{ "9605/astro-ph9605114_arXiv.txt": { "abstract": "We present the highest spatial and spectral resolution near-infrared data to date of the $\\sim~10^{13}~\\htwo~L_{\\sun}$ {\\sl IRAS} source FSC 15307+3252 at $z = 0.93$, apparently the most luminous galaxy in the known Universe. Deep $K$-band (2.2 \\micron) images taken in 0\\farcs4 seeing at the W.\\ M.\\ Keck Telescope reveal three components: (A) a bright elliptical source with a compact nucleus, (B) a resolved circular companion separated from component A by 2\\farcs0 (8$h^{-1}$~kpc for $q_{0} = 0.5$), and (C) a faint irregular component 1\\farcs7 from A. The surface brightness profile of F15307-A is well-characterized by a de~Vaucouleurs $r^{1/4}$ law with $r_{e} = 1\\farcs4 \\pm 0\\farcs2$ (6\\hone~kpc), a size comparable to local giant ellipticals. The nucleus of component A is stellar in appearance with extended structure, possibly a second nucleus $\\sim$~0\\farcs5 away. Our 1.1--1.4~\\micron\\ spectrum of the F15307 system with a resolution of 330 km~s\\perone\\ shows strong emission lines of \\oi\\ \\lam\\lam6300, 6364; blended \\ha~+~\\nii\\ \\lam\\lam6548, 6583; and \\sii\\ \\lam\\lam6716, 6731. The $\\sim$~900~km~s\\perone\\ width of the forbidden lines and the relative strengths of the emission lines are characteristic of Seyfert 2 galaxies. The \\ha\\ line also has a broad (1900 km~s\\perone) component. In light of the recent discovery that FSC 10214+4724, previously the most luminous known galaxy, is a gravitationally-lensed system, we explore the possibility that F15307 is also lensed. Quantitative arguments are inconclusive, but aspects of F15307's morphology do suggest lensing; the system bears a strong resemblance to quadruple-image gravitational lenses. On the other hand, given the $r^{1/4}$ profile, the close companions, and the active nucleus, F15307 may in fact be a giant elliptical galaxy caught in the act of galactic cannibalism, a scenario which could also account for its unparalleled luminosity. ", "introduction": "During the course of an \\IRAS\\ color-selected survey for extremely luminous IR-bright galaxies, Cutri \\etal\\ (1994) identified FSC 15307+3252 as an $\\sim 1.0 \\times 10^{13}\\ h^{-2} L_{\\sun}$ galaxy at a redshift of 0.926 ($q_{0} = 0.5$, $H_{0} = 100h$ km~s\\perone~Mpc\\perone). They found its restframe UV/blue optical spectrum resembles a Seyfert 2 galaxy; Soifer \\etal\\ (1994) found a similar result for the restframe red optical emission lines though they had insufficient spectral resolution to measure linewidths. Hines \\etal\\ (1995) have found broad \\ion{Mg}{2} $\\lambda$2798 emission and a power-law continuum in polarized light, leading them to argue the system contains a buried quasar. IR imaging by Soifer \\etal\\ (1994) in 1\\arcsec\\ seeing shows the system is composed of a bright extended source with one or two close companions. The one known galaxy believed to be more luminous than F15307, the $\\sim 5 \\times 10^{13}\\ h\\pertwo\\ L_{\\sun}$ source FSC 10214+4724 at $z = 2.286$, is now known to be the first example of a gravitationally-lensed Seyfert 2 galaxy. Its $I$-band flux is magnified by a factor of 100 (\\cite{eis96}), and the $K$-band magnification is around 10--20 (\\cite{gra95,bro95}). In hindsight, this result is not surprising. Many known lensed systems are $z \\gtrsim 1$ quasars. In the local universe, the space density of luminous ($L \\gtrsim 10^{11} L_{\\sun}$) IR galaxies exceeds that of quasars (\\cite{soi86}); if this fact holds at higher redshifts, one naturally expects gravitational lensing of IR-bright galaxies. \\IRAS\\ sources at $z \\gtrsim 0.5$ are prime suspects for this phenomenon since the associated magnification would allow these objects to be detected at significant redshifts. Statistical estimates support this line of reasoning (\\cite{bro95,tre95}). However, while lensed quasars are relatively easy to identify since lensing of point sources produces distinctive sets of multiple images, lensed extended sources, like IR-bright galaxies, are more difficult to recognize for two reasons: (1) their total magnification is less, and (2) they form extended images which require high angular resolution to resolve, \\eg, sub-arcsecond interferometric imaging is needed to identify lensed high redshift radio lobes (\\eg, \\cite{bla92}). Therefore, high resolution imaging of F15307 is necessary in order to determine whether its extraordinary luminosity arises from gravitational lensing or intrinsic phenomena such as massive starbursts and/or an active nucleus. If F15307 and other high-$z$ \\IRAS\\ sources are gravitationally lensed like F10214, this discovery will have applications beyond understanding the nature of these objects. Lensed extended sources are useful tools for probing the mass distribution of the lensing galaxies since they offer more lines of sight through the lens than lensed point sources (\\eg, \\cite{koc91}). Imaging provides a more effective tool to search for lensing than spectroscopy, since the latter typically requires high S/N to search for discrepant redshifts from continuum features. Targets found with morphologies suggestive of lensing can then be spectroscopically examined to determine a redshift for the foreground lens. Ultimately, statistics of these lensed systems will quantify the magnification bias afflicting the high end of the \\IRAS\\ luminosity function. In this paper we present 0\\farcs4 resolution $K$-band imaging and moderate resolution ($\\lambda/\\Delta\\lambda$ = 990) near-IR (1.1--1.4 \\micron) spectroscopy of FSC 15307+3252. Our imaging data identify three components all within 2\\arcsec. The near-IR (restframe optical) spectrum displays emission lines of \\oi, \\ha~+~\\nii, and \\sii\\ which resemble a Seyfert~2-type spectrum. The morphology of the system is similar to quadruple-image gravitational lenses, though at the limit of our resolution, we cannot discount the possibility the system is involved in a close interaction and/or merger of 2--3 separate components; in particular, the brightest component appears to be a large elliptical galaxy in the process of assembling. Throughout the paper we assume $q_{0} = 0.5$ and $H_{0} = 100h$ km~s\\perone~Mpc\\perone. With this choice of cosmology, 1\\farcs0 corresponds to 4.2\\hone\\ kpc at a redshift of 0.926. ", "conclusions": "We have presented the highest spatial and spectral resolution near-IR observations to date of the $\\sim~10^{13}~\\htwo~L_{\\sun}$ \\IRAS\\ galaxy FSC~15307+3252 located at $z = 0.93$, apparently the most luminous known galaxy. We find the following results: \\noindent 1. Deep $K$-band images with 0\\farcs4 resolution reveal at least three components to the system. The brightest, component A, is elliptical with a compact nucleus. Component B, is resolved and apparently circular, and the faintest component, C, has an irregular morphology. \\noindent 2. The $K$-band surface brightness profile of F15307-A is well-described by a de~Vaucouleurs $r^{1/4}$ law with $\\mu_{e} = 20.1 \\pm 0.3$~mag~arcsec\\pertwo\\ and $r_{e} = 1\\farcs4 \\pm 0\\farcs2$ (6\\hone~kpc) after correction for seeing effects. Its effective radius is comparable to local giant ellipticals. After removal of the de~Vaucouleurs profile, the core of F15307-A shows a compact nucleus with extended structure $\\sim$~0\\farcs5 to the southwest, possibly a second nucleus. \\noindent 3. Our 1.1--1.4 \\micron\\ (restframe optical) spectrum with a resolution of 330~km~s\\perone\\ shows strong emission lines of \\oi, \\ha~+~\\nii, and \\sii\\ with velocity widths typical of Seyfert~2 galaxies. The line excitation is also consistent with such a classification. \\ha\\ also has a strong $\\sim$~1900~km~s\\perone\\ component but lacks a very broad $\\sim$~10$^{4}$~km~s\\perone\\ component unlike the polarized \\mgii\\ \\lam2798 line (\\cite{cut94}). The line emission may be extended on scales of $\\sim$~1\\arcsec\\ (4\\hone\\ kpc). \\noindent 4. The morphology of F15307 is reminiscent of known gravitational lensed objects, particularly quadruply-imaged sources such as MG~J0414+0534. Quantitative arguments are inconclusive, though if the system is lensed, the absence of an obvious foreground lens imply the lensing galaxy is underluminous for its mass. The fact that the components are extended means even if the system is lensed, the $z=0.93$ source must be an intrinsically luminous galaxy. \\noindent 5. Alternatively, F15307 may be an interacting system with an intrinsically large luminosity, similar to local ultraluminous \\IRAS\\ galaxies. Some indications exist that the system is not heavily extincted. The $r^{1/4}$ profile suggests F15037-A is an elliptical galaxy. It may be in the process of forming at $z=0.93$ or else it formed at $z > 0.93$ and we are now observing its interaction/merger with components B and C. Additional observations should determine the nature of F15307. \\HST\\ imaging should be able to identify if the system is lensed but is not essential; ground-based IR observations in excellent seeing or high resolution radio imaging should also suffice. Color information will be useful --- if the system is lensed, the foreground lensing galaxy, most likely an elliptical, should be distinct from the multiple images of the background lensed Seyfert. Narrow-band imaging centered on emission lines will be a good test for lensing as will long slit spectroscopy to compare the spectra of components A and B. One additional observation which would serve as an empirical test is to search for CO emission from F15307 since the only two definite detections of CO emission at high redshift are from the lensed sources F10214 and the Cloverleaf quasar (\\cite{sol92,bar94}). Regardless of which way the issue is settled -- if the system is a lensed Seyfert galaxy or an interacting elliptical --- the system will be worthy of further scrutiny." }, "9605/astro-ph9605052_arXiv.txt": { "abstract": "We show that the sharp cutoff in the hard X-ray spectrum of NGC 4151, unusual for Seyfert 1 galaxies, can be reconciled with the average Seyfert 1 spectrum if we assume that the central source is completely hidden from our line of sight by the thick part of the accretion disk or by the broad emission line clouds. The observed X-ray radiation is produced by scattering of the Seyfert 1-type spectrum in the higher, cooler parts of the accretion disk corona, or in a wind. A sharp cutoff appears as a result of the Compton recoil effect. This model naturally explains a discrepancy regarding the inclination of the central source, inferred to be low (face-on) from observations of the iron $K\\alpha$ emission line, but inferred to be high on the basis of optical and UV observations. ", "introduction": "\\label{sec:intro} The brightest Seyfert galaxy in X-rays, NGC 4151, has a significantly different spectrum from the average Seyfert 1 spectrum. The average hard X-ray Seyfert 1 spectrum is well described by a power-law with exponential cutoff at energy, $E_{\\rm c}\\sim 300-1000$ keV, and a Compton reflection component. The spectrum of NGC 4151 has a much sharper decline in hard X-rays and no clear signature of a reflection component. While the X-ray spectra of both an average Seyfert 1 and NGC 4151 can be well described by models invoking thermal Comptonization of the soft radiation from the accretion disk in a hot corona, the corona in NGC 4151 is required to be much thicker (Thomson optical depth $\\taut\\sim2$) and much cooler ($\\Te\\sim 40-50\\kev$) than the corona of Seyfert 1s, for which $\\taut\\sim 0.2-0.3$ and $\\Te\\sim 200-300$ keV (Zdziarski et al. 1995, 1996). In this Letter we argue that the intrinsic spectrum of NGC 4151 does not differ from that of Seyfert 1s, if we assume that the direct component is hidden from our line of sight by the outer parts of the accretion disk or by the broad emission line region (BLR) close to the central source (Jourdain \\& Roques 1995) and that the observed X-ray radiation is due to scattering in the higher, cooler parts of the accretion disk corona or in a wind. The observed Compton-scattered component has much sharper cutoff than the intrinsic spectrum due to the Compton recoil effect. We show also that the primary X-ray spectrum of NGC 4151 is consistent with thermal Comptonization in active regions in the vicinity of a relatively cold accretion disk and that optical depths and temperatures of the hot plasma do not differ from those of Seyfert 1s. Non-thermal models cannot be ruled out, as a strong annihilation line will be smeared out by scattering. The scattered component is further filtered through a complex absorber. The absorption clearly visible in the X-ray spectrum of NGC 4151 can be provided by the extended ``atmosphere'' of the accretion disk or BLR. The edge-on orientation of the NGC 4151 nucleus is strongly supported by the biconical geometry of the [OIII] $\\lambda$5007 region (Evans et al. 1993; Pedlar et al. 1993). The observed geometry requires the observer to be located outside the cone of UV radiation which photoionizes the oxygen. Recent observations of the profile of the iron $K\\alpha$ line, showing an extended luminous red wing and a sharp cutoff on the blue side, suggest an accretion disk viewed face-on (Yaqoob et al. 1995). This can be reconciled with the edge-on geometry deduced from the [OIII]$\\lambda$5007 image, if the central source is observed through the radiation scattered by electrons in an extended corona or wind. Finally, after correcting the UV and X-ray luminosities for dilution due to scattering, one also finds that NGC 4151 has luminosity ratios, $L_{UV}/L_{OIII}$ and $L_X/L_{OIII}$, typical of Seyfert 1s (Mulchaey et al. 1994). ", "conclusions": "\\label{sec:intro} The brightest Seyfert galaxy in X-rays, NGC 4151, has a significantly different spectrum from the average Seyfert 1 spectrum. The average hard X-ray Seyfert 1 spectrum is well described by a power-law with exponential cutoff at energy, $E_{\\rm c}\\sim 300-1000$ keV, and a Compton reflection component. The spectrum of NGC 4151 has a much sharper decline in hard X-rays and no clear signature of a reflection component. While the X-ray spectra of both an average Seyfert 1 and NGC 4151 can be well described by models invoking thermal Comptonization of the soft radiation from the accretion disk in a hot corona, the corona in NGC 4151 is required to be much thicker (Thomson optical depth $\\taut\\sim2$) and much cooler ($\\Te\\sim 40-50\\kev$) than the corona of Seyfert 1s, for which $\\taut\\sim 0.2-0.3$ and $\\Te\\sim 200-300$ keV (Zdziarski et al. 1995, 1996). In this Letter we argue that the intrinsic spectrum of NGC 4151 does not differ from that of Seyfert 1s, if we assume that the direct component is hidden from our line of sight by the outer parts of the accretion disk or by the broad emission line region (BLR) close to the central source (Jourdain \\& Roques 1995) and that the observed X-ray radiation is due to scattering in the higher, cooler parts of the accretion disk corona or in a wind. The observed Compton-scattered component has much sharper cutoff than the intrinsic spectrum due to the Compton recoil effect. We show also that the primary X-ray spectrum of NGC 4151 is consistent with thermal Comptonization in active regions in the vicinity of a relatively cold accretion disk and that optical depths and temperatures of the hot plasma do not differ from those of Seyfert 1s. Non-thermal models cannot be ruled out, as a strong annihilation line will be smeared out by scattering. The scattered component is further filtered through a complex absorber. The absorption clearly visible in the X-ray spectrum of NGC 4151 can be provided by the extended ``atmosphere'' of the accretion disk or BLR. The edge-on orientation of the NGC 4151 nucleus is strongly supported by the biconical geometry of the [OIII] $\\lambda$5007 region (Evans et al. 1993; Pedlar et al. 1993). The observed geometry requires the observer to be located outside the cone of UV radiation which photoionizes the oxygen. Recent observations of the profile of the iron $K\\alpha$ line, showing an extended luminous red wing and a sharp cutoff on the blue side, suggest an accretion disk viewed face-on (Yaqoob et al. 1995). This can be reconciled with the edge-on geometry deduced from the [OIII]$\\lambda$5007 image, if the central source is observed through the radiation scattered by electrons in an extended corona or wind. Finally, after correcting the UV and X-ray luminosities for dilution due to scattering, one also finds that NGC 4151 has luminosity ratios, $L_{UV}/L_{OIII}$ and $L_X/L_{OIII}$, typical of Seyfert 1s (Mulchaey et al. 1994)." }, "9605/astro-ph9605028_arXiv.txt": { "abstract": "{\\baselineskip 0.4cm The Sloan Digital Sky Survey (SDSS) is a project to definitively map $\\pi$ steradians of the local Universe. An array of CCD detectors used in drift-scan mode will digitally image the sky in five passbands to a limiting magnitude of $r' \\sim 23$. Selected from the imaging survey, $10^6$ galaxies and $10^5$ quasars will be observed spectroscopically. I describe the current status of the survey, which is due to begin observations early in 1997, and its prospects for constraining models for dark matter in the Universe.} ", "introduction": "Systematic surveys of the local Universe ($z \\simlt 0.2$) can provide some of the most important constraints on dark matter, particularly through the measurement of the clustering of galaxies and clusters of galaxies on large scales. Most existing galaxy and cluster catalogues are based on photographic plates \\cite{msel90, chm89}, and there is growing concern that such surveys might suffer from severe surface-brightness selection effects, so that they are missing a substantial fraction of the galaxy population. In addition, the limited volume of existing redshift surveys means that even low-order clustering statistics, such as the galaxy two-point correlation function, cannot reliably be measured on scales beyond $100 \\hMpc$, an order of magnitude below the scale on which COBE has measured fluctuations in the microwave background radiation. A collaboration has therefore been formed with the aim of constructing a definitive map of the local universe, incorporating digital CCD imaging over a large area in several passbands and redshifts for around one million galaxies. In order to complete such an ambitious project over a reasonable timescale, it was decided to build a {\\em dedicated} 2.5-metre telescope equipped with a large CCD array imaging camera and multi-fibre spectrographs. The collaboration comprises around 100 astronomers and engineers from University of Chicago, Fermilab, Princeton University, Institute for Advanced Study, Johns Hopkins University, US Naval Observatory, University of Washington and the JPG---a group of astronomers in Japan. The total cost of the survey is around \\$30 million, and funding sources include the Alfred P. Sloan Foundation, the National Science Foundation and the participating institutions. ", "conclusions": "It is probably no exaggeration to claim that the Sloan Digital Sky Survey will revolutionize the field of large scale structure. Certainly we can expect to rule out large numbers of presently viable cosmological models, as illustrated in Figure~\\ref{fig:P_k}. As well as measuring redshifts for a carefully controlled sample of $10^6$ galaxies and $10^5$ quasars, the survey will also provide high quality imaging data for about 100 times as many extragalactic objects, from which one can obtain colour and morphological information. In addition to measuring the basic cosmological parameters $\\Omega$ and $h$ discussed in the preceding section, the SDSS will also allow us to measure the properties of galaxies as a function of their colour, morphology and environment, providing valuable clues to the process of galaxy formation. \\begin{figure}[htbp] \\parbox{10cm}{ \\epsfxsize=10cm \\epsfbox{slice.ps} } \\parbox{6cm}{ \\caption[]{Redshift-space distribution of galaxies in a $6\\dg$ slice from a large, low-density CDM $N$-body simulation generated by Changbom Park.} \\label{fig:slice} } \\end{figure} Finally, I cannot resist the temptation to give a visual impression of what we might expect to see with the SDSS redshift survey. Figure~\\ref{fig:slice} shows the distribution of 62,295 galaxies in a $6\\dg$ slice from a simulation carried out by Changbom Park, assuming a low-density CDM model. This slice represents just {\\em one sixteenth} of the million galaxy redshifts we will be measuring with the Sloan survey. I leave it to the readers imagination to dream up all the projects they would love to carry out given such a data-set. The work described here has been carried out by many people throughout the SDSS collaboration, and I thank all my colleagues warmly. I am particularly grateful to Chris Stoughton and Michael Vogeley for providing Figures~\\ref{fig:stripes} and Figure~\\ref{fig:P_k} respectively, and to Philippe Canal for translating the Abstract into French. My attendance at the meeting was supported by a generous grant from the EEC." }, "9605/astro-ph9605046_arXiv.txt": { "abstract": "Irregular dust grains are subject to radiative torques when irradiated by interstellar starlight. It is shown how these radiative torques may be calculated using the discrete dipole approximation. Calculations are carried out for one irregular grain geometry, and three different grain sizes. It is shown that radiative torques can play an important dynamical role in spinup of interstellar dust grains, resulting in rotation rates which may exceed even those expected from $\\HH$ formation on the grain surface. Because the radiative torque on an interstellar grain is determined by the overall grain geometry rather than merely the condition of the grain surface, the resulting superthermal rotation is expected to be quite long-lived. By itself, long-lived superthermal rotation would permit grain alignment by normal paramagnetic dissipation on the ``Davis-Greenstein'' timescale $\\tau_\\DG$. However, radiative torques arising from anisotropy of the starlight background can act directly to alter the grain alignment on times short compared to $\\tau_\\DG$. Radiative torques must therefore play a central role in the process of interstellar grain alignment. The radiative torques depend strongly on the grain size, measured by $a_\\eff$, the radius of a sphere of equal volume. In diffuse clouds, radiative torques dominate the torques due to $\\HH$ formation for $a_\\eff=0.2\\micron$ grains, but are relatively unimportant for $a_\\eff\\leq0.05\\micron$ grains. We argue that this may provide a natural explanation for the observation that $a_\\eff\\gtsim0.1\\micron$ grains in diffuse clouds are aligned, while there is very little alignment of $a_\\eff\\ltsim0.05\\micron$ grains. We show that radiative torques are ineffective at producing superthermal rotation within quiescent dark clouds, but can be very effective in star-forming regions such as the M17 molecular cloud. ", "introduction": "Polarization of starlight by aligned interstellar dust grains was discovered nearly half a century ago (Hiltner 1949a,b; Hall 1949; Hall \\& Mikesell 1949), but the processes responsible for the observed alignment remain uncertain. Davis \\& Greenstein (1951) observed that interstellar grains were expected to be rotating rapidly due to Brownian motion, and proposed that these spinning grains could be aligned with the local magnetic field by paramagnetic dissipation. However, further study of the statistical mechanics of grain alignment (Jones \\& Spitzer 1967; Purcell \\& Spitzer 1971) raised questions about the ability of the interstellar magnetic field to achieve the observed degree of alignment, since random gas-grain collisions would tend to oppose the alignment process. Purcell (1975, 1979) first recognized that interstellar grains were expected to have superthermal rotational velocities as the result of systematic torques, the most important of which appeared to be due to the process of $\\HH$ formation on the grain surface. As discussed by Purcell, superthermal rotation due to torques which are fixed in body coordinates can enhance the degree of grain alignment, since the ``thermal'' torques due to random collisions with gas atoms now have little effect on the direction of the grain angular momentum, allowing paramagnetic dissipation to inexorably bring the angular momentum into alignment with the galactic field. The systematic torques considered by Purcell were due to processes taking place at the grain surface -- $\\HH$ formation, photoelectric emission, and inelastic collisions with gas atoms -- but the grain surface may be altered due to contamination or erosion on relatively short time scales. The resulting changes in direction of the systematic torque can cause the grain to occasionally undergo short periods when its rotation is ``spun down''; during these ``crossover'' episodes the grain may become disaligned (Spitzer \\& McGlynn 1979). Because of this disorientation during ``crossover'', it was not clear whether ordinary paramagnetic dissipation plus superthermal rotation driven by ``Purcell torques'' can account for the observed grain alignment. In addition, dust grains were observed to be aligned in some dense molecular regions where ``Purcell torques'' were expected to be ineffective due to a low H/H$_2$ ratio, attenuation of the ultraviolet radiation required for photoelectric emission, and near-equality of gas and grain temperatures. As a result, there has been renewed interest in alternatives, including the possibility that grains may be superparamagnetic (Jones \\& Spitzer 1967; Duley 1978; Martin 1995; Goodman \\& Whittet 1995), or that grain alignment is due to gas-grain streaming (Gold 1952; Lazarian 1994, 1995a; Roberge, Hanany, \\& Messinger 1995). Lazarian (1995b) has emphasized the possible importance of grain ``helicity'', since helical grains can be driven to superthermal rotational velocities, and possibly aligned, when exposed to either streaming gas atoms or anisotropic radiation. Harwit (1970a,b) suggested that the quantized angular momentum of the photon could lead to rapid rotation of a grain following absorption and emission of many photons, and proposed that the anisotropy of starlight could result in a tendency for interstellar grains to spin with their angular momentum vectors parallel to the Galactic plane. Dolginov (1972) observed that interstellar grains might have different absorption and scattering cross sections for left- and right-handed circularly polarized light, so that the grain angular momentum could be changed if illuminated by unpolarized but anisotropic radiation. This effect was further discussed by Dolginov \\& Mytrophanov (1976) for particles in the Rayleigh limit, and by Dolginov \\& Silant'ev (1976) for larger particles but with refractive index close to unity so that the Rayleigh-Gans approximation could be used. Dolginov \\& Mytrophanov noted that this process could lead to both rapid rotation and possible alignment. Unfortunately, Dolginov and collaborators were unable to calculate the torques on grains with realistic compositions and sizes. That irregular interstellar grains should be subject to radiative torques is not surprising. We consider two macroscopic examples for illustration. Fig.\\ \\ref{fig:targs}a shows a four-fold symmetric target with square top and bottom, with each of its four rectangular sides divided into perfectly absorbing and perfectly reflecting halves. In the geometric optics limit the normal component of the radiation pressure force will be twice as large on the reflecting sections as on the absorbing sections; as a result, an isotropic radiation field illuminating this target will produce a positive torque along axis $\\ahat_1$. However, incident radiation which is either parallel or antiparallel to $\\ahat_1$ will not produce any torque on this target. Fig.\\ \\ref{fig:targs}b shows a target obtained by starting with the shape of Fig.\\ref{fig:targs}a and removing four wedges from the top and four from the bottom, with the resulting shape being symmetric under reflection through the centroid. Fig.\\ref{fig:targs}b is an example of a shape with ``helicity''. From symmetry it is clear that an isotropic radiation field will produce no torque on this target: whatever torque is exerted on the ``top'' half of the grain will be cancelled by an opposite torque on the ``bottom'' half. However, anisotropic illumination can produce a torque on this target. If, for example, the surfaces are all perfectly reflecting, then incident radiation which is antiparallel to $\\ahat_1$ will produce a torque parallel to $\\ahat_1$, while radiation parallel to $\\ahat_1$ will produce a torque antiparallel to $\\ahat_1$. These two examples show that macroscopic objects will be subject to radiative torques unless they are highly symmetric; thus irregular targets should generally be subject to radiative torques. Interstellar grains are, of course, comparable to or smaller than the wavelength of the illuminating radiation, but one does not expect the radiative torques to vanish when target geometries such as Fig. \\ref{fig:targs} are reduced to sizes comparable to the wavelength. In this paper we discuss the forces and torques on grains of arbitrary shape and with sizes which are neither large nor small compared to the wavelength of the incident radiation. We show how these forces and torques can be calculated using the discrete dipole approximation. Quantitative results are obtained for one particular irregular grain shape. The first part of this paper, \\S\\S\\ref{sec:DDA}-\\ref{sec:target_orient}, is devoted to development of the theory of scattering by irregular particles to enable efficient computation of radiative torques. This is carried out within the conceptual (and computational) framework of the discrete dipole approximation. In \\S\\ref{sec:dda_results} we report results of extensive computations for one specific irregular grain geometry and composition, and three different sizes, $a_\\eff=0.2$, 0.05, and $0.02\\micron$ ($a_\\eff$ is the radius of a sphere of equal volume). Readers primarily interested in the implications for grain rotation may elect to skip \\S\\S\\ref{sec:DDA}-\\ref{sec:dda_results}, and proceed directly to \\S\\ref{sec:interstellar}, where we discuss the effects of starlight and gas drag under realistic conditions in interstellar diffuse clouds, and \\S\\ref{sec:superthermal}, where the resulting superthermal rotation is evaluated. It is seen in \\S\\ref{sec:diffuse} that moderately anisotropic starlight can torque $a_\\eff=0.2\\micron$ grains in diffuse clouds up to extremely large rotational velocities, exceeding even the superthermal rotation due to $\\HH$ formation. Smaller ($a_\\eff\\ltsim 0.05\\micron$) grains, on the other hand, are only weakly affected by radiative torques. We also examine the importance of radiative torques within quiescent dark clouds (\\S\\ref{sec:dark}), and within active star-forming regions (\\S\\ref{sec:starforming}). Our results are summarized in \\S\\ref{sec:summary}. Our principal result is that the torques exerted on interstellar grains by background starlight are dynamically very important for grains with $a_\\eff\\gtsim0.1\\micron$. These torques will produce extreme superthermal rotation of interstellar grains in both diffuse clouds and star-forming clouds. In a separate paper (Draine \\& Weingartner 1996) we examine the role of these radiative torques in the alignment of interstellar grains with the galactic magnetic field. ", "conclusions": "} The principal results in this paper are as follows: \\begin{enumerate} \\item We show how forces and torques on an irregular grain may be calculated using the discrete dipole approximation. \\item We report numerical results (in Fig.\\ \\ref{fig:qpr_kvslambda} and Table \\ref{tab:grain_props}) for $\\khat\\!\\cdot\\!\\bQ_{pr}(\\lambda)$, the component of the radiation pressure efficiency vector parallel to the radiative flux for one particular irregular grain geometry, where the grain is assumed to be spinning around its principal axis $\\ahat_1$ of largest moment of inertia. \\item We report numerical results for the ``radiation torque efficiency vector'' $\\bQ_\\Gamma(\\lambda)$, (in Figs.\\ \\ref{fig:qgam_a1vslambda_0.2} -- \\ref{fig:qgam_alignvsTheta_0.05}) for one irregular grain geometry. The torque depends upon the angle $\\Theta$ between the incident flux and the grain rotation axis $\\ahat_1$. \\item In interstellar diffuse clouds, radiative torques will drive $a_\\eff\\gtsim0.1\\micron$ grains to extreme superthermal rotation. \\item Radiative torques will dominate the torques due to $\\HH$ formation for $a_\\eff\\gtsim0.1\\micron$ interstellar grains. For these grains, the superthermal rotation is expected to be very long-lived, since it depends upon global properties of the grain, rather than the relatively short-lived surface properties which determine superthermal rotation due to $\\HH$ formation, photoelectric emission, or variations in surface accomodation coefficient. \\item In an isotropic radiation field, the long-lived superthermal rotation of $a_\\eff\\gtsim0.1\\micron$ grains due to radiative torques would facilitate alignment of these grains with the Galactic magnetic field by the Davis-Greenstein mechanism of paramagnetic relaxation. \\item Since the rotation of smaller ($a\\ltsim0.05\\micron$) grains is not dominated by radiative torques, alignment of these grains with the Galactic magnetic field would be limited due to random variations in the torque associated with $\\HH$ formation on the grain surface. This may explain why $a_\\eff\\gtsim0.1\\micron$ grains in diffuse clouds are aligned, while there is evidently minimal alignment of the $a_\\eff\\ltsim0.05\\micron$ grains which dominate the extreme ultraviolet extinction. \\item Radiative torques appear to be able to drive grains to superthermal rotation in star-forming regions, such as M17, where the ratio of anisotropic radiation to gas pressure is relatively high, thereby potentially explaining the observed alignment of far-infrared emitting dust in M17 and other star-forming regions with warm dust. In cold dark clouds, on the other hand, radiative torques are unable to drive the grains to superthermal rotation, consistent with the observed lack of aligned grains deep in quiescent dark clouds. \\item In addition to the torque component parallel to the grain rotation axis $\\ahat_1$ (which drives superthermal rotation), anisotropy of the radiation field can result in radiative torque components perpendicular to the grain angular momentum; these components can affect grain alignment directly. \\end{enumerate}" }, "9605/astro-ph9605192_arXiv.txt": { "abstract": "The stable clustering hypothesis is a key analytical anchor on the nonlinear dynamics of gravitational clustering in cosmology. It states that on sufficiently small scales the mean pair velocity approaches zero, or equivalently, that the mean number of neighbours of a particle remains constant in time at a given physical separation. N-body simulations have only recently achieved sufficient resolution to probe the regime of correlation function amplitudes $\\xi \\sim 100-10^4 $ in which stable clustering might be valid. In this paper we use N-body simulations of scale free spectra $P(k)\\propto k^n$ with $-2\\leq n \\leq 0$ and of the CDM spectrum to apply two tests for stable clustering: the time evolution and shape of $\\xi(x,t)$, and the mean pair velocity on small scales. We solve the pair conservation equation to measure the mean pair velocity, as it provides a more accurate estimate from the simulation data. For all spectra the results are consistent with the stable clustering predictions on the smallest scales probed, $x < 0.07 \\ x_{nl}(t)$, where $x_{nl}(t)$ is the correlation length. The measured stable clustering regime corresponds to a typical range of $200\\lsim \\xi \\lsim 2000$, though spectra with more small scale power ($n\\simeq 0$) approach the stable clustering asymptote at larger values of $\\xi$. We test the amplitude of $\\xi$ predicted by the analytical model of Sheth \\& Jain (1996), and find agreement to within $20\\%$ in the stable clustering regime for nearly all spectra. For the CDM spectrum the nonlinear $\\xi$ is accurately approximated by this model with $n \\simeq -2$ on physical scales $\\lsim 100-300 h^{-1} {\\rm kpc}$ for $\\sigma_8=0.5-1$, and on smaller scales at earlier times. The growth of $\\xi$ for CDM-like models is discussed in the context of a power law parameterization often used to describe galaxy clustering at high redshifts. The growth parameter $\\epsilon$ is computed as a function of time and length scale, and found to be larger than $1$ in the moderately nonlinear regime -- thus the growth of $\\xi$ is much faster on scales of interest than is commonly assumed. ", "introduction": "The stable clustering hypothesis is one of the few analytical handles on the deeply nonlinear regime of gravitational clustering. It states that the mean relative velocity of particle pairs in physical coordinates is zero. Hence in comoving coordinates the mean relative velocity exactly cancels the Hubble recession velocity between pairs of particles. As we will see below, this is equivalent to the statement that the mean number of neighbours of a particle in physical coordinates remains constant in time. The stable clustering hypothesis invokes the physical picture of a virialized cluster which has separated out from the expanding background, and is neither expanding nor contracting. Since on small scales, any statistical measure is dominated by the contribution from dense clusters, the clustering should statistically be stable. This hypothesis leads to predictions for the evolution in time of the autocorrelation function $\\xi$. In the case of scale free spectra which display self-similar scaling, the slope of $\\xi(x)$ in the small scale regime is predicted as well. For $\\xi\\gg 1$ it is extremely difficult to make analytical approximations to the growth of clustering. Hence the stable clustering hypothesis has been very useful in relating the shape of $\\xi$ and the power spectrum $P(k)$ in the nonlinear regime to the initial spectrum. Peebles (1974) and Gott \\& Rees (1975) implemented the first such applications. The widely used property of hierarchical scaling of the higher order moments of the density in terms of its second moment also derives from the dynamics of stable clustering. As emphasized in the next section, this property requires additional assumptions of stability at each order in the distribution. N-body simulations are the ideal tool to test stable clustering. Efstathiou et al. (1988) carried out a pioneering study of self-similar evolution, and tested the small scale $\\xi$ and $v$ for stable clustering. Their data were consistent with the stable clustering slope for $\\xi$ on the smallest scales, but their $32^3$ particle simulations lacked the resolution to give any definitive conclusion. Recently Padmanabhan et al. (1995) and Colombi, Bouchet \\& Hernquist (1995; hereafter CBH), have tested the stable clustering predictions for $\\xi, v$, and in the latter case for the hierarchical form of the higher moments $S_3$, $S_4$ and $S_5$ as well. While Padmanabhan et al. (1995) found departures from stable clustering in their $\\Omega=1$ simulations, CBH verified the stable clustering prediction in their tests of $\\xi$. However, they found small departures from the hierarchical relation for the higher moments. In this paper we use ${\\rm P^3 M}$ (particle-particle/particle-mesh) simulations with $100^3-144^3$ particles to test stable clustering for power law spectra with $-2\\leq n\\leq 0$, and for the CDM spectrum. We measure $\\xi$ and $v$, for which we use the pair conservation equation to obtain estimates with greater accuracy than allowed by direct measurements. Our approach and numerical resolution is similar to that of CBH, with the advantage that we have $4-10$ times as many particles. We do not however test for the higher moments as they do. While stable clustering predicts the slope of $\\xi$, its amplitude can be approximated by additional assumptions as done in the analytical model of Sheth \\& Jain (1996). We test their predictions against the measured amplitude in the N-body data. We also test for stable clustering in two high resolution CDM simulations and identify the range of scales and epochs on which it is an adequate approximation. We begin in the next section with the relevant BBGKY equations through which the stable clustering hypothesis leads to the predictions for $\\xi$ and the higher moments. In Section 3 we outline a secondary infall model which can be connected with the nonlinear form of $\\xi$, and discuss the dynamical effects which might invalidate stable clustering. Section 4 contains a description of the N-body simulations, and an analysis of the effects of limited numerical resolution on small scales. Section 5 presents the main results for $\\xi$, with the mean pair velocity results in Section 5.1, and results for the CDM spectrum in Section 5.2. We conclude in Section 6. ", "conclusions": "The results presented in this paper can be summarized as follows. \\noindent $\\bullet$ The shape and evolution of the correlation function $\\xi(a,x)$ is consistent with the stable clustering prediction of equation (\\ref{stable3}). We have verified this result with the power spectrum measured from the simulations presented here as well. \\noindent $\\bullet$ Direct measurement of the mean pair velocity is not sufficiently accurate on small scales. We have therefore solved the pair conservation equation to estimate $-v/Hr$ which approaches unity on small scales, as required for consistency with the results for $\\xi$. \\noindent $\\bullet$ We find that the onset of stable clustering occurs at $x/x_{nl}(a) = 0.07$ for all spectra tested. This provides a useful way to demarcate the stable clustering regime for generic spectra. The range of $\\xi$ over which stable clustering is verified is typically $200<\\xi<2000$; it is higher for initial spectra with more small scale power ($n\\simeq 0$). \\noindent $\\bullet$ For the CDM spectrum we find the range of scales for $0.2^{1/2} \\approx 1$, where $\\rho$ is the density field and $\\bar \\rho$ its mean) the linear theory breaks down (see e.g. \\cite{z-nov83}, \\cite{sh-z89}). The most widespread method to deal with the complex dynamics at the nonlinear stage is to run N-body simulations generating the initial condition as a realization of a Gaussian random process (\\cite{kly-sh83}). In N-body simulations of this type the gravitational forces generated by the density distribution is calculated at each time step. The trajectory of every particle is integrated in a self-consistently varying gravitational field. Cosmological N-body simulations have played the most significant role in testing (and in most cases rejecting) the models for dark matter. Here we are interested in a different aspect of the problem of the LSS formation. We are trying to formulate simple physical {\\it macroscopic} principles controlling the nonlinear stage of gravitational clustering. Long ago Zel'dovich (1970) suggested a very elegant, analytical approximation to describe the beginning of the nonlinear stage in cosmological scenarios assuming smooth initial conditions. Quantitatively it can be expressed as a requirement that the initial power spectrum of density fluctuations has a steep cutoff on small scales (steeper than $P(k) \\propto k^{-3}$). Mathematically, the Zel'dovich Approximation (ZA) is a one step mapping from the Lagrangian space into the Eulerian space at a time $t,$ given by \\begin{equation} {\\bf r}({\\bf q},t)=a(t)[{\\bf q} -D(t) \\nabla \\Phi({\\bf q})] \\end{equation} where ${\\bf r}$ and ${\\bf q}$ are the Eulerian and Lagrangian coordinates, respectively; $a(t)$ is the scale factor describing the homogeneous expansion of the Universe; $D(t)$ is a known function of time describing the growth of perturbations; and $\\Phi({\\bf q})$ is the potential of the initial velocity field: ${\\bf v}_0 \\propto -\\nabla \\Phi({\\bf q})$. With the aid of the above mapping one can calculate the density at the final time $t$ using the conservation of mass. However, cosmological observations almost certainly exclude scenarios having no perturbations on small scales. Small scale power is required to explain the existence of quasars and galaxies at very high redshifts. Two modifications---the Truncated Zel'dovich Approximation (TZA) (\\cite{kof-etal92}, \\cite{Col-etal93}) and the Adhesion Approximation (AA) (\\cite{gur-sai-sh89})---have been suggested in an attempt to extend the scope of the ZA and to make it more useful for general cosmological scenarios (for a brief review see e.g.~\\cite{sh94} and for more exhaustive discussion of various approximations see \\cite{sathya-etal95}, \\cite{sah-col95}). A comparison with gravitational N-body simulations shows that these two approximations fairly accurately describe nonlinear gravitational clustering (\\cite{mel-sh-wei94}, \\cite{sathya-etal95}). Here we describe another approximation to the nonlinear gravitational evolution of the density and velocity perturbations which is numerically almost as simple as the ZA but completely universal and much superior to any approximation method suggested so far. It consists of two elements: \\begin {itemize} \\item a transformation of variables and \\item an assumption that in the dense regions the local gravitational interaction can be approximated by the diffusion of a generalized momentum (see below for a definition of the generalized momentum). \\end {itemize} The latter assumption is similar to the AA but in this model the generalized momentum is locally conserved. ", "conclusions": "Summarizing, we conclude that the proposed approximation mimics the large-scale gravitational evolution at late nonlinear stages quite well (positions of clumps, filaments, pancakes) -- better than any other known approximation. This implies that the two simple assumptions: \\begin {itemize} \\item the generalized gravitational force on large scales ($l\\ge k_{nl}^{-1}$) equals the velocity : ${\\partial \\varphi / \\partial x_i} \\approx - v_i({\\bf x},D)$ and \\item the conservation of mass and the local ($l\\le k_{nl}^{-1}$) conservation of the generalized momentum, ${\\bf p} = \\eta {\\bf v} $, \\\\ \\end {itemize} explain fairly well the nonlinear gravitational clustering on large scales. In a very general sense the COMA falls in the class of sticky particle methods used in the numerical hydrodynamics and also resembles the lattice gas models used in modeling turbulence and similar phenomena. An interesting question is whether the COMA guarantees complete hierarchical clustering or not. Due to numerical errors some small clumps may miss merging with the larger ones passing by without the collision. We have not seen this phenomena in our simulations and believe that it should not be a serious problem for the method. We believe that after a thorough testing the approximation can be a practical tool for cosmological studies of large-scale processes which do not require a resolution better than a few $Mpc,$ such as large-scale streaming velocities, spatial distribution of rich clusters of galaxies, statistics of voids, etc. In such low resolution calculations the COMA can be more efficient than N-body simulations if very large volumes and large statistical ensembles are required." }, "9605/astro-ph9605009_arXiv.txt": { "abstract": "In the powerful, high redshift radio galaxies, it is believed that the dominant source of ionization for the interstellar gas is the hard radiation field associated with the active nucleus. The photon source is generally external to the clouds being ionized and so the geometrical perspective from which the gas is observed and the presence and distribution of dust must be properly accounted for in the diagnostic process. In this paper, we examine the formation of the three strong lines: CIV$\\lambda$1549, Ly$\\alpha$\\ and CIII]$\\lambda$1909 which are often observed in the nuclear and extended emission from these sources. We find that the observed trends, in particular the high CIV$\\lambda$1549/Ly$\\alpha$ ratio, are often better explained by geometrical (viewing angle) effects than by the presence of large quantities of dust either within or outside the excited clouds. We show that neutral condensations along the line-of-sight, by reflecting photons near the wavelength of Ly$\\alpha$, can increase the observed CIV/Ly$\\alpha$ ratio. The existence of HI absorption clouds (i.e., mirrors) external to the emission region leads also to the presence of large, diffuse haloes of what appears to be pure, narrow Ly$\\alpha$\\ emission. ", "introduction": "The strong, spatially extended, rest-frame ultraviolet emission lines observed in high redshift radio galaxies provide one of the principal diagnostics in establishing the state of the interstellar medium in galaxies at early epochs. The presence of a blue continuum and emission lines from regions aligned with the radio axis (McCarthy et~al. 1987; Chambers et~al. 1987) warned us that much of the observed optical radiation might be associated with the nuclear activity and so may not be giving us a clear picture of the stellar processes which are of such interest in studies of galaxy formation and evolution. Subsequent work has shown, indeed, that much of the blue light is scattered, polarized nuclear radiation (e.g., Tadhunter et~al. 1989; di Serego Alighieri et~al. 1993; Cimatti et~al. 1993) and that the emission lines have a high ionization state and cannot result from stellar photoionization (McCarthy 1993). It is clearly necessary, therefore, to reach a clear understanding of the physical processes involved in the formation of the various lines and continua to be able to disentangle the stellar and the AGN-related sources. For objects at high\\,$z$, the UV rest-frame lines are shifted into the optical band and the spectrum is generally dominated by Ly$\\alpha$, CIV$\\lambda$1549, HeII$\\lambda$1640 and CIII]$\\lambda$1909. The strength of the high ionization lines suggests the presence of a hard photoionizing continuum which could originate at the AGN itself (Robinson et~al. 1987) or be associated with fast shocks generated in extranuclear regions by the radio jets (Sutherland, Bicknell \\& Dopita 1993). The strong radio/optical asymmetries observed in these objects which exhibit the `alignment effect' (McCarthy et~al. 1991a) may simply result from a one-sidedness in the distribution of material. It it is clear, however, that correlated line and continuum asymmetries could be produced by dust scattering and line fluorescence for sources where the radio axis falls significantly away from the plane of the sky. In this work, we concentrate on modeling the high excitation lines for which rather extreme ratios relative to Ly$\\alpha$ have recently been reported. The presence of dust has been universally invoked to explain the weakness of Ly$\\alpha$ which is a resonance line and therefore, due to multiple scattering, more susceptible to absorption. We explore the fact that any resonance line will be extremely sensitive to geometrical factors, an aspect of the problem which has so far been overlooked in modeling the UV lines. If in radio-galaxies the distant gas clouds are photoionized from the outside by partially collimated UV radiation emitted by the nucleus, the line formation process --- particularly for the resonance lines --- is very different from internally ionized HII regions. The escape of resonance line photons is strongly influenced by the presence of spaces between the line emitting clouds. We have collected from the literature the observed line ratios for a number of high~z radio-galaxies in which no contribution from any nuclear BLR is apparent. We have built a diagnostic diagram consisting of the lines CIV$\\lambda$1549/Ly$\\alpha$ {\\it vs.} CIV$\\lambda$1549/CIII]$\\lambda$1909, in which we compare the position of the objects with photoionization models which not only consider the effects of internal dust but also those of the viewing perspective --- the angle between the incoming ionizing radiation and the observer's line of sight. Our concentration on the particular class of radio galaxies is purely for pragmatic reasons. It is these objects, which we presume to harbour a powerful quasar which is hidden at optical/ultraviolet wavelengths to our line of sight, which are most readily found and studied at the high redshifts where we have access to the ultraviolet spectrum from groundbased observations. Our conclusions should be equally applicable to other classes of AGN. For some objects, Ly$\\alpha$ is observed to be fainter with respect to CIV than predicted by dust-free photoionization models. The explanation previously proposed to explain the weakness of Ly$\\alpha$ with respect H$\\alpha$ or H$\\beta$ has been dust destruction of resonant Ly$\\alpha$ photons. This is {\\it not} borne out by our calculations in which we have used arbitrary amounts of dust and found that this cannot simultaneously weaken Ly$\\alpha$ while leaving the CIV/CIII] ratio relatively unchanged since resonant CIV suffers also from dust absorption. Alternatively, by varying the proportions of the illuminated and the shadowed cloud faces which contribute to the observed spectrum, we are better able to match the data. % geometric explanation could naturally explain that some of the % brightness asymmetries noted by McCarthy et~al. (1991a) on % sides of the nucleus. As we find that geometry alone (with or without internal dust) can in principle explain most of the specific line ratios observed (fainter Ly$\\alpha$ compared with either CIV or HeII), we also discuss the possibility of a patchy outer halo of neutral gas to account for the diffuse Ly$\\alpha$ seen in some cases to extend much beyond the CIV emitting region and even the outermost radio lobes. Reflection by cold gas of the brighter Ly$\\alpha$ emitting side of the ionized clouds would lead to a narrower profile for such a diffuse component. Another possibility is that part of the beamed nuclear {\\it continuum and BLR} radiation might be reflected at the wavelength of Ly$\\alpha$ by thin matter-bounded photoionized gas at very large distances from the nucleus leading to a diffuse Ly$\\alpha$ component aligned with the radio axis. It appears to us that geometrical perspective effects are an essential component of the interpretation of the UV spectrum of radio-galaxies whether or not dust is present. Furthermore, a spectrum in which only Ly$\\alpha$ appears does not necessarily imply starburst activity, other lines must be observed before the existence of an HII region can be inferred. ", "conclusions": "" }, "9605/astro-ph9605186_arXiv.txt": { "abstract": "We present an analytical method for studying the changes of the orbital characteristics of binary systems with circular orbits due to a kick velocity imparted to the newborn neutron star during a supernova explosion (SN). Assuming a Maxwellian distribution of kick velocities we derive analytical expressions for the distribution functions of orbital separations and eccentricities immediately after the explosion, of orbital separations after circularization of the post-SN orbits, and of systemic velocities of binaries that remain bound after the explosion. These distributions of binary characteristics can be used to perform analytical population synthesis calculations of various types of binaries, the formation of which involves a supernova explosion. We study in detail the dependence of the derived distributions on the kick velocity and the pre-SN characteristics, we identify all the limits imposed on the post-SN orbital characteristics, and we discuss their implications for the population of X-ray binaries and double neutron star systems. We show that large kick velocities do not necessarily result in large systemic velocities; for typical X-ray binary progenitors the maximum post-SN systemic velocity is comparable to the relative orbital velocity prior to the explosion. We also find that, unless accretion-induced collapse is a viable formation channel, X-ray binaries in globular clusters have most probably been formed by stellar dynamical interactions only, and not directly from primordial binaries. ", "introduction": "Studies of the radio pulsar population (e.g., Gunn \\& Ostriker\\markcite{G70} 1970; Helfand \\& Tademaru\\markcite{H77} 1977; Harrison, Lyne \\& Anderson\\markcite{H93} 1993; Lyne \\& Lorimer\\markcite{L94} 1994) have shown that pulsars move in the Galaxy with very high space velocities, ranging from $20$ to $2000$\\,km\\,s$^{-1}$, and that their galactic distribution has a large scale height, of the order of $1$\\,kpc. The origin of these high velocities is often attributed to a kick velocity imparted to the neutron star at the time of the supernova explosion. Early studies by Dewey \\& Cordes\\markcite{D87} (1987) and Bailes\\markcite{B89} (1989) concluded that the mean magnitude of the kick velocity is of the order of $100-200$\\,km\\,s$^{-1}$. In a more recent study, which takes into account new measurements of pulsar proper motions, a new electron density model, and a selection effect against fast pulsars, Lyne \\& Lorimer (1994) found the mean kick velocity to be $\\sim 450\\pm 90$\\,km\\,s$^{-1}$. Additional observational evidence in support of a kick velocity imparted to neutron stars at birth are related to the existence of a high--velocity population of O,\\,B runaway stars (e.g., Stone\\markcite{S91} 1991), as well as to supernova remnant -- pulsar associations, studies of which yield kick velocities up to $2000$\\,km\\,s$^{-1}$ (Caraveo\\markcite{C93} 1993; Frail, Goss, \\& Whiteoak\\markcite{F94} 1994). In contrast to Dewey \\& Cordes (1987), Iben \\& Tutukov\\markcite{I96} (1996) have recently concluded that the hypothesis of natal kicks imparted to neutron stars is unnecessary. They have found that the transverse velocity distribution of pulsars in the solar neighborhood, as well as that of O,\\,B runaway stars, massive X-ray binaries, and double neutron stars, can be explained by the recoil velocity due to symmetric supernova explosions. However, they reach this conclusion by assuming (i) that all stars are members of binary systems and (ii) that neutron stars formed by massive single stars (formed only by mergers) or in wide binary systems rotate too slowly to become radio pulsars. Although, their results are marginally consistent (mean predicted velocities are $\\sim 100-150$\\,km\\,s$^{-1}$) with the old pulsar distance scale (Harrison et al. 1993), they are not consistent with the more recent results of Lyne \\& Lorimer (1994). Over the years, several theories have been put forward in an effort to explain the origin of kick velocities (e.g., Harrison \\& Tademaru\\markcite{H75} 1975; Chugai\\markcite{C84} 1984; Duncan \\& Thomson\\markcite{D92} 1992; Herant, Benz \\& Colgate\\markcite{H92} 1992; Janka \\& M\\\"{u}ller\\markcite{J94} 1994; Burrows, Hayes, \\& Fryxell\\markcite{F95} 1995; Burrows \\& Hayes\\markcite{H96} 1996). Even a small asymmetry during the collapse of the core can give a kick to the remnant of the explosion. The asymmetry may be related either to neutrino emission or to mass ejection during the supernova, and may be caused by the magnetic field or rotation of the collapsing core, or by hydrodynamic instabilities, such as Rayleigh-Taylor or convective motions. In any case, the mechanism responsible for the kick velocity is still not well understood, and it appears that fully three-dimensional numerical simulations of the core collapse will be required in order to settle this issue. Several authors have previously studied the effect of an asymmetric supernova explosion on binary parameters, focusing on various aspects of the problem. Early work by Flannery \\& van den Heuvel\\markcite{F75} (1975), Mitalas\\markcite{M76} (1976), Sutantyo\\markcite{78} (1978), and Hills\\markcite{H83} (1983) addressed the problem of deriving expressions of post-SN orbital characteristics for a specific kick velocity for both circular and eccentric pre-SN orbits. They also derived survival probabilities for kick velocities of constant magnitude and random direction. The one-to-one link between pre-SN and post-SN parameters is broken when kick velocities are allowed to have a distribution over both magnitude and direction, in which case there exists a distribution of post-SN characteristics, even for pre-SN binaries with specific orbital parameters. Wijers, van Paradijs, \\& van den Heuvel\\markcite{W92} (1992) were the first to address this problem. They derived an analytic expression for the distribution of post-SN orbital separations and eccentricities only, which however was also convolved with a distribution of pre-SN orbital separations. More recently Brandt \\& Podsiadlowski\\markcite{B95} (1995) addressed the same problem using numerical methods (Monte Carlo simulations). The resulting distributions are again convolved with pre-SN period distributions, and, in this case, are calculated only for specific stellar masses, in an effort to compare them with observation. Because these distributions are calculated numerically, information about the allowed ranges of post-SN characteristics, the shape of multi-dimensional distributions, and their dependence on the pre-SN and kick-velocity characteristics is limited. Our purpose here is to derive analytical expressions of various post-SN characteristics for the realistic case of kick velocities with a distribution in both magnitude and direction. The derived distributions are general, and apply to any circular binary systems that experience asymmetric supernova explosions. The study presented in this paper has been motivated by our interest in performing population synthesis calculations for low-mass X-ray binaries. Monte Carlo techniques have been widely used in such calculations modeling various kinds of binary systems (e.g., Dewey \\& Cordes 1987; de Kool\\markcite{92} 1992; Romani\\markcite{R92} 1992). Another method is based in creating a multi-dimensional grid of initial binary parameters and tracing the evolution of systems through a sequence of evolutionary stages for each set of initial parameters (Kolb\\markcite{93} 1993; Iben, Tutukov, \\& Yungel'son\\markcite{I95} 1995 and references therein). Both of these numerical methods have the same problem: although the goal is to calculate the characteristics of the final population, the sampling procedure is applied on the initial population, and therefore it is possible that the final population is under-sampled, even if the sampling of the primordial population appears adequate. Another problem with both methods is related to statistical accuracy: the initial sets of parameters cover a wide range, of which only a small part is populated by progenitors of interest, especially in the case of X-ray binaries, which have very small birth rates; therefore, with these methods it is necessary to study a very large number of primordial binaries in order for a statistically significant number of systems to survive. Both of these problems are absent in population synthesis calculations performed analytically, where distributions of primordial binaries over orbital characteristics are transformed through a sequence of evolutionary stages, using Jacobian transformations. In this way, the regions in parameter space populated by the progenitors of interest are identified and the final population is calculated directly. This method has been formulated and applied to the study of cataclysmic binaries by Politano\\markcite{P96} (1996) (see also Politano, Ritter, \\& Webbink\\markcite{P89} 1989; Politano \\& Webbink\\markcite{P90} 1990). Apart from the absence of the problems discussed above, the analytical method has the additional advantage that the shape of final distributions is calculated exactly, revealing fine details and subtle features, such as sharp peaks, infinities, or definite limits imposed on the final parameters. Also, the various dependences of these parameters and their distributions on the initial parameters can be identified and studied in detail. In order to use the analytical method in population synthesis of neutron-star binaries, it is necessary to develop an analytical tool for the modeling of asymmetric supernova explosions. Our purpose in this paper is to present such a method based on Jacobian transformations for computing analytically the probability distributions of several orbital characteristics of post-SN binaries. These distributions include (\\S\\,2) the orbital separations and eccentricities immediately after the supernova explosion, the circularized orbital separations, and (\\S\\,3) the systemic velocities. They are derived for circular pre-SN orbits and for kick velocities that are randomly distributed not only in direction but also in magnitude (Maxwellian distribution). The derived expressions can be used in synthesis calculations of any kind of binaries that experience supernova explosions during their evolution. The analytical character of the derivation enables us to perform detailed parameter studies and identify those characteristics of the kick velocities or the pre-SN binaries that govern the behavior of the post-SN distribution functions. Expressions for the limiting cases of very large or very small kick velocities relative to the pre-SN orbital velocities are also derived. We identify the limits imposed on the post-SN parameters and discuss their physical interpretation. In addition, we calculate survival probabilities (\\S\\,4) as functions of the pre-supernova (pre-SN) orbital characteristics and the mean kick velocity. Finally, we examine several implications of our results (\\S\\,5) for the progenitors of high- and low-mass X-ray binaries, double neutron stars, and their populations in globular clusters. A list of the symbols used throughout the paper is given in Appendix A. The study of a few special cases is included in Appendices B and C. ", "conclusions": "The expressions derived here provide a tool necessary in analytical population syntheses of neutron star binaries. The additional step needed in such syntheses is to convolve the distribution over post-SN parameters with the distribution of pre-SN binaries over masses and orbital separations (see also Wijers et al. 1992). This link depends on the type of final systems and the specifics of their formation mechanism. In addition, the distribution functions of systemic velocities and their correlation with orbital separations and eccentricities (or circularized orbital separations) can be used in studying the motion of neutron star binaries in the Galactic potential, and in modeling their spatial distribution in the Galaxy. The results of the study presented in this paper have a number of important implications concerning the population of neutron star binaries: There exists a correlation between orbital separations and eccentricities, which is independent of the characteristics of the binary or the magnitude of the kick velocity. For post-SN orbits much wider than the pre-SN orbit, the total energy of the binary significantly increases, and the system remains bound only in a highly eccentric orbit. On the other hand, the eccentricity may be low ($e\\lesssim 0.4$) only if the post-SN orbital separation is comparable to that before the explosion. The discovery of a double neutron star system of modest eccentricity could therefore be used to infer the size of the orbit of its progenitor, provided that the gravitational radiation decay time scale for the orbit were long enough for such losses to be negligible. The ratio of the post-SN systemic velocity, $V_{sys}$, to the pre-SN relative orbital velocity, $V_r$, is restricted in a relatively narrow range of values. Both lower and upper limits depend only on the stellar masses involved. For the ranges of progenitor masses relevant to HMXBs, LMXBs, and double neutron star binaries we find $V_{sys}^{max}\\lesssim 1.5\\,V_r$. Since LMXB progenitors are more tightly bound than those of HMXBs, and hence have higher relative orbital velocities than HMXB progenitors, the systemic velocities of LMXBs are expected to be higher than those of HMXBs. It is also clear that measurements of systemic velocities of neutron star binaries do not necessarily reveal information about the kick velocities imparted to neutron stars in individual systems. Instead, they can be used to infer typical relative orbital velocities prior to the supernova explosion. Although the allowed range of systemic velocities is independent of the kick velocity, the probability distribution within this range does depend on the r.m.s. magnitude of kick velocities relative to the pre-SN orbital velocities. In the limit of very small kicks the distribution sharply peaks at values close to the lower end of the range. As the r.m.s. of the kick velocities increases the distribution becomes broader and its peak shifts to higher velocities. For kicks much higher than the pre-SN relative orbital velocities, the shape of the distribution remains unaffected, and further increases of the r.m.s. kick velocity only decrease the binary survival rate, without altering the velocity distribution of bound post-SN systems. Measurements of the systemic velocities of neutron star binaries will possibly prove quite significant in distinguishing between symmetric and asymmetric explosions with high kicks imparted to the neutron stars. The incidence of X-ray binaries in globular clusters relates to their smallest possible systemic velocity and to how this velocity compares with the escape velocity from the cluster. For LMXBs formed via the explosion of the He-star remnant of a common envelope phase, typical parameters for the progenitors yield $V_{sys}^{min} \\simeq 100\\,$km s$^{-1}$ (Kalogera \\& Webbink 1996). The direct-SN channel (Kalogera\\markcite{K196} 1996; Kalogera 1996) is fed by binaries with orbits which are much wider, but still small enough to avoid disruption by dynamical interactions. Typical parameters in this case yield $V_{sys}^{min} \\simeq 20\\,$km s$^{-1}$. Estimates of the escape velocities from the cores of globular clusters that contain LMXBs range from $30$\\,km\\,s$^{-1}$ to $60$\\,km\\,s$^{-1}$ (for NGC 1851, 6440, 6441, 6624, M15, and Lil 1); more loosely bound clusters such as Ter 1 and 2 have central escape velocities of the order of $10$\\,km\\,s$^{-1}$ (Webbink\\markcite{W85} 1985; van Paradijs\\markcite{V95} 1995). It is therefore clear that post-SN binaries formed in globular clusters from primordial binaries via the He-SN channel have a very small chance of remaining in the clusters and becoming X-ray binaries. LMXBs formed via the direct-SN channel, on the other hand, will remain in the clusters, but their formation rate is too low to account for a significant fraction of the LMXB population in globular clusters. Barring accretion-induced collapse as an alternative formation channel, it therefore appears that low-mass X-ray binaries observed in globular clusters must have formed through stellar exchanges and captures, rather than directly from primordial binaries. We have already applied the analytical method presented here to study low-mass X-ray binaries formed via different evolutionary channels. The results of these population synthesis calculations will be presented elsewhere (Kalogera \\& Webbink 1996; Kalogera 1996)." }, "9605/astro-ph9605096_arXiv.txt": { "abstract": "Recent timing observations of PSR J0045-7319 reveal that the neutron star/B star binary orbit is decaying on a time scale of $|\\Porb/\\dot\\Porb|=0.5$ Myr, shorter than the characteristic age ($\\tau_c=3$ Myr) of the pulsar (Kaspi et al.~1996a). We study mechanisms for the orbital decay. The standard weak friction theory based on static tide requires far too short a viscous time to explain the observed $\\dot\\Porb$. We show that dynamical tidal excitation of g-modes in the B star can be responsible for the orbital decay. However, to explain the observed short decay timescale, the B star must have some significant retrograde rotation with respect to the orbit --- The retrograde rotation brings lower-order g-modes, which couple much more strongly to the tidal potential, into closer ``resonances'' with the orbital motion, thus significantly enhancing the dynamical tide. A much less likely possibility is that the g-mode damping time is much shorter than the ordinary radiative damping time. The observed orbital decay timescale combined with a generic orbital evolution model based on dynamical tide can be used as a ``timer'', giving an upper limit of $1.4$ Myr for the age of the binary system since the neutron star formation. Thus the characteristic age of the pulsar is not a good age indicator. Assuming standard magnetic dipole braking for the pulsar and no significant magnetic field decay on a timescale $\\lo 1$ Myr, the upper limit for the age implies that the initial spin of the neutron star at birth was close to its current value. ", "introduction": "One of the fundamental questions in the study of pulsars concerns the initial conditions of neutron stars at birth. In particular, the initial spin of neutron star is related to such issues as angular momentum coupling in the progenitor stars, supernova explosion mechanisms and gravitational wave generation from core collapse and nascent neutron stars. Unfortunately, except for the Crab pulsar, for which the initial spin can be directly inferred from the measured pulsar period $P_p$ and its time-derivatives $\\dot P_p,\\,\\ddot P_p$ and the known age, our knowledge about this quantity is rather limited. Statistical studies of the evolution of pulsar population (e.g., Narayan 1987), the energetics of pulsar nebulae (Helfand \\& Becker 1987) and possible old pulsar/supernova remnant associations (Kaspi et al.~1996b) give some indications that neutron stars are formed rotating at a moderate spin period $10-100$ ms. However, all these methods suffer from uncertainties, and other independent constraints on the initial spins of neutron stars are highly valuable. The PSR J0045-7319 binary contains % a radio pulsar ($P_p=0.93\\,$s) and massive B-star companion in an eccentric, $51.17\\,$ days orbit (\\cite{Kaspi94}). This system has recently been shown to exhibit spin-orbit precessions due to the rapid, misaligned rotation of the B star, which strongly suggests that the neutron star received a kick at birth from asymmetric supernova (\\cite{Lai95,Kaspi96a}). Recent timing observations also reveal that the orbit is decaying on a time scale $|\\Porb/\\dot\\Porb|=0.5\\,$ Myr, shorter than the pulsar's characteristic age $\\tau_c=P_p/(2\\dot P_p)=3\\,$Myr (\\cite{Kaspi96a}). In this paper, we study the physical mechanisms for the rapid orbital decay, and demonstrate the potential of using the orbital decay time to constrain the age and initial spin of the pulsar. The fiducial numbers we adopt for the current PSR J0045-7319 system are: pulsar mass $M_p=1.4M_\\odot$, companion mass $M_c=8.8M_\\odot$, radius $R_c=6.4R_\\odot$, and orbital period $\\Porb=51.17$ days, semi-major axis $a=20R_c$, eccentricity $e=0.808$ (\\cite{Kaspi96a,Bell95}). ", "conclusions": "Our analyses of PSR J0045-7319 binary orbital decay show that the B star companion is most likely to have a retrograde rotation with respect to the orbit. Since the spin of the B star is expected to have been aligned with the orbital angular momentum before the supernova, the current misaligned configuration could have come about only if the neutron star received a kick at birth due to asymmetry in the supernova. The kick velocity must (i) have had a component out of the original orbital plane in order to misalign ${\\bf L}$ and ${\\bf S}$; (ii) have had a significant component in the direction opposite to the orbital velocity of the progenitor in order to reverse ${\\bf L}$. The current timing data yield two degenerate solutions for the range of the spin-orbit inclination angle, allowing for both prograde and retrograde rotation (Kaspi et al.~1996a). Long-term (i.e., some fraction of the precession period $\\sim 500$ years) timing observation should distinguish these two possibilities. Dedicated optical observation of the companion may also give useful constraints on the excited modes (Kumar et al.~1995). Our analyses have also demonstrated that the orbital decay can be used to put concrete constraints on the pulsar age and initial spin. The tide-induced orbital decay of the PSR B1259-63/Be star binary (the only other known radio pulsar/main sequence star binary) is too slow to be observable owing to its larger orbital separation at periastron. Finding more systems similar to PSR J0045-7319 will allow for determination of systematic constraints on the physical conditions of neutron stars at birth and supernova characteristics." }, "9605/astro-ph9605119_arXiv.txt": { "abstract": " ", "introduction": "The universe is not transparent to high energy gamma-rays due to interactions with low energy photons of the extragalactic radiation fields, the most important process being photon-photon pair production. For example, interactions in the cosmic microwave background radiation give a mean interaction length of less than 10 kpc at $10^6$ GeV as has been known since soon after the discovery of the microwave background \\cite{Gould,Jelley}. The threshold for interactions on the microwave background is $\\sim 10^5$ GeV, and at lower energies interactions on the infrared and optical backgrounds limit the transparency at TeV energies (e.g. \\cite{StdeJS,Pro93}) Other components of the extragalactic background radiation are discussed in the review of Ressel and Turner \\cite{Res90}. Above $\\sim 10^{10}$ GeV interactions with the radio background become more important than the microwave background in limiting the transparency of the universe to gamma-rays and controlling any resulting electromagnetic cascades. Both the infrared and radio backgrounds are poorly known due to our location within our Galaxy which emits and absorbs at these wavelengths. The radio background was measured over twenty-five years ago \\cite{Cla70}, but the fraction of this radio background which is truly extragalactic, and not contamination from our own Galaxy, is still debatable. A theoretical estimate \\cite{Ber69} was made about the same time which gave a quite different spectrum, particularly at low frequencies. In recent cascade calculations \\cite{ProtJohns95,Elb95,Lee96,ProtStan96} the estimate of ref.~\\cite{Cla70} has been used. It is this very uncertain radio background which will provide target photons for UHE $\\gamma$-rays above $\\sim 10^{10}$ GeV. While gamma-ray astronomy is not currently undertaken at $\\sim 10^{10}$ GeV energies, it is important to know the photon-photon mean interaction length at these energies because cascading involving gamma-rays at these energies occurs in top-down models for the origin of the highest energy cosmic rays. The highest energy cosmic rays have energies of 200 EeV \\cite{Hay94,Yos95} and 300 EeV \\cite{Bir95}, and are well above the ``Greisen-Zatsepin-Kuzmin cut-off'' \\cite{Gre66,Zat66} at 50 EeV in the spectrum of cosmic ray protons due to pion photoproduction in the microwave background, which is expected if the cosmic rays originate further than a few tens of Mpc ({\\it e.g.}, \\cite{GrigBer,RB93}). Of the various models proposed to account for the origin of these high energy cosmic rays \\cite{Biermann&Strittmatter,RB93,Mil95,Wax95,Vie95}, one of the more tantalizing speculations is that the highest energy cosmic rays may be ultimately due to the decay of supermassive X particles \\cite{Bha92,Sig94,Bha95,Sig95}, themselves radiated during collapse or annihilation of topological defects, remnants of an early stage in the evolution of the Universe. The X particles have GUT-scale masses of $\\sim 10^{16}$ GeV or lower, depending on the theory, and decay into leptons and quarks at lower energies. The quarks themselves fragment into a jet of hadrons which, it is supposed, could produce the highest energy cosmic rays, although there is some debate as to whether a sufficiently large fraction of the energy of the defect could end up in high energy particles \\cite{Hin95}. In any case, much of the radiation is likely to emerge in the electromagnetic channel and initiate an electromagnetic cascade in the ambient radiation field, in which collisions with radio photons play an important role. In this paper we make a new calculation of the extragalactic radio background down to kHz frequencies based on the infrared luminosity function of normal galaxies recently determined from IRAS source counts, the observed radio--infrared correlation, and the luminosity function of radio galaxies, together with recent models for radio spectra of these objects. Finally, we calculate the mean free path for $\\gamma$-rays in the extragalactic radio background radiation. ", "conclusions": "Motivated by a new interest in electromagnetic cascades through the universe at extremely high energies, we have made a new calculation of the extragalactic radio background radiation down to kHz frequencies. The main contribution to the background is from normal galaxies and is uncertain due to uncertainties in their evolution. The 60 micron source counts from IRAS above 0.3 Jy appear consistent with no evolution provided there is a new source population (possibly AGN) contributing below 0.3 Jy. An alternative interpretation of the data is that there is strong evolution of normal galaxies giving agreement with the source counts above 3 Jy and below 0.1 Jy (but not for $0.1 < S_\\nu < 3$ Jy). This gives rise to a factor of 5 uncertainty in the radio intensity at kHz frequencies, and this translates to a factor of 5 uncertainty in the mean free path at $10^{12}$ GeV. If there is a new source population contributing to the infrared source counts it may also be important in determining the infrared background which limits the transparency of the universe to TeV energy gamma rays. Clearly, it is vital to determine the nature of the sources which dominate the 60 micron counts below 0.3 Jy. We calculated the radio background for the two assumptions about the evolution of normal galaxies, and in both cases the background we obtain exceeds previous estimates at low frequencies. By examining Fig.~\\ref{fig:ggee_radio.eps} we find that for the radio background calculated in this paper photon-photon pair production on the radio background is the dominant interaction process for photons over four or five decades of energy from $3 \\times 10^{10}$ -- $5 \\times 10^{10}$ GeV to $10^{15}$ -- $5 \\times 10^{15}$ GeV, above which double pair production on the microwave background dominates. We estimate the mean free path to be $\\sim 1$ -- 5 Mpc at $10^{12}$ GeV. Using the radio background estimated by Clark \\protect \\cite{Cla70} photon-photon pair production on the radio background would only be important only up to $10^{13}$ GeV, and the mean free path at $10^{12}$ GeV would be a factor of 3 -- 10 larger. This difference will be very important in electromagnetic cascades initiated by particles with energies up to the GUT scale produced at topological defects." }, "9605/astro-ph9605163_arXiv.txt": { "abstract": "Here we speculate on what observations are telling us about the difference between radio-loud and radio-quiet QSOs. The observations are (i) the relation between ultraviolet-optical luminosity and `jet power', (ii) the dependences of emission and absorption line spectra, and the spectral energy distribution, on radio core-dominance, assumed to be an indicator of orientation, (iii) the spectral differences between radio-loud and radio-quiet QSOs, and (iv) the inverse relation between the strength of broad, blended Fe\\,II multiplets and [O\\,III]\\,$\\lambda$5007, and the apparently-related association between Fe\\,II strength, reddening, broad absorption lines, and scattering polarization. We present and discuss a picture in which there are two main variables: (i) the inclination of the plane of the host galaxy to the axis of the inner jet (the central engine's rotation axis), and (ii) the angle of the line-of-sight to this rotation axis. The radio-loud QSOs are those with jets aiming away from the plane of the host galaxy. ", "introduction": "Some hypotheses proposed to explain why $\\sim$90\\% of QSOs\\footnote {`QSO' refers to all luminous AGN (L$\\ga 10^{11}$\\,L$_{\\sun}$, H$_0 = 100$\\, km s$^{-1}$\\,Mpc$^{-1}$. A radio-loud QSO is one having F$_{\\rm5GHz}$/F$_{4400} \\ga 10$, where F is the rest frame flux-density in mJy. Such strong radio emission is assumed to indicate powerful radio jets.} are radio quiet include (i) an evolutionary phenomenon where radio-loudness is a short-lived phase in the existence of all QSOs, or a series of short-lived phases (Schmidt 1970), (ii) the result of differences in mass concentration in the host galaxy nucleus (Heckman 1983), (iii) the result of fundamental angular momentum differences (Wilson \\& Colbert 1995), (iv) the result of poorly-collimated sub-relativistic wind in radio-quiet QSOs (RQQs) (Boroson, Persson \\& Oke 1985). Some hypotheses simply discuss conditions under which jets might form, but do not attempt to explain all known differences between radio-loud QSOs (RLQs) and RQQs. We take a different approach, by first examining the relation between ultraviolet-optical luminosity and jet power (see the chapter, {\\it Accretion and Jet Power}). There, we concluded that jet power (represented approximately by unbeamed radio power) is directly related to the Big Blue Bump luminosity, for RLQs and RQQs, while the radio luminosity is a factor of $\\sim$1000 less in the RQQs. Then we argued that the generally great similarity of the Big Blue Bump, non-synchrotron X-ray emission, and the emission line spectra implied a very similar central engine mechanism, independent of radio-emission. This, together with the relations between unbeamed radio and Big Blue Bump luminosity, led us to the hypothesis that the central engines of RQQs and RLQs (fueling, accretion, and power available to generate a jet) are essentially identical. There is some theoretical support for this, but no single hypothesis is clearly favoured. ", "conclusions": "" }, "9605/astro-ph9605177_arXiv.txt": { "abstract": "Measuring the angles of muons and electrons in air showers is proposed as a method for studying the primary cosmic-ray mass composition near the knee of the cosmic-ray energy spectrum at a few $10^{15}$\\,eV. Conventional tracking detectors at existing air shower arrays could serve this purpose, like the CRT detectors at the HEGRA array. When the average radial muon angles are examined as a function of shower core distance, the experimental resolution can be very well calibrated from the tangential angle distribution. The method is particularly promising for measuring changes in the average mass number of the primary cosmic rays with energy. The method is described and experimental and theoretical constraints are discussed. ", "introduction": "Despite the fact that ultra-high energy (UHE) cosmic rays are known for decades, their sources and the acceleration mechanisms are still under debate. Sources are only detectable by $\\gamma$-rays produced in interactions near the sources. In the very-high energy (VHE) range near 1\\,TeV more and more $\\gamma$-ray sources are revealed by the imaging Cherenkov technique. On the contrary, no clear source detections have been made in the UHE domain above about 100\\,TeV, except perhaps a few episodic cases. Mainly for reasons of the required power, the dominant sources of cosmic rays up to about 100\\,TeV and probably up to the {\\em knee} of the cosmic-ray energy spectrum at a few $10^{15}$\\,eV are believed to be supernova remnants in the Sedov phase. The change of the spectrum near the knee presumably reflects a change in the origin and the takeover of another, yet unclear type of sources at energies above the knee. A change in the cosmic-ray propagation with a decreasing Galactic containment has also been considered. In either case, the change in the slope of the spectrum should be accompanied by a change in the mass composition of cosmic rays. In the case of a change of sources across the knee, the composition could change dramatically. A much less spectacular change of the composition is expected in the case of decreasing containment. Direct measurements well below the knee \\cite{Asakimori-1993ab,Ichimura-1993b} show indeed a substantial change in the mass composition already at energies around 100\\,TeV. In particular, the fraction of protons seems to diminish with increasing energy. Due to their small collection areas the balloon-borne direct experiments run out of statistics above several hundred TeV. Indirect methods using ground-based experiments are, so far, not able to classify individual cosmic rays unambiguously by their mass. Such methods are more appropriate for evaluating some average mass number. Most notably, the results of the Fly's Eye group \\cite{Gaisser-1993} indicate a rather heavy composition well above the knee. If taken at face value, their results represent a composition of mainly very heavy nuclei, like iron, at $10^{17}$\\,eV. Experiments measuring the composition right at the knee of the spectrum obtained either ambiguous or even conflicting results. Results with no significant change \\cite{Zhu-1990,Ahlen-1992b} or a slight increase of heavy elements \\cite{Khristiansen-1994} have been reported. Other groups found more significant increases of heavy elements \\cite{Ren-1988a,Freudenreich-1990,Mitsui-1995} or, on the other hand, predominantly protons \\cite{Cebula-1990}. Further measurements are needed, if the cosmic-ray composition should help to resolve the question where cosmic rays are accelerated. The method proposed in this paper should be relatively easy to implement at sites where an air-shower array with an angular resolution below one degree already exists. The method is mainly a measurement of the longitudinal shower development by the angles of muons with respect to the shower axis. It does not require to measure many muons in a single shower because it uses only the {\\em inclusive} angular distributions, nor is accurate timing required. Indeed, if several muons are measured in one event, they are treated separately. Not only the average muon angles but also the average electron angles with respect to the shower axis are sensitive to the primary composition. Because the detector response is, in general, better understood for muon tracks than for electron tracks, this paper focuses mainly on the muons. Using the tracking detectors and the air-shower array, the method can be supplemented by traditional methods like the average $\\mu/e$ ratio or the muon lateral distribution. Although one can think of complex experiments dedicated to measuring the cosmic-ray composition, like KASKADE \\cite{Rebel-1993}, where more pieces of information are collected, the purpose of this paper is to demonstrate that even the muon angles alone provide significant information about the composition. The proposed method relies on shower simulations to obtain an absolute value of an average mass number, just like other indirect methods. If suitable tracking detectors are used, it has the advantage that essentially all required detector parameters for the simulation can be obtained from the measured data as a function of shower size. Therefore, it can be particularly sensitive to changes in the composition across the measured shower size spectrum, even if a comparison with simulations using different interaction models may yield different absolute values. An analysis of data taken with ten CRT detectors -- tracking detectors of 2.5\\,m$^2$ sensitive area each \\cite{CRT-NIM-1} -- and the HEGRA air-shower array \\cite{Fonseca-1995} on La Palma is in progress \\cite{future-CRT-results}. In the data of CRT and HEGRA both muon and electron tracks are analysed. Although the intention of this paper is to promote the method to other air-shower experiments, the simulations shown in this paper are specific to the combination of the CRT and HEGRA experiments. These simulations take into account the response of both components -- the tracking detectors and the air-shower array -- in much detail. After an outline of the method, the specific simulations are described to demonstrate that the method can be very well applied with existing detector technology. Experimental requirements for application of the method and limitations by shower simulations are shown in a more general context, not specific to CRT and HEGRA. ", "conclusions": "The average radial angle of particles are sensitive to the cosmic-ray mass composition. Muons have, among other particles in air showers, many advantages. Their intrinsic angular distribution is very narrow and, thus, the tangential-angle distribution can be used to calibrate the radial-angle resolution as a function of shower size. Muons can be distinguished from other particle types very well. The larger number of muons in showers initiated by heavy primaries compensates for the $N_e$ shower selection bias which favours light primaries. Like any other indirect measurement of some average of the cosmic-ray composition, that method requires comparison of measured data with simulations. Compared to many other indirect methods, the muon radial-angle method has two major advantages: First, the most important detector effects to be included in the simulation can be measured very well and, second, systematic errors, for example due to the interaction model, can be easily checked by comparing measurements at low energies (a few hundred TeV) with simulations for directly measured compositions as in \\cite{Asakimori-1993ab}. Despite some systematic uncertainties in the shower simulations an average mass number ($\\langle\\ln A\\rangle$) can be derived and compared with direct measurements well below the knee. Regardless of that, the muon radial-angle method can be very sensitive to changes in the composition. The radial-angle method would not require a very large experimental effort if existing air-shower arrays are supplemented with suitable tracking detectors." }, "9605/astro-ph9605082_arXiv.txt": { "abstract": "This paper combines data from the three preceding papers in order to analyze the multi-waveband variability and spectral energy distribution of the Seyfert~1 galaxy NGC~4151 during the December 1993 monitoring campaign. The source, which was near its peak historical brightness, showed strong, correlated variability at X-ray, ultraviolet, and optical wavelengths. The strongest variations were seen in medium energy ($\\sim$1.5~keV) X-rays, with a normalized variability amplitude (NVA) of 24\\%. Weaker (NVA = 6\\%) variations (uncorrelated with those at lower energies) were seen at soft $\\gamma$-ray energies of $\\sim$100~keV. No significant variability was seen in softer (0.1--1~keV) X-ray bands. In the ultraviolet/optical regime, the NVA decreased from 9\\% to 1\\% as the wavelength increased from 1275~\\AA\\ to 6900~\\AA. These data do not probe extreme ultraviolet (1200~\\AA\\ to 0.1~keV) or hard X-ray (2--50~keV) variability. The phase differences between variations in different bands were consistent with zero lag, with upper limits of $\\ls$0.15~day between 1275~\\AA\\ and the other ultraviolet bands, $\\ls$0.3~day between 1275~\\AA\\ and 1.5~keV, and $\\ls$1~day between 1275~\\AA\\ and 5125~\\AA. These tight limits represent more than an order of magnitude improvement over those determined in previous multi-waveband AGN monitoring campaigns. The ultraviolet fluctuation power spectra showed no evidence for periodicity, but were instead well-fitted with a very steep, red power-law ($ a = -2.5 $). If photons emitted at a ``primary\" waveband are absorbed by nearby material and ``reprocessed\" to produce emission at a secondary waveband, causality arguments require that variations in the secondary band follow those in the primary band. The tight interband correlation and limits on the ultraviolet and medium energy X-ray lags indicate that the reprocessing region is smaller than $\\sim$0.15~lt-day in size. After correcting for strong (factor of $\\gs$15) line of sight absorption, the medium energy X-ray luminosity variations appear adequate to drive the ultraviolet/optical variations. However, the medium energy X-ray NVA is 2--4 times that in the ultraviolet, and the single-epoch, absorption-corrected X-ray/$\\gamma$-ray luminosity is only about 1/3 that of the ultraviolet/optical/infrared, suggesting that at most $\\sim$1/3 of the total low-energy flux could be reprocessed high-energy emission. The strong wavelength dependence of the ultraviolet NVAs is consistent with an origin in an accretion disk, with the variable emission coming from the hotter inner regions and non-variable emission from the cooler outer regions. These data, when combined with the results of disk fits, indicate a boundary between these regions near a radius of order $ R \\approx 0.07 $~lt-day. No interband lag would be expected as reprocessing (and thus propagation between regions) need not occur, and the orbital time scale of $\\sim$1~day is consistent with the observed variability time scale. However, such a model does not immediately explain the good correlation between ultraviolet and X-ray variations. ", "introduction": "\\label{intro} Two of the most constraining observed properties of active galactic nuclei (AGN) are their large luminosities over a broad range of energies ($\\gamma$-ray through infrared) and their rapid variability (implying a small source size unless the emission is highly beamed). The inferred large energy densities have led to a standard model of the ultimate energy source being the release of gravitational potential energy of matter from an accretion disk surrounding a supermassive black hole (e.g., Rees 1984). Although this general model has broad support, the specific physical processes that produce the complex, broadband spectral energy distributions (SEDs) observed from AGN have not been clearly identified. It is believed that a mix of processes is important. The ultraviolet and optical emission may be primary radiation from an accretion disk (Shields 1978; Malkan \\& Sargent 1982; Malkan 1983). In low-luminosity objects starlight will contribute as well. Thermal dust emission is an important ingredient of the infrared band (Barvainis 1987; Sanders \\et 1989). The high-energy (X-ray and $\\gamma$-ray)emission is not well understood. There are a variety of models for their origin ranging from electromagnetic cascades in an $e^+ e^-$ pair plasma (Zdziarski \\et 1990) to thermal Comptonization models (Haardt \\& Maraschi 1993; Haardt, Maraschi, \\& Ghisellini 1994). Furthermore, gas near the central source may reprocess at least some of the primary radiation via Compton scattering, absorption, and fluorescent processes (Guilbert \\& Rees 1988; Lightman \\& White 1988; George \\& Fabian 1991; Matt, Fabian, \\& Ross 1993). Determination of the mix of physical processes that produce these large, broadband luminosities is a major unresolved issue in AGN research, and multi-waveband variability studies are potentially highly constraining. Causality arguments imply that if emission in a ``secondary\" band is produced when photons from a ````primary\" band are reprocessed in material near the central engine, then variations in the secondary band could not be seen to lead those in the primary band. Furthermore, if the emission in any given waveband is a combination of two independent components (with presumably independent variability behavior), then measurement of broadband spectral variability might allow them to be separated. Finally, if a characteristic variability time scale could be measured, it could be compared with those indicative of different physical processes (e.g., with the expected viscous, orbital, light-travel time scales). In spite of the potential power of this approach, it has not until recently been exploited because of the very large amount of telescope time required. In several experiments designed to measure the size of the broad-line region in the Seyfert 1 galaxy NGC 5548, variations at $\\sim$1400~\\AA\\ were seen to track those at $\\sim$2800~\\AA\\ and $\\sim$5000~\\AA\\ to within $\\ls$1--2 day (Clavel \\et 1991; Peterson \\et 1991; Korista \\et 1995). This was taken to imply an ultraviolet-optical propagation time that is too short to be associated with any dynamics mediated by viscosity, such as variations in the mass inflow rate, in a standard $\\alpha$-disk (Krolik \\et 1991; but see \\S 4.2. below). Similar problems were noted in ultraviolet and optical monitoring of NGC~4151 by Ulrich \\et (1991). Krolik \\et (1991) suggested that variation in the different wavebands in NGC~5548 were coordinated by a photon signal. Nandra \\et (1992) suggested that this signal might be X-ray heating (reprocessing). Several authors constructed specific models of X-ray illuminated accretion disks to account for the NGC~5548 data (Collin-Souffrin 1991; Rokaki \\& Magnan 1992; Molendi, Maraschi, \\& Stella 1992; Rokaki, Collin-Souffrin, \\& Magnan 1993) as well as for NGC~4151 (Perola \\& Piro 1994). A strong test of the idea that the ultraviolet is produced by reprocessing X-ray photons could be made by measuring the time relationship between fluctuations in the ultraviolet and the X-rays, but previous attempts (e.g., Clavel \\et 1992) lacked adequate temporal resolution. In order to attempt this test, an international consortium of AGN observers undertook a campaign to intensively monitor a single Seyfert~1 galaxy, NGC~4151, at ultraviolet, X-ray, $\\gamma$-ray, and optical wavelengths for $\\sim$10 days in December 1993. These data are described in detail in the three preceding papers (Paper I--Crenshaw \\et 1996; Paper II--Kaspi \\et 1996; and Paper III--Warwick \\et 1996); they are summarized in the following section. In this paper, the multi-wavelength data are analyzed in combination. The measurement of the multi-waveband variability, temporal correlations, phase lags, and the broadband optical--through--$\\gamma$-ray SED are analyzed in \\S~3 and the scientific implications are briefly discussed in \\S~4. ", "conclusions": "\\label{discussion} These results have important implications for models that attempt to explain the ultraviolet emission from AGN. There are currently two broad classes of such models. The first hypothesizes that the bulk of the ultraviolet luminosity is produced internally by viscosity in the inner regions of an accretion disk surrounding a central black hole, and the second, that the observed ultraviolet emission is produced in gas illuminated and heated by the source that we observe at high energies. Of course, the true picture could be a combination of these processes, a hybrid in which both intrinsic emission from an accretion disk and reprocessing of X-ray emission are important (and, indeed, may feed back upon each other), or conversely, it may be that neither of these models is relevant. \\subsection{Mass and Size Scales} \\label{scales} Although the specific processes responsible for AGN emission have not been clearly identified, there is broad support for the general model of a black hole and accretion disk (see \\S~1). In this model, the emission from normal (non-blazar, radio-quiet) Seyfert~1s like NGC~4151 is relatively isotropic, not significantly Doppler-boosted or beamed towards Earth. In this case, it is possible to use variability to place relatively model-independent limits on the central black hole mass (and therefore the size scale). The most general is the Eddington limit, which requires only that the source be gravitationally bound and possess a high degree of spherical symmetry. The minimum central mass given by this limit is $$ M_E = { { L_E \\sigma_e } \\over { 4 \\pi G c m_p } }, \\eqno(3) $$ where $ L_E $ and $ M_E $ are the Eddington luminosity and mass, $\\sigma_e$ is the Thompson cross-section, and $ m_p $ is the proton mass. As the integrated luminosity of NGC~4151 is $ \\sim 4 \\times 10^{43} $~erg s$^{-1}$, the Eddington mass is $ M_E \\approx 3 \\times 10^{5} M_\\odot $. For a source surrounding a black hole of mass $M_{BH}$, and Schwarzschild radius $R_S$, the minimum variability time scale ($t_{min}$) can be estimated from the size ($r_{min}$) of the smallest stable orbit, which is $$ r_{min} \\approx ct_{min} \\approx 3R_{S} \\approx 6GM_{BH}/c^2 \\eqno(4) $$ for a Schwarzschild black hole. For $ M_{BH} \\gs M_E \\approx 3 \\times 10^{5} M_\\odot $, this implies $ r_{min} \\gs 3 \\times 10^{11} $~cm or $ t_{min} \\gs 10 $~sec, which is not a significant constraint on data which were sampled every hour. A larger but more model-dependent constraint assumes Keplerian orbits and uses the correlation between the widths of emission lines and the distances estimated from their lags to estimate the central mass. In the form in which this estimate is generally presented, the inferred mass is the true mass if the clouds travel on circular orbits. If the clouds are gravitationally bound, but non-gravitational forces (e.g. radiation pressure or hydrodynamics) affect cloud motions, the real mass is greater than this estimate; if the motions are unbound, the real mass is smaller than this estimate. Clavel \\et (1987, 1990) used this method to derive a central mass of $ M \\approx 4 \\times 10^7 M_\\odot $ for NGC~4151. This corresponds to a smallest stable orbit of $ r_{min} \\approx 4 \\times 10^{13}~{\\rm cm} \\approx 20 $~lt-min. Again, this relatively weak constraint is not significant for these data. \\subsection{Thermal Accretion Disk Models} \\label{disk} If the ultraviolet/optical continuum is optically thick thermal emission, the variability amplitudes can be used to constrain the temperature distribution. The simplest non-trivial general case is a flat, azimuthally symmetric disk with a local blackbody temperature that drops with radius as some power-law: $ T(r) = T_O (r/r_o)^{-\\alpha} $. When $\\alpha$ is 3/4, this is a fair approximation of a standard accretion disk, except at the smallest radii. By contrast, in a disk that radiates predominantly by reprocessed energy (see \\S~4.3.), $\\alpha$ can be smaller, depending on the geometry of both the disk and the source of the primary radiation. If the local emission is described by a blackbody, the contribution of an annulus to the total disk flux density at a given frequency $\\nu$ is $$ S_\\nu \\propto \\int_{x_1}^{x_2} {x^{2/\\alpha-1} \\over e^{-x}-1} dx, \\eqno(5) $$ where $ x = h \\nu /k T(r) $, and the starting and ending points of the integral are defined by the temperatures at the inner and outer radii of the ring. The increasing amplitude of variations with observing frequency is then naturally attributed to changing emission from the hotter regions (that is, the inner disk radii). There is a test of the simplest case that produces simultaneous multi-wavelength variations, in which the emission from the outer disk ($x > x_2$) is constant, and all of the variability is produced by a complete, simultaneous modulation of the emission from the inner disk ($0 < x < x_2$). The only free parameter is the radius that separates the variable and constant parts of the disk, and this can be determined from the NVA at a single wavelength. For example, using the 1275~\\AA\\ variability amplitude of 8.6\\% gives $x_2 = 0.50$ for $\\alpha = 3/4$ or $ x_2 = 1.38 $ for $ \\alpha = 1/2 $. This corresponds to a boundary at the disk radius where the temperature is 215,000 or 78,000 K, respectively. The last two columns of Table~2 show how the percentage flux would drop if all of the emission inside this radius (the putative variable component) went to zero, including the effects of starlight. There is good agreement between the simple thermal model and the observed wavelength dependence of the variability amplitude for the standard accretion disk case, $ \\alpha = 3/4 $. This is not a strong function of how the inner boundary is chosen; for the $ \\alpha = 1/2 $ case, truncating the integration to between $ x_1 = 0.7 $ and $ x_2 = 1.38 $ changes the result by only 20\\%. The success of this simple exercise motivated the fitting of the ultraviolet/optical SED with a standard model of a geometrically thin, optically thick accretion disk (e.g., following the formalism of Sun \\& Malkan 1989). Aside from the starlight, no additional long-wavelength component was included in the models, so no attempt was made to fit fluxes longward of 2~$\\mu$m. If the disk is assumed to be viewed face-on, and the black hole is spinning rapidly (Kerr metric), the best-fit model parameters are $ M_{BH} = 1 \\times 10^8 M_\\odot $ and $ \\dot M = 0.01 M_\\odot$ yr$^{-1}$. If on the other hand the black hole is assumed stationary (Schwarzschild case), the best-fit parameters are $ M_{BH} = 4 \\times 10^7 M_\\odot $ and $ \\dot M = 0.025 M_\\odot$ yr$^{-1}$. In either case, the accretion rate corresponds to 0.6\\% of the Eddington rate. The black hole mass inferred from the Schwarzschild fit agrees with the Keplarian value obtained by Clavel \\et (1987, 1990). These fits give higher weight to the higher signal-to-noise optical continuum than to the ultraviolet continuum where the disk light dominates, which in turn requires a hotter disk and consequently a lower black hole mass ($1 - 2 \\times 10^7~\\rm M_\\odot$). All the disk fits would give significantly larger black hole masses if the disk had a non-zero inclination. Integrating the multi-waveband disk emission out to a boundary radius of $ R \\approx 2 \\times 10^{14}~{\\rm cm} \\approx 0.07 $~lt-day shows that approximately 30\\%, 20\\% and 5\\% of the total disk flux at 1275~\\AA, 2688~\\AA, and 5125~\\AA\\ is produced in the inner disk. (These numbers refer to the Kerr model, but are not very model-dependent; Malkan 1991.) After correcting for the effects of galactic starlight in the $\\sim 10''$ aperture, the 5125~\\AA\\ emission from the inner disk falls to $\\sim$4\\%. For $ M_{BH} \\approx 0.4 - 1 \\times 10^8~M_\\odot $, this radius corresponds to $ R \\approx 6 - 15~R_S $ These fractions are approximately the same as the largest peak-to-peak variations observed in these bands during the intensive 10 day multi-waveband monitoring campaign. Thus, one consistent explanation for the decline in variability with increasing wavelength is that the variations occur entirely inside the inner disk. At a distance $ \\approx 0.07 $ lt-day from a $ 4 \\times 10^7~M_\\odot $ black hole, the orbital time scale is $\\sim$1~day, whereas the dominant fluctuations clearly occur on longer time scales (i.e., the 1275~\\AA\\ peak-to-peak variation was only 42\\% over the entire 10 day intensive campaign). Thus, they could be associated with either orbital mechanics or thermal fluctuations in the inner disk. It must also be noted that this simple disk model does not produce any X-ray emission, although this is also likely to originate within the inner regions. \\subsection{Reprocessing Models} \\label{reprocessing} These data also can be used to constrain models in which the ultraviolet radiation is produced in gas that is heated by the same X-ray continuum that we observe directly at higher energies. In this model, time variations in the ultraviolet and high energy fluxes should be closely coupled: the ultraviolet becomes stronger shortly after the high energy flux rises, and the high energy flux may itself respond to changes in the ultraviolet flux if the ultraviolet photons provide seeds for Compton upscattering into the higher energy band. The delays in both cases are essentially due to the light travel time between the two source regions. Consequently, the (reprocessed) ultraviolet emission should vary simultaneously with the (primary) X-rays on time scales longer than the round-trip light-travel time between the emitting regions (e.g., Clavel \\et 1992). The strong correlation between the ultraviolet and X-ray variations therefore supports the reprocessing hypothesis. The lack of any lag within the ultraviolet could be explained in two ways: either the sub-regions responsible for variations in different wavelengths are likewise very close to each other, or, as with the accretion disk model, only the hottest part of the region is varying. In the context of this model, the lack of any detectable lag implies that the X-ray and ultraviolet emitting regions are separated by $\\ls$0.15~lt-day, ($ 1/2 \\times 0.3$~lt-day, because the light must travel in both directions), so the bulk of the reprocessing must occur in the central regions. Perola \\& Piro (1994) applied a more detailed reprocessing model to earlier X-ray/ultraviolet observations and predicted that high time resolution monitoring would measure lags of order 0.03--0.1~day (rather close to but still formally consistent with the measured limits of $\\ls$0.15--0.3~day). The reprocessing model is supported by the broad profile of the iron K$\\alpha$ line, which suggests relativistic effects associated with an origin very close to a central black hole (Yaqoob \\et 1995). However, the \\ASCA\\ observations (and previous medium X-ray observations) found no evidence for any significant ``hard tail\" in the X-ray spectrum (Paper III; Maisack \\& Yaqoob 1991). While the presence of the iron line implies reprocessing by some material, the lack of a ``reflection hump'' suggests that the material is not optically thick to Compton scattering, as would be expected in the putative reprocessing disk. An associated problem is the overall energy budget. The total X-ray/$\\gamma$-ray flux must be adequate to produce the observed ultraviolet/optical/infrared flux, and the variable high energy flux must also equal or exceed that at lower energies. The observed, integrated 0.1--1~$\\mu$m flux is $ \\sim 11 \\times 10^{-10} $ erg cm$^{-2}$ s$^{-1}$. As strong Ly$\\alpha$ and C~IV emission indicates that the ultraviolet bump extends to wavelengths substantially shorter than 1000~\\AA, the intrinsic, integrated flux is probably larger by a factor of $\\sim$3, corresponding to a total ultraviolet/optical/infrared flux of order $ \\sim 30 \\times 10^{-10} $ erg cm$^{-2}$ s$^{-1}$. The observed, integrated 1--2~keV and 2--10~keV fluxes are $ \\sim 0.05 \\times 10^{-10} $ erg cm$^{-2}$ s$^{-1}$ and $ \\sim 2.4 \\times 10^{-10} $ erg cm$^{-2}$ s$^{-1}$, respectively After correction for line-of-sight absorption (which is particularly important at 1--2~keV), the intrinsic, integrated fluxes rise to $ \\sim 0.9 \\times 10^{-10} $ erg cm$^{-2}$ s$^{-1}$ and $ \\sim 3.6 \\times 10^{-10} $ erg cm$^{-2}$ s$^{-1}$, for a total of $ \\sim 4.5 \\times 10^{-10} $ erg cm$^{-2}$ s$^{-1}$. This is not adequate to power the lower energies, but inclusion of the GRO data and interpolating between ASCA and GRO yields a (rather uncertain) integrated 1--200~keV flux of order $ \\sim 15 - 20 \\times 10^{-10} $ erg cm$^{-2}$ s$^{-1}$. This would be of order the amount necessary to power the lower energies. However, the fact that the $\\gamma$-ray variations differ from those in all other wavebands suggests that the bulk of the 10--200~keV emission (which dominates the X-ray/$\\gamma$-ray flux) arises in a component that does not fully participate in the reprocessing. In this case, the X-ray/$\\gamma$-ray luminosity would still be a factor of order $\\sim$3 too small, so at most $\\sim$1/3 of the observed infrared/optical/ultraviolet flux could be due to reprocessing. However, this cannot be independently verified because the \\ASCA\\ sampling above 2~keV is inadequate to characterize the variability, and indeed the entire 10-50~keV spectrum is interpolated, not observed. Although the absolute X-ray luminosity changes are observed to be small compared to those in the ultraviolet/optical, spectral fits indicate that the X-rays are highly (factor of $\\sim$15--20) absorbed, and the intrinsic, absorption-corrected variations have more than enough power to drive the ultraviolet/optical variations. However, the NVA, which measures the fractional (as opposed to absolute) variations is 24\\% in the X-rays, while it is only 9\\%, 5\\%, 4\\%, and 1\\% at 1275~\\AA, 1820~\\AA, 2688~\\AA, and 5125~\\AA, respectively. This indicates that at most 35\\%, 20\\%, 15\\%, and 4\\% of the emission at 1275~\\AA, 1820~\\AA, 2688~\\AA, and 5125~\\AA\\ could be due to reprocessing, with the rest coming from a component with different (slower) variability. As with the previous analysis, this would indicate that at most $\\sim$1/3 of the ultraviolet/optical/infrared can be reprocessed emission from higher energies. \\subsection{Summary} \\label{summary} \\begin{enumerate} \\item NGC~4151 showed significant variability over time scales of days, so the emitting region must be smaller than of order a few light days across, assuming the emission is not beamed. The limits on the interband lags indicate that, if there is reprocessing of flux between bands, none of the emission regions could be larger than $\\sim$0.15~lt-day. The lower limit to the central black hole mass derived from the Eddington limit is small ($ M_{BH} \\gs 3 \\times 10^5~M_\\odot $), corresponding to a minimum variability time of only 10 sec, which is not a significant constraint. \\item Accretion disk fits to the SED yield a central black hole with a mass of $ 0.4-1 \\times 10^8 M_\\odot $, accreting well below the Eddington limit. The fact that the low NVAs decrease from medium energy X-ray to ultraviolet to optical wavebands is consistent with the accretion disk model if the bulk of the variable ultraviolet/optical emission originates in a region $\\sim$0.07~lt-day ($ \\sim 10 R_S $) from the center. This model gives is no immediate explanation of the link between ultraviolet and X-ray variations. \\item The reprocessing model predicts a strong correlation between ultraviolet and X-ray variability, which is observed. Because the NVAs become systematically smaller at longer wavelengths, and because the absorption corrected X-ray/$\\gamma$-ray luminosity is only much smaller than in the ultraviolet/optical/infrared, and at most $\\sim$1/3 of the lower energy emission could be produced by reprocessing. \\end{enumerate} This suggests that perhaps the ultraviolet arises in a disk powered partially by illumination by an X-ray source and partially by internal viscosity and accretion. Determining the exact mix of these emission components will require probing the ultraviolet/X-ray bands at the shortest accessible time scales. It is of particular importance to extend the coverage to the gap at X-ray energies harder than 2~keV. This is the goal of the upcoming coordinated {\\it XTE/IUE}/ground-based observations of NGC~7469, scheduled for the middle of 1996, and it is hoped that they will shed further light on this important question." }, "9605/astro-ph9605010_arXiv.txt": { "abstract": "Presently, most observations of absorption lines from interstellar and intergalactic matter have sufficient resolution to show most of the structure at differing radial velocities of the absorber. This added information allows one to go beyond the practice of just obtaining equivalent widths. As with measurements of $W_\\lambda$, however, it is important to sense and correct for the fact that some parts of a profile may arise from absorption peaks that are strong enough to be saturated. This effect may be unrecognized, or at least underappreciated, in those cases where the narrowest velocity structures are degraded by the convolution of the true spectrum by the instrumental profile. Using a procedure that is virtually identical to the curve of growth method for equivalent widths, one can compare at any velocity the apparent optical depths $\\tau_a$ of two lines that have significantly different transition probabilities. If their ratio is smaller than the ratio of the lines' values of $f\\lambda$, the actual saturation is more severe than that indicated by the values of $\\tau_a$. This paper describes a simple procedure for selectively boosting $\\tau_a$ of the weaker of the two lines so that unresolved saturated structure is accounted for. This enables one to obtain a very nearly correct answer for the column density per unit velocity. (The lost velocity detail is not restored however.) Two synthetic, test examples of very complex, saturated profiles are analyzed with this method to show how well it works. A demonstration with real observations is also presented. An explicit, easily-computed formula that is a very close approximation to the real correction factors is given, to make data analysis and error estimation more convenient. ", "introduction": "Over recent years, improvements in spectrographs and detectors have brought forth substantial gains in the quality of observations of absorption features arising from either interstellar gases in front of stars in our Galaxy or material in very distant systems in front of quasars. Most modern observations of these features have good signal-to-noise ratios, accurate determinations of the zero intensity level, and sufficient wavelength resolution to break the overall absorption profiles into subcomponents at different Doppler shifts. These advances have allowed us to progress beyond the simple practice of measuring and interpreting just the total equivalent widths of the absorptions. Now, with the ability to discern the added dimension of velocity in the absorption features, an observer is presented with new opportunities for more detailed interpretations. With this expansion, however, come new challenges and responsibilities, ones that extend beyond the framework of analysis techniques that were connected with equivalent widths. Except for features that we are sure must arise from regions with elevated temperatures, we are rarely confident that all of the substructures within the radial velocity peaks have been completely discerned by the spectrograph. There is evidence that, as a rule, observations taken at successively higher resolutions reveal finer details than those registered before; good examples can be seen in the interstellar Na~I absorption features recorded by Wayte, Wynne-Jones \\& Blades \\markcite{2056} (1978), Blades, Wynne-Jones \\& Wayte \\markcite{304} (1980), Welty, Hobbs \\& Kulkarni \\markcite{262} (1994) and Barlow, et al. \\markcite{3122} (1995) and some molecular lines observed by Crawford, et al. \\markcite{2651} (1994) and Crane, Lambert \\& Sheffer \\markcite{304} (1995). Ultimately, the intrinsic dispersion of Doppler velocities (partly thermal, partly turbulent) may be the only limiting factor in the fineness of the real features. With typical temperatures of cool gas complexes extending below 100K and negligible turbulence, we can expect velocity dispersion parameters $b$ that could be as small as 0.2 km~s$^{-1}$ (for atoms with a mass of about 40 amu), a value that is still significantly narrower than most present-day instrumental profiles. Unfortunately, as we shall see in the discussion that follows, the consequences of instrumental smoothing are more serious than just a loss of velocity detail. Observers must often face the challenge of determining how badly saturated the absorptions were before the smoothing took place. This is an important step in deriving trustworthy conclusions about the amount of material that caused the absorption. An observer's ultimate objective is usually to determine not only the total column density $N$ of an absorber, but also how the atoms, ions or molecules are distributed over different radial velocities. For the original form of the spectrum $I(v)$ that has not been degraded by a convolution with the instrumental profile, the column density as a function of Doppler velocity $v=(\\lambda - \\lambda_0)/(c\\lambda_0)$ is equal to the absorption feature's optical depth $\\tau(v)=\\ln [I_0/I(v)]$ multiplied by the constant factor $(m_ec)/(\\pi e^2f\\lambda)$ ($I_0$ is the intensity of the unabsorbed continuum). What one observes in actual practice, however, is an apparent intensity $I_a(v)$ that is a smoothed form of the real intensity profile $I(v)$. Even so, as long as the smoothing is not too severe, one can derive an approximate representation that is called the {\\it apparent} optical depth $\\tau_a(\\lambda) = \\ln[I_0/I_a(v)]$, an interpretative concept first used for high resolution recordings of lines in the visible part of the spectrum by Hobbs \\markcite{1080,1081,1083,1085,1086} (1971, 1972, 1973, 1974a, b) and later invoked for UV lines by Savage, et al. \\markcite{1149} (1989), Jenkins, et al. \\markcite{1367} (1989), Savage, Massa \\& Sembach \\markcite{29} (1990), Joseph \\& Jenkins \\markcite{1728} (1991), Sembach, Savage \\& Massa \\markcite{119} (1991) and Tripp, Sembach \\& Savage \\markcite{2551} (1993) in their analysis of some IUE and IMAPS data. More recently, spectra of exceptionally good quality and resolution have been produced by the GHRS echelle spectrograph on the Hubble Space Telescope, and representations of $\\tau_a$ have been important tools for understanding these data \\markcite{1965,1966,2369,2519,2630,311} (Cardelli et al. 1991; Savage et al. 1991; Savage, Cardelli, \\& Sofia 1992; Sofia, Savage, \\& Cardelli 1993; Savage, Sembach, \\& Cardelli 1994; Cardelli \\& Savage 1995). Important properties of $\\tau_a$ have been explained in detail by Savage \\& Sembach \\markcite{110} (1991). The papers cited above have made it clear that apparent optical depths are useful functions for deriving column densities and extracting linear representations for all of the kinematical information that is available. The information conveyed by the $\\tau_a$ functions represents a significant improvement over the single numbers that signify the equivalent widths of entire profiles or resolved pieces of profiles. Nevertheless, we must be aware of some limitations that arise in certain circumstances \\markcite{1367,1728} (Jenkins et al. 1989; Joseph \\& Jenkins 1991). The real physical processes that created the recorded intensities consisted of an exponential attenuation of the light, followed by an instrumental smearing of the spectrum. The derivation of $\\tau_a$ is an attempt to reconstruct a linear representation for the amount of absorbing material by unraveling the exponential absorption law, but it disregards the convolution by the instrumental profile that followed. Normally, we are accustomed to interpreting functions where there is simply a loss of detail caused by smoothing. But unfortunately $\\tau_a$ does {\\it not} represent just a smoothed version of the real $\\tau$. Instead, we find that the smoothing has deaccentuated the extremes in $\\tau$, and the nonlinear operation used to construct $\\tau_a$ creates a representation of $\\tau$ that is both smoothed {\\it and distorted}. There are only two circumstances where $\\tau_a$ represents an unbiased reflection of the sought-after distribution: (1) All of the velocity details of the profile were fully resolved so that $\\tau_a$ is identical to $\\tau$, or (2) $\\tau\\ll 1$ everywhere, so that the $\\ln[I_0/I(\\lambda)]$ is essentially equivalent to the linear representation $[I_0-I(\\lambda)]/I_0$ whose integral over any $\\lambda$ interval is not changed by the convolution operation. In the first case, all of the information is recovered, while in the second, the only repercussion is a loss of velocity detail. In short, in the course of interpreting $\\tau_a(v)$ an observer must be vigilant about the possible loss of evidence that narrow peaks in absorption are badly saturated. There is a danger that instrumental smearing has created a picture where the reduction of intensity {\\it appears} to be weak and thus far from saturation. The same argument holds for stronger features. Even if one can sense that some saturation must be evident because the intensity is significantly below the continuum level, smoothing of the bumps could cause one to underestimate its severity and then misjudge the actual amount of material in the line of sight. A straightforward way to sense and measure the amount of hidden saturation is to observe two or more lines with differing transition probabilities from the same species. If, at any velocity $v$, the apparent optical optical depths in the smoothed spectra exhibit a scaling that is weaker than the progression of the respective lines' $f\\lambda$ values, then there is good reason to believe that in some places the unresolved saturated structures are stronger than a general level suggested by the apparent (smoothed) intensity values. The object of this paper is to demonstrate how one can correct for this effect and derive reasonably accurate representations of column density as a function of velocity. The method to be outlined has a relationship with the conventional curve of growth analysis for equivalent widths that is stronger than just a simple analogy. As the arguments in \\S\\ref{concepts} will show, the two methods have nearly identical mathematical foundations. The principal advantage of correcting $\\tau_a$ rather than $W_\\lambda$ is that we do not sacrifice the information contained in velocity peaks that can be resolved. Hence one can explore, for instance, how the abundances of different species change with velocity, rather than just determining the overall abundance ratios at all velocities within some large complex of components. In their instructive overview on how to derive, interpret and exploit the apparent optical depths of interstellar features, Savage \\& Sembach \\markcite{110} (1991) likewise addressed the problem of how to cope with the misrepresentations of the real optical depth levels caused by instrumental smearing. They proposed that one should measure the disparity in inferred column densities {\\it integrated over velocity} for two lines and then apply, according to a specific prescription, a global, multiplicative (upward) correction to the entire profile of the weaker line.\\footnote{This correction procedure may be applied to any two lines of arbitrarily different strengths (within reason), but Savage \\& Sembach supplied correction factors only for lines that had a 2:1 ratio for $f\\lambda$.} The method advocated here uses a different approach that is an improvement over the one described by Sembach \\& Savage. Corrections are applied on the spot at individual velocities, without regard to what is happening elsewhere. The two methods will be compared in \\S\\ref{comparison}. A very different tactic for analyzing saturated, blended features is to build a model of the real absorption complex by defining such parameters as the strengths, widths and velocity centroids of individual components \\markcite{1769,1819,19,1872,2671,1988,2481,262,2462,2701,250,304} (Vidal-Madjar et al. 1977; Ferlet et al. 1980; Welsh, Vedder, \\& Vallerga 1990; Hobbs \\& Welty 1991; Welsh et al. 1991; Welty, Hobbs, \\& York 1991; Spitzer \\& Fitzpatrick 1993, 1995; Vallerga et al. 1993; Fitzpatrick \\& Spitzer 1994; Welty, Hobbs, \\& Kulkarni 1994; Crane, Lambert, \\& Sheffer 1995). One then solves (or searches) for a minimum in the $\\chi^2$ values as parameters for the theoretical representation of the instrumentally blended complex are compared with the observations. In cases where independent information can help to constrain the choice of free parameters (such as much higher resolution observations of other species), this method can be successful. While such model building has the potential of helping us to understand some details that may not be evident in a display of smoothed optical depths, it has the disadvantage of usually relying on human judgement to define the constraints on the parameters and the method of converging to a minimum $\\chi^2$. Also, the models contain specific assumptions about the functional forms of the components, with the usual choice being a Gaussian (or Voigt) profile. By contrast, the derivation of $\\tau_a$ is a simple, mechanical process that places no such requirements on the investigator and does not rely on any specific models, even when the corrections discussed later in this paper are implemented. ", "conclusions": "\\label{recipe} The basic principles developed in \\S\\ref{concepts} and the demonstrations in \\S\\ref{demo} and \\S\\ref{real_obs} show that it is possible, even under fairly harsh circumstances of unresolved saturation, to derive good measurements of the column densities of absorbing substances as a function of velocity if two or more lines with different transition probabilities are observed. The analysis method proposed in this paper has a special virtue, in that it avoids the requirement for model building: one is not forced to try to reconstruct exactly what profiles should have looked like before they were smoothed by the instrument. Obviously, how well the method works depends on a number of experimental conditions, such as ratio of $f\\lambda$ of two lines, the signal-to-nose ratio of the spectrum, how well various kinds of systematic error are controlled, and the accuracy in the match of the two velocity scales. It is not easy to give guidelines here on these issues, since there are so many possibilities. A formal evaluation of how the errors can propagate through the mathematical transformations can give some guidance. This sort of error analysis combined with common sense are probably the best tools for judging the reliability of the final results. One must be wary of the trap where a disproportionately large fraction of the gas is located in very narrow features that are fully saturated in both lines, but where most of the absorption is caused by high-velocity fluff that is unsaturated. This condition is especially likely to arise when there is a bimodal distribution in the widths and strengths of the components in the ensemble. One should be alert for physical circumstances that could produce this state, such as lines of sight that have the right mixture of contributions from cold H~I and much hotter H~II regions, cases where both quiescent and shock-accelerated gases are present, or, when one is looking through entire galaxies, there is a mixture of disk and halo gases. That being said, it is reassuring to see from the demonstration in \\S\\ref{demo} that the analysis is remarkably tolerant to the existence of components that span a wide range of properties (as long as they are not too bizarre). Even a power law for the distribution of $\\tau_0$ is acceptable: see Jenkins \\markcite{1355} (1986) for details. To summarize how the correction method works, we review in the form of a recipe how one would apply it in practice: \\begin{enumerate} \\item For a given absorber, obtain spectra of two lines that have values of $f\\lambda$ that differ by a large enough factor to show when saturation might be taking place. \\item On the basis of what the lines look like, coupled with any independent evidence (e.g. higher quality observations of other species) or a general knowledge of the physical situation, decide that the pitfall discussed in the above paragraph does not apply. If it could, do not proceed further. Also, the analysis should not be undertaken if $\\tau_a(v)$ is very large (the threshold for rejection should depend on how accurately the intensities are measured). \\item For each line, measure $I_0/I_a(v)$ and evaluate its natural logarithm to obtain $\\tau_a(v)$. \\item At every velocity $v$, use Eq.~\\ref{x} to evaluate the quantity $x(v)$ from measurements of $R(v)$, the ratio of the strong line's $\\tau_a(v)$ to that of the weak line, along with the two lines' $f\\lambda$'s. \\item From $(f\\lambda)_{\\rm strong}/(f\\lambda)_{\\rm weak}$, determine appropriate values for the coefficients $a_0$ through $a_4$ from Table~\\ref{coef}. If necessary, intermediate values can be found by interpolation. \\item For every $v$, evaluate the correction $C_R(v)$ by the use of Eq.~\\ref{logC} and the coefficients derived in the preceding step. \\item Derive the column density of the absorber per unit velocity by taking the product of the weak line's $\\tau_a(v)$ and its enhancement factor $C_R(v)$, and multiplying it by the constants in front of the integral in Eq.~\\ref{N}. Numerically, the latter equals $3.767\\times 10^{14}/f\\lambda$, if $\\lambda$ is expressed in \\AA\\ and the column density per unit velocity has the units ${\\rm cm}^{-2}({\\rm km~s}^{-1})^{-1}$. \\end{enumerate}" }, "9605/astro-ph9605142_arXiv.txt": { "abstract": "During the fifth flight of the Microwave Anisotropy Experiment (MAX5), we revisited a region with significant dust emission near the star Mu Pegasi. A 3.5 cm$^{-1}$ low frequency channel has been added since the previous measurement (\\cite{mei93a}). The data in each channel clearly show structure correlated with IRAS 100 \\micron\\ dust emission. The spectrum of the structure in the 6, 9 and 14 cm$^{-1}$ channels is described by $I_{\\nu}\\propto\\nu^{\\beta}B_{\\nu}(T_{dust})$, where $\\beta$ = 1.3 and $T_{dust}$ = 19~K and $B_{\\nu}$ is the Planck function. However, this model predicts a smaller amplitude in the 3.5 cm$^{-1}$ band than is observed. Considering only linear combinations of the data independent of the best fit foreground spectrum for the three lower channels, we find an upper limit to CMBR fluctuations of $\\Delta T/T = \\langle \\frac{C_l~l(l+1)}{2\\pi}\\rangle^{\\frac{1}{2}} \\leq 1.3\\times 10^{-5}$ at the 95\\% confidence level. The result is for a flat band power spectrum and does not include a 10\\% uncertainty in calibration. It is consistent with our previous observation in the region. ", "introduction": "Cosmic Microwave Background Radiation (CMBR) anisotropy measurements provide a means of constraining various cosmological models. Several groups have reported measuring CMBR anisotropies at 0.5 to 1\\arcdeg\\ (\\cite{che95,cla94,deb94,dev94,gun95,net95,ruh95}). However, disentangling the primodial fluctuatations from foreground sources is problematic even if the foreground is understood. The third flight of MAX made an observation in a medium constrast dust region near the star Mu Pegasi and measured anisotropy smaller than seen elsewhere in the same flight (\\cite{gun93,mei93a}). In order to confirm this measurement, we returned to the Mu Pegasi region with an additional low frequency band centered at 3.5 cm$^{-1}$. ", "conclusions": "We have presented new results from a search for CMBR anisotropy with high sensitivity at 0\\fdg5 angular scales near the star Mu Pegasi. Free-free and synchrotron radiation are excluded as the main source of signal on amplitude and spectral arguments. There are no strong point sources in the field. The morphology of the observed structure is consistent with known interstellar dust but not the spectrum. The structure in the 6, 9 and 14 cm$^{-1}$ channels is fit by a single dust model power law $I_{\\nu} \\propto \\nu^{\\beta} B_{\\nu}(T_{dust})$, where $\\beta = 1.3$, and $T_{dust} = 19$~K. We cannot rule out the possibility that the structure is a correlated combination of dust and CMBR or dust and free-free radiation. Linear combinations of the data independent of the best fit spectrum yield a $\\Delta T/T~<~1.3 \\times 10^{-5}$. (95\\% confidence level) The results are consistent with our previous observation in the region. These data are available from the authors." }, "9605/astro-ph9605127_arXiv.txt": { "abstract": "We investigate the possible role of an accretion disk instability in producing the giant outbursts seen in GRO J1744-28. Specifically, we study the global, time dependent evolution of the Lightman-Eardley instability which can develop near the inner edge of an accretion disk when the radiation pressure becomes comparable to the gas pressure. Broadly speaking, our results are compatible with earlier works by Taam \\& Lin and by Lasota \\& Pelat. The uniqueness of GRO J1744-28 appears to be associated with the constraint that, in order for outbursts to occur, the rate of accretion at the inner edge must be within a narrow range just above the critical accretion rate at which radiation pressure is beginning to become significant. \\medskip \\medskip Subject Headings: accretion disks: instabilities $-$ X-rays: bursts $-$ pulsars: individual (GRO J1744-28) ", "introduction": "On 2 December 1995 the Burst and Transient Source Experiment (BATSE) on the {\\it Compton Gamma Ray Observatory} ({\\it CGRO}) discovered a new source which maintained a high persistent flux level, and also showed outbursts with a duration of about 10 seconds during which time the X-ray flux increased by about 4-5 (Kouveliotou et al. 1996). The source has subsequently been studied in detail by the {\\it Rossi X-ray Timing Explorer} ($=${\\it RXTE}, cf. Swank et al. 1996). Subsequent investigation of this unusual source showed it to reside in a binary star system with an orbital period of 11.8 days (Finger et al. 1996). The pulsar has a spin period of 0.467 seconds (Finger et al. 1996) and concomitant corotation radius $1\\times10^8$ cm $(M_1/1.4\\msun)^{1/3}$. Several papers have already appeared which attempt to address broad issues connected with the evolutionary status of the system and the strength of the magnetic field on the pulsar (e.g., Lewin et al. 1996, Daumerie et al. 1996, Lamb et al. 1996, Sturner \\& Dermer 1996). The question has naturally arisen as to the cause of the outbursts. The two main models being discussed at present are (1) thermonuclear flashes of material accumulated on the surface of the neutron star, and (2) some as yet unspecified accretion disk instability which causes a periodic storage and dumping of some material in the inner disk. In the light curve one sees a dip and recovery period following each outburst, during which time the light asymptotically approaches its pre-outburst level. Also, the spectrum does not change dramatically going from quiescence to outburst. This behavior may not favor the thermonuclear flash model (Lewin et al. 1993, 1996). The most obvious disk instability to invoke for the outbursts is the Lightman-Eardley (LE) instability (Lightman \\& Eardley 1974). This instability develops in viscous accretion disks when the radiation pressure becomes comparable to the gas pressure. Several papers have already investigated the global, nonlinear evolution of accretion disks which are LE unstable (Taam \\& Lin 1984=TL, Lasota \\& Pelat 1991=LP). These investigators showed that the instability first develops at the inner edge of the disk and propagates outward as a heating wave of high viscosity material, much like the heating wave associated with the classical limit cycle instability in dwarf novae and X-ray novae. The instability does not propagate far, and the heated matter with its increased viscosity rapidly accretes onto the central star and produces a brief burst. Figure 1 shows a $\\sim1$ hr stretch of data obtained 13 March 1996 with the Proportional Counter Array (PCA) instrument on {\\it RXTE}. Three outbursts were seen $-$ with durations of $\\sim$10 seconds and recurrence times of $\\sim$1000 seconds. The light curves shown in TL and LP bear a striking resemblance to those seen in GRO J1744-28, in particular one sees the broad dip and recovery phase after a burst has ended. The main shortcoming of the TL and LP bursts insofar as they might pertain to GRO J1744-28 is that they recur every few seconds and last for less than one second. These time scales are both much faster than observed. In their modeling TL and LP (1) set the viscosity parameter $\\alpha$ to its maximal value of 1, and they (2) took the inner disk edge to equal roughly the radius of the neutron star ($\\sim10^6$ cm), whereas we suspect that in GRO J1744-28 the pulsar has a strong magnetic field. In this {\\it Letter} we quantify the increases in the outburst time scales due to setting $\\alpha$ to a more reasonable value, and to increasing $r_{\\rm inner}$. \\section {General Physical Considerations} The limit cycle found by TL and LP is unlike the standard limit cycle for dwarf novae (see Cannizzo 1993a for a recent review). In the standard dwarf nova model, the locus of steady state solutions forms an S-curve when plotted as effective temperature versus surface density (Meyer \\& Meyer-Hofmeister 1981). For the LE instability, however, there is no upper stable branch. (This situation has recently changed [Abramowicz et al. 1988].) Following the discovery of the LE instability in the 1970's, this lack of an upper stable branch was viewed as a severe limitation of the instability which might restrict its usefulness. The earliest time dependent studies of the LE instability solved only the viscous diffusion equation for surface density. TL and LP simultaneously solved both the diffusion equation and the thermal energy equation for temperature, and therefore considered rather more general accretion disks which need be neither steady (i.e., ${\\dot M} $ constant with radius) nor in thermal equilibrium. The fundamental obstacle to progress in accretion disk research has been the lack of understanding of the physical mechanism responsible for the viscous dissipation. In a recent study of the time dependent evolution of accretion disks in black hole X-ray binaries, Cannizzo et al. (1995$=$CCL) found that, to reproduce the observed $\\sim30-40$ day exponential decays of the X-ray fluxes in the soft X-ray transients, the Shakura-Sunyaev viscosity parameter $\\alpha$ must take the form $\\alpha=\\alpha_0(h/r)^n$, where $\\alpha_0 \\simeq 50$ and $n=1.5$. In this study we adopt $\\alpha=50(h/r)^{1.5}$, keeping in mind that this form may not be valid when radiation pressure begins to play a role. In the limit of large $\\alpha$, we do not allow $\\alpha$ to exceed $0.25$. One may gain some rough understanding of the criterion for instability by considering scalings for physical properties at the local maximum in $\\Sigma$ associated with the transition to radiation pressure domination. Using the Shakura-Sunyaev ``middle'' region for which $P=P_{\\rm gas}$ and $\\kappa=\\kappa_{\\rm es} = 0.34$ cm$^2$ g$^{-1}$, the rate of accretion at which the gas and radiation pressure are equal is \\begin{equation} {\\dot M}_{\\rm crit} = 8.3\\times 10^{18} \\ {\\rm g} \\ {\\rm s}^{-1} \\ \\alpha^{-1/8} \\Omega^{-7/8} \\mu^{-1/2} \\end{equation} \\noindent (Shakura \\& Sunyaev 1973). Here $\\Omega$ is the local angular frequency (assumed to be Keplerian) and $\\mu$ is the mean molecular weight ($=0.617$). The temperature associated with the LE unstable branch and with $\\Sigma_{\\rm crit}$ is $T_{\\rm crit} = 2.11\\times 10^6 \\ {\\rm K} \\ \\alpha^{-1/4} \\ \\Omega^{1/4}$. Combining this with the law $\\alpha=50(h/r)^{1.5}$ and the condition of hydrostatic equilibrium $h\\Omega = \\sqrt{{\\cal R}T/\\mu}$ gives \\begin{equation} {\\dot M}_{\\rm crit} = 1.5\\times 10^{18} \\ {\\rm g } \\ {\\rm s}^{-1} \\ \\ r_8^{1.26} \\ m_1^{-0.55}. \\end{equation} The viscous diffusion time at the inner edge $ t_{\\nu, \\ {\\rm crit} } =$ $ {r_{\\rm inner}}^2 / \\nu_{\\rm crit} = 1200$ s $ \\ r_8^{0.58} \\ m_1^{ 0.79}$, where $\\nu_{\\rm crit} =$ $ (2\\alpha_{\\rm crit}/3\\Omega_{\\rm inner})$ $ ({\\cal R}T_{\\rm crit}/\\mu)$, $r_8=r_{\\rm inner}/10^8$ cm, and $m_1 = M_1/1\\msun$. This time scale is roughly the observed recurrence time scale for outbursts in GRO J1744-28. \\section {Model} The model we use is the same as that described in detail in TL and LP. This is a time dependent model which follows the evolution of surface density and temperature. The heating and cooling functions are evaluated separately, and the radial flow of energy $-$ from both advection and diffusion $-$ is included. The radial pressure gradient and departures from Keplerian flow are not included. Our numerical code is a modified version of the one used previously for modeling dwarf novae and X-ray novae (cf. Cannizzo 1993b, Cannizzo et al. 1995). In this study we utilize a grid spacing for which $\\Delta r\\propto \\sqrt{r}$, and take $N=40$ radial grid points. For the pulsar mass we adopt $M_1 = 1.4\\msun$. The inner and outer disk radii are taken to be $r_{\\rm inner}= 10^{7.5}$ cm and $r_{\\rm outer} = 10^9$ cm, respectively. The value of $r_{\\rm inner}$ was chosen to be less than the corotation radius, in order to be consistent with the observed spin-up of the pulsar. The value of $r_{\\rm outer}$ was chosen to be large enough so that the heating front never comes close to reaching it. Figure 2 shows a sample light curve from our model, for a mass transfer rate into the outer disk of $1.5\\times 10^{18}$ g s$^{-1}$. We show a 3000 s history of (1) the rate of mass loss at the inner disk edge, and (2) the mass of the accretion disk. For this model, the observed burst durations of $\\sim10$ s and recurrence times of $\\sim1000$ s are reproduced. There is also a dip and recovery following each major outburst $-$ although the dip is somewhat deeper and faster than observed. Figure 3 shows the evolution of the disk in $Z=P_{\\rm radiation}/P_{\\rm gas}$, $\\Sigma$, and $h/r$. We show 100 seconds of evolution centered on the second burst in Figure 2, spanning the time from 1480 to 1580 seconds. Each curve in Fig. 3 is separated by 2 seconds. The $t=0$ curve corresponds to just prior to the onset of the outburst. The ratio $Z$ has just begun to exceed $\\sim1$ in the inner disk. At slightly later times $Z$ increases rapidly to $\\sim10$ as the local gas heats and matter accretes onto the pulsar, but then quickly drops back down to $<1$ as the decreased surface density forces a return to the gas pressure dominated branch. The second panel in Figure 3 reveals how the heating front is propagated as a local enhancement in $\\Sigma$. This is quite similar to what is seen in computations of the classical limit cycle instability (Cannizzo 1993b). Finally, the third panel shows that $h/r$ is always considerably less than unity $-$ varying from a few percent in quiescence to $\\sim0.1$ in outburst. Figure 4 shows the evolution of the disk at two radial grid points near the inner disk edge in $(T,\\Sigma)$ space. The dashed line shows the standard equilibrium relation derived from taking the heating and cooling functions to be equal and assuming the viscosity to couple to $P_{\\rm gas} + P_{\\rm radiation}$ (as in our model). The dotted curve shows the equilibrium track for which the viscosity couples to the gas pressure only. In quiescence the evolutionary track closely follows the thermal equilibrium curve. The deviation between the actual evolution and the equilibrium curve becomes stronger for the evolution at $4\\times 10^7$ cm as $\\Sigma_{\\rm crit}$ is approached. In Figure 4 we see that, after an annulus has made a transition to the LE state, it eventually migrates to smaller surface density (due to removal of matter from the inner edge), and finally proceeds back down to the gas pressure dominated branch. At this point we observe the build-up in $\\Sigma$ associated with material from further out flowing in to refill the cavity. The evolution for the annulus at $1.1\\times 10^8$ cm is slightly different. This annulus is further away from the site of the initial trigger, and only makes the transition to the high state by virtue of having the heating front sweep past. The surface density drops after the heating wave passes, and rapid cooling forces a return to the gas pressure dominated branch. The evolutionary trends shown in Figure 4 are similar to those displayed by LP. ", "conclusions": "We have shown how the LE instability operating in the inner edge of an accretion disk can be used to account for the giant outbursts seen in the bursting pulsar GRO J1744-28. In accordance with the time dependent calculations of TL and LP, we find that the LE instability never has a chance to go strongly into the non-linear regime because the rapid loss of material from the inner edge which happens once the inner disk starts to become LE unstable prevents $P_{\\rm radiation}/P_{\\rm gas}$ from running away to a high value. The material that is evacuated onto the pulsar during an accretion event is replenished by material flowing in from further out, hence the dip and recovery in the light curve following an outburst. TL and LP found much shorter outburst time scales (i.e., $t_{\\rm recurrence} \\simeq $ a few seconds) than we do because they took larger $\\alpha$ values ($\\alpha=1$) and smaller $r_{\\rm inner}$ values ($\\simeq 10^6$ cm). The uniqueness of GRO J1744-28 might be associated with the possibility that ${\\dot M}$ onto the pulsar could only exceed ${\\dot M}_{\\rm crit}(r_{\\rm inner})$ by some marginal amount $-$ whose precise value remains to be determined $-$ for the outbursts to occur. If the mass transfer rate were too large, there may exist a permanent region of radiation pressure domination at smaller radii, and not the oscillation we find between $P_{\\rm radiation}>P_{\\rm gas}$ and $P_{\\rm radiation}>1$ for these systems, and outbursts of the type considered in this {\\it Letter} could not occur. Further work must be done to determine how the size of the zone of instability varies with $r_{\\rm inner}$ and hence ${\\dot M}_{\\rm crit}$. One consequence of eqn. (2) is that, as the long-term, mean mass accretion rate onto the pulsar decreases and the persistent flux diminishes, the outbursts in GRO J1744-28 should cease. As of $\\sim1$ May 1996, plus or minus several days, with the persistent {\\it RXTE} PCA flux level at $\\sim0.1$ Cb, the giant outbursts have indeed stopped occurring." }, "9605/astro-ph9605194_arXiv.txt": { "abstract": "Using our catalogue of V$_{26.5}$ isophotal magnitudes for 6756 galaxies in a region covering 60~$\\times$~25~arcmin$^2$ in the center of the Coma cluster, plus 267 galaxies in a region of 9.7~$\\times$~9.4~arcmin$^2$ around NGC~4839, we derive the luminosity function in the magnitude range 13.5$\\leq V_{26.5} <$ 21.0 (corresponding to the absolute magnitude range $-22.24 < M_{V26.5} \\leq -14.74$). The luminosity function for this region is well fitted by the combination of a gaussian in its bright part and of a steep Schechter function (of index $\\alpha =-1.8$) in its faint part. Luminosity functions derived for individual regions surrounding the brightest galaxies show less steep slopes, strongly suggesting the existence of environmental effects. The implications of such effects and galaxy formation scenarios are discussed. ", "introduction": "The shape of the luminosity function (LF) of galaxies gives strong constraints on cosmological parameters and formation scenarios since it is closely related to the galaxy mass function (MF) and therefore to the spectrum of initial perturbations (see Binggeli et al. 1988 for a review). For instance, the hierarchical model predicts a MF characterized by an exponential cut-off above a given mass ($M^*$) and a power law (with index $\\alpha$) at low masses, where the index $\\alpha $ is related to the slope n of the power spectrum as $\\alpha=(9-n)/6~$ with $-3$ colors, and impact parameters $D$. We found no correlations at the 2.5$\\sigma$ level between the measured absorption properties and galaxy properties. Of primary significance is the fact that the QSO--galaxy impact parameter apparently does not provide the primary distinguishing factor by which absorption properties can be characterized. The absorption properties of {\\Mg} selected galaxies exhibit a large scatter, which, we argue, is suggestive of a picture in which the gas in galaxies arises from a variety of on--going dynamical events. Inferences from our study include: (1) The spatial distribution of absorbing gas in and around galaxies does not appear to follow a simple galactocentric functional dependence, since the gas distribution is probably highly structured. (2) A {\\it single} systematic kinematic model apparently cannot describe the observed velocity spreads in the absorbing gas. It is more likely that galaxy/halo events giving rise to absorbing gas each exhibit their own systematic kinematics, so that a heterogeneous population of sub--galaxy scale structures are giving rise to the observed cloud velocities. (3) The absorbing gas spatial distribution and overall kinematics may depend upon gas producing events and mechanisms that are recent to the epoch at which the absorption is observed. In any given galaxy, these distributions likely change over a $\\sim$~few Gyr timescale (few dynamical times of the absorbing clouds), which provides one source for the observed scatter in the absorption properties. Based upon these inferences, we note that any evolution in the absorption gas properties over the wider redshift range ($0.4\\leq z\\leq 2.2$) should be directly quantifiable from a larger dataset of high--resolution absorption profiles. ", "introduction": "\\pagestyle{myheadings} \\markboth{\\sc \\hfill Churchill, Steidel, \\& Vogt \\hfill} {\\sc \\hfill Churchill, Steidel, \\& Vogt \\hfill} The {\\MgII} doublet, as seen in absorption in the spectra of background QSOs (cf.~\\cite{ss92}), is known to arise in the low ionization gas associated with a population of ``normal'' field galaxies that exhibit little to no evolution in their rest frame $\\left< B-K\\right>$ colors since a redshift of $z \\sim 1.0$ (\\cite{sdp94}, hereafter SDP). Galaxies selected by the known presence of {\\Mg} absorption represent a wide range of colors, from late--type spirals to the reddest ellipticals, have $L_B$ and $L_K$ luminosity functions consistent with local luminosity functions in which morphological types later then Sd are excluded, and exhibit a strong correlation between color and $L_K$ (fainter galaxies are bluer). These facts suggests that a wide range of morphological types are undergoing the processes that give rise to {\\Mg} absorbing gas, but that isolated low mass ($L_K < 0.07L_K^{\\ast}$) ``faint blue galaxies'' are not. Now that we have a first look at what types of galaxies are being selected by their {\\Mg} absorption cross section, we can undertake studies from which we hope to infer the spatial distribution and line--of--sight kinematics of the absorbing gas and to examine connections, if any, between the absorbing gas and galaxy properties. If correlations between galaxy and absorption properties can be established, where galaxies are directly accessible to imaging and spectroscopy, then we may be able to infer the properties of higher redshift galaxies simply by classifying their absorption properties. The hope is that we may chart the general evolution of galaxies and of their gas kinematic, chemical, and ionization conditions back to the epoch of the earliest QSOs (\\cite{steidel93a}; \\cite{bergeron94}; \\cite{welty96}; \\cite{charlton96}; \\cite{bechtold96}; \\cite{halopaper}). A more direct motive for this study is to examine the model of $z \\leq 1$ galaxy halos suggested by Lanzetta \\& Bowen (1990, 1992). They suggested that intermediate redshift galactic halos are roughly identical, have absorbing gas spatial number density distributions $\\propto r^{1-2}_{\\rm gal}$, and likely exhibit systematic rotational or radial flow kinematics. The primary test for this picture is the prediction that the {\\it observed}\\/ differences in the absorption properties from one system to another are predominantly due to the QSO--galaxy impact parameter. Based upon several studies (\\cite{pb90}; \\cite{bb91}; \\cite{lanzetta92}; \\cite{lebrun93}; \\cite{steidel93b}; \\cite{bbp95}; \\cite{s95}), a consensus has emerged in which the ``galaxy/halo'' model (first proposed by \\cite{bachall69}) is favored over the ``galactic fragments'' (cf.~\\cite{yanny92}) and ``dwarf satellites'' (\\cite{york86}) models. Whatever the true nature of {\\Mg} absorbing gas, the bottom line is that a relatively luminous galaxy within $\\sim 40$~kpc of the QSO line of sight appears to be a prerequisite for the detection of {\\Mg} absorption (\\cite{s95}). If all scenarios contribute at some level, statistical correlations between absorption and galaxy properties predicted by the galaxy/halo model (\\cite{lb92}; \\cite{lanzetta92}; \\cite{cc96}) would be ``diluted'' by the more stochastic kinematics expected from merging dwarf satellite galaxies or accreting {\\it gaseous}\\/ sub--galactic fragments. That is, if the local environments around {\\Mg} absorbing galaxies are populated by satellite galaxies and by fragments of on--going galaxy/halo events (i.e.~accretion, superbubbles, merging), systematic trends with impact parameter, or any other galaxy property, would be difficult to detect due to a large scatter in the absorption properties. In this paper, we report on observations of the {\\Mg} ($\\lambda 2796$) absorption line obtained with a resolution of $\\sim 6$~{\\kms} and signal--to--noise ratios $\\sim 30$, and explore correlations between the absorption properties and the IR/optical luminosities and colors, impact parameters, and redshifts of the identified associated galaxies. ", "conclusions": "As a first step toward developing a better appreciation of the spatial distributions and kinematics of low ionization absorbing gas associated with galaxies, we have presented the {\\Mg} $(\\lambda 2796)$ absorption profiles for 15 $z < 1$ galaxies, developed simple kinematic indicators of the profiles, and searched for statistically significant correlations between the absorbing gas and galaxy properties. \\begin{enumerate} \\item Using Spearman and Kendall non--parametric rank correlation tests, we found no evidence for 2.5$\\sigma$--level correlations between the absorbing gas and galaxy properties. We performed Monte--Carlo Spearman and Kendall tests in which we randomly assigned our measured absorption properties to the full SDP sample of galaxies. These tests revealed that our 15 galaxies are a fair representation of the SDP dataset and that the Spearman and Kendall results provide reliable indicators for the presence or non--presence of correlations. \\item In Table 3, we have listed the eight tests for which the Spearman and Kendall results are weakly suggestive of correlations. Since trends in absorption properties with the QSO--galaxy impact parameter, $D$, are an important test of the galaxy/halo model, we have performed maximum likelihood least square fits to those tests that included $D$ (i.e.~DR, $N_{\\rm c}$, and $W_{\\rm r}$ versus $D$). For these fits, we modeled the uncertainty in the measured absorption properties as scatter due to Poisson fluctuations, which are predicted when sampling a finite number of absorbing clouds along the line of sight through a galaxy halo. All LSF slopes were consistent with zero, which is indicative of no statistically significant dependence with $D$ for these absorption properties. \\item Since the number of clouds shows no significant dependence with $D$, both the rotation and radial flow kinematic models predict an anti--correlation of the median absolute deviation of cloud velocities with impact parameter. As illustrated in Fig.~5., we found no clear trend in $A(\\Delta v)$ with $D$. If anything, the weak positive correlation suggested by the rank correlation tests is suggestive of a scenario in which more than one kinematic model may be needed to explain the data. Perhaps the inner 20~kpc are dominated by the systematic kinematics expected for galaxies (morphology dependent?), whereas the higher impact parameter kinematics is dominated by accretion and merging of various types of ``halo'' material. \\item We have found that the QSO--galaxy impact parameter apparently does not provide the primary distinguishing factor by which absorption properties can be characterized. This fact suggests that we should investigate the degree to which galaxy morphologies and, in the case of disk galaxies, orientations with respect to the QSO light path play a role in distinguishing between observed absorption properties. \\item Since {\\Mg} absorption properties exhibit a level of scatter greater than that predicted by a simple Poisson fluctuation model, our data do not provide a level of constraint necessary for us to infer functional relations that describe the spatial and kinematic distributions of {\\Mg} absorbing gas around galaxies. If weak correlations are in fact present, they exhibit a large enough scatter that a fair sample of 15 systems has not yielded unequivocal results. \\item As one possible interpretation, we have tentatively suggested a picture of intermediate redshift galactic halos in which the distribution and kinematics of the low ionization absorbing gas is dominated by the events and mechanisms that give rise to the gas recent to the epoch of observation. These halos would be dynamically active with evolving gaseous conditions dependent upon local environmental influences, as expected with tidally stripped dwarf satellite galaxies, infalling gaseous sub--galactic fragments, superbubbles, and in the case of disk galaxies, with high velocity clouds, galactic fountains, and the warped extended disks themselves. Our observational results are not suggestive of a picture in which galaxy halos underwent a single epoch of dynamical formation in the past. Rather, these galaxies have experienced multiple and episodic merging and have undergone internal events that give rise to extended (though somewhat patchy) regions of low ionization absorbing gas. \\item If the {\\Mg} absorbing gas from these events has a dynamical time of $\\sim$ 1 Gyr, the gas producing events, spread out both spatially and temporally, would not give rise to halos comprised of multiple coalescing and evaporating absorbing clouds that yield a near--unity covering factor. Such halos would be expected to exhibit systematic kinematics and have an approximately spherically symmetric spatial number density distribution that scales with galactocentric radius. Instead, these events may give rise to $\\sim$~few Gyr sub--galactic gaseous structures so that the overall spatial distribution and kinematics of absorbing gas in any one galaxy would be expected to change over a few cloud dynamical times. The important point is that the data are not suggestive of the continual processing of gas that would give rise to an apparently ``steady state'' halo over the 10~Gyr evolution of the galaxy. \\item Since the dynamical time is roughly an order of magnitude shorter than the overall look--back time over which complex {\\Mg} absorption is seen around galaxies, and since QSO absorption lines likely sample gas produced in events recent to the epoch at which it is observed, we should be able to directly track evolution in the absorption properties. A larger database of HIRES {\\Mg} profiles would be instrumental for directly quantifying evolution in the absorbing gas properties over the redshift range $0.4 \\leq z \\leq 2.2$. Such evolution may provide information helpful for ruling out various type of events or absorbing structures and for quantifying possible major shifts in epochs from one type of pre--dominant galaxy/halo gas processing phase to another. \\end{enumerate} A more comprehensive appreciation of the spatial and kinematic properties of low ionization absorbing will require a sizable unbiased sample of high resolution absorption profiles (unbiased in that the distribution of galaxy luminosities, colors, impact parameters, and absorption rest equivalent widths are consistent with having been drawn from the observed distributions of {\\Mg} selected galaxies). It is important that surveys of QSO fields be complete to a small limiting rest frame luminosity and that the selection of these fields be unbiased with regard to the presence or non--presence of intervening absorbing galaxies. Unless the gas kinematics in spiral/disk and elliptical galaxies are distinguishable as seen in high resolution profiles, it is not likely the {\\Mg} absorption properties can be used to infer the type of galaxy associated with the absorbing gas at the highest redshifts, where the galaxy properties are difficult to obtain. However, we may be able to roughly infer the region of the galaxy sampled by the line of sight or something about its current or recent environmental dynamical activity. Ultimately, the observed evolutionary properties of gas derived from QSO absorption line studies are likely to yield direct quantities from which the formation and evolution time scales of 10$^{12-13}$~M$_{\\sun}$ structures in the universe can be better understood." }, "9605/astro-ph9605075_arXiv.txt": { "abstract": "Line-of-sight velocity distributions are crucial for unravelling the dynamics of hot stellar systems. We present a new formalism based on penalized likelihood for deriving such distributions from kinematical data, and evaluate the performance of two algorithms that extract $N(V)$ from absorption-line spectra and from sets of individual velocities. Both algorithms are superior to existing ones in that the solutions are nearly unbiased even when the data are so poor that a great deal of smoothing is required. In addition, the discrete-velocity algorithm is able to remove a known distribution of measurement errors from the estimate of $N(V)$. The formalism is used to recover the velocity distribution of stars in five fields near the center of the globular cluster $\\omega$ Centauri. ", "introduction": "The most complete kinematical information obtainable for a distant stellar system is the distribution of line-of-sight velocities at every point in the image. Velocity distributions are crucial for understanding the dynamical states of slowly-rotating stellar systems like elliptical galaxies and globular clusters, since velocity dispersions alone place almost no constraints on the form of the potential unless one is willing to make ad hoc assumptions about the shape of the velocity ellipsoid (\\cite{dem92}). Velocity distributions are also useful when searching for kinematically distinct subcomponents (e.g. \\cite{fri88}; \\cite{rif92}). The velocity distribution at point ${\\bf R}$ in the image of a stellar system, $N({\\bf R},V)$, can be related to the data in different ways depending on the nature of the observations. In a system like a globular cluster, for which the data usually consist of individual stellar velocities, the velocity distribution is just the frequency function of stellar velocities defined by those stars with apparent positions near to ${\\bf R}$. Since measured velocities are always in error, the observed and true $N(V)$'s are related via a convolution integral. In a distant, unresolved galaxy, one typically measures the integrated spectrum of many stars along a line of sight. The observed spectrum is then a convolution of the velocity distribution of these stars with the broadening function of the spectrograph, and the spectrum of a typical star. With both sorts of data, the goal is to find a function $N(V)$, at some set of points ${\\bf R}$, such that $\\sum_i L\\{Y_i;N(V)\\}$ -- the log likelihood of observing the data $Y_i$ given $N$ -- is large. Maximizing this quantity over the space of all possible functions $N(V)$ is unlikely to yield useful results, however, since any $N(V)$ that maximizes the likelihood (assuming it exists, which it often will not) is almost certain to be extremely noisy. This is obviously true if the data are related to the model via a convolution, since the process of deconvolution will amplify the errors in the data. But it is equally true if $N(V)$ is simply the frequency function of observed velocities, since the most likely distribution corresponding to an observed set of $V$'s is just a sum of delta functions at each of the measured velocities. One is therefore forced to place smoothness constraints on the solution. But smoothing always introduces a bias, i.e. a systematic deviation of the solution from the true $N(V)$. The nature of the bias is obvious when the smoothing is carried out by imposing a rigid functional form on $N(V)$, since the true function will almost certainly be different from this assumed form. But even nonparametric smoothing generates a bias since it effectively averages the data over some region. Furthermore, because the required degree of smoothing increases with the amplitude of the noise in the data, the error from the bias goes up as the quality of the data falls. An ideal algorithm for estimating $N(V)$ would therefore be one in which the bias introduced by the smoothing was effectively minimized, so that the derived $N(V)$ was close to the true function even when the data were so poor that a great deal of smoothing was required. One way to accomplish this is to make use of prior knowledge about the likely form of $N(V)$. Many studies of stellar and galactic systems have shown that $N(V)$ is often close to a Gaussian. This fact suggests that we infer $N(V)$ by maximizing a quantity like \\begin{equation} \\log{\\cal L}_p = \\sum_i L\\{Y_i;N(V)\\} - \\alpha P(N) , \\end{equation} the ``penalized log likelihood,'' where the penalty functional $P(N)$ is large for any $N(V)$ that is noisy and zero for any $N(V)$ that is Gaussian. A natural choice for such a penalty functional has been suggested by \\cite{sil82}: \\begin{equation} P_G(N) = \\int_{-\\infty}^{+\\infty}\\left[(d/dV)^3\\log N(V)\\right]^2 dV. \\end{equation} This functional assigns zero penalty to any $N(V)=N_0 \\exp[-(V-V_0)^2/2\\sigma^2]$, i.e. any Gaussian velocity distribution, and a large penalty to any $N(V)$ that is rapidly varying. The limiting estimate as the smoothing parameter $\\alpha$ tends to infinity is the normal distribution that best corresponds, in a maximum-likelihood sense, to the data. Thus varying $\\alpha$ takes one from an estimate of $N(V)$ that is very noisy but that reproduces the data well, to the ``infinitely smooth'' maximum likelihood Gaussian fit to $N(V)$. When the data are copious and accurate, the degree of smoothing required, i.e. the value of $\\alpha$, will be small and the inferred $N(V)$ will be close to the true function. When the data are poor, $\\alpha$ must be increased to deal with the noise; however even a very large value of $\\alpha$ will yield an $N(V)$ that is nearly Gaussian and that is therefore likely to be close to the true velocity distribution. Regardless of the quality of the data, there will always be a formally optimal choice of $\\alpha$ that yields a solution that is closest in some sense to the true $N(V)$ -- neither too noisy nor too biased. Here we apply penalized likelihood methods to the recovery of velocity distributions from kinematical data of two sorts: Doppler-broadened spectra, and discrete velocities. There are of course a large number of excellent algorithms already in use for extracting velocity distributions from absorption-line spectra (\\cite{fri88}; \\cite{ben90}; \\cite{riw92}; \\cite{kum93}; \\cite{vdf93}; \\cite{saw94}). Is another approach really needed? Many of the existing algorithms are essentially nonparametric and hence yield unbiased estimates of $N(V)$ when the signal-to-noise ratio of the data is large. Their behavior given data with small S/N is more variable, however, due to the different ways in which they carry out the smoothing. For instance, in algorithms that represent the unknown $N(V)$ via a basis-set expansion, \\begin{equation} N(V) = \\sum_{k=1}^K C_k N_k(V), \\end{equation} the smoothing is accomplished by truncating the expansion after a finite number of terms. Adding more terms decreases the bias by giving the algorithm more freedom to match the true $N(V)$; however the level of fluctuations in the solution increases as the bias falls since the high-order terms will always try to reproduce the noise in the data. The optimal estimate for data of a given quality will therefore contain only a limited number of terms, and if the data are poor, this number will be small; hence the solution will be biased toward the functional form selected for $N_1(V)$. Of course one can choose $N_1$ to be the normal distribution (e.g. \\cite{vdf93}) but its mean and variance must be specified, and the optimal choices for both parameters will depend in some complex way on the number of terms retained in the expansion and on the level of noise in the data. Worse, one does not have complete freedom in this approach to adjust the smoothing to its optimal level since the basis set is fixed and its terms are discrete. Most of the spectral deconvolution schemes currently in use have continuously-adjustable smoothing and so do not suffer from this latter defect. However few of these schemes incorporate any prior knowledge about the likely form of $N(V)$ and so the solutions they return given noisy data tend to be unphysical, with functional forms that are determined primarily by the mechanics of the smoothing. (In fact it is a common practice to fall back on parametric methods when the data are poor.) For instance, both the Wiener-filtered algorithm of Rix \\& White (1992) and the kernel-based algorithm of Kuijken \\& Merrifield (1993) yield $N(V)\\approx {\\rm constant}$ in the limit of infinite smoothing. Since real velocity distributions are unlikely to be well approximated by constant functions, the estimates produced by these schemes can be substantially biased. The approach advocated here is neither better nor worse than the existing ones when the data are of high quality. However it has an advantage when the data are poor, since even a large degree of smoothing is likely to bias the solution only slightly. Furthermore the amount of smoothing can be adjusted with infinite precision by varying $\\alpha$. In practice it may be difficult to find the optimal choice of $\\alpha$ given noisy data, but there are bootstrap techniques for choosing $\\alpha$ that work well in most cases; and one can always elect to be guided by physical intuition when deciding how smooth $N(V)$ should be. Most important, even a gross overestimate of $\\alpha$ will yield no worse than a Gaussian fit to the velocity distribution, which is perhaps the best that can be hoped for when the signal-to-noise ratio or the number of observed velocities is small. (Much of the uncertainty in $N(V)$'s derived from absorption line spectra is due to systematic errors such as incorrect continuum subtraction, template mismatch, limited resolution, etc. These problems afflict every spectral deconvolution scheme and have been treated at length by other authors. We have nothing new to say about these systematic effects and will simply ignore them -- our focus is on the uncertainty in $N(V)$ that is generated by noise in the data rather than by systematic errors.) Below we evaluate the performance of penalized-likelihood algorithms for estimating $N(V)$ from spectral data (\\S2) and from discrete velocities (\\S3). The former sort of data are routinely obtained for distant galaxies and the latter for globular clusters, clusters of galaxies and systems of emission-line objects around galaxies. The same formalism works equally well in both cases; essentially all that needs to be changed is the form of the matrix that relates the observable quantities to $N(V)$. We also show how the cross-validation score can be used to estimate the optimal degree of smoothing from the data. We then (\\S4) apply the formalism to the recovery of the velocity distribution near the center of the globular cluster $\\omega$ Centauri using a new sample of stellar radial velocities from an imaging spectrophotometer. ", "conclusions": "" }, "9605/astro-ph9605133_arXiv.txt": { "abstract": "Conditions for the establishment of small density perturbations in a self-gravitating two component fluid mixture are studied using a dynamical system approach. It is shown that besides the existence of exponentially growing and decaying modes, which are present for values of the perturbation wave-number $k$ smaller than a critical value $k_{_M}$, two other, pure oscillatory, modes exist at all scales. For $k < k_{_M}$, the growing mode always affects both components of the fluid and not only one of them. Due to the existence of a resonance between the baryonic and the dark perturbations, it is shown that the onset of structure formation in the post recombination epoch is substantially enhanced in a narrow scale band around another critical value $k_{c}$. For dark matter particles having a mass $\\sim 30$ eV, the corresponding critical mass scale for the establishment of density perturbations at the time of recombination is of the same order of magnitude as the galactic one. ", "introduction": "The study of the mechanisms responsible for the formation of structures in the universe was started by the pioneer work of Jeans (1902, 1928). Studying the conditions under which a cloud of gas (in a static background) becomes gravitationally unstable under its own gravity Jeans concluded that perturbations with masses smaller than a \"critical\" value $M_{_J}$ (the Jeans mass) do not grow and behave like acoustic waves whereas perturbations with a mass $M$ bigger than $M_{_J}$ grow under the effect of their self-gravity, leading to gravitationally bound structures. Since then, the mechanism proposed by Jeans has been extensively applied as a criterion of stability in several models of galaxy formation. However, by the recombination epoch (which is believed to be the one after which baryonic perturbations could begin to grow), the critical scale predicted by the classical Jeans theory is not at all related to the galactic scale. Instead, it is well known that just before recombination the critical Jeans mass is $\\sim 10^{16-17}$M$_{\\odot}$, (i.e. the mass of rich clusters or even superclusters of galaxies), and immediately after recombination the Jeans mass drops abruptly, more than 10 orders of magnitude, to a value $\\sim 10^{5-6}$M$_{\\odot}$, which is related to the mass of globular clusters (Weinberg 1972; Zel'dovich \\& Novikov 1983). The origin of this discrepancy between the Jeans mass, before and after recombination, and the mass of a typical galaxy, a few $10^{11}$M$_{\\odot}$, has not been, up to now, well understood. One should emphasize, however, that these values for the Jeans mass just before and just after recombination epoch are obtained assuming a baryon-dominated universe. On the other hand, the observation of flat galactic rotation curves at large galactic radii as well as high galaxy velocity dispersions in clusters has led to the missing mass problem and to the dark matter conjecture to solve it. This fact has, in particular, led to the hypothesis that dark matter halos exist around galaxies. The existence of dark matter therefore also implies that when studying the dynamics and the formation of structures in the universe one cannot use the simple Jeans stability criterion for a one component gas, but one has to study how does the gravitational instability arise in a mixture of at least two components. This formulation of the problem leads to a different Jeans mass, as well as to a better understanding of the origin of galactic mass spectrum. This will be the main goal of this paper. We must note that, after we finished this work, it was pointed out to us by Dr. Varun Sahni that this problem had already been studied, using a different formalism, by some russian authors like Grishchuk \\& Zel'dovich (1981) or Polyachenko \\& Fridman (1981). Although having reached some of our conclusions, such studies lack most of the features present in this work. In particular they do not refer to the existence of the resonance we shall point out in this paper. Since it is generally accepted that dark matter is constituted by WIMPs, (Weakly Interacting Massive Particles) in this study we shall consider the case for which the two components of the cosmic fluid interact only gravitationally. The two fluid components that we shall consider will be a baryonic one and a hot dark matter (HDM) one, hereafter component $B$ and $D$ respectively. The latter being assumed to be made of neutrino-like particles. Although the numerical results obtained in this paper refer to the particular case of HDM, one should point out that the formalism here developed is quite general and applies to any type of a two-component mixture. In Sect. \\ref{sec.equ} we shall establish the linear coupled equations which describe the dynamical system for the density perturbations in the two-component fluid we wish to study. We shall then develop, in Sect. \\ref{sec.qual}, a qualitative analysis of the dynamical system. In Sect. \\ref{sec.sol} we shall study the behaviour, in phase-space, of the trajectories representing the general solution of the dynamical system. This analytical study will be complemented with some numerical plots in order to clarify some of the qualitative results obtained. For numerical purposes we shall consider that the onset of gravitational instability occurs in a flat $(\\Omega = 1)$ universe at recombination epoch, after the decoupling between radiation and baryonic matter, when the radiation temperature is $\\sim 3000$ K (Kolb \\& Turner 1990). We shall assume that the density parameter $\\Omega_B$ has a value in agreement with the limits imposed by standard nucleosynthesis (Walker et al. 1991). Assuming $0.5 \\leq$ h $\\leq 1$, where h is the Hubble constant in units of $100$ Km/s/Mpc, i.e. h = H$_0/$($100$ Km/s/Mpc), such a value is $\\sim 0.05$. The neutrino-like particles which constitute the dark matter component are assumed to have a mass compatible with the assumption of being already non-relativistic by the recombination epoch. It will be shown later in this paper that this value for the mass of the dark matter particles seems to provide a good fit for the galactic mass spectrum. In Sect. \\ref{sec.res} we shall describe the occurence of a resonance which, in our opinion, is responsible for the formation of structure at the typical galactic scales. The relation between the existence of the resonance, the galactic scale and the mass of dark matter particles is discussed in Sect. \\ref{sec.gxf}. Finally in Sects. \\ref{sec.con} and \\ref{sec.fut} we shall point out the main results presented in this paper and outline some open questions as well as the research paths we intend to follow in the near future. ", "conclusions": "\\label{sec.con} It is clear from the results obtained in this work that it is incorrect to use the Jeans criterion for a 1-component fluid to a 2-component mixture, for two main reasons: \\begin{enumerate} \\item The Jeans scale for the mixture does not correspond to any of the Jeans scales for the components taken separately. \\item Moreover, in a 2-component mixture there are always present, at all scales, oscillations in the two components, which correspond to acoustic waves. The same is not true for a one component system. \\end{enumerate} However the main result of this work is, as we have shown, that, in a two-component fluid, a resonance between the two components of the fluid must always occur provided that the component with a greater density is the one with a greater sound speed, see Eq. (\\ref{eq.19-f}). One can therefore put some constraints on the nature of the dark matter if galaxies are to be formed by such a resonant effect. In fact, assuming that the density parameter of the universe is $\\Omega = 1$ and adopting a value for the density of the baryonic component in agreement with standard light-element nucleosynthesis, one is led to the conclusion that the universe is dominated by dark matter, i.e. $W \\! {_{_D}} > W \\! {_{_B}}$. In such a case, if $c_{_B} > c_{_D}$ (case of CDM), one concludes from Eq. (\\ref{eq.19-f}) that no resonance between the two components is possible and therefore, the galactic scale would not be a preferred one, as it seems to be. One is therefore led to believe that most, if not all, of the {\\em dark matter present in the universe is hot}, i.e. it is constituted by light neutrino-like particles as implied by the condition for the existence of a strong resonance, i.e. $c_{_D} \\gg c_{_B}$, (see Eq. (\\ref{eq.104}) and comments following it). This resonance is linked to the fact that at the critical scale $l_{c}$, there is an enhancement of the number of particles in both components, (but particularly in the baryonic one), which participate in the collapse mode, instead of participating in the acoustic modes as it happens for other scales. This effect is only significant in a narrow resonant band in the length, or mass, scale of the perturbations. This, we believe, is the reason for the formation of galactic structures at the time of recombination with their characteristic range of mass scales. This effect occurs at the galactic scales provided that the dark matter component is made of neutrino-like particles with masses of the order of $30\\,$eV. This value for the mass of the neutrino-like particles is below the upper bounds imposed by cosmological constraints on the neutrino's mass (Peebles 1993), assuming a flat universe, and remarkably close to the value predicted by Sciama's Decaying Dark Matter Hypothesis (Sciama 1990a; Sciama 1990b). We must also note that, from the numerical results obtained in the preceding sections, this mass scale is of the order of $10^{13}$M$_{\\odot}$ which gives a baryonic mass, in the same scalelength, of the order of $\\frac{ \\; \\rho_{_B} } { \\rho_{_D} } 10^{13}$M$_{\\odot}$, which lies in the range of the masses of typical galaxies (a few $10^{11}$M$_{\\odot}$). One should point out, however, that the resonant scale $l_{c}$ is particularly sensitive to the mass of the particles constituting the dark component, see Fig. \\ref{fig.mD}." }, "9605/astro-ph9605168_arXiv.txt": { "abstract": "We considered the Inverse Compton Scattering (ICS) of charged particles onto photons whose distribution is a Black Body Radiation (BBR) deriving the exact energy and angular differential distribution in the general case and in its most useful expansions. These results can be successfully applied in high energy accelerators experiments to evaluate the ICS contribution from the thermal photons in the cavity as well as in astrophysics where the ICS of cosmic rays plays a relevant role in a variety of phenomena. In particular we show how our formulae reproduce the ICS energy spectrum recently measured at LEP, how it could be considered a key tool in explaining the Gamma Ray Bursts (GRB) , SGRs energy spectrum. Finally we predicted the presence of a low gamma flux, nearly detectable at hundred of TeV from SNRs SN1006 as well as, at lower energy (tens TeV, due to gamma ray cascading in cosmic BBR), from relic extragalactic highest cosmic rays sources born by jets in AGN,as blazars 3C279,Mrk421,Mrk 501. ", "introduction": " ", "conclusions": "" }, "9605/astro-ph9605054_arXiv.txt": { "abstract": "We have refined the analysis of the data from the \\FIRAS\\ (Far InfraRed Absolute Spectrophotometer) on board the \\COBE\\ (COsmic Background Explorer). The \\FIRAS\\ measures the difference between the cosmic microwave background and a precise blackbody spectrum. We find new tighter upper limits on general deviations from a blackbody spectrum. The RMS deviations are less than 50 parts per million of the peak of the CMBR. For the Comptonization and chemical potential we find $|y|<$\\ymin\\ and $|\\mu|<$\\mumin\\ (95\\% CL). There are also refinements in the absolute temperature, \\tcbrpm, and dipole direction, $(\\ell,b)=(264.14^\\circ\\pm0.30,48.26^\\circ\\pm0.30)$ (95\\% CL), and amplitude, \\adippm. All of these results agree with our previous publications. ", "introduction": "The{~\\FIRAS}~(Far~Infrared~Absolute~Spectrophotometer) instrument aboard the \\COBE\\ (COsmic Background Explorer) satellite (Boggess \\etal\\ 1992 and references therein; Bennett \\etal\\ 1992a) was designed to measure the spectrum of the cosmic microwave background radiation (CMBR). In the simple hot Big Bang model the spectrum has a blackbody form, but it could be distorted by energy release after a redshift $z \\sim3\\times10^6$ (Peebles 1971, Sunyaev \\& Zel'dovich 1980). After the annihilation of positrons and the decoupling of neutrinos until $ z \\sim 3 \\times 10^4$, the CMBR was the dominant energy field. The number of photons exceeds the number of baryons by a factor $\\sim 10^9$, so excellent sensitivity is required to detect even large radiant energy releases. Spectral distortion limits from the FIRAS were presented by \\specpaper. These were based on $\\sim 40$\\ days of high Galactic latitude data from a single detector and scan mode. The dipole spectrum was also determined (Fixsen \\etal\\ 1994a) from this single detector. \\analysispaper\\ found that the spectrum and dipole are consistent with a simple Big Bang model. All of the previous work in this frequency range (2 to 21 \\icm) was based on part of the data from a single detector. This paper uses all of the low frequency data from the 10 month mission, except for the first month when settings were frequently readjusted to reach the optimum condition, approximately doubling the statistical weight of the results. There have been several improvements in the calibration that we note, but the basic calibration process remains the same. The instrument was recalibrated using the method described in \\calpaper. The calibration was applied to the sky data, producing spectra from 2 to 21~\\icm\\ (5000 to 480 $\\mu$m). Five important improvements were made to the calibration: (1) a bias in some pixels is corrected; (2) insufficiently sampled pixels ``borrow\" data from neighboring pixels to determine a template for deglitching (removing effects of cosmic ray hits on the detector); (3) data with a large number of glitches (cosmic ray hits) are deweighted relative to data with few glitches; (4) we use 320 points in the spectrum rather than 256; and (5) the data are ``destriped\" after the calibration. Each of these processes is described in more detail below. ", "conclusions": "The FIRAS spectrum of the cosmic microwave background radiation agrees with a blackbody spectrum to high accuracy. The CMBR monopole and dipole spectra are the result of fitting a model including a dust map derived from the DIRBE data. The CMBR dipole has a spectrum consistent with its thermal origin and a Doppler shift. The dipole itself has a differential thermal spectrum the temperature of which, \\tdippm, agrees with the monopole temperature. The Doppler shift implies that the Sun's peculiar velocity relative to the comoving frame is $371\\pm1$ km/s (95\\% CL) toward \\dipdir, in agreement with the microwave results from the DMR. The CMBR temperature is \\tcbrpm, where the error is dominated by our estimate of the thermometry errors. The weighted rms deviation from the fit is \\rmspct\\ of the peak brightness. The limit on $|y|$ is \\ymin\\ and the limit on $|\\mu|$ is \\mumin\\ (95\\% CL)." }, "9605/astro-ph9605112_arXiv.txt": { "abstract": "We have developed a new stellar population synthesis model designed to study early-type galaxies. It provides optical and near-infrared colors, and line indices for 25 absorption lines. It can synthesize single age, single metallicity stellar populations or follow the galaxy through its evolution from an initial gas cloud to the present time. The model incorporates the new isochrones of the Padova group and the latest stellar spectral libraries. We have applied our model to new data for a set of three early-type galaxies, to find out whether these can be fitted using single-age old metal-rich stellar populations, as is normal practice when one uses other stellar models of this kind. The model is extensively compared with previous ones in the literature to establish its accuracy as well as the accuracy of this kind of models in general. Using the evolutionary version of the model we find that we cannot fit the most metal-rich elliptical galaxies if we keep the IMF constant and do not allow infall of gas. We do however reproduce the results of Arimoto \\& Yoshii (1986) for the evolution of the gas, and produce colors, and, for the first time with this type of models, absorption line-strengths. It is in fact possible to fit the data for the elliptical galaxies by varying the IMF with time. Our numerical model is in good broad agreement with the analytical {\\em simple model}. We prefer however to calculate the evolution of the gas numerically instead of using the {\\em simple model}, since it offers more flexibility, and even improved insight, when comparing with observations. In the present paper we describe the model, and compare a few key observables with new data for three early-type {\\em standard} galaxies. However the data, as well as our fits, will be discussed in much more detail in a second paper (Vazdekis {\\it et al.} 1996), where some conclusions will be drawn about elliptical galaxies on the basis of this model. ", "introduction": "\\subsection{Population Synthesis} The information that is available about galaxies primarily relates to their morphology, internal kinematics, and spectral energy distribution. The further away one goes, the less important become the first two, compared to the third. Clearly, if one wants to study galaxy evolution, study of the electromagnetic spectrum is of maximum importance. Since the spectrum of a galaxy generally consists of a combination of stellar spectra, emission from gas, and possibly non-thermal radiation, partly extinguished by dust, and since also stellar spectra exist in a very large number of varieties, it is clear that understanding the spectrum of a galaxy is very difficult. To study complicated spectra it is necessary to first understand the spectral energy distributions of relatively simple objects. For this reason we will discuss here a model that analyzes the spectra of early-type galaxies. These objects appear to contain relatively little dust extinction and gaseous interstellar medium, and to have little recent star formation. They have, for these reasons, been the most studied objects in the current literature on population synthesis. There have been a number of accepted ways to attack the problem of understanding the spectrum of an elliptical. To understand why we adopt our current method, we will summarize shortly some of the population synthesis methods most often used in the literature. A stellar population synthesis program tries to find a combination of stars for which the integrated spectrum agrees with the observed spectrum of the object under study. In practise the problem is often underconstrained, i.e. a number of combinations of stars can be found which are able to fit the spectrum. To overcome this problem one generally forces the solution to obey certain constraints. These range from simple continuity requirements (e.g. the luminosity function should decrease monotonically) to the requirement that the distribution of stars is determined completely by stellar evolution calculations. Models with very few physical constraints are generally called {\\em empirical} population synthesis models, as opposed to {\\em evolutionary} models. Empirical models have been used with some success by Spinrad \\& Taylor (1971), Faber (1972), O'Con\\-nell (1976, 1980) and Pickles (1985). These papers often make use of linear programming to obtain their results. Some workers, notably Bica (1988), have attempted to take into account evolutionary effects by using, as units of population, distributions of stars observed in clusters of our Galaxy, instead of individual stars. Evolutionary models use a theoretical isochrone or HR diagram, convert isochrone parameters to observed spectra in some way and, finally, integrate along the isochrone. They all need to make an assumption about which {\\em initial mass function} IMF to use. Also, the models need a recipe prescribing when the stars have been formed. Since the IMF is not very well known at the present time, its treatment is not very different from one model to another. However, as far as the {\\em star formation rate} (SFR) is concerned, some models assume that all stars are formed at the same time, others prescribe that the SFR has to decrease exponentially with time, while still others explicitly try to describe the whole formation of a galaxy from a gas cloud and form stars when the physical conditions in the gas are adequate. Examples of this kind of evolutionary models can be found in Tinsley (1968,1972,1978a,1978b,1980), Searle {\\it et al.} (1973), Tinsley \\& Gunn (1976), Turnrose (1976), Whitford (1978), Larson \\& Tinsley (1978), Wu {\\it et al.} (1980), VandenBerg (1983), Bruzual (1983,1992), Stetson \\& Harris (1988), Renzini \\& Buzzoni (1986), Rocca-Volmerange \\& Guiderdoni (1987,1988,1990), Guiderdoni \\& Rocca-Volmerange (1987,1990,1991), Yoshii \\& Takahara (1988), Rocca-Volmerange (1989), Buzzoni (1989), Charlot \\& Bruzual (1991), Lacey {\\it et al.} (1993) and Bruzual \\& Charlot (1993). Some of these models not only predict colors but also line-strengths notably those of Peletier (1989) and Worthey (1994). There are also models which combine evolutionary population predictions with considerations of chemical evolution. These models follow the evolution of the gas and make use of isochrones of more than one metallicity (solar). Examples of these {\\em chemo-evolutionary} population synthesis models are Arimoto \\& Yoshii (1986,1987), Casuso (1991), Bressan {\\it et al.} (1994) as well as the model presented in this paper. Note that for this type of models only the global metallicity, Z, is normally taken into account to determine the stellar populations. However it is in principle possible to follow the abundance distribution separately for each of several important elements in the gas. Examples of these so called chemical evolution models can be found in Larson (1972), Matteucci \\& Tornambe (1987), Tosi (1988) and there are many more. However, calculating colors and especially absorption line-strengths in such models has not been attempted up to now. Finally, among this kind of models there are a few which combine chemical evolution with dynamics, e.g. Theis, Burkert \\& Hensler (1992). One cannot say that one type of model is better than another. In general, more observables and physical parameters can be calculated if one makes more assumptions. If no assumptions are made about the physics, as in the empirical models, one may end up with solutions that are unphysical. If however wrong assumptions are made, one will not learn anything about the stellar evolution history either. We show later in this paper that our results can be reproduced using the {\\em simple} analytical model and possibly with infall. This means that we could have replaced the part of the model that deals with the evolution of the gas by some analytical calculations. However, we have preferred to build up the numerical machinery, since it offers much more flexibility, and even improved insight. It is clear that our understanding of all these aspects is improving with time, which means that the models that are to be applied can legitemately be more and more complicated, and in this context we have developed the evolutionary population synthesis code presented in this paper. For the reasons mentioned above it should never be used as a static black box out from which a theoretical fit to the data is to be taken, but as an evolving tool, which might help in disentangling stellar populations in a composite system. \\subsection{Evolutionary synthesis in general, and its problems} If one wants to calculate the final spectrum of a galaxy that has evolved from a gas cloud, one has to integrate over time the spectra of all stars that are still {\\em living} at the current time. The number of stars formed at a certain epoch is determined by the star formation rate. Little is known about this, so many models give it a prescribed form, and let it decrease e.g. exponentially. In this paper we assume that the SFR is proportional to the gas density (Schmidt 1959). The gas density itself and the chemical evolution of the gas is calculated taking into account the original gas, and the metal-enriched gas that is ejected by stars. The yields for the various elements needed for this calculation are not especially well known, and better knowledge would significantly improve the model. Other factors that may affect the SFR, such as inflow or outflow, are not considered in the context of the present models. The stars living at the current epoch contain stellar populations with a mixture of ages and metallicities. To calculate the final spectrum we decompose the stars into single stellar populations (SSP) each of a single age and metallicity, and calculate their spectra. To do this, one needs in the first place theoretical isochrones. The parameters of the isochrones depend, amongst others, on opacities of ions and molecules, and are reasonably well known for the early stages of stellar evolution. However for later phases such as the AGB and the Post-AGB, evolutionary calculations are very complicated, and could still benefit from significant improvement. The isochrones are much better for solar and sub-solar metallicity than for metal rich stars, because the former can be, and have been, tested observationally on globular clusters. In general, the relative composition of the elements heavier than Helium in the models is close to solar; only recently have people included for example oxygen-enhancement (Vandenberg 1992) or $\\alpha$-element enhancement (Weiss {\\it et al.} 1995). The following step is to obtain a spectrum for a star with physical parameters given by the isochrones. Model atmospheres needed for this (e.g. Kurucz 1992) appear to be reasonably reliable in the blue. In the red, molecular opacities make them, for the time being, much less reliable. For that reason several authors (Faber {\\it et al.} 1985, Gorgas {\\it et al.} 1993 and Worthey {\\it et al.} 1994) have developed a method that depends much more on observations. They use a grid of observed stars with various theoretical parameters to determine fitting functions that can be used to calculate an absorption line index for any combination of theoretical isochrone parameters. The problem however is that these fitting functions at the moment are available only for a limited number of absorption lines, since one needs many stars of various types and metallicities to make them. If one wants to carry out population synthesis, one needs to cover as large a wavelength range as possible, and also at as high a spectral resolution. This is to cover many colors and line indices, since in principle every color and absorption line is affected in a different way by the parameters above: the SFR, the IMF, the metallicity and abundance ratios etc. In practice a model with complete coverage from UV to near-IR is hard to implement, because of lack of fitting functions, color calibrations etc., and the observations are hard to obtain. In this paper we are concentrating on early-type galaxies, for which high spectral resolution is less important, due to their large velocity dispersions. We have produced model output for colors and lines that are relatively easy to obtain and reproduce, and that allow us to separate effects due to various relevant physical parameters. To some extent we are limited by the availability of libraries of stars, especially for the fitting functions, so this aspect too, can be significantly improved in the future. The layout of the paper is as follows. In Section 2 we will describe how we obtain colors and absorption line indices for a single stellar population, emphasizing differences from previous studies, and especially any improvements. In Section 3 we introduce our chemical evolutionary model. In Section 4 we apply our model to a limited set of data from three standard galaxies, for which the data is presented in an accompanying paper (Vazdekis {\\it et al.} 1996, {\\bf Paper II}). We perform the fits for an SSP (the {\\em static} option) and for a full evolutionary case. In Section 5 the conclusions are presented. Finally, in Paper II, apart from presenting the observational basis of the data-set used here, we carry out a comprehensive fit of the whole set of indices and colors on the basis of the scenarios suggested in this paper. In particular, we compare the fits obtained assuming a single-age single-metallicity stellar population or using the full chemical evolution model. We also discuss the relations between elements. ", "conclusions": "We have developed a stellar population model to apply to early-type galaxies. It produces optical and near-infrared colors, and absorption line strengths in lines from 4100 - 8800~\\AA~on the Lick system, is applicable to systems of intermediate or old age, and metallicity larger than 0.1 Z$_\\odot$. The model is chemo-evolutionary, i.e. it calculates the properties of a stellar system, starting from a primordial gas cloud. However, it can easily be used to predict the properties of systems with a single age and metallicity. The model colors and line strengths are determined by integrating stellar observables along theoretical isochrones, in this way obtaining Single Stellar Populations (SSPs), and then integrating these SSPs over time. The model uses isochrones with solar metal abundance ratios. As far as possible empirical calibrations have been used to convert theoretical isochrone values to observables for individual stars. Some properties of the models are: \\begin{figure} \\plotone{f24.eps} \\caption{The ($V-K$)-Mg$_{2}$ diagram for models which reach solar metallicity in an initial period of 0.2~Gyr. for a bimodal IMF. We can see that the Mg$_{2}$ index is always lower than the observational data. As can be deduced from Fig. ~21 the Mg$_{2}$ index is expected to decrease with increasing $t_{0}$. The metallicities in the three galaxies must therefore clearly be higher than solar.} \\end{figure} \\begin{itemize} \\item Extensive comparisons with models from other authors show that there is broad overall agreement in the colors and line strengths. We have also made independent estimates of the errors in our observables. \\item Our chemical evolutionary model is in good agreement with Arimoto \\& Yoshii (1986). We present optical and IR colors which are likely to be improved as a result of new calibration relations. Also, for the first time, we give integrated line strengths for an evolutionary model. \\item We find that for a closed box approximation the most metal rich elliptical galaxies cannot be fitted with a single IMF that is constant in time. To solve this problem, we propose a scenario invoking an IMF skewed towards high-mass stars during a short, initial period (smaller than 1 Gyr), followed by preferential low-mass star formation in the remaining time. \\item We have briefly tested the model here by fitting it to a few key colors and line strength indices, using a new data set for 3 standard early-type galaxies. In general, satisfactory results are reported. A much more comprehensive comparison of theory with observations is given in Paper II. \\end{itemize} To conclude, we need to make a few statements about the applicability of this model. Given the nature of this type studies, the numbers given in the text will soon cease to be the most accurate possible, because better isochrones become available, or better calibrations linking one parameter to another. Therefore, we will try to update the model as time goes on, and interested people can always obtain the most recent version electronically from the authors. There are however a few areas in which we think that further effort by the astronomical community is needed to improve models of this kind. These are: \\begin{itemize} \\item We show that absorption line strengths are generally more accurate than integrated colors. To change this situation better color-color relations are needed, especially for very high and very low metallicities. \\item Inclusion of more absorption line observations will make this kind of models more useful. Especially in the near-UV or near-IR very little work has been done, except in the region of the Ca II triplet. More libraries like the one of Worthey {\\it et al.} (1994) are urgently needed. \\item It looks as if a substantial part of the uncertainties are due to incorrect treatment of the later stages of stellar evolution, such as the AGB. Theoretical work in this area would be very valuable. \\end{itemize}" }, "9605/astro-ph9605089_arXiv.txt": { "abstract": "Using the exceptional monitoring capabilities of the MACHO project we present here the optical history of the LMC supersoft source (SSS) RX~J0513.9-6951, for a continuous 3 year period. Recurring low states, in which the optical brightness drops by up to a magnitude, are observed at quasi-regular intervals. This provides a crucial insight into the nature of the SSS and, in particular, a chance to investigate the poorly understood behaviour of their accretion discs. Analysis of the high state data reveals a small modulation of semi-amplitude $\\sim$~0.02 magnitudes at P$=$0.76278$\\pm$0.00005~days, a period which is consistent with the current ``best'' suggested spectroscopic value. ", "introduction": "{\\it ROSAT} observations have considerably enlarged the new class of high luminosity X-ray objects, the so-called ``supersoft sources'' (SSSs) characterised by their EUV temperatures (Tr\\\"{u}mper 1992). SSSs were first detected in the Large Magellanic Cloud in 1979-1980 with the {\\it Einstein} X-ray Observatory (Long, Helfand \\& Grabelsky, 1981). Until recently, little progress had been made in determining the exact nature of these elusive systems, the high level of X-ray absorption rendering them undetectable in the Galactic plane. Most currently known SSS are therefore extragalactic and, as such, they are optically faint. The current inventory of supersoft objects (Hasinger 1994; Cowley et al.\\ 1996; Kahabka \\& Tr\\\"umper 1996) is of the order of 11 in the Magellanic Clouds, 15 in M31 and 7 Galactic sources, with candidates existing also in M101, NGC253 and M33. It appears now, through ROSAT observations, that the SSS do not form a strictly homogeneous class, some having been identified with a planetary nebula nucleus (Wang 1991), a PG~1159 star (Cowley et al.\\ 1995) and symbiotic systems (e.\\ g.\\ Hasinger 1994). However, the bolometric luminosities of these objects ($L_{\\rm bol} \\sim~10^{37}$~erg\\,s$^{-1}$) are typically an order of magnitude less than the original {\\it Einstein} sources, CAL~83 and CAL~87. Among the {\\it ROSAT} discoveries are several systems, including RX~J0513.9-6951 (hereafter RX~J0513-69) which show the hallmarks of the original LMC SSS. Typically, $L_{\\rm bol} \\sim~10^{38}$~erg\\,s$^{-1}$ and T$_{\\rm bb} \\sim 30$~eV. Spectroscopic studies (Smale et al.\\ 1988; Pakull et al.\\ 1988) readily identified them as low mass X-ray binaries (LMXBs), yet the nature of the compact object and the source of the soft emission proved elusive. Previously, X-rays of such low energy had only been observed in certain types of cataclysmic variables (CVs), but these accreting white dwarf binary systems are typically about a million times fainter than the SSS (see e.\\ g.\\ Warner 1995). In 1990, CAL~87 was proposed to be a black hole binary, on the basis of a radial velocity analysis (Cowley et al.\\ 1990). The following year, a paper appeared advocating the scenario of a neutron star accretor, shrouded in a dense cocoon of ionised matter (Greiner, Hasinger \\& Kahabka 1991). However, neither model seemed to provide a natural explanation for the extremely soft X-ray emission. The most significant progress occurred when van den Heuvel et al.\\ (1992) proposed a model for the SSS which involved a white dwarf primary undergoing accretion at a rate $ \\simgt 10^{-7} {\\rm M}_{\\odot}$~yr$^{-1}$. It was shown that steady nuclear burning on the white dwarf surface could produce the extremely soft X-ray emission at the required luminosities. However, such high accretion rates require a donor star more massive than the white dwarf, in order to sustain thermally unstable mass transfer. We have therefore undertaken a programme of optical spectroscopy and photometry, to test the predictions of this model. In particular, we focus on the LMC group, since the accurately known distance of these high luminosity SSSs is a vital key in understanding their nature. We present here the results of long-term optical photometry of the transient LMC source, RX~J0513-69, which was discovered in the ROSAT All Sky Survey (Schaeidt, Hasinger \\& Tr\\\"umper 1993). Remarkably, these observations were acquired as a serendipitous by-product of the MACHO project (Alcock et al.\\ 1995a), owing to the location of RX~J0513-69 in a frequently monitored field. We are thus afforded an unprecedented opportunity to study the long term behaviour of this source which, at $V \\sim 16-17$, would normally be impossible. ", "conclusions": "Recently, Crampton et al.\\ (1996) reported variations of only $\\sim0.3$~mag, noting that the optical counterpart, identified as HV~5682, has historically shown variations of up to $\\sim1$~mag. Placing these observations in the context of the MACHO light curve, it is clear that both findings are consistent with the data presented here. In the more usual optical high states, variations of up to $\\sim0.3$~mag commonly occur on timescales of days (see Fig.~1). Clearly, the more dramatic variation of $\\sim 1$~mag can be identified with transitions to the rather more infrequent low states, detection of which requires extended monitoring of the type reported here. The optical luminosity in this system is expected to be dominated by the EUV/soft X-ray heated accretion disc, which has an absolute visual magnitude $M_{V} \\approx -2$ in the high state, at the high extreme of LMXBs in general (van Paradijs \\& McClintock 1995). Indeed, it is remarkable that {\\em all} the LMC LMXBs are optically so luminous. This may be compared to typical values of $M_{V} = +4$ to $+7$ for CVs (van Paradijs 1983). Even if we apply the Warner (1987) empirical relation: \\begin{equation} M^{\\rm{\\scriptsize{disk}}}_{{\\small{v}}} = 5.74 - 0.259~{\\rm P}_{\\small{orb}}({\\rm hr}) \\hspace{1cm} ({\\rm P}_{\\small{orb}} \\simlt 15~{\\rm hr}) \\end{equation} for the brightness of dwarf novae discs at maximum, using $P_{\\small{orb}} \\approx 18$~hr, we obtain $M_{V} = +1.1$, substantially fainter than observed for RX~J0513-69. This suggests that there is an additional source of optical luminosity in the system, consistent with the van den Heuvel et al.\\ (1992) scenario of a white dwarf undergoing surface nuclear burning. Using our orbital period of $P=0.76278$~d, we may calculate the mean density, $\\overline{\\rho}$, of the companion star under the assumption that it fills its Roche lobe. We combine Kepler's third law and the Eggleton (1983) relation for a Roche-lobe filling star: \\begin{equation} \\frac{R_{L_2}}{a}=\\frac{0.49q^{-2/3}}{0.6q^{-2/3} + \\mbox{ln}(1+q^{-1/3})}, \\end{equation} where $R_{L_2}$ is the radius of a sphere with the same volume as the secondary Roche lobe, $a$ is the binary separation, and $q$ is the binary mass ratio ($\\equiv {\\rm M}_{\\scriptsize{compact}}/ {\\rm M}_{\\scriptsize{secondary}}$) to obtain: \\begin{equation} \\overline{\\rho} = \\frac{0.161}{{\\rm P}^2(1+q)} \\left (0.6 + q^{2/3} \\ln(1+q^{-1/3}) \\right )^3 {\\rm g}~{\\rm cm}^{-3}, \\end{equation} where $P$ is in days. For values of $q \\simlt 1$, as required by the van den Heuvel et al.\\ 1992 model, the implied mean density is $\\sim 0.2-0.3$~g\\,cm$^{-3}$. This is consistent with that of a $\\sim 2.5-3.0~{\\rm M}_{\\odot}$ main sequence star (of spectral type $\\sim$ A0). The light from such a star would still be dominated by the accretion disk/compact object luminosity, since for an LMC distance modulus of 18.5 (e.\\ g.\\ Panagia et al.\\ 1991) its apparent magnitude would be $\\sim 19$, significantly fainter than the observed brightness of RX~J0513-69 of $V \\sim 17$." }, "9605/astro-ph9605199_arXiv.txt": { "abstract": "We propose a strategy for searching for isolated stellar mass black holes in the solar neighborhood with the Sloan Digital Sky Survey. Due to spherical accretion of the inter-stellar medium and the ambient magnetic field, an isolated black hole is expected to emit a blended, thermal synchrotron spectrum with a roughly flat peak from the optical down to the far infra-red. We find that the Sloan Survey will be able to detect isolated black holes, in the considered mass range of 1--100$M_{\\odot}$, out to a few hundred parsecs, depending on the local conditions of the ISM. We also find that the black holes are photmetrically distinguishable from field stars and they have a photometry similar to QSOs. They can be further singled out from QSO searches because they have a featureless spectrum with no emission lines. The Sloan Survey will likely find hundreds of objects that meet these criteria, and to further reduce the number of candidates, we suggest other selection criteria such as infra-red searches and proper motion measurements. Estimates indicate that dozens of black holes may exist out to a few hundred parsecs. If no black hole candidates are found in this survey, important limits can be placed on the local density of black holes and the halo fraction in black holes, especially for masses greater than about $20 M_{\\odot}$. ", "introduction": " ", "conclusions": "" }, "9605/astro-ph9605002_arXiv.txt": { "abstract": "Two new methods are proposed for linear regression analysis for data with measurement errors. Both methods are designed to accommodate intrinsic scatter in addition to measurement errors. The first method is a direct extension of the ordinary least squares (OLS) estimator to allow for measurement errors. It is quite general in that a) it allows for measurement errors on both variables, b) it allows the measurement errors for the two variables to be dependent, c) it allows the magnitudes of the measurement errors to depend on the measurements, and d) other `symmetric' lines such as the bisector and the orthogonal regression can be constructed. We refer to this method as BCES estimators (for Bivariate Correlated Errors and intrinsic Scatter). The second method is a weighted least squares (WLS) estimator, which applies only in the case where the `independent' variable is measured without error and the magnitudes of the measurement errors on the 'dependent' variable are independent from the measurements. Several applications are made to extragalactic astronomy: The BCES method, when applied to data describing the color-luminosity relations for field galaxies, yields significantly different slopes than OLS and other estimators used in the literature. Simulations with artificial data sets are used to evaluate the small sample performance of the estimators. Unsurprisingly, the least-biased results are obtained when color is treated as the dependent variable. The Tully-Fisher relation is another example where the BCES method should be used because errors in luminosity and velocity are correlated due to inclination corrections. We also find, via simulations, that the WLS method is by far the best method for the Tolman surface-brightness test, producing the smallest variance in slope by an order of magnitude. Moreover, with WLS it is not necessary to ``reduce'' galaxies to a fiducial surface-brightness, since this model incorporates intrinsic scatter. ", "introduction": "Linear regression analysis is used extensively in everyday astronomical research. The distinguishing feature of many astronomical data sets is the presence of intrinsic scatter in addition to heteroscedastic measurement errors (i.e. the size of the error can vary from observation to observation). A few notable examples in extra-galactic astronomy include relations between X-ray temperatures and velocity dispersions for galaxy clusters, the color-luminosity relations for field galaxies, the Tully-Fisher relation (and other ``Fundamental Plane'' relations), and the Tolman test. In this paper we consider the latter three examples. Neglect of measurement errors and intrinsic can bias the derived slopes of these relations, thus potentially leading to incorrect astrophysical deductions. Willick (1991) has performed a detailed study of the effects of intrinsic scatter and measurement error on the estimated slope of the Tully-Fisher relation. An additional issue pertains to biases associated with the correlation of measurement errors between observables. This occurs, for example, in color-luminosity relations and the Tully-Fisher relation. There are some cases where the measurement error is negligible in one variable. For example, in the case of the Tolman surface-brightness test, the error in redshift is usually negligible compared to the error and intrinsic scatter in surface-brightness. Regression model found in statistics text books rarely accommodate heteroscedastic measurement errors in more than one variable, and the recent paper Isobe \\etal (1991) (IFAB hereafter) deals exclusively with data that have no measurement errors. Indeed, accommodating heteroscedastic measurement errors and intrinsic scatter is mentioned in Feigelson \\& Babu (1992) as one of the outstanding problems in linear regression. The only currently available regression methods that deal with heteroscedastic measurement errors are based on the assumption that the true variables (in the absence of measurement error) have no intrinsic scatter. That is, the true points are assumed to lie exactly on a straight line, which implies they have correlation one. Software packages which perform regressions under this assumption are mentioned in Feigelson \\& Babu (1992), including ORDPACK (Boggs \\etal 1990), which also does nonlinear regression. A more accessible reference is Press {\\it et al.} (1988). This assumption, however, is violated in many astronomical data sets. In this paper we address the important problem of fitting regression models with data having heteroscedastic measurement errors of known standard deviation, and entirely unknown intrinsic scatter. We define a {\\it statistical model} for data with astronomical (heteroscedastic) measurement errors which allows the possibility of correlated errors between both variables of interest, and the possibility that the size of the measurement error depends on the observation. This model should prove useful for addressing other problems with such data, including intrinsic variance function estimation, goodness-of-fit, comparing $k$ multivariate samples etc). Very important is the distinction we draw between the case where the size of the measurement error (standard deviation in statistical parlance) depends on the measurement and the case where it does not. Both cases are equally common in astronomical data sets (e.g. background-limited versus source-limited observations). However, procedures that weigh the measurements according to the variance of the measurement error can give biased results if this variance depends on the observation, as we discuss in the next section. We describe here two different regression methods. Both of our methods pertain only to linear (as opposed to nonlinear) regression and are based on transparent ideas that make them very intuitive. The first method is a direct generalization of the OLS estimator which applies quite generally. The second method is a weighted least squares (WLS) estimator which applies when only the `response' variable is subject to measurement error and the size of the measurement error does not depend on the observation. We only consider simple linear regression here (i.e.\\ only one `explanatory' variable); extensions of this method to multiple regressions will appear in a sequel paper. The paper is organized as follows. In the next section we introduce the basic idea of our method. The statistical model for data with measurement errors is presented in subsection 2.1. In subsection 2.1 we consider the general case where both the response and the explanatory variable are subject to potentially correlated measurement errors, and the magnitude of these errors may depend on the measurements. We use the acronym BCES($X_2|X_1$) to denote the present generalization of the OLS($X_2|X_1$), which minimizes the residuals in $X_2$ (i.e. $X_2$ is the dependent variable). In subsection 2.2 we consider the case where only the response variable is subject to measurement error whose magnitude does not depend on the measurement, and we introduce a competing procedure based on WLS. In Section 3 we study other versions of the first method, namely the BCES-bisector and BCES-orthogonal regression; these regression lines are defined in terms of BCES($X_2|X_1$) and BCES($X_1|X_2$). In Section 4 we apply these methods to an astronomical data set and use simulations as a methodological tool to investigate the small-sample performance of the four BCES estimators (for color-luminosity relations) and the WLS estimator (for the Tolman test). Relevance to the Tully-Fisher relation is discussed. We consider more general application of BCES in Section 5. The mathematical derivations are given in the Appendix. \\newpage ", "conclusions": "To our knowledge, the methods presented here are the only algorithms that apply to data with both measurement errors and intrinsic scatter. When is it necessary to use one of the above methods over the techniques discussed in IFAB or FB? There are two basic criteria for selecting a statistical model to use for studying correlations in data, bias and uncertainty. Their relative importance depends somewhat on the specific scientific objective, however the conclusion is the same: When in doubt, the BCES and WLS models should be used. However, the WLS model should be used {\\it only} in the approximation where the $X_1$ variable is measured without error. If the purpose is to test a theory which predicts correlation slopes and/or zeropoints for some set of observables, then bias is the principal criterion. The statistical model which best approximates the real data is expected to give the least-biased regression, and so the choice becomes an issue of approximation. Because astronomy largely consists of passive observations and not active experiments, there is rarely an `explanatory' variable free of measurement error. Moreover, correlations between variables for astronomical systems almost always have intrinsic scatter, which is simply a reflection of these systems' complex, multi-variate dependencies. The `Fundamental Plane' for elliptical galaxies is one good astronomical example of this complexity (cf.\\ Santiago \\& Djorgovski 1993). For cases where the intrinsic scatter may be {\\it much larger} than measurement error, or vice-versa, the methods in IFAB or those outlined in FB, respectively, may provide acceptable approximations. However, at this time we cannot quantify ``much larger''. The methods presented here are valid in general and, since they reduce to the methods considered in IFAB in the case of no measurement errors, {\\it we recommend that the present methods be used in all cases.} There are some situations where differential measurements are designed simply to detect differences in slope between samples. Examples of this were described for the CL relation. Here, the most accurate regression estimate may be desired, and should be assessed via simulations of artificial data sets, as we have illustrated for the BCES family of models. However, if the statistical model is incorrect, then the estimated variance does not necessarily include effects of bias, which may differ from sample to sample. While bootstrap estimates of the variance may be 'unbiased,' the same is not necessarily true of the slope. To put it another way, if the null hypothesis is that two samples are the same, and this is to be confirmed by comparing regression properties, any statistical model may yield results consistent with the hypothesis. However, if the statistical model is incomplete or unrepresentative of the data, the comparison is only consistent and cannot validate the hypothesis. Again, BCES models are the most general and should provide the least-biased estimates of regression slopes and variances. Within a family of regressions models (e.g.\\ BCES or OLS), the choice of particular regression (($X_2|X_1$), ($X_1|X_2$), etc.) is only an issue of accuracy, and {\\it not} bias. As has been emphasized in IFAB and again here, {\\it the different regression methods give different slopes even at the population level.} All slopes are related to the second moments of the bivariate distribution of the data. Again, the most accurate regression should be assessed via simulations. In the case where the $X_1$ variable is measured without error, our simulations for two different artificial data sets revealed that the WLS estimator has smaller variance than BCES($X_2|X_1$). However WLS is consistent only when the error magnitude is independent from the observation. While the BCES estimators are consistent under general conditions, the simulations suggest they can be improved under the additional assumption that the measurement errors on $X_1$, $X_2$ are independent from the observations. Weighted versions of the BCES estimators under this additional assumption will be the subject of a forthcoming paper. The present procedures resulted from an interdisciplinary collaboration of astrophysicists and mathematical statisticians via the newly founded {\\it Statistical Consulting Center for Astronomy} (SCCA). Further information about SCCA can be obtained through the World Wide Web (http://www.stat.psu.edu/scca/homepage.html), or by contacting SCCA@stat.psu.edu. A FORTRAN package which includes the algorithms in this paper and IFAB, including bootstrap resampling error analysis, is available via anonymous ftp (contact mab@astro.psu.edu). The work of MGA was supported in part by NSF grant DMS-9208066. MAB acknowledges support from NASA through grant HF-1028.02-92, from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under contract NAS5-26555. \\appendix" }, "9605/astro-ph9605144_arXiv.txt": { "abstract": "The galaxy population in the intermediate-redshift ($z=0.228$) rich cluster Abell 2390 is investigated. We present velocities, colors, and morphological information for an exceptionally large sample of 323 galaxies (216 cluster members) in a 46$^\\prime \\times 7^\\prime$ (6 $h^{-1}$ Mpc $\\times$ 1 $h^{-1}$ Mpc) strip centered on the cD galaxy. This sample of confirmed cluster members is second only to that for the Coma cluster in terms of sample size and spatial coverage in the cluster rest frame, and is the first to trace the transition between a rich cluster and the field at intermediate redshift. The galaxy population in the cluster changes gradually from a very evolved, early-type population in the inner 0.4 \\hmpc\\ of the cluster to a progressively later-type population in the extensive outer envelope of the cluster from 1 to 3 \\hmpc\\/ in radius. Radial gradients in galaxy $g-r$ color, 4000 \\AA\\/ break, H$\\delta$ and [O II] line strengths and morphology are seen in the cluster, and are investigated by comparing the data to models computed with the GISSEL spectral synthesis package. The results suggest that the cluster has been gradually built up by the infall of field galaxies over $\\sim 8$ Gyr and that star formation has been truncated in infalling galaxies during the accretion process. The morphological composition of the cluster is shown to be consistent with such a scenario. If true for other clusters, infall-truncated star formation as seen in Abell 2390 may explain both the Butcher-Oemler effect and the large fraction of S0 galaxies in clusters. Only $\\simlt$5\\% of the galaxies observed in Abell 2390 exhibit evidence for star formation at levels stronger than those seen in typical late-type systems. This suggests that starbursts do not play a major role in driving cluster galaxy evolution at the redshift of Abell 2390, although infall-induced starbursts leading to truncated star-formation may have played a role in the earier history of the cluster. Evidence is found for at least one subcomponent on the West side of the cluster, which is likely to be infalling at the epoch of observation. ", "introduction": "\\noindent Within the hierarchical gravitational instability theory, clusters of galaxies are created by merging of smaller clusters. Such merged clusters may have no memory of their initial conditions, or they may retain the radial gradients of the progenitors. More specifically, ``violent relaxation''~\\cite{Lynden-Bell:1967} erases nearly all memory of the initial structures (but see \\citeNP{Quinn:1986}), whereas steady accretion formation~\\cite{Gunn:1972} builds the cluster slowly and continuously over a Hubble time, so that the orbits remain stratified in a radial age sequence. Nearly equal mass mergers will be quite ``violent'', but the steady accretion of individual galaxies and small groups on to a pre-existing cluster leaves the structure of the initial cluster relatively unaffected. The ability of the cluster to continue to accrete material at low redshift depends on the initial overdensity profile of the cluster and $\\Omega$~\\cite{Gunn:1972}. If a cluster is uniformly mixed then we presume that the last merger was quite violent. Cluster galaxies are generally red, and the combination of their mean color and the {\\em dispersion} in color allows a limit to be put on how closely in time the galaxies formed, and thus on the epoch of initial galaxy formation. Observed gradients in galaxy populations can be used to trace the cluster's accretion history, and to test simple galaxy evolution models. There is likely to be a close relationship between population gradients in clusters and the ``Butcher-Oemler Effect'' (the increase in the fraction of blue cluster members with redshift). HST observations of the intermediate redshift clusters CL 0939+4713 ($z=0.41$; \\shortciteNP{Dressler:1994}), Abell 370 ($z=0.39$; \\shortciteNP{Couch:1994}), and AC 114 ($z=0.31$; \\shortciteNP{Couch:1994}) have shown that in these three clusters the relative fraction of spirals, S0 galaxies, and ellipticals is similar to that seen in the {\\em field} at the current epoch. These observations suggest that the Butcher-Oemler effect is mostly due to an excess population of late-type systems, and not due to a population of starbursting, early-type systems. If CL 0939+4713, Abell 370, and AC 114 (the only clusters for which morphological studies at $z \\sim 0.3 - 0.4$ have been published) are representative of rich clusters at intermediate redshift, then the cluster galaxy population has evolved since $z\\sim 0.4$ into the early-type-dominated population seen in nearby clusters \\cite{Dressler:1980}. The narrow color-magnitude envelope for the red galaxies in the clusters studied with HST led both \\shortciteN{Dressler:1994} and \\shortciteN{Couch:1994} to conclude that the old population in these clusters is similar to ellipticals and S0s seen at the current epoch, and hence that galaxy evolution in clusters is dominated by the fading or destruction of cluster spirals. Other evidence for cluster galaxy evolution was discovered by \\citeN{Dressler:1983}, who found that a substantial number of galaxies in intermediate redshift clusters have enhanced Balmer absorption for their color. These authors coined the term ``E+A galaxy'' to describe these objects, noting that their spectra could be matched with a mixture of an elliptical galaxy and an A-type stellar population, and that their colors were intermediate between those of early-type systems and spirals. Since Balmer lines are enhanced as the main-sequence turnoff moves through A stars, which occurs $\\sim 1$ Gyr after star-formation (or a starburst) ceases, the spectroscopic characteristics and colors of E+A galaxies have led most authors to conclude that E+A systems are the remnants of starbursts that have recently occurred in old galaxies. However, others ({\\it e.g.} \\citeNP{Couch:1987}) show that it is hard to distinguish between 1 Gyr old starbursts in early-type systems and late-type systems whose star-formation has simply been truncated without an initial starburst, and in view of this ambiguity prefer the term ``H$\\delta$-strong'' (HDS) to ``E+A''. More recently, \\citeN{Charlot:1994} have shown that, solely on the basis of optical colors and spectra, it is virtually impossible to distinguish between a major starburst in an elliptical and one in a spiral if star formation ceases after the burst. The only unambiguous way to identify these starbursts is to catch them {\\em during} the burst when their [O~II] emission is strong and their colors are blue. In this paper we examine the galaxy population in the intermediate redshift cluster Abell 2390 ($\\alpha_{\\rm 1950} = 21:51:14.3$, $\\delta_{\\rm 1950} = +17:27:34.9$, $z=0.228$). The data were obtained as part of the Canadian Network for Observational Cosmology (CNOC) dynamical survey of X-ray-luminous clusters of galaxies \\shortcite{Carlberg:1994}. Abell 2390 is a large, rich cluster with a sizable hot intracluster medium ($L_x=5.5 \\times 10^{44}$ erg s$^{-1}$; \\citeNP{McMillan:1989}). We use the observed colors, spectral features and morphologies of the galaxies to put limits on the star-formation histories of cluster galaxies and on the cluster's accretion history. The plan of this paper is as follows. In \\S2, we describe our spectroscopic and photometric data and analysis, and outline the automated procedure used to obtain the morphological classifications. In \\S3, we discuss the rich spatial and velocity structure of the cluster. We demonstrate that Abell 2390 contains a very old, red, centrally condensed component, and that galaxies in the extensive outer envelope of the cluster show a radial gradient in which bluer, later type galaxies are found systematically at larger radii. We also identify a distinct group of galaxies (red as well as blue: the `NW Group') that appear to constitute a small cluster that is merging with Abell 2390. In \\S4, we discuss the galaxies with current star formation ([O II] emission line galaxies) and those galaxies which have recently experienced a significant decrease in their star formation rates (strong Balmer absorbers). In \\S5, we discuss how we have used the GISSEL spectral synthesis package \\shortcite{Bruzual:1993} to calculate the line strengths and colors of galaxies for various galaxy evolution models. In \\S6, we compare the data with these models. In \\S7, we show that the gradients in galaxy color, spectroscopic line measures, and morphology are consistent with a scenario in which the the outer part of the cluster is built up slowly over a Hubble time, while star formation is truncated in infalling galaxies. In this picture, the radial gradients in Abell 2390 are due to systematic changes in the ages of the stellar populations in the galaxies as a function of radius. Abell 2390 is similar to other rich clusters at intermediate redshifts, and we speculate that truncated star formation may play an important role in the Butcher-Oemler effect and lead to the formation of cluster S0 galaxies. We also discuss evidence for merging and interactions in our imaging data. Our conclusions are summarized in \\S8. ", "conclusions": "Our analysis leads to the following conclusions: 1. Galaxies in the central $0.4$ \\hmpc\\/ of Abell 2390 are red and have low dispersions in velocity, color, and spectral line strengths as well as high central concentrations. These properties suggest that they are coeval E/S0 galaxies with ages $\\simgt 8$ Gyr (assuming that their star formation timescales are $\\sim 1$ Gyr and that mean metallicities are approximately solar). These objects are likely to be the first generation of galaxies formed in the proto-cluster. 2. Large scale accretion from the field along the West side of the cluster is suggested by the spatial-velocity structure of the cluster, and by the the skewed distribution of line emitters (which occur almost exclusively in the West half of the cluster). The most obvious structural subgroup in Abell 2390, the NW Group, may be part of this infall pattern. This group of galaxies is more evolved than its surroundings and is presumably the core of a smaller cluster being accreted onto the main component. 3. Radial gradients exist in the colors, spectral features and morphologies of the cluster galaxies. These radial gradients are interpreted as an age sequence in which the mean age of the galaxies decreases with radius as a consequence of truncated star formation in spirals accreted from the field. Many galaxies in the extensive outer envelope of the cluster have properties intermediate between E/S0s and field spirals. These galaxies are analogous to the ``anemic spirals'' seen in local clusters \\cite{vandenBergh:1976}, and they are likely to be transitional objects in an evolutionary sequence in which field spirals are transformed into into cluster S0s. While the blue fraction of the cluster rises strongly as a function of radius, even at the edges of our dataset the galaxy population remains redder than the field. 4. Only $\\simlt 5$\\% of the galaxies in Abell 2390 show signs of star formation at levels higher than those seen in normal Sbc galaxies. The large number of H$\\delta$ strong objects relative to active galaxies suggests that star formation has been halted in many galaxies, and that in most cases this truncation has occurred in systems that have not undergone starbursts. This suggests that truncation in the star formation rates of cluster members is more closely linked to a gradual mechanism such as stripping by the hot intracluster medium than to starbursts. We cannot rule out the possibility that some ($\\sim$25) H$\\delta$-strong objects are post-starburst systems, but if so then the epoch of cluster starbursts must ended $\\simgt 1$Gyr before the epoch of observation. 5. The blue fraction in Abell 2390 is typical of that seen in ``Butcher-Oemler'' clusters at $z\\sim 0.25$. The recent HST results of \\citeNP{Couch:1994} and \\citeNP{Dressler:1994} suggest that the increased blue fraction in high-redshift clusters is due to a high proportion of blue disk galaxies. If Abell 2390 is really a ``typical'' rich cluster at intermediate redshift, then truncated star formation leading to the transformation of the blue disks in high redshift clusters may be the physical mechanism driving the Butcher-Oemler effect. Future papers will compare Abell 2390 to other CNOC clusters (which span the redshift range $0.2 \\leq z \\leq 0.5$) in order to determine whether similar mechanisms are driving galaxy evolution in other X-ray luminous clusters. \\vskip 10pt \\centerline" }, "9605/astro-ph9605165_arXiv.txt": { "abstract": "We have performed quasi-simultaneous radio flux density measurements at 2.7 and 10 GHz for all PG quasars with radio flux densities between 4-200~mJy. We find that a large fraction of these sources are variable, flat-spectrum quasars. This brings the total fraction of flat-spectrum quasars with a ratio between radio and optical flux of $R>10$ --- a value previously used to define a radio-loud quasar --- to 40\\% in the PG quasar sample. We also find that the median $R$-parameter of these flat-spectrum quasars is {\\it lower} than those of steep-spectrum radio-loud quasars. This contradicts the predictions of the unified scheme and the idea that all flat-spectrum, core-dominated quasars are relativistically boosted lobe-dominated quasars. We show that this discrepancy is due to a population of flat-spectrum radio-intermediate quasars with $25R>200$ are compact flat-spectrum radio quasars and constitute a population of flat-spectrum radio-intermediate quasars (RIQ). This confirms an earlier prediction for the radio-intermediate quasars by FMB95 which was based on a subsample of the PG quasars. Together with data from the literature we have now almost complete spectral information for PG quasars down to $R\\sim1$. If one uses the definition for a radio-loud source of $R>10$ (K89) we find severe inconsistencies in the content of the PG quasar sample with the simple unified scheme. According to the unified scheme flat-spectrum, core-dominated sources are the relativistically boosted counterparts to steep-spectrum, lobe-dominated sources. Therefore, they should be rare and they should have higher radio flux densities than steep-spectrum sources. However, if we treat the flat-spectrum quasars as a single population, the flat-spectrum sources are quite frequent ($40\\%$) in the PG sample and the majority has lower flux densities and lower $R$-parameters than steep-spectrum quasars. Under these prerequisites our observations exclude that core-dominated quasars are generally the boosted counterparts of {\\em lobe-dominated, steep-spectrum \\RLQ{}}. We point out that this problem can be easily circumvented if one assumes that the distributions of flat- and steep-spectrum quasars are both bi-modal. In this case one would separate radio-loud and radio-weak steep-spectrum sources at $R\\simeq25$ and radio-loud and radio-weak flat-spectrum quasars at a higher value of $R\\sim250$, where the latter number is fairly uncertain due to the small number of flat-spectrum quasars. As a consequence, the fraction of flat-spectrum quasars would be only of the order $10\\%$ for {\\em both}, radio-loud and radio-weak quasars. This fraction of flat-spectrum sources as well as the relative enhancement of the radio cores in radio-loud and \\RWQ{} between flat- and steep-spectrum sources is consistent with average Lorentz factors of $2-4$ and now fits well into the unified scheme for \\RLQ{}. The implication of this suggestion is that \\RWQ{} are as much subject to relativistic boosting as are \\RLQ{}, and the \\FIQ{} are just the boosted counterparts to \\RWQ{} --- this agrees well with the jet-disk symbiosis idea for radio-weak and radio-loud quasars proposed by Falcke \\& Biermann 1995 and FMB95, which postulates that the central engines in quasars produce initially very similar radio jets. It is known, that a large fraction of Seyfert galaxies, which are believed to be the low-power counterparts to quasars, have collimated bi-polar radio outflows (Ulvestad \\& Wilson 1989). Radio morphological studies of \\RWQ{} also show evidence of jet-related structures (K89). Hence it is not surprising to find jets in radio-weak quasars. However, so far no Seyfert galaxy has shown evidence for relativistic motion in its radio jets (although this is not yet excluded for the cores). Therefore, the \\FIQ{} could be an important clue for the understanding of jets in radio-weak sources. It may, for example, be that the jet speed is somehow related to the total luminosity or to the Eddington luminosity of the central engine and becomes relativistic only for high-power engines. There are also a few other arguments that support the link between the \\RWQ{} and the \\FIQ{}. While the \\RWQ{} in the PG sample have absolute UV luminosities that stretch from $10^{44}$erg/sec to $10^{48}$erg/sec, steep-spectrum \\RLQ{} are only found only in the interval $10^{46}$erg/sec$1$), but they also point out that core-dominated \\RLQ{} too have relatively strong \\ion{Fe}{2}, moving them closer to \\RWQ{}. We note that 4 of their core-dominated 5 sources are \\FIQ{} and hence might be boosted \\RWQ{}. Our interpretation can be tested further by VLBI observations of the \\FIQ{} and studies of their host galaxies. One would expect to see a very compact nucleus in these sources, and possibly core-jet structures and superluminal motion as seen in many lobe- and core-dominated radio-loud quasars (e.g.~Hough et al.~1992 and Zensus, Cohen, \\& Unwin 1995). However, if the \\FIQ{} are indeed radio-weak quasars, one expects the limits for the resolved, and extended emission (i.e.~radio lobes) to be very low, with fluxes corresponding to $R$-parameters of unity or less. This is in marked contrast to what one expects to see for a boosted radio-loud quasar and is a testable prediction. Moreover, as the host-galaxies are markedly different between radio-loud and \\RWQ{} one expects to find a substantial fraction of spiral host galaxies for the \\FIQ{}. We also need a larger optically selected quasar sample with deep VLA observations and quasi-simultaneous flux-measurements to directly prove the bi-modality of flat-spectrum quasars. If these tests fail, the \\FIQ{} would constitute a major puzzle for our understanding of the radio properties of quasars and one would have to invoke other, possibly more exotic explanations for the \\FIQ{}. Finally we wish to point out that without spectral information the \\FIQ{} can spoil all studies concerned with the radio properties of quasars and the difference between radio-loud and \\RWQ{}. At least in an optically selected sample one would simply overestimate the number of radio-loud sources in certain regimes. This is especially critical for the determination of the paucity of radio-loud quasars found at low powers (see Falcke et al.~1995b), where some \\FIQ{} could be falsely classified as \\RLQ{}." }, "9605/astro-ph9605059_arXiv.txt": { "abstract": "The 4.2-day orbit of the newly discovered planet around 51~Pegasi is formally unstable to tidal dissipation. However, the orbital decay time in this system is longer than the main-sequence lifetime of the central star. Given our best current understanding of tidal interactions, a planet of Jupiter's mass around a solar-like star could have dynamically survived in an orbit with a period as short as $\\sim10\\,$hr. Since radial velocities increase with decreasing period, we would expect to find those planets close to the tidal limit first and, unless this is a very unusual system, we would expect to find many more. We also consider the tidal stability of planets around more evolved stars and we re-examine in particular the question of whether the Earth can dynamically survive the red-giant phase in the evolution of the Sun. ", "introduction": "A new era in astronomy has begun recently with the first clear detections of several extra-solar planets, first around a millisecond pulsar (Wolszczan 1994) then around several solar-type stars (Mayor \\& Queloz 1995; Marcy \\& Butler 1996). These discoveries will no doubt lead to significant improvements in our understanding of many processes related not only to planet formation, structure and evolution, but also, as we illustrate in this paper, to stellar astrophysics. The new planets have brought many surprises. In particular, the existence of a Jupiter-type planet with a very short orbital period of $4.2\\,$d around 51~Peg\\markcite{ref1} (Mayor \\& Queloz 1995) is very puzzling. Not only is it difficult to fit such an object into accepted scenarios for planet formation but it turns out, as we show below, that its orbit is unstable to tidal dissipation. Orbital decay is therefore inevitable in this system, and the Jupiter-mass companion will ultimately spiral into the star. However, in this system, we will show that the orbital decay timescale is longer than the main-sequence lifetime of the solar-like star, consistent with the planet's surviving to the present. We will then investigate tidal survival in general for Jupiter-like planets in close orbits around solar-type stars. In the 51~Peg system, we can be sure that the planet will not survive any post-main-sequence evolution of the central star. By the time the star has grown to about twice its current radius, the orbital decay rate will have exceeded the evolution rate. This last point brings us to reconsider the fate of our own planet Earth. Current stellar evolution calculations\\markcite{ref2} (Sackmann, Boothroyd, \\& Kraemer 1993), taking into account the mass loss from the Sun and the resulting expansion of the Earth's orbit, predict that the Earth will not be engulfed even when the Sun reaches its maximum radius at the tip of the giant branch. However, as the mass-loss rate increases with the expansion of the solar envelope, so does the tidal decay rate of the Earth's orbit and we will show here that, as a result, the Earth may well not survive after all. ", "conclusions": "" }, "9605/astro-ph9605090_arXiv.txt": { "abstract": "We present spectroscopy and photometry of the LMC supersoft binary system RX~J0513.9-6951. We derive a refined spectroscopic period of P$=0.761\\pm0.004$~d, which is consistent with the value obtained from long term photometric monitoring (P$=0.76278\\pm0.00005$~d). We see bipolar outflow components of He{\\sc ii} and H$\\beta$, with velocities of $\\sim 3800$\\,km\\,s$^{-1}$, strongly suggesting that the compact object is a white dwarf. Using all the available optical and X-ray data, we construct a theoretical model to explain the principal features of the unusual variability of this source. In particular, we note that X-ray outbursts have only been seen at times of optical minima. From this, we conclude that the most likely cause of the X-ray outbursts is a photospheric contraction during a nuclear shell burning phase, rather than a thermonuclear flash or shocked emission. The system probably comprises a relatively massive white dwarf accreting at a high rate ($\\sim 10^{-6} M_{\\odot}~{\\rm yr}^{-1}$) from an evolved donor star, and is observed close to pole-on. ", "introduction": "The supersoft X-ray sources (SSS) are a class of luminous ($L_{\\mbox{bol}} \\sim~10^{37} - 10^{38}$\\ergsec) objects, with a characteristic radiation temperature of $(1-10)~\\times~10^5$\\,K. Seven such sources are now known in the Galaxy, 11 in the Magellanic Clouds, 15 in M31 and candidates exist also in M101, NGC~253 and M33 (see reviews by Hasinger 1994; Kahabka \\& Tr\\\"{u}mper 1996; Cowley \\etal 1996). The most popular theoretical model for the SSS consists of a binary system in which a white dwarf accretes mass from a subgiant companion at such a high rate that it burns hydrogen steadily at its surface (van den Heuvel \\etal 1992; Rappaport \\etal 1994). The difference between SSS and ordinary cataclysmic variables is in the high accretion rates (by a factor $\\sim 100-1000$) in the SSS. More recently, Yungelson \\etal (1995) have shown that three major binary subpopulations may contribute to the Galactic population of SSS with: (i)~low mass main sequence donors, (ii)~low mass subgiant donors, and (iii)~(super)giant donors. The transient supersoft source RX~J0513.9--6951 (hereafter 0513--69) was discovered in outburst during the ROSAT All Sky Survey (Schaeidt, Hasinger \\& Tr\\\"{u}mper 1993). In 1990 October/November the source brightened in X-rays by about a factor of 20 during a period of $\\sim~10$ days. A formal black body fit to the PSPC data gave a temperature of about 40\\,eV and a bolometric luminosity of $\\sim 2\\times10^{38}$\\ergsec, for a column density of N$_{\\rm {\\scriptsize H}} = 9.4 \\times 10^{20}$~cm\\,$^{-2}$. The source has been monitored roughly every three months between November 1992 and October 1993 and was found to be three times in an off-state and once, on 20/22 July 1993, in an on-state, with a similar brightness to that observed in the first outburst (Schaeidt 1996). Furthermore, a series of weekly HRI pointings between 3~November 1994 and 3~March 1995 revealed a third X-ray outburst around the end of December 1994. A typical turn-on time of $\\sim 6$~d (from survey data) and turn-off time of $\\simlt 1$ week (from the HRI pointings) were thus proposed for this source by Schaeidt (1996). This object has been identified with a $\\sim 17$~mag emission-line star in the LMC (Pakull \\etal 1993; Cowley \\etal 1993). Spectroscopic observations by Crampton \\etal (1996), hereafter C96, showed that the spectrum is dominated by He~{\\sc ii} emission lines and H$+$He{\\sc ii} blends. Their radial velocity measurements suggested a binary period of 0.76~d, but no orbital photometric variations were found. However, we have recently published a $\\sim3$~year light curve of 0513--69, from observations made during the MACHO project (Alcock \\etal 1996). This photometry revealed a high level of optical variability, including recurrent low states, in which the brightness drops by $\\sim 1$~mag every $\\sim 100-200$~days. The extended time-base over which these observations were made enabled us to detect an orbital modulation, although of small semi-amplitude ($\\sim 0.02$~mag). The photometric period thus derived, P$=0.76278\\pm0.00005$~d, is consistent with the independent spectroscopic result. In the current work, we present further spectroscopic and photometric observations of 0513--69, in which we see some unusual features, including evidence for high velocity outflows and optical variability on timescales as short as $\\sim 3$~h. We then use all the available optical and X-ray data in an attempt to construct a comprehensive theoretical model for the source. The spectroscopic observations are described in \\S~2, and the photometry in \\S~3. In \\S~4, we present a refined spectroscopic period, and consider the implications of the derived binary parameters and mass function. A discussion and the proposed model follow. ", "conclusions": "We will now discuss the implications of the observations presented here, as well as of other available data, for models of the system. \\subsection{The Nature of the Compact Object} The first thing we would like to establish is the nature of the compact object. To this goal, we note that observations of young stellar objects (\\eg Reipurth \\& Heathcote 1993), of AGN (\\eg Blandford 1993), of SS~433 (\\eg Vermeulen 1993) and of the Galactic black hole candidates GRS~1915+105 (Mirabel \\& Rodriguez 1994) and GRO~1655-40 (Hjellming \\& Rupen 1995) {\\it all} indicate that the velocities of jets are always of the order of {\\it the escape velocity from the central object}. The observations presented in \\S~2 (see also C96) indicate bipolar outflows or jet speeds of $V_{\\rm bipolar} \\sim~3800$\\kmsec. If interpreted as an escape velocity, the observed value of $V_{\\rm bipolar}$ corresponds to a value of the mass to radius ratio of the compact object of $M/R~\\sim 40~M_{\\odot}/R_{\\odot}$, {\\it which is typical for a white dwarf}. Indeed, outflows with velocities of this order have been observed in cataclysmic variables (\\eg Drew 1991; Drew, Hoare \\& Woods 1991). Since the value of $M/R$ identifies the accreting object unambiguously as a white dwarf, we check further if the observed luminosity is consistent with a white dwarf burning hydrogen in a shell. For such an object, the luminosity is related to the white dwarf mass by (\\eg Iben \\& Tutukov 1989) \\begin{equation} L/L_{\\odot} \\simeq 4.6\\times10^4 (M_{\\rm WD}/M_{\\odot} - 0.26). \\end{equation} Note that this relation differs somewhat from the usual Paczy\\'{n}ski-Uus relation (Paczy\\'{n}ski 1970; Uus 1970) which is appropriate for AGB stars which have both hydrogen and helium burning shells. The bolometric luminosity of 0513--69 is probably between $9.5\\times10^{37}$\\ergsec (obtained from an LTE model atmosphere fit; Reinsch \\etal 1996) and $2\\times10^{38}$\\ergsec (obtained assuming a black body fit; Schaeidt, Hasinger \\& Tr\\\"umper 1993). Using Eqn.~1 with these values gives a mass of $\\sim 0.8-1.4\\,M_{\\odot}$, again consistent with a white dwarf. From the above discussion we therefore conclude that the compact object in 0513--69 is almost certainly a white dwarf. \\subsection{The Accretion Rate} Much of the optical luminosity of the system is probably generated in the accretion disk (although some fraction may represent the effects of nuclear burning and of illumination of the accretion disk and the secondary star by the hot white dwarf). For a distance modulus of 18.5 to the LMC and $E_{B-V} = 0.1$ (\\eg Panagia \\etal 1991), we obtain (in the optical high states) $M_V~\\simeq~-2$. {\\it If} we assume that the entire luminosity comes from a standard accretion disk then, using the fact that the luminosity of the accretion disk is given approximately by (Webbink \\etal 1987) \\begin{equation} M^{\\rm disk}_V \\simeq -9.48 - \\frac{5}{3} \\log \\left( \\frac{M_{\\rm WD}}{M_{\\odot}} \\frac{\\dot{M}}{M_{\\odot} {\\rm yr}^{-1}} \\right) - \\frac{5}{2} \\log~(2\\cos i)~, \\end{equation} where $\\dot{M}$ is the accretion rate and $i$ is the inclination angle, we obtain for $M_{\\rm WD} = 1M_{\\odot}$ and $i \\simeq 10^{\\rm o}$ (see \\S~4.2), an accretion rate of $\\dot{M}~\\simeq~10^{-5} M_{\\odot}~{\\rm yr}^{-1}$. This accretion rate is of the order of the Eddington value, and it indicates that at least some fraction of the optical light is due to illumination (and perhaps nuclear burning on the white dwarf surface). It probably remains true, however, that the accretion rate in this system is extremely high. Another indication of the fact that the accretion rate in 0513--69 may be higher than in other similar systems (\\eg CAL~83) comes from the observation of the bipolar outflow (\\S~2.2 and \\S~5.1). Typically, the mass flux in jets is of the order of 1--30\\% of the disk accretion rate (\\eg Lizano \\etal 1988), and while not all the objects which exhibit jets have luminosities near the Eddington limit (although SS~433 does), it is certainly the case that the intermittent nature of the jets in young stellar objects seems to be associated with episodes of an increased accretion rate through the disk (\\eg Reipurth \\& Heathcote 1993). The observed drops in the optical luminosity, by $\\sim 0.8$~mag (\\S~3), if interpreted as a reduction in the accretion rate, correspond to a decrease in $\\dot{M}$ by a factor $\\sim$~3. We should note, however, that if the optical luminosity is actually dominated by reprocessed radiation from the accretion disk and/or the secondary star, both being irradiated by the steady burning white dwarf, then the decrease in $\\dot{M}$ could be by a larger factor. Such occasional drops in the accretion rate are observed in many nova-like variables and in particular in the group of cataclysmic variables known as VY Scl stars (\\eg Shafter 1992; Robinson \\etal 1981; Honeycutt 1995). Similarly to the case of 0513--69, the downward transitions in VY Scl stars also occur on a timescale of tens of days (\\eg Hudec, Huth \\& Fuhrmann 1984; Liller 1980; Rosino, Romano \\& Marziani 1993; Honeycutt 1995). Further evidence for the relation between the bipolar outflows and the accretion rate may be inferred from comparison of spectroscopic observations obtained during both high and low states. Optical spectroscopy obtained during a low state in December 1993 (C96; Reinsch \\etal 1996) revealed the equivalent widths of the emission lines to be significantly weaker than in high state observations. We shall return to the question of what can cause the drops in the mass transfer rate when we discuss a comprehensive model for the system in \\S~5.4 below. \\subsection{The Cause of the X-ray Outbursts} There are four main ways in which an accreting white dwarf can exhibit transient X-ray outbursts: (i)~the outbursts may represent some phases in thermonuclear flashes occurring when a critical mass for ignition is accumulated (\\eg Iben 1982; Prialnik \\& Kovetz 1995), examples of this behaviour being provided by classical novae; (ii)~the X-ray outbursts may be the consequence of a photospheric contraction during a nuclear shell burning phase (even if the burning was steady; \\eg MacDonald, Fujimoto \\& Truran 1985; \\\"Ogelman \\etal 1993; Krautter \\etal 1996); again, this behaviour has been observed in some nova systems; (iii)~the X-ray luminosity may be generated in shocks resulting from the interaction of an ejected shell with the ISM; (iv)~the outbursts may simply represent epochs in which the X-ray source is not shielded by intervening material (\\eg Pakull 1996). Examining the X-ray data {\\it alone} it is difficult to rule out regular thermonuclear flashes as a possible cause for the recurrent X-ray outbursts (this was, in fact, the model proposed by Kahabka 1995). However, when the X-ray data are examined {\\it together} with the optical data, flashes caused by the accumulation of a critical mass become extremely unlikely. The reason is simply the fact that the second and the third X-ray outbursts observed in the system in July 1993 and in December 1994 occurred {\\it during optical minima} (see Fig.~3), while {\\it no outbursts were observed during optical high states} (Schaeidt 1996; Pakull \\etal 1993). If this represents the rule (rather than being an accident), then it is very difficult to reconcile with a thermonuclear flash model, which is normally accompanied by radius expansion and an increased optical luminosity (see \\eg Livio 1994 for a discussion). Even if a thermonuclear flash was able to produce a decrease in the optical luminosity (for example, if it led only to a modest expansion, but which nevertheless managed to destroy the disk), this would {\\it follow} the X-ray rise, contrary to what is probably observed (see \\S~5.4 and Fig.~3). We may thus rule out the thermonuclear flash model. The shock emission model ((iii) above) may also be eliminated as a possible source for the increase in the X-rays, since the ejection of a shell is normally a consequence of significant expansion (\\eg Prialnik \\& Kovetz 1995). We are therefore left with the episodic unveiling of a permanent X-ray source or contraction during a steady shell burning phase as the most probable origins for the increase in the X-ray luminosity (see Pakull \\etal 1993; Pakull 1996). In the former model, the white dwarf is burning steadily all the time, but is visible (in X-rays) only during phases of low mass transfer rate (see \\S~5.4 for a possible cause of such phases). At other times, the wind and bipolar outflow are optically thick to soft X-rays. It should be noted that the decrease in the optical should precede the rise in the X-rays, which is probably consistent with the available data (see \\S~5.4). We may investigate whether the outflow can indeed shield the source using the following simplified approximation. If we assume a spherical outflow, characterised by a velocity law of the type $V=V_{\\infty} \\left ( 1 - R_{\\rm WD}/r \\right )^{\\beta}$, where $V_{\\infty}$ is the outflow velocity at a large distance, then we can calculate the optical depth in the outflow, \\begin{equation} \\tau = \\frac{\\sigma}{4\\pi m_p V_{\\infty} R_{\\rm WD}} f(X, \\beta) \\dot{M}_{\\rm outflow}. \\end{equation} Here, $m_p$ is the proton mass, $\\sigma$ is the absorption cross-section to the soft X-rays, $\\dot{M}_{\\rm outflow}$ is the mass outflow rate and $f(X, \\beta)$ is a function of $X \\equiv R_{\\rm WD}/R_{\\rm S}$, where $R_{\\rm S}$ is the sonic radius in the outflow and $\\beta$ is the exponent in the velocity law. For values of $\\beta$ in the range $1.0-4.5$ and $X \\sim 1/50$, both typical for nova-like variables (\\eg Knigge 1995), $f(X, \\beta) \\sim 0.02$. If we use, for example, the photoelectric absorption cross-section at $0.28-0.40$~keV from Morrison \\& Mc\\,Cammon (1983), $V_{\\infty} \\sim 4000$~km\\,s$^{-1}$, and $R_{\\rm WD} \\sim 10^9$~cm, we obtain that the source will be totally obscured ($\\tau \\sim 5$) for $\\dot{M}_{\\rm outflow} \\simgt 3 \\times 10^{-9} M_{\\odot}$~yr$^{-1}$. This number should not be taken as representing the real value, since the actual obscuration depends crucially on the geometry of the real outflow from the accretion disk (\\eg Knigge, Woods \\& Drew 1995), especially in a nearly pole-on system. Whilst the above discussion does indicate that a scenario of this type is, in principle, viable, we find the white dwarf photospheric contraction model more reasonable; this is discussed fully in \\S~5.4 below. It is important to note that the appearance of a relatively short lived X-ray phase due to contraction of the photosphere, during shell burning, has been established observationally for both GQ Mus (\\\"{O}gelman \\etal 1993; Shanley \\etal 1995) and V1974~Cyg (Krautter \\etal 1996). This puts us now in a position where we can attempt to propose a comprehensive model for the system, taking all the available observational data into consideration. \\subsection{A Comprehensive Model of Photospheric Contraction} The principal features of the photospheric contraction model which emerge as a result of the discussion in the previous sections are the following. The system consists of a white dwarf which may be fairly massive (both because of the constraints imposed by the accretion luminosity, see \\S~5.2, and by the inclination angle, \\S~4.2; see also below), which accretes from an {\\it evolved} companion. The accretion rate is normally very high (perhaps $\\sim10^{-6} M_{\\odot}~$yr$^{-1}$), at a value which is near the top of the steady burning strip in the $\\dot{M} - M_{WD}$ plane (\\eg Nomoto 1982). Under these conditions, the white dwarf is slightly inflated (by perhaps no more than a factor $\\sim3$ in radius; Kovetz \\& Prialnik 1994), and most of the shell luminosity is probably emitted in the UV. The mass transfer rate, and concomitantly the optical luminosity, suffer occasional drops by about a factor~3 or more. This is a very similar phenomenon to the one exhibited by VY Scl stars and some nova-like variables (\\eg Honeycutt 1995; Honeycutt, Robertson \\& Turner 1995). The important point here is that 0513--69, like the VY Scl stars, experiences only {\\it downward} transitions. Livio \\& Pringle (1994) suggested a model for VY Scl stars, in which the reduced mass transfer rate is a consequence of a magnetic spot covering the $L_{1}$ region. VY Scl stars are normally found in the period range 3--4 hrs and in the Livio \\& Pringle model, this is a consequence of the fact that when the rotation rate of the star (which is coupled to the orbit) increases, so does the magnetic activity and the fraction of the stellar surface covered with spots (\\eg K\\\"urster \\etal 1992). One may therefore wonder why the secondary in 0513--69, which has an orbital period of $\\sim~0.76$~d, should exhibit a similar behaviour. However, it should be remembered that the secondary in 0513--69 is evolved. The physical quantity which characterizes the magnetic activity is the Rossby number, $P_{\\rm rot}/\\tau_{\\rm C}$, where $\\tau_{\\rm C}$ is the convective overturn time in the envelope (\\eg Schrijver 1994). Since evolved stars have deeper convective envelopes (longer $\\tau_{\\rm C}$) than main sequence stars, they exhibit the same level of activity at longer $P_{\\rm rot}$ (see \\eg Schrijver 1994 for a review). In fact, the orbital period of 0513-69 is close to the range spanned by the magnetically active RS~CVn stars. Once the accretion rate drops, the photosphere contracts slightly (\\eg Kovetz \\& Prialnik 1994; Kato 1985), raising the effective temperature and thus producing an increase in the X-ray luminosity. It is important to note in this respect that the decrease in the optical luminosity, {\\em precedes} the rise in the X-rays. Fig.~3 shows the times at which the X-rays were known to be off (arrows marked ``NX'') and on (arrows marked ``X''), in relation to the optical behaviour. Using the fact that the X-ray rise time is of order 6~days (Schaeidt 1996 - see also \\S~1), we may be fairly confident that, at least in the X-ray outburst of December 1994 (day number $\\sim$\\, 1715 in Fig.~3), the optical had already started to fall before the X-rays turned on. In this respect, the episodic unveiling model (discussed in \\S~5.3 above) is also consistent with the available data. However, Reinsch \\etal (1996) have shown that the optical low states of 0513--69 are accompanied by a reddening of $\\sim 0.1$~mags, which is quantitatively consistent with the decreased disk illumination resulting from a contraction in the white dwarf radius. Furthermore, the photospheric contraction model is able to provide a natural explanation of details in the light curve morphology, as described below. The increased X-ray flux irradiates the companion star and, either by inflating material above the secondary's photosphere and causing it to be transferred (\\eg Ritter 1988), or by heating the magnetic spot area (which is generally cooler, \\eg Parker 1979), causes the mass transfer rate to increase again. This produces the step-like behaviour of the optical light curve when the luminosity increases, or the small jump in the optical luminosity in the middle of the low state (around day 1539, Fig.~3). The following should also be noted: in {\\it all} cases, the luminosity immediately following the end of one of these low states is slightly higher than the average between these events (see Fig.~3). This is entirely consistent with the above model, since the temporary blocking of the mass transfer (\\eg by a magnetic spot), plus the effect of the irradiation of the secondary by the X-rays, is likely to result in a somewhat increased mass transfer rate, once the blocking is removed. A question which needs to be addressed is whether the contraction and expansion of the white dwarf photosphere can occur on the observed timescale ($\\sim$ 1 week). An examination of the results of Kovetz \\& Prialnik (1994) and Kato (1996) reveals that this is indeed possible, if the white dwarf is massive ($M_{\\rm WD} \\sim 1.3-1.4~M_{\\odot}$). This can be easily understood if we realise that the contraction timescale can be reasonably approximated by the duration of the mass-ejection phase (Livio 1992): \\begin{equation} \\tau_{\\rm duration} \\simeq \\xi \\left( \\frac{M_{\\rm WD}}{M_{\\rm C}} \\right)^{-1} \\left[ \\left( \\frac{M_{\\rm WD}}{M_{\\rm C}} \\right) ^{-2/3} - \\left( \\frac{M_{\\rm WD}}{M_{\\rm C}} \\right) ^{2/3} \\right] ^{3/2}, \\end{equation} where $\\xi$ is nearly a constant and $M_{\\rm C}$ is the Chandrasekhar mass. Using a value for $\\xi \\approx 51$~days, which fits the observations of 84 novae in M31 and 15 novae in the LMC (Della Valle \\& Livio 1995), gives a contraction timescale of less than 4 days for a $1.3 M_{\\odot}$ white dwarf. Assuming that the main ingredients of the model outlined above are correct, we may ask what is the cause for the difference in the X-ray behaviour of 0513--69 and similar sources (such as CAL~83). The main difference is probably in the ratio of the mean mass transfer rate to the rate at which steady burning occurs (for the given white dwarf mass). This ratio is probably higher for 0513--69, a hypothesis which is supported by the greater optical luminosity of this system ($V_{\\scriptsize mean} \\sim 16.8$ in the high states, compared with $V_{\\scriptsize mean} \\sim 17.3$ for CAL~83; Cowley \\etal 1993). Evidence for a high mass transfer rate is provided both by the brightness of the accretion disk, and by the fact that a bipolar outflow is not observed in CAL~83 (C96). Finally, we should point out that the main model discussed in the present work (\\S~5.4) is based on the probable observation that the rise in X-rays came {\\it after} the optical luminosity was observed to drop. Thus, it can be tested directly by long-term monitoring of the system in the optical and X-ray regimes. In particular, the model predicts that increases in the X-ray luminosity should follow drops (by $\\sim$~1~mag) in the optical luminosity. If future observations will show that this is indisputably the case, then the model of photospheric contraction will be further strengthened." }, "9605/astro-ph9605084_arXiv.txt": { "abstract": "The analytical phase-space distribution function (DF) of spherical self--consistent galaxy (or cluster) models, embedded in a dark matter halo, where both density distributions follow the Hernquist profile, with different total masses and core radii (hereafter called HH models), is presented. The concentration and the amount of the stellar and dark matter distributions are described by four parameters: the mass and core radius of the {\\it reference} component, and two dimensionless parameters describing the mass and core radius of the {\\it halo} component. A variable amount of orbital anisotropy is allowed in both components, following the widely used parameterization of Osipkov-Merritt. An important case is obtained for a null core radius of the halo, corresponding to the presence of a central black hole (BH). Before giving the explicit form for the DF, the necessary and sufficient conditions that the model parameters must satisfy in order to correspond to a {\\it consistent} system (i.e., a system for which each physically distinct component has a positive DF), are analytically derived. In this context it is proved that globally isotropic HH models are consistent for any mass ratio and core radii ratio, even in the case of a central BH. In this last case the analytical expression for a lower limit of the anisotropy radius of the host system as a function of the BH mass is given. These results are then compared with those obtained by direct inspection of the DF. In the particular case of global isotropy the stability of HH models is proved, and the explicit formula for the differential energy distribution is derived. Finally, the stability of radially anisotropic HH models is briefly discussed. The expression derived for the DF is useful for understanding the relations between anisotropy, density shape and external potential well in a consistent stellar system, and to produce initial conditions for N-body simulations of two-component galaxies or galaxy clusters. ", "introduction": "Recent ground based observations (\\cite{msz95}), and with the Hubble Space Telescope show that the spatial luminosity distributions of elliptical galaxies approach a power-law form $\\rho(r)\\propto r^{-\\gamma}$ at small radii, with $0\\leq\\gamma\\leq 2.5$ (\\cite{cra93,jaf94,fer94,lau95,kor95,byu96}). These findings increase considerably the interest of theorists in the study of cuspy models. Two important families of spherical dynamical models with a central divergent density that have been explored so far are the $R^{1/m}$ models and the so-called $\\gamma$-models. The dynamical properties of models whose surface brightness distribution follows the $R^{1/m}$-law, introduced by Sersic (1968) as a natural generalization of the de Vaucouleurs law (\\cite{dev48}), have been extensively studied (\\cite{cio91,cl96}). Particularly, their deprojected density increases toward the center as $r^{-(m-1)/m}$ for $m>1$; unfortunately two major problems afflict these models: their deprojected density cannot be expressed analytically in terms of known functions, and no galaxies with $\\gamma >1$ can be accurately modeled in their central regions. The family of the $\\gamma$-models, in some way anticipated by Hernquist (\\cite{her90}, hereafter H90), has been widely explored (\\cite{deh93,car93,tre94}) and it represents a generalization of the well known Hernquist (H90) and Jaffe (\\cite{jaf83}) density distributions. As shown by the previous authors, many of the dynamical properties of the $\\gamma$-models can be expressed analytically. In particular the Hernquist model (hereafter H model) in projection well resembles the de Vaucouleurs law, and an exhaustive analytical investigation of its properties is possible (H90). It is now accepted that a fraction of the mass in galaxies and clusters of galaxies is made of a dark component, whose density distribution differs from that of the visible one. The shape of the dark matter distribution is not well constrained by observations, but numerical simulations of dissipationless collapses seem to favor a peaked profile, consistent with the scale-free nature of the gravitational field (\\cite{dc91,white96}, and references therein). From these considerations it follows that the obvious generalization of the one-component spherical models (the dynamicists zero-th order approximation of real galaxies) is not only in the direction of the actively developed modeling of axisymmetric and triaxial systems [see, e.g., de Zeeuw (1996) for a recent review] but also in the study and construction of two-component analytical models, a field far less developed. From this point of view the zero-th order approximation of realistic galaxies is the construction of analytical spherically symmetric {\\it two-component} galaxy models. When studying a dynamical model (single or multi-component) the fact that the Jeans equations have a physically acceptable solution is not a sufficient criterion for the validity of the model: the essential requirement to be met by any acceptable dynamical model is the positivity of the DF of each physically distinct component. A model satisfying this minimal requirement (much weaker than the model stability) is called a {\\it consistent} model. Two general strategies can be used to construct a consistent model or check whether a proposed model is consistent: the ``$f$ to $\\rho$'' and the ``$\\rho$ to $f$'' approaches (\\cite{bt87}, Chap. 4, hereafter BT87). An example of the first approach is the extensive survey of two--component, spherical, self--consistent galaxy models carried out by Bertin and co-workers (\\cite{bss92}). They assume for the stellar and dark matter components two distribution functions of the $f_{\\infty}$ form (and so positive by choice) (\\cite{bs84}). The main problem with this approach is that generally the spatial density is not expressible in terms of known functions, and so only numerical investigations are feasible. In the second approach the density distribution is given, and assumptions on the model internal dynamic are made, making the comparison with the data simpler. But the difficulties inherent in the operation of recovering the DF in many cases prevent a simple consistency analysis. In particular, in order to recover the DF of spherical models with anisotropy two techniques have been developed from the original Eddington (1916) method for isotropic systems: the Osipkov-Merritt technique (\\cite{osi79,mer85}, hereafter OM), and the case discussed by Cuddeford and Louis (\\cite{culo95}, and references therein). Examples of {\\it numerical} application of the OM inversion to two-component spherical galaxies can be found in the literature (see, e.g., \\cite{cp92}, hereafter CP92; \\cite{czm95}). For axisymmetric systems recently a new inversion technique, less restrictive than the classical ones (\\cite{lyb62,hun75,dej86}), has been found (\\cite{hq93}). If one is just interested in the consistency of a stellar system the previous methods give \"too much\", i.e., give the DF. A simpler approach, at least for spherically symmetric multicomponent systems with OM anisotropy -- as the case discussed in this paper -- is given by a method described by CP92, that requires information only on the radial density profiles of each component. Despite all these efforts, a small number of one-component systems in which both the spatial density and the DF are analytically known is at our disposition, and in the more interesting case of two-component systems only the very remarkable axisymmetric Binney-Evans model is known (\\cite{bin81,eva93}). It is therefore of particular interest the result here proved that also the DF of HH models with OM anisotropy is completely expressible in an analytical way. This family of models is made by the superposition of a stellar and a dark matter distribution both following the Hernquist profile, with different total masses and core radii. The concentration and the amount of the stellar and dark matter distributions are described by four free parameters, and the orbital anisotropy is allowed in both components, following the OM prescription. A particularly interesting case is obtained for a null core radius of the \"halo\", so mimicking a central BH. The study of HH models is also useful for many different reasons: to provide an analytical DF for a two-component cuspy system for which the analytical solution of the Jeans equations is also available (\\cite{clr96}); to investigate the r\\^ole of anisotropy and mass distribution of each component in determining the positivity of their DF; to compute in an accurate and \"easy\" way the model line-profiles, to arrange initial conditions for numerical simulations of two-component systems. In Section 2 I briefly review the method presented in CP92, formulating it in a way suitable for its application to the present problem. Then in Section 3 I introduce the HH models, and use the previous method to discuss the limits imposed on their parameters by the positivity of the DF of the two components. It is proved that globally isotropic HH models are consistent for any mass ratio and core radii ratio, even in the case of a central BH. In this last case the analytical expression for a lower limit of the anisotropy radius of the host system as a function of the BH mass is given. In Section 4 I derive the DF for HH models, and their differential energy distribution in the case of global isotropy; some velocity sections of the DF are also shown. In the case of a dominant halo it is found that the DF of an HH component can be expressed only through elementary functions. A particular case -- corresponding to a Hernquist model with a central BH -- is extensively discussed. In Section 5 the exact boundary of the region of consistency in the parameter space is obtained using the DF, and the results are compared with those given in Section 3. In the same section the stability of globally isotropic HH models is proved, and a discussion on the stability of the anisotropic case is given. Finally in Section 6 the main results are summarized. ", "conclusions": "In this paper an extensive analytical investigation of two-component spherical galaxy (or cluster) models, made of the sum of two Hernquist density distributions with different physical scales, is carried out. A variable amount of orbital anisotropy is also allowed in both components. These models, characterized by a power-law density profile in their central regions -- both in the visible and in the dark matter distribution -- reproduce the main properties of early-type galaxies as revealed by Hubble Space Telescope observations, and also of the dark matter distribution as obtained in recent N-body simulations. The main results presented in this paper can be summarized as follows: \\begin{enumerate} \\item The analytical expression for the DF of HH models with general OM anisotropy is presented and discussed, even for the particular case of an Hernquist model with a central BH. The special case of a dominant dark halo is also discussed, and it is shown that under this assumption the DF can be asymptotically expressed using just elementary functions. In the case of global isotropy the analytical expression for the differential energy distribution of both components is obtained. Some velocity sections of the DF are shown and discussed. \\item The necessary and sufficient conditions that the model parameters must satisfy in order to correspond to a consistent system (i.e., a system for which each physically distinct component has a positive DF) are analytically derived using the method introduced in CP92. It is proved that globally isotropic HH models are consistent for any mass ratio and core radii ratio, even in the special case in which the \"halo\" reduces to a BH. In the case of a central BH and of variable anisotropy for the host system, the analytical expression for a minimum anisotropy radius as a function of the BH mass is given. \\item The region in the parameter space in which HH models are consistent is subsequently explored using the DF. The main result is that the presence of a massive halo does not affect significantly the maximum anisotropy that can be sustained by a consistent model. It is shown that the presence of a halo with a core radius larger than that of the reference component allows a slightly higher degree of anisotropy with respect to the one-component Hernquist model. On the contrary, a halo with a smaller core radius imposes a larger value for the minimum anisotropy radius than that proper of the H model. The most restrictive case is that of a central BH. In any case, for a given core radius of the halo there is a lower limit to the minimum anisotropy radius that approaches an asymptotic value for a dominant halo mass. \\item Finally, it is proved that isotropic HH models are stable, except for the case of a central BH, when no conclusions can be drawn. For anisotropic models the stability parameter against radial orbit instability is briefly discussed, and it is shown that with high probability the most anisotropic {\\it consistent} HH models are unstable. \\end{enumerate}" }, "9605/astro-ph9605171_arXiv.txt": { "abstract": "We calculate the deflection of a light ray caused by the gravitational field of a cosmic string loop in the weak field limit and reduce the problem to a single quadrature over a time slice of the loop's world sheet. We then apply this formalism to the problem of gravitational lensing by cosmic string loops. In particular, we find an analytic solution for the special case of a circular loop perpendicular to the optical axis. As examples of more complicated loops, we consider two loops with higher frequency Fourier modes. The numerical analysis illustrates the general features of loop lenses. Our estimates, using typical parameters for GUT scale loops, show that the stringy nature of loop lenses can be observed for lensing systems involving high redshift galaxies ($z \\sim 2$), and we suggest that gravitational lensing can confirm the existence of GUT scale strings if they are the seeds for large scale structure formation. ", "introduction": "\\label{intro} Current research focuses on two scenarios for the formation of structure in the universe: the first where structure formation was seeded by adiabatic perturbations produced during an inflationary epoch and the second where structure accretes around isocurvature perturbations produced by topological defects such as cosmic strings, global monopoles or textures. In the latter scenario it should be possible to directly detect the presence of topological defects in the present universe leading to immediate confirmation of the scenario. On the other hand, the lack of direct evidence for topological defects in the present universe can lead to constraints on the defect scenario for structure formation and perhaps be considered as circumstantial evidence in favor of the inflationary alternative. Thus it is quite important to consider specific distinctive signatures of the various topological defects that can be used to directly observe them. Let us specifically consider cosmic strings, the model which will be relevant to the work in this paper (for a review of cosmic strings, see Ref. \\cite{vilenkin}). A number of observable features produced by cosmic strings of mass density suitable for structure formation have been discussed in the literature. These include discontinuous patterns in the microwave background radiation \\cite{bennett92}, generation of a gravitational wave background that could be detected by noise in the millisecond pulsar timing \\cite{barc} and gravitational lensing \\cite{vil1,chrn,gott,paczynski,hindmarsh}. The ongoing observations of anisotropies in the microwave background radiation are expected to yield stronger constraints or positive results over the next decade or so. The millisecond pulsar observations can only impose tighter constraints on the string scenario since a positive detection of gravitational waves does not specifically imply the existence of cosmic strings. There has also been sporadic effort over the last decade to work out the gravitational lensing signature of cosmic strings but, perhaps due to the difficulties encountered in understanding the evolution of the string network, no distinctive result emerged from these analyses. However, an analytical framework for describing the string network has been constructed over the last few years and the time seems ripe to reconsider gravitational lensing as a tool for searching for strings. The timing is also right from the observational viewpoint since several new initiatives are underway that promise to survey much wider and deeper regions of the sky. In this paper we investigate gravitational lensing by cosmic string loops\\footnote{Gravitational lensing by global monopoles and textures is likely to be less interesting since only a few of these are expected to occur within our horizon. Also, their spherical symmetry will lead to lensing that is harder to differentiate from that due to conventional sources.}. We begin in Sec. II by estimating the probability of string lensing and in so doing we review some of the relevant properties of cosmic strings. Our estimates are based on recent results for the string network evolution summarized in Ref. \\cite{vilenkin}. Next, in Sec. III, we consider photon propagation in the metric of a loop. The problem appears to be quite difficult at first because the oscillating loop is a complicated time dependent gravitational source. Yet we are able to show that the problem reduces to one that is static where a specific time slice of the loop's world sheet is sufficient to determine the gravitational lensing effects. In other words, the bending of light by a string loop is equivalent to the bending of light by a static curved rod with non-uniform energy density, a result similar to that for the energy shift of a photon propagating in a string loop background first derived by Stebbins \\cite{stebbins}. We also rederive the energy shift of the photon in the Appendix and recover a logarithmic term that appears to have been eliminated by the regularization procedure used in Ref. \\cite{stebbins}. Once we have set up the formalism for an arbitrary loop and described some rudiments of gravitational lensing theory (Sec. \\ref{basic}), we apply it to treat the lensing due to a circular loop that is oriented in a plane normal to the optical axis (Sec. \\ref{circlesec}). The results for the circular loop are in agreement with the assumption in Ref. \\cite{chrn} that the photons passing through the loop remain undeflected. The deflection of a photon trajectory not threading the loop can also be described quite simply and the whole problem can happily be solved by hand without resorting to numerical evaluation. The perpendicular circular loop, however, is a very special case as even a change in the orientation of the loop yields qualitatively different results, and loops with less symmetry have completely different lensing behavior. The assumption that photons passing through the loop remain undeflected fails for general loops. We study the lensing due to several generic loops numerically and provide image maps that promise to distinguish cosmic string lensed images from more conventional gravitational lensing events (Sec. \\ref{numerical}). Here we also show that the Einstein radius of the string loop is comparable to the typical loop size for any value of the string tension and so the stringy nature of the loop plays a crucial role in determining the structure of the lensed images. Effective techniques --- for example, techniques that replace the string loop by a point mass plus perturbations --- are unlikely to yield successful approximations leading us to conclude that string loop lenses ought to be observationally distinct from garden variety astrophysical lenses. In Sec. \\ref{discussion} we summarize and discuss our main results. We also qualitatively discuss the effects of long strings and describe further work to come. Finally, Sec. \\ref{conclusion} contains some concluding remarks. ", "conclusions": "\\label{conclusion} In this paper we have derived a method for calculating the deflection of light rays due to the gravitational field of an oscillating string loop. We have shown that this problem can be reduced to an effective static problem, greatly simplifying calculations. The formalism was then applied to the problem of gravitational lensing by cosmic strings, and using typical loop parameters, we have shown that a loop lens produces images on arc second scales, similar to galactic size objects. Specifically, we find that for $G \\mu \\sim (1-2)~10^{-6}$ --- values consistent with structure formation, microwave background anisotropies and millesecond pulsar timing limits --- strings can produce images separated on arc second scales which would be observable by both ground based telescopes and the Hubble space telescope and would have features that are distinctly different from other dark lens candidates. This suggests that string loops can be definitively observed as gravitational lenses. Furthermore, the lensing due to long strings would appear like a linear sequence of lensings due to loops and these would be the unmistakable fingerprints of cosmic strings." }, "9605/astro-ph9605047_arXiv.txt": { "abstract": "\\openup1\\jot We investigate how the qualitative structure of Doppler peaks in the angular power spectrum of the cosmic microwave anisotropy is affected by basic assumptions going into theories of structure formation. We define the concepts of ``coherent'' and ``incoherent'' fluctuations, and also of ``active'' and ``passive'' fluctuations. In these terms inflationary fluctuations are passive and coherent while topological defects are active incoherent fluctuations. Causality and scale invariance are shown to have different implementations in theories differing in the above senses. We then extend the formalism of Hu and Sugiyama to treat models with cosmic defects. Using this formalism we show that the existence or absence of secondary Doppler peaks and the rough placing of the primary peak are very sensitive to the fundamental properties defined. We claim therefore that even a rough measurement of the angular power spectrum $C_l$ shape at $1000$. Other parameters $B$, $\\mu_0$ are scaling parameters, specifying a length scale (the break radius) and a scale for projected density. For flattened nuclei, the parametrization applies on the major or minor axis or in a shell averaged sense. Interpreting this class of density profiles requires a new class of dynamical models. Previous dynamical models mostly have a finite core. A recent set of cuspy models, including the $\\gamma/\\eta$ models discovered by Dehnen (1994) and Tremaine et al. (1995), and a even wider range of analytical models by Zhao (1996), often do not match the light of nuclei outside the break radius. Unlike these models the observed light profiles are often much shallower at large radius, and in principle correspond to a divergent mass if extrapolated to infinity. Hence it is necessary to explore dynamical models consistent with a general double-power-law profile, including those with a divergent mass. The existence of a universal parametrization constitutes a major advantage for theoretical study of their dynamical properties. It makes it possible to study observed galactic nuclei as a class spanned by the three slope parameters $(\\alpha_1, \\beta_1, \\gamma_1)$, and constrain the models with the steady state dynamics without necessarily using data of individual systems explicitly. In this paper, we give some results which immediately follow from the above surface brightness profiles. We will concentrate on the simple class of spherical isotropic models with main emphasis on their simple analytical results. While spherical models with a $f(E)$ distribution function are famous for admitting mathematical solutions, and are often used as a compromise for more realistic but less tractable anisotropic/flattened/triaxial models, the actual implementation of the spherical models is in fact very tedious, and rarely admits simple analytical results. These significantly complicate the first-level simple interpretation of photometric and kinematic data. The standard inversion using Eddington formula involves at least three integrations and two derivatives (analytical or numerical) to get $f(E)$ from a surface density profile. To further make a prediction on line profile requires computing a three dimensional integral (see e.g., Dehnen 1994) at each grid point in the projected radius vs. velocity plane. For the current problem, one is interested in a class of models with a range of density profiles. The main challenge is to present the results in a manageable and easily interpretable way. Virtually no rigorous analytical solutions are known for the projected models given by Eq.(1). Even for some related analytical models (Zhao 1996, Dehnen 1994, Tremaine et al. 1995), the expressions of the distribution function and projected density and dispersion are generally very lengthy, typically involving more than half a dozen analytic terms with no clear physical meaning and with possible large cancellations between terms. As a result, the relations between observable and model quantities are obscured. In this paper we build a set of spherical dynamical models with simple functional forms for the intrinsic volume density and $f(E)$. We fit these to the double-power-law projected density models. We set the scaling quantities, $\\mu_0$ and $B$ as unity, and vary the dimensionless parameters $(\\alpha_1, \\beta_1, \\gamma_1)$ in a 3D parameter space to simulate a complete set of radial profiles of the surface light. Because of the way the fitted models are tailored, the residuals of the fits are typically smaller than the uncertainties in the data so that the models are practically consistent with the double-power-law surface brightness profile. The main results of the paper are summarized in several universal formulae for the volume density, the phase space density, the line-of-sight velocity profiles. The model results can be presented directly with the fitting formulae and a few numerically fitted parameters. To demonstrate the applications, we compute the system parameters for about 25 observed galaxies and give them in tables. With these the intrinsic and projected quantities of the model are fully determined, and it involves virtually no further calculation to predict the line-of-sight velocity distributions. The paper is organized as follows. In Section 2 we fit the surface brightness profiles with analytical volume density models. Section 3 gives the analytical expression for the model potential. Section 4 gives the deprojected phase space density by matching the volume density and the potential. In Section 5, the distribution functions are re-projected to yield line-of-sight velocity distributions as well as the dispersion and kurtosis of the profiles, all on a grid of projected radius. We illustrate the model applications in Section 6. We summarize in Section 7. Asymptotic relations for the model quantities are given in Appendix A. Some alternative analytical approximations with rigorous asymptotic solutions are given in Appendix B. A simple formula for the line profiles of the models is derived in Appendix C. Although similar models can be built for anisotropic spherical systems with a black hole, and the techniques are also generalizable to oblate $f(E,J_z)$ systems, we leave these generalized models for a later study (Zhao and Syer 1996). The three-dimensional $(\\alpha_1,\\beta_1, \\gamma_1)$ parameter space of the spherical models is already very big, and at least two more dimensions would be necessary to cover spherical models with black hole and anisotropy. Also while the isotropic models are most likely stable, many simulations are needed to examine the stability of anisotropic or black hole models before applying them to observations. ", "conclusions": "In summary, a large number of galactic nuclei obey a parametrized double-power-law surface brightness radial profile (Byun et al. 1996). We find that their intrinsic volume density fits a similar universal double-power-law with a comparble residual. We further explore spherical isotropic models consistent with these profiles, and find a simple fitting formula for the distribution function $f(E)$ as well. These parametrizations are tailored so that their functional forms reduce to power-laws at large or small radius. These analytical models also simplify the procedures to interpret photometric and kinematic data of galactic nuclei. We demonstrate the models with a simple application to a group of observed galactic nuclei, and predict the radial runs of their velocity dispersion and kurtosis. Tables for computed models as well as FORTRAN programs to run additional models are available at site http://ftp.ibm-1.mpa-garching.mpg.de/pub/hsz. Galactic nuclei are generally flattened with a possible central black hole and velocity anisotropy. For these models the distribution function is generally a function of two or three integrals, $f=f(E,J_z,I_3)$. Still the simple spherical model here can provide some simple insights which help to build these more complex models. We expect that an $f(E,J_z,I_3)$ with its energy dependence similar to the fitting formula for isotropic models here will give a plausible fit to anisotropic flattened systems if with a double-power-law radial profile. I thank Dave Syer for a critical reading of the manuscript and many helpful comments." }, "9605/astro-ph9605072_arXiv.txt": { "abstract": "We investigate the hydrodynamics of a variant of classical Bondi-Hoyle-Lyttleton accretion: a totally absorbing sphere moves at various Mach numbers (3 and 10) relative to a medium, which is taken to be an ideal gas having a velocity gradient (of 3\\% or 20\\% over one accretion radius) perpendicular to the relative motion. We examine the influence of the Mach number of the flow and the strength of the gradient upon the physical behaviour of the flow and the accretion rates of the angular momentum in particular. The hydrodynamics is modeled by the ``Piecewise Parabolic Method'' (PPM). The resolution in the vicinity of the accretor is increased by multiply nesting several grids around the sphere. Similarly to the 3D models without gradients published previously, models exhibit non-stationary flow patterns, although the Mach cone remains fairly stable. The accretion rates of mass, linear and angular momenta do not fluctuate as strongly as published previously for 2D models, but similarly to the 2D models, transient disks form around the accretor that alternate their direction of rotation with time. The average specific angular momentum accreted is roughly between 7\\% and 70\\% of the total angular momentum available in the accretion cylinder and is always smaller than the value of a vortex with Kepler velocity around the surface of the accretor. The fluctuations of the mass accretion rate in the models with small gradients (2\\%) are similar to the values of the models without gradients, while the models with large gradients (20\\%) exhibit larger fluctuations. The mass accretion rate is maximal when the specific angular momentum is zero, while the specific entropy tends to be smaller when the disks are prograde. ", "introduction": "} The simplicity of the classic Bondi-Hoyle-Lyttleton (BHL) accretion model makes its use attractive in order to roughly estimate accretion rates and drag forces in many different astrophysical contexts, ranging from wind-fed X-ray binaries (e.g.~Anzer \\& B\\\"orner~1996), over supernovae (e.g.~Chevalier~1996), and galaxies moving through intracluster gas in a cluster of galaxies (Balsara at al.~(1994), to the black hole believed to be at the center of our Galaxy (Ruffert \\& Melia~1994; Mirabel et al.~1991). In the BHL scenario a totally absorbing sphere of mass $M$ moves with velocity $v_\\infty$ relative to a surrounding homogeneous medium of density $\\rho_\\infty$ and sound speed $c_\\infty$. It has been investigated numerically by many workers (e.g.~Ruffert 1994 and 1995, and references therein). Usually, the accretion rates of various quantities, like mass, angular momentum, etc., including drag forces are of interest as well as the properties of the flow, (e.g.~distribution of matter and velocity, stability, etc.). All results pertaining to total accretion rates are in qualitative agreement (to within factors of two, ignoring the instablitites of the flow) with the original calculations of Bondi, Hoyle and Lyttleton (e.g.~Ruffert \\& Arnett~1994). The BHL recipe for accretion in the axisymmetric case for pressureless matter is the following. A ring of material with radius $b$ (which is identical to the impact parameter) far upstream from the accretor and thickness d$b$ will be focussed gravitationally to a point along the radial accretion line downstream of the accretor. At this point the linear momentum perpendicular to the radial direction is assumed to be cancelled. Then, if the remaining energy of the matter at this point is not sufficient for escape from the potential, this material is assumed to be accreted. The largest radius $b$ from which matter is still accreted by this procedure turns out to be the so-called Hoyle-Lyttleton accretion radius (Hoyle \\& Lyttleton~1939, 1940a, 1940b, 1940c; Bondi \\& Hoyle~1944) \\begin{equation} R_{\\rm A} = \\frac{2GM}{v_\\infty^2} \\quad, \\label{eq:accrad1} \\end{equation} where $G$ is the gravitational constant. The mass accretion rate follows to be \\begin{equation} \\dot{M}_{\\rm HL} = \\pi R^2_{\\rm A} \\rho_\\infty v_\\infty \\quad. \\label{eq:accmass1} \\end{equation} I will refer to the volume upstream of the accretor from which matter is accreted as accretion cylinder. However, if the assumption of homogeneity of the surrounding medium is dropped, e.g.~by assuming some constant gradient in the density or the velocity distribution, the consequences on the accretion flow remain very unclear. Using the same conceptual procedures, one can calculate (Dodd \\& McCrea, 1952; Illarionov \\& Sunyaev, 1975; Shapiro \\& Lightman, 1976; Wang, 1981) how much angular momentum is present in the accretion cylinder for a non-axisymmetric flow which has a gradient in its density or velocity perpendicular to the mean velocity direction. Then, assuming that the angular momentum will be accreted together with the mass, it is only a small step to conclude that the amount of angular momentum accreted is equal to (or at least is a large fraction of) the angular momentum present in the accretion cylinder. Note, that if the velocity is a function of position, then by virtue of Eq.~(\\ref{eq:accrad1}) also the accretion radius varies in space. Thus the cross section of the accretion cylinder (perpendicular to the axis) is not circular. However, the reasoning of BHL calls for a cancelling of linear momentum perpendicular to the radial accretion line before matter is accreted. Together with this linear momentum also angular momentum is cancelled and so the matter accreted has zero angular momentum by construction! This point was first discussed by Davies \\& Pringle~(1980), who were able to construct two-dimensional flows with small non-vanishing gradients for which the accreted angular momentum was exactly zero, by placing the accretion line appropriately. Thus, following these analytic investigations two opposing views are voiced about how much angular momentum can be accreted: either a large or a very small fraction of what is present in the accretion cylinder. Numerical simulations thus are called for to help solve the problem. In this paper I would like to compare the accretion rates of several quantities (especially angular momentum) of numerically modeled accretion flows with gradients to the previous results of accretion without gradients (e.g.~Ruffert~1994). One has to change some of the parameters of the flow (Mach number, size of the accretor) in order to get a good overview of which features are generic and which specific to that combination of parameters. Although several investigations of {\\it two}-dimensional flows with velocity gradients exist (Anzer et al.~1987; Fryxell \\& Taam~1988; Taam \\& Fryxell~1989; Ho et al.~1989), {\\it three}-dimensional simulations are scarse due to their inherently high computational load. Livio et al.~(1986) first attempted a three-dimensional model including gradients, but due to their low numerical resolution the results were only tentative. Also in the models of Ishii et al.~(1993) was the accretor only coarsly resolved, while the results of Boffin (1991) and Sawada et al.~(1989) are only indicative, because due to the numerical procedure the flows remained stable (too few SPH particles in Boffin~1991 and local time stepping in Sawada et al.~1989 which is appropriate only for stationary flows). A simulation that was numerically better resolved was performed later by Ruffert \\& Anzer (1995), but since only one model was presented, the results cannot be taken as conclusive either. I intend to remedy these shortcomings in the present paper. In section~\\ref{sec:numer} I give only a short summary of the numerical procedure used. Sections~\\ref{sec:descr1} to~\\ref{sec:descr3} present the results, which I analyze and interpret in Sect.~\\ref{sec:analy}. Section~\\ref{sec:conc} summarizes the implications of this work. \\begin{table*} \\caption[] { Parameters and some computed quantities for all models. ${\\cal M}_\\infty$ is the Mach number of the unperturbed flow, $\\varepsilon_{\\rm v}$ the parameter specifying the strength of the gradient, $\\gamma$ the ratio of specific heats, $R_\\star$ the radius of the accretor, $g$ the number of grid nesting depth levels, $\\delta$ the size of one zone on the finest grid, $\\epsilon$ the softening parameter (zones) for the potential of the accretor (see Ruffert, 1994), $t_{\\rm f}$ the total time of the run (units: $R_{\\rm A}/c_{\\infty}$), $\\overline{\\dot{M}}$ the integral average of the mass accretion rate, $S$ one standard deviation around the mean $\\overline{\\dot{M}}$ of the mass accretion rate fluctuations, $\\widehat{\\dot{M}}$ the maximum mass accretion rate, $\\dot{M}_{\\rm BH}$ is defined in Eq.~(3) of Ruffert \\& Arnett (1994), $l_{\\rm x}$, $l_{\\rm y}$, $l_{\\rm z}$, are the averages of specific angular momentum components together with their respective standard deviations $\\sigma_{\\rm x}$, $\\sigma_{\\rm y}$, $\\sigma_{\\rm z}$, $s$ is the entropy (Eq.~(4) in Ruffert \\& Arnett~1994), the number $N$ of zones per grid dimension is 32, and the size of the largest grid is $L=32R_{\\rm A}$ (except for model~RL for which it is $L=128R_{\\rm A}$). } \\label{tab:models} \\tabcolsep = 1.6mm \\begin{flushleft} \\begin{tabular}{lccccccccrclcrclrclrclc} \\hline\\\\[-3mm] Model & ${\\cal M}_\\infty$ & $\\varepsilon_{\\rm v}$ & $\\gamma$ & $R_\\star$ & $g$ & $\\delta$ & $\\epsilon$ & $t_{\\rm f}$ & $\\overline{\\dot{M}}$&\\ppmm&$S$ & $\\widehat{\\dot{M}}$ & $l_{\\rm x}$&\\ppmm&$\\sigma_{\\rm x}$ & $l_{\\rm y}$&\\ppmm&$\\sigma_{\\rm y}$ & $l_{\\rm z}$&\\ppmm&$\\sigma_{\\rm z}$ & $s$ \\\\ & & & & ($R_{\\rm A}$) & & ($R_{\\rm A}$) & & & \\multicolumn{3}{c}{($\\dot{M}_{\\rm BH}$)} & ($\\dot{M}_{\\rm BH}$) & \\multicolumn{3}{c}{~($1.5\\,\\varepsilon_{\\rm v}R_{\\rm A}v_0$)} & \\multicolumn{3}{c}{~($1.5\\,\\varepsilon_{\\rm v}R_{\\rm A}v_0$)} & \\multicolumn{3}{c}{~($1.5\\,\\varepsilon_{\\rm v}R_{\\rm A}v_0$)} & (${\\cal R}$) \\\\[0.5mm] \\hline\\\\[-3mm] IT & 3 &-0.03&5/3& 0.02&10 & $1/512$& 8 & 4.82 & 0.72&\\ppmm&0.04 & 0.78 & 0.00&\\ppmm&0.01 & 0.00&\\ppmm&0.02 & +0.20&\\ppmm&0.04 & 2.1 \\\\ % IS & 3 &-0.03&5/3& 0.02& 9 & $1/256$& 3 & 13.9 & 0.53&\\ppmm&0.09 & 0.80 & 0.00&\\ppmm&0.13 & 0.05&\\ppmm&0.17 & +0.12&\\ppmm&0.24 & 2.2 \\\\ % IM & 3 &-0.03&5/3& 0.10& 7 & $1/64$ & 4 & 26.6 & 0.79&\\ppmm&0.06 & 0.90 & -0.01&\\ppmm&0.11 & 0.00&\\ppmm&0.13 & +0.68&\\ppmm&0.33 & 2.2 \\\\ % IM*& 3 &-0.03&5/3& 0.10& 7 & $1/64$ & 4 & 8.37 & 0.82&\\ppmm&0.08 & 0.91 & +0.02&\\ppmm&0.06 & -0.08&\\ppmm&0.14 & +0.69&\\ppmm&0.45 & 2.2 \\\\[1mm] % JS & 10&-0.03&5/3& 0.02& 9 & $1/256$& 3 & 2.93 & 0.45&\\ppmm&0.09 & 0.68 & -0.04&\\ppmm&0.17 & -0.08&\\ppmm&0.35 & +0.18&\\ppmm&0.28 & 5.3 \\\\ % JM & 10&-0.03&5/3& 0.10& 7 & $1/64$ & 4 & 10.3 & 0.72&\\ppmm&0.05 & 0.79 & +0.01&\\ppmm&0.06 & -0.07&\\ppmm&0.33 & +0.26&\\ppmm&0.35 & 5.2 \\\\[1mm] % KS & 3 &-0.20&5/3& 0.02& 9 & $1/256$& 3 & 6.89 & 0.54&\\ppmm&0.09 & 0.78 & 0.00&\\ppmm&0.02 & -0.01&\\ppmm&0.03 & +0.07&\\ppmm&0.02 & 1.8 \\\\ % KM & 3 &-0.20&5/3& 0.10& 7 & $1/64$ & 4 & 20.3 & 0.95&\\ppmm&0.19 & 1.30 & 0.00&\\ppmm&0.02 & 0.00&\\ppmm&0.02 & +0.26&\\ppmm&0.06 & 1.6 \\\\[1mm] % LS & 10&-0.20&5/3& 0.02& 9 & $1/256$& 3 & 1.94 & 0.35&\\ppmm&0.08 & 0.53 & +0.02&\\ppmm&0.03 & +0.01&\\ppmm&0.05 & +0.09&\\ppmm&0.03 & 5.2 \\\\ % LM & 10&-0.20&5/3& 0.10& 7 & $1/64$ & 4 & 8.54 & 0.72&\\ppmm&0.17 & 1.11 & 0.00&\\ppmm&0.04 & 0.00&\\ppmm&0.05 & +0.25&\\ppmm&0.09 & 4.7 \\\\[1mm] % RL &0.6&-0.20& 5/3& 1.00& 6 & $1/8$ & 5 & 63.1 & 36.3&\\ppmm&0.14 & 36.4 & 0.00&\\ppmm&0.00 & 0.00&\\ppmm&0.00 & -0.49&\\ppmm&0.04 & 0.18\\\\[1mm] % ST & 3 &-0.03&4/3& 0.02& 10 & $1/512$& 8 & 4.60 & 1.01&\\ppmm&0.09 & 1.29 & 0.00&\\ppmm&0.05 & +0.01&\\ppmm&0.07 & +0.51&\\ppmm&0.23 & 4.4 \\\\ % SS & 3 &-0.03&4/3& 0.02& 9 & $1/256$& 3 & 9.24 & 1.01&\\ppmm&0.12 & 1.46 & +0.02&\\ppmm&0.15 & +0.03&\\ppmm&0.25 & +0.36&\\ppmm&0.40 & 5.2 \\\\ % \\hline \\end{tabular} \\end{flushleft} \\end{table*} ", "conclusions": "} For the first time a comprehensive numerical {\\it three}-dimensional study is presented of wind-accretion with a velocity gradient using a high resolution hydrodynamic code. I vary the following parameters: Mach number of the relative flow (Mach~3 and~10), strength of the velocity gradient perpendicular to this flow (3\\% and 20\\% over one accretion radius), radius of the accretor (0.02, 0.1 and 1 accretion radius), and adiabatic index (5/3 and 4/3). The results are compared among the models with differing parameters, to some previously published simulations, and also to the analytic estimates of the specific angular momentum of the matter that is accreted (Eq.~(\\ref{eq:specmomang}), which assumes that all angular momentum in the accretion cylinder is actually accreted). \\begin{enumerate} \\item All models with a small enough accretor (with a size less or equal than 0.1~accretion radii) exhibit active unstable phases, very similar to the models without gradients. The accretion rates of mass, linear and angular momentum fluctuate with time, although not as strongly as published previously for 2D models (e.g.~Fryxell \\& Taam 1988). Similarly to the 2D simulations, transient disks form around the accretor that alternate their direction of rotation with time. \\item Depending on the model parameters, the average specific angular momentum accreted is roughly between 7\\% and 70\\% of the analytical estimate. For the models with small velocity gradients (3\\%) the accreted specific angular momentum is roughly a factor of~10 smaller than the value of a vortex with Kepler velocity around the surface of the accretor. This factor is roughly~3 for models with a large gradient of~20\\%. \\item The mass accretion rates of all models with velocity gradients are equal, to within the fluctuation amplitudes, to the rates of the models without gradients (published previously). \\item The fluctuations of the mass accretion rate in the models with small gradients (3\\%) are also similar to the values of the models without gradients, while the models with large gradients (20\\%) exhibit larger fluctuations. So large gradients either amplify existing instability mechanisms or generate new ones. \\item Marginal correlations are found, connecting the mass accretion rate, the specific angular momentum, and the specific entropy during the temporal evolution. The mass accretion rate is maximal when the specific angular momentum is zero, while the specific entropy tends to be smaller when the disks are prograde (i.e.~when the specific angular momentum is negative, in our units). \\end{enumerate} Movies in mpeg format of the dynamical evolution of some models are available in the WWW at {\\tt http:\\nix//www.mpa-garching.mpg.de\\nix/\\lower0.7ex\\hbox{$\\!$\\~~$\\!$}mor\\nix/bhla.html}" }, "9605/astro-ph9605134_arXiv.txt": { "abstract": "The light curve of a distant Type Ia supernova acts like a clock that can be used to test the expansion of the Universe. SN~1995K, at a spectroscopic redshift of $z = 0.479$, provides one of the first meaningful data sets for this test. We find that all aspects of SN~1995K resemble local supernova Ia events when the light curve is dilated by $(1+z)$, as prescribed by cosmological expansion. In a static, non-expanding universe SN~1995K would represent a unique object with a spectrum identifying it as a regular Type Ia supernova but a light curve shape and luminosity which do not follow the well-established relations for local events. We conclude that SN~1995K provides strong evidence for an interpretation of cosmological redshifts as due to universal expansion. Theories in which photons dissipate their energy during travel are excluded as are age-redshift dependencies. ", "introduction": "The nature of galaxy redshifts has usually been interpreted as due to a general expansion of the universe. However widely accepted clear experimental proof of this fundamental assumption of most cosmological models has been lacking. The main argument in favor of expansion is the observed nearly perfect blackbody energy distribution of the cosmic background radiation (Mather et al. 1990, Peebles et al. 1991). The Tolman surface brightness test (Tolman 1930) fundamentally probes for expansion as well, but implementation of this test has proven difficult (Sandage \\& Perelmutter 1991, Pahre et al. 1996), as galaxy evolution has to be evaluated independently. The interpretation of redshifts as due to universal expansion has been questioned (e.g. Arp 1987, Arp et al. 1990). Observations of the apparent clustering of high-redshift quasars around low-redshift galaxies (Burbidge et al. 1971, Arp 1987) and the anomalous distribution of redshifts in groups (Arp 1994) have been used to argue against cosmological expansion. A theory linking observed redshifts to the ages of the objects has been developed to explain these findings (Narlikar \\& Arp 1993). A direct test of the nature of cosmological redshifts is provided by the observable effects of time dilation on time variable phenomena at large redshifts. In an expanding universe these redshifts are directly related to the change in the scale parameter inducing a change of distant clock rates for a local observer. The light curve of a distant supernova is predicted to be stretched in the observer's frame by a factor $(1+z)$ compared to the rest frame of the object (Wilson 1939, Rust 1974, Colgate 1979, Tammann 1979, Leibundgut 1990, Hamuy et al. 1993). Although the light curves of nearby events display, in general, a fairly uniform shape (Barbon et al. 1973, Leibundgut 1988), recent high-precision photometry shows that SNe~Ia exhibit differences in their light curves which are related to their luminosities (Phillips 1993, Hamuy et al. 1995, Riess et al. 1995a). To observe the real effect one needs a well observed, spectroscopically classified SN~Ia at a considerable redshift and a thorough understanding of the varieties of light curve shapes. Attempts to measure the cosmological time dilation with SNe~Ia have been made before. A sample of nearby events ($z < 0.05$) was investigated by Rust (1974). For such low redshifts, errors in photometry and the real variations in light curve shape mask the effect of time dilation. The light curve of the distant SN~1988U was employed for a first test ($z=0.31$; N\\o rgaard-Nielsen et al. 1989, Leibundgut 1991), but the observations do not cover the maximum and no definite answer could be found. Recently, the light curve data on other distant supernovae have been used for a similar analysis (Goldhaber et al. 1996). Here we describe the time dilation test with observations of SN~1995K, a spectroscopically confirmed SN~Ia with a well-observed light curve. ", "conclusions": "The photometry of SN~1995K extending over about 50 days provides sufficient data to probe the effect of time dilation on a clock running at a cosmological distance. We find that including the time dilation expected from universal expansion makes SN~1995K comparable to local SNe~Ia and a fair representative of its class. The spectrum, color, luminosity at maximum, and the light curve shape are all very similar to what is observed in local Type Ia supernova. Together with more SNe~Ia at cosmological distances it can be used to determine the deceleration parameter and contributions of non-baryonic mass to the cosmic mass density. On the other hand, assuming a static universe, SN~1995K had the slowest photometric evolution of all known SNe~Ia despite appearing spectroscopically indistinguishable from local events. The photometry of SN~1995K cannot be approximated by any light curve shape of nearby events and, in a non-expanding universe, does also not follow the decline-luminosity relation established for nearby events. It is even less luminous than the mean of local supernovae and would constitute a unique and peculiar SN~Ia. We take this as a clear vindication of an expanding universe. Further supernovae at redshifts beyond 0.1 provide additional checks (cf. Goldhaber et al. 1996). Such distant objects are currently discovered at a regular rate (Perlmutter et al. 1995a,b, 1996, Kirshner et al. 1995, Garnavich et al. 1996a,b) and will provide additional tests for consistency. The importance of extensive light curve coverage as early and as long as possible must be stressed. It is only these observations which provide enough leverage to perform this test. The early and late phase photometry is also of paramount importance for an accurate determination of the deceleration parameter $q_0$ in order to identify the best local counterpart and find the most appropriate luminosity. Direct observation of the detailed spectral evolution of a distant supernova provides a further test. Here the changes in line shifts and relative strengths would reveal the apparently retarded evolution of the supernova." }, "9605/astro-ph9605187_arXiv.txt": { "abstract": " ", "introduction": "A crude estimate of the gravitational luminosity of an object of mass $M$, mean radius $R$ and internal velocities of order $V$ can be derived from the quadrupole formula \\cite{Blanc96}: \\be \\label{e:quadru,L} L \\sim {c^5\\ov G} \\, s^2 \\l( {R_{\\rm s} \\ov R} \\r) ^2 \\l( V \\ov c \\r) ^6 \\ , \\ee where $R_{\\rm s} := 2 G M / c^2$ is the Schwarzschild radius associated with the mass $M$ and $s$ is some asymmetry factor: $s=0$ for a spherically symmetric object and $s\\sim 1$ for an object whose shape is far from that of a sphere. According to formula (\\ref{e:quadru,L}), the astrophysical objects for which $s\\sim 1$, $R\\sim R_{\\rm s}$ and $V \\sim c$ may radiate a fantastic power in the form of gravitational waves: $L\\sim {c^5/ G} = 3.6\\times 10^{52}$ W, which amounts to $10^{26}$ times the luminosity of the Sun in the electromagnetic domain! A neutron star has a radius quite close to its Schwarzschild radius: $R \\sim 1.5 - 3 \\, R_{\\rm s}$ and its rotation velocity may reach $V\\sim c/2$ at the equator, so that they are a priori valuable candidates for strong gravitational emission. The crucial parameter to be investigated is the asymmetry factor $s$. It is well known that a uniformly rotating body, perfectly symmetric with respect to its rotation axis does not emit any gravitational wave ($s=0$). Thus in order to radiate gravitationally a neutron star must deviate from axisymmetry. P.~Haensel's lecture \\cite{Haens96} investigates the deviation from axisymmetry resulting from irregularities (``mountains'') in the solid crust or from the neutron star precession. In the present lecture, we investigate two other mechanisms which generate a deviation from axisymmetry: (i) the spontaneous symmetry breaking resulting from the development of a triaxial instability in a rapidly rotating neutron star (\\S~\\ref{s:symbreak}) and (ii) the distortion induced by the internal magnetic field of the neutron star (\\S~\\ref{cw,pulsars}). ", "conclusions": "\\subsection{Spontaneous symmetry breaking} From the results presented in Table~\\ref{t:resu,EOS}, it appears that only neutron stars whose mass is larger than $1.74\\, M_\\odot $ meet the conditions of spontaneous symmetry breaking via the viscosity-driven instability. The above minimum mass is much lower than the maximum mass of a fast rotating neutron star for a stiff EOS ($3.2\\ M_\\odot $ \\cite{SaBGH94}). Note that the critical period at which the instability happens ($P=1.2$ ms) is not far from the lowest observed one ($1.56$ ms). The question that naturally arises is : do these heavy neutron stars exist in nature ? Only observations can give the answer; in fact, the numerical modelling of a supernova core and its collapse \\cite{Mulle96} cannot yet provide us with a reliable answer. The masses of 17 neutron stars (all in binary systems) are known \\cite{ThAKT93}. Among them, four masses (all in binary radio pulsars) are known with a precision better than $10\\% $ and they turn out to be around $1.4\\ M_\\odot $ (see Table III in A.~Wolszczan's lecture \\cite{Wolsz96}). Among the X-ray binary neutron stars, two of them seem to have a higher mass: 4U 1700-37 and Vela X-1 ($1.8\\pm 0.5\\ M_\\odot $ and $1.8\\pm 0.3\\ M_\\odot $ respectively). These objects show that neutron stars in binary systems may have a mass larger than $1.7\\ M_\\odot $. A natural question that may arise is: why do X-ray binary neutron stars, which are believed to be the progenitors of binary radio pulsars, would have a mass larger than the latter ones ? We have not yet any reliable answer to this question. A first (pessimistic) answer is that the measurements of X-ray neutron star masses are not as reliable (compare the error bars of the masses of the binary radio pulsars with the ones of the X-ray binaries in Fig.~3 of ref.~\\cite{ThAKT93}). Actually it should be noticed that the error bars of the X-ray pulsars do not have the same statistical meaning as the error bars of the binary radio pulsars \\cite{Lindb96}: they give only the extremum limits of neutron star masses in the X-ray binary. Consequently $1.4\\ M_\\odot $ is not incompatible with these masses. If this is really the case forget all we have said about the above instability mechanisms: only the CFS mechanism for $m > 2 $ can work, provided that the viscosity is low enough, which does not seem to be the case (especially if the ``mutual friction'' in the superfluid interior is taken into account \\cite{LindM95}). A related question arises naturally: why are the observed masses of millisecond radio pulsars almost identical ? Following the standard model, a millisecond radio pulsar is a recycled neutron star, spun up by the accretion of mass and angular momentum from a companion. The observed mass and angular velocity are those of the end of the accretion process. Consequently the accreted mass depends on the history of the system and on the nature of the companion. By supposing ``per absurdo'' that all neutron stars are born with the same mass, it is difficult to understand why the accreted mass is the {\\em same} for all neutron stars. A possible answer is that this could result from some observational selection effect. For example, suppose that accreted matter quenches the magnetic field, it is then easy to imagine that the final external magnetic field depends on the mass of the accreted plasma. If the accreted mass is large enough, the magnetic field can be lower than the critical value for which the pulsar mechanism works. On the contrary, if the accreted mass is quite small, the magnetic field is large and the life time of the radio pulsar phase is shorter and consequently more difficult to observe. Let us conclude by saying that a lot of questions are still open about these systems. If we knew everything about neutron stars, such an observation would be a waste of time. The only thing that we can recommend is to stay open minded. \\subsection{CW emission from pulsars} In this lecture, we have also investigated the CW emission resulting from the magnetic field induced distortion of neutron stars. The computations presented in \\S~\\ref{s:mag,num,res} show that the distortion at fixed magnetic dipole moment depends very sensitively on the magnetic configuration. The case of a perfect conductor interior with toroidal electric currents is the less favorable one, even if the currents are concentrated in the crust. Stochastic magnetic fields (that we modeled by considering counter-rotating currents) enhance the deformation by several orders of magnitude and may lead to a detectable amplitude for a pulsar like the Crab. As concerns superconducting interiors --- the most realistic configuration for neutron stars --- we have studied type I superconductors numerically, with a simple magnetic structure outside the superconducting region. The distortion factor is then $\\sim 10^2$ to $10^3$ higher than in the normal (perfect conductor) case, but still insufficient to lead to a positive detection by the first generation of kilometric interferometric detectors. We have not studied in detail the type II superconductor but have put forward some argument which makes it a promising candidate for gravitational wave detection. \\ack{We warmly thank Joachim Frieben and Pawel Haensel for their careful reading of the preliminary version of these notes.} \\bigskip\\goodbreak \\noindent{\\bf Problem}: Show that, at fixed angular momentum, the kinetic energy of an incompressible fluid in a cylinder is minimal for rigid rotation. \\bigskip \\noindent{\\em Solution}: Let $\\Omega(\\rho,z)$ be the angular velocity ($\\rho=\\sqrt{x^2+y^2})$. The kinetic energy of the fluid is given by $T=\\int_V 1/2\\ n\\Omega^2(\\rho,z)\\rho^2 \\, dV $ where $n$ is the density of the fluid (assumed to be constant). We have to find an extremum of this quantity under the constraint that the angular momentum $L=\\int_V n\\, \\Omega(\\rho,z)\\rho^2 \\, dV $ has a fixed value. By means of the Lagrangian multiplier technique, this amounts to find an extremum of \\be \\int_{V} {1\\ov 2}\\, n\\, \\Omega^2(\\rho,z)\\rho^2 \\, dV + \\lambda\\int_{V}n\\, \\Omega(\\rho,z)\\rho^2 \\, dV \\ , \\ee where $\\lambda$ is the Lagrangian multiplier. By performing the variation with respect to $\\Omega$ we obtain \\be \\int_{V}(\\Omega(\\rho,z)\\rho^2 +\\lambda \\rho^2)\\, \\delta \\Omega \\, dV =0 \\ , \\ee from which $\\Omega={\\rm const}$. \\appendix \\label{a:hydro} {\\bf RELATIVISTIC HYDRODYNAMICS IN AN ACCELERATED \\\\ FRAME} \\bigskip In this appendix, we examine how to re-write the equation of momentum-energy conservation \\be \\label{e:div(T)=0} \\nabla_\\mu T^{\\mu\\alpha} = 0 \\ee as a system of evolution equations with respect to a given observer $\\cal O$, the evolved variables being the energy density and the fluid velocity, both measured by $\\cal O$. We consider perfect fluids only: \\be \\label{e:Tab,fluide} T^{\\alpha\\beta} = (e+p) \\, u^\\alpha u^\\beta + p\\, g^{\\alpha\\beta} \\ , \\ee so that the equation for the fluid velocity will constitute a relativistic generalization of the {\\em Euler equation} of classical hydrodynamics. The observer $\\cal O$ is completely arbitrary; he is simply described by its 4-velocity $v^\\alpha$. Strictly speaking we consider a {\\em family} of observers $\\cal O$ (a {\\em congruence} of worldlines), so that $v^\\alpha$ constitutes a smooth vector field on spacetime. A fundamental tensor field related to $\\cal O$ is the projection operator onto the 3-space $P$ orthogonal to $v^\\alpha$: \\be q_{\\alpha\\beta} := g_{\\alpha\\beta} + v_\\alpha\\, v_\\beta \\ . \\ee The 3-space $P$ is made of spacelike vectors and can be thought as the ``physical'' three-dimensional space ``felt'' by the observer $\\cal O$. Note that if $\\cal O$ is rotating ($\\omega_{\\alpha\\beta}\\not = 0$, see below), the vector space $P$ is not integrable in global 3-surfaces. The motion of the observer $\\cal O$ through spacetime is characterized by the Ehlers decomposition of $\\nabla_\\beta v_\\alpha$ (see, e.g., Sect.~4.1 of ref.~\\cite{HawkE73}) \\be \\nabla_\\beta v_\\alpha = \\omega_{\\alpha\\beta} + \\theta_{\\alpha\\beta} - a_\\alpha v_\\beta \\ , \\ee where \\be \\omega_{\\alpha\\beta} := q_\\alpha^{\\ \\, \\mu} q_\\beta^{\\ \\, \\nu} \\nabla_{[\\nu} \\, v_{\\mu]} \\ee is the {\\em rotation 2-form} of $\\cal O$, \\be \\label{e:expansion,tens} \\theta_{\\alpha\\beta} := q_\\alpha^{\\ \\, \\mu} q_\\beta^{\\ \\, \\nu} \\nabla_{(\\nu} \\, v_{\\mu)} \\ee is the {\\em expansion tensor} of $\\cal O$ and \\be a_\\alpha := v^\\mu \\nabla_\\mu v_\\alpha \\ee is the {\\em 4-acceleration} of $\\cal O$. For a 4-vector $W^\\alpha$ lying in the ``physical space'' $P$ of $\\cal O$ ($v_\\mu W^\\mu = 0$), we introduce the {\\em 3-covariant derivative} with respect to $\\cal O$ as \\be \\overline\\nabla_\\alpha W_\\beta := q_\\alpha^{\\ \\, \\mu} q_\\beta^{\\ \\, \\nu} \\nabla_\\mu W_\\nu \\ . \\ee This definition results in the following relation between the 4-covariant and the 3-covariant derivatives: \\be \\nabla_\\alpha W_\\beta = \\overline\\nabla_\\alpha W_\\beta - v_\\alpha\\, v^\\mu \\nabla_\\mu W_\\beta + ( \\theta_{\\alpha\\mu} W^\\mu - \\omega_{\\alpha\\mu} W^\\mu ) v_\\beta \\ , \\ee from which the following relation between the 4-divergence and the 3-divergence is immediately derived: \\be \\nabla_\\mu W^\\mu = \\overline\\nabla_\\mu W^\\mu + a_\\mu W^\\mu \\ . \\ee The fluid motion as seen by the observer $\\cal O$ is specified by the {\\em Lorentz factor} \\be \\Gamma := - v_\\mu u^\\mu \\ , \\ee and the {\\em 3-velocity} \\be V^\\alpha := {1\\ov \\Gamma} q^\\alpha_{\\ \\, \\mu} u^\\mu \\ . \\ee $V^\\alpha$ belongs to $P$ and is the fluid velocity as measured by the observer $\\cal O$ with his clock and his ruler. The following relations are immediate consequences of the above definitions: \\begin{eqnarray} u^\\alpha & = & \\Gamma (V^\\alpha + v^\\alpha) \\label{e:u(V,v)} \\\\ \\Gamma & = & (1-V_\\mu V^\\mu)^{-1/2} \\ . \\end{eqnarray} The fluid energy density as measured by $\\cal O$ is given by the formula \\be E = T_{\\mu\\nu} \\, v^\\mu v^\\nu \\ , \\ee or, according to the form (\\ref{e:Tab,fluide}) of $T_{\\mu\\nu}$, \\be \\label{e:E(e,p)} E = \\Gamma^2 (e+p) - p \\ . \\ee From this expression, it is clear that the kinetic energy of the fluid with respect to $\\cal O$ is included in the energy density $E$ via the Lorentz factor $\\Gamma$. Having set these definitions, let us now examine the equations of motion deduced from the momentum-energy conservation, Eq.~(\\ref{e:div(T)=0}), which, using the perfect fluid form (\\ref{e:Tab,fluide}) of $T_{\\alpha\\beta}$, can be written as \\be \\label{e:div(T),u} (e+p) u^\\mu \\nabla_\\mu u^\\alpha + \\nabla_\\mu \\l[ (e+p) u^\\mu \\r] \\, u^\\alpha + \\nabla^\\alpha p = 0 \\ee The evolution equation for the fluid energy density $E$ as measured by $\\cal O$ is obtained by projecting Eq.~(\\ref{e:div(T),u}) along $v^\\alpha$. Invoking Eqs.~(\\ref{e:u(V,v)}) and (\\ref{e:E(e,p)}), one obtains after straightforward calculations \\be \\label{e:evol,E} v^\\mu \\nabla_\\mu E + \\overline\\nabla_\\mu \\l[ (E+p) V^\\mu \\r] + (E+p) ( 2 a_\\mu V^\\mu + \\theta_\\mu^{\\ \\, \\mu} + \\theta_{\\mu\\nu} V^\\mu V^\\nu ) = 0 \\ . \\ee The relativistic generalization of the Euler equation is obtained by projecting Eq.~(\\ref{e:div(T),u}) onto $P$, by means of $q_{\\alpha\\beta}$. After straightforward calculations (at a certain stage, use must be made of Eq.~(\\ref{e:evol,E})) one obtains \\begin{eqnarray} & & v^\\mu \\nabla_\\mu V^\\alpha - a_\\mu V^\\mu v^\\alpha + V^\\mu \\overline\\nabla_\\mu V^\\alpha + (\\omega^\\alpha_{\\ \\, \\mu} + \\theta^\\alpha_{\\ \\, \\mu} ) V^\\mu - (a_\\mu V^\\mu + \\theta_{\\mu\\nu} V^\\mu V^\\nu) V^\\alpha \\nonumber \\\\ & & \\qquad = - {1\\ov E+p} \\l( \\overline\\nabla^\\alpha p + V^\\alpha v^\\mu \\nabla_\\mu p \\r) - a^\\alpha \\label{e:Euler,vdV} \\ . \\end{eqnarray} Note that the first two terms on the left-hand side, $v^\\mu \\nabla_\\mu V^\\alpha - a_\\mu V^\\mu v^\\alpha$, constitute the {\\em Fermi-Walker derivative} \\cite{HawkE73} of $V^\\alpha$ with respect to $v^\\alpha$. The Fermi-Walker derivative measures the rate of change {\\em within} $P$ of $V^\\alpha$ with respect to the proper time of $\\cal O$. If the observer $\\cal O$ has set up a local coordinate system, with respect to which the length of the vectors in $P$ are evaluated, a derivative operator more convenient than $v^\\mu \\nabla_\\mu$ is the {\\em Lie derivative} along $v^\\alpha$, $\\pounds_v$. The term which naturally appears on the left-hand side of Eq.~(\\ref{e:Euler,vdV}) is then the {\\em convected derivative} of $V^\\alpha$ \\cite{CartQ72}, \\cite{Carte80} : \\be D_v V^\\alpha := \\pounds_v V^\\alpha - a_\\mu V^\\mu v^\\alpha = v^\\mu \\nabla_\\mu V^\\alpha - (\\omega^\\alpha_{\\ \\, \\mu} + \\theta^\\alpha_{\\ \\, \\mu}) V^\\mu - a_\\mu V^\\mu v^\\alpha \\ . \\ee The Euler equation (\\ref{e:Euler,vdV}) then becomes \\begin{eqnarray} & & D_v V^\\alpha + V^\\mu \\overline\\nabla_\\mu V^\\alpha + 2(\\omega^\\alpha_{\\ \\, \\mu} + \\theta^\\alpha_{\\ \\, \\mu} ) V^\\mu - (a_\\mu V^\\mu + \\theta_{\\mu\\nu} V^\\mu V^\\nu) V^\\alpha \\nonumber \\\\ & & \\qquad = - {1\\ov E+p} \\l( \\overline\\nabla^\\alpha p + D_v p \\, V^\\alpha \\r) - a^\\alpha \\label{e:Euler,DV} \\ . \\end{eqnarray} In the Newtonian limit, $D_v$ reduces simply to $\\partial/\\partial t$. Moreover, the $V^\\mu \\overline\\nabla_\\mu V^\\alpha$ gives the classical term $(\\vec V \\cdot \\vec\\nabla)\\vec V$ and $2\\, \\omega^\\alpha_{\\ \\, \\mu} V^\\mu$ gives the Coriolis term $2\\, \\vec\\omega\\times\\vec V$, induced by the rotation of the observer $\\cal O$ with respect to some inertial frame. The terms involving $\\theta_{\\alpha\\beta}$ are due to the non-rigidity of the frame set up by the observer $\\cal O$. On the right-hand side, the classical $(1/\\rho) \\vec\\nabla p$ term is recognized, supplemented by the special relativistic term $(\\partial p/\\partial t) \\, \\vec V$. The last term, the acceleration $-a^\\alpha$, contains gravitational as well as centrifugal forces." }, "9605/astro-ph9605008_arXiv.txt": { "abstract": "\\bigskip Using HST and the WFPC2 we have acquired very deep V- and I-band photometry of stars in NGC 2420 and NGC 2477 to study cluster luminosity functions at approximately solar metallicity. We have determined these cluster luminosity functions down to $M_I$ = 10.5 (0.2 M$_{\\odot}$) and find that the luminosity function of NGC 2420 turns over at $M_I$ $\\approx$ 9.0, and possibly stops altogether by $M_I$ $\\approx$ 9.5. The luminosity function of NGC 2477 may flatten at $M_I$ $\\geq$ 9.5. We compare our open cluster luminosity functions to the solar neighborhood field star luminosity function of Kroupa, Tout \\& Gilmore (1993) and the four published HST globular cluster luminosity functions: $\\omega$ Cen (Elson {\\it et al.}\\ 1995), 47 Tuc (De Marchi \\& Paresce 1995b), M 15 (De Marchi \\& Paresce 1995a), and NGC 6397 (Paresce, De Marchi \\& Romaniello 1995). We find a smooth relation between the location of the luminosity function turn-over and the metallicity for all these low mass star samples which matches the expected $M_I$ versus [Fe/H] trend for a model star of $\\approx$ 0.27 M$_{\\odot}$ (Saumon 1995; Alexander {\\it et al.}\\ 1996). We interpret this smooth and systematic behavior in the cluster luminosity functions as strong evidence in favor of an invariant initial mass function and a metallicity-dependent mass-luminosity relation. ", "introduction": "One of the most fundamental aspects of the stellar content of galaxies is the distribution by mass of newly formed stars, the initial mass function (IMF). Evidence supporting or restricting variations in the IMF for very low mass stars is of profound importance for an understanding of the mass content of the universe, the dynamical evolution of open and globular clusters, the chemical evolution of galaxies, and the physics of star formation. While developments in star formation theory (e.g. Shu 1991) and observations (e.g. Evans 1991) continue to increase our understanding of the complexities and processes involved in star formation, any understanding of how the IMF does, or does not, depend on environment and metallicity is still elusive. For low mass stars, which are the subject of this paper, large surveys (see Reid \\& Gilmore 1982; Hawkins \\& Bessell 1988; Stobie, Ishida \\& Peacock 1989; Bessell \\& Stringfellow 1993) have provided a fairly well determined measure of the field star luminosity function near the Sun. Extensive modelling is required to derive the corresponding stellar initial mass function. However, there is reasonable agreement (cf. Kroupa {\\it et al.}\\ 1993 and Tinney 1995 for recent references) that the luminosity function shows a broad maximum near $M_I \\approx +9.5$, while the underlying mass function (MF) breaks away from an approximate power-law increase below 0.5 M$_{\\odot}$. Star count surveys in the near-IR (e.g. Hu {\\it et al.}\\ 1994) and in the optical with HST (Bahcall {\\it et al.}\\ 1994; Santiago, Gilmore \\& Elson 1995), and most recently from the Hubble Deep Field (Elson, Santiago \\& Gilmore 1996), suggest that the field stars of the Galactic thick disk and halo have a luminosity function which is not significantly distinguishable from that of the solar neighborhood down to masses near the hydrogen burning limit. This is a remarkable result, given that these stellar populations differ considerably in local density, and by a factor of forty in mean chemical abundance. Field star analyses are, however, subject to many uncertainties, in particular imprecise distance determination (Kroupa {\\it et al.}\\ 1993). The derivation of an initial mass from a color and apparent magnitude of an object which may be an unresolved binary star of unknown age, distance, and metallicity remains a statistical goal, rather than a precise tool. By contrast, in clusters the primary uncertainties of differential ages, abundances and distances are removed. Hence, extensive surveys of the open clusters near the Sun have been undertaken (e.g. Pleiades: Hambly \\& Jameson 1991; Hyades: Reid 1993; Praesepe: Williams, Rieke \\& Stauffer 1995; Hambly {\\it et al.}\\ 1995). Such clusters are however primarily young, so that interpretation suffers from the limitation that evolutionary models for pre-main sequence stars of low mass are not yet well tested. Ideally, one wants clusters older than perhaps 1 Gyr, covering a wide range of metallicities. In the past year there has been a vast improvement in the quality and quantity of data on the low mass end of the stellar luminosity function (LF) from observations of globular clusters with the refurbished HST (e.g.\\ Elson {\\it et al.}\\ 1995; De Marchi \\& Paresce 1995a, 1995b; Paresce, De Marchi \\& Romaniello 1995). These four globular cluster studies have already provided good stellar LFs to $M_I \\geq 10$ ($\\approx$ 0.2 M$_{\\odot}$), and they will soon be supplemented by at least seven more HST globular cluster studies. In this paper we report deep HST observations of the LFs in two open clusters, which allow us to extend the metallicity range represented by these four globular clusters ($-2.2 < [Fe/H] < -0.7$) up to solar abundance. Thus, for the first time we now have cluster luminosity functions extending to very low stellar masses and covering more than 2 dex in metallicity, and can therefore study the effect of metallicity on stellar luminosity functions. In this paper we search for a systematic dependence of the IMF on some parameter to provide clues to the physics of star formation. ", "conclusions": "Using HST and the WFPC2 we have acquired very deep V- and I-band photometry of stars in NGC 2420 and NGC 2477 to study cluster luminosity functions at approximately solar metallicity. We have determined these cluster luminosity functions down to $M_I$ = 10.5 (0.2 M$_{\\odot}$) and find that the LF of NGC 2420 turns over at $M_I$ $\\approx$ 9.0, and possibly stops altogether by $M_I$ $\\approx$ 9.5. The LF of NGC 2477 may flatten at $M_I$ $\\geq$ 9.5. We compare our open cluster luminosity functions to the solar neighborhood field star luminosity function of Kroupa {\\it et al.}\\ (1993) and the four published HST globular cluster luminosity functions: $\\omega$ Cen (Elson {\\it et al.}\\ 1995), 47 Tuc (De Marchi \\& Paresce 1995b), M 15 (De Marchi \\& Paresce 1995a), and NGC 6397 (Paresce, De Marchi \\& Romaniello 1995). We find a smooth relation between the location of the luminosity function turn-over and the metallicity for all these low mass star samples which matches the expected $M_I$ versus [Fe/H] trend for a model star of $\\approx$ 0.27 M$_{\\odot}$ (Saumon 1995; Alexander {\\it et al.}\\ 1996). We interpret this smooth and systematic behavior in the cluster luminosity functions as strong evidence in favor of an invariant initial mass function and a metallicity-dependent mass-luminosity relation." }, "9605/astro-ph9605193_arXiv.txt": { "abstract": "\\\\ \\noindent Causal seed models, such as cosmological defects, generically predict a distinctly different structure to the CMB power spectrum than inflation, due to the behavior of the perturbations outside the horizon. We provide a general analysis of their causal generation from isocurvature initial conditions by analyzing the role of stress perturbations and conservation laws in the causal evolution. Causal stress perturbations tend to generate an isocurvature pattern of peak heights in the CMB spectrum and shift the first compression, i.e.~main peak, to smaller angular scales than in the inflationary case, unless the pressure and anisotropic stress fluctuations balance in such a way as to reverse the sense of gravitational interactions while also maintaining constant gravitational potentials. Aside from this case, these causal seed models can be cleanly distinguished from inflation by CMB experiments currently underway. ", "introduction": "\\label{sec-introduction} It is now widely recognized that features in the power spectrum of Cosmic Microwave Background (CMB) anisotropies can be a gold mine of information for cosmology. A great deal of experimental effort is being expended in order to map the CMB accurately over a wide range of angular scales from the ground, balloons and eventually space. In addition to providing valuable information about the cosmological parameters, it is becoming clear that the CMB can teach us much about how the fluctuations were generated in the early universe. For example in \\cite{ourpaper}, it was claimed that by studying the acoustic signature of the anisotropy spectrum one can test the inflationary paradigm for fluctuation generation (see \\cite{Lid} and references therein for other inflationary tests). The key idea in differentiating inflation from other models of structure formation, such as defects \\cite{CriTur,Magetal,Duretal}, is the behavior of the gravitational potential fluctuations outside the horizon. In inflation, these potentials are approximately constant while in a viable defect model, or indeed any isocurvature model, they start out vanishingly small and are generated as a mode enters the horizon. Coupled with the effects of photon backreaction, this distinction implies a different structure in the anisotropy spectrum on small angular scales, allowing for a test of the inflationary paradigm. Specifically it was claimed that, with some exotic exceptions, isocurvature models produced spectra whose peaks were phase shifted with respect to the inflationary models \\cite{ourpaper}. In a very rough sense, the inflationary driving force excites a cosine mode whereas the isocurvature one excites a sine mode. Even if the phase shift were closer to $\\pi$ rather than $\\pi/2$ radians \\cite{Magetal}, causing the peaks to line up with the inflationary model once again, the non-monotonic modulation of the peak heights by baryon drag would allow the defect and inflationary spectra to be distinguished. We refer the reader to \\cite{ourpaper} for more details. In this paper, we specialize the discussion to causal {\\it scaling} models by applying Turok's \\cite{turokletter} mode expansion techniques to the underlying stress perturbations. These fluctuations are the fundamental source of gravitational instability in any isocurvature model \\cite{Bar,KodSas}. Detailed discussions of stress perturbations, conservation laws, and gauge in relativistic perturbation theory as well as their role in causality arguments are given in the Appendices \\ref{sec-perturbation} and \\ref{sec-causal} respectively. We explicitly enforce energy-momentum conservation and thus self-consistently include the response and backreaction of the photon-baryon fluid to the gravitational sources \\cite{ourpaper}. We show that except for one special case, the resultant CMB spectra are easily distinguished from their inflationary counterpart. If the dynamical effects of isotropic and anisotropic stress are exactly balanced, a novel situation may arise in which the sense of gravity is reversed and hence also the predictions for the acoustic features in the CMB. We discuss in detail the model of Turok \\cite{turoknew} which utilizes this mechanism in Appendix \\ref{sec-mimic}. Thus out of the general class of causal models with scaling properties only this one case may be confused with inflation from its acoustic signature. ", "conclusions": "\\label{sec-discussion} All of the causal models for the formation of large scale structure currently being considered can be divided into two classes: (a) inflationary models, which have curvature fluctuations on superhorizon scales and (b) scaling seeded-models, such as strings and textures. In the latter case, there are no initial curvature fluctuations and stress fluctuations only generate them through the causal redistribution of matter under energy-momentum conservation \\cite{Bar,KodSas}. We have presented a thorough discussion of this process that can be used to study the general properties of any model that proposes a causal mechanism for large scale structure formation without postulating an inflationary epoch. We apply these techniques to study a representative class of scaling models inspired by Turok \\cite{turokletter}. For models dominated by white noise isotropic stress fluctuations, the acoustic signature in the CMB angular power spectrum follows the canonical signature of a baryon-isocurvature model. Physically, this robust signature arises from the ability of photon-backreaction to drive the acoustic oscillation \\cite{ourpaper}, a feature that must be included in a self-consistent calculation. Models dominated by anisotropic stress fluctuations tend to be even more extreme, with main features pushed toward smaller scales. Hence both classes are easily distinguished from inflation by experiments currently underway (see Fig.~\\ref{fig:family}). A realistic model, such as strings or textures, may contain additional complications beyond the simple toy-models explored in this paper, such as tensor and vector contributions as well as reionization. It can also require non-linear evolution of the sources that couple the normal modes discussed here and leave non-gaussian signatures in the CMB and/or cause decoherence in the oscillation \\cite{Magetal}. However, such complications are likely to make alternate models less, rather than more, like inflation. The analysis in this paper also reinforces the conclusions of \\cite{ourpaper}: in an inflationary model, even peaks are produced by rarefaction waves and odd peaks are produced by compression waves. On the other hand in isocurvature models, even peaks are produced by compression waves and odd peaks are produced by rarefaction waves. As long as the energy density in radiation at decoupling is significant and gravitational potential wells represent overdense regions, such a model cannot reproduce the inflationary CMB signature without the equivalent of putting in the features by hand. \\bigskip \\noindent{\\it Acknowledgements:} We thank \\href{http://www.sns.ias.edu/$\\sim$jnb}{J.N. Bahcall}, \\href{http://physics7.berkeley.edu/cmbserve/ferreira.html}{P.G. Ferreira} and \\href{http://www-astro-theory.fnal.gov/Personal/stebbins/welcome.html}{A. Stebbins} for useful discussions, as well as \\href{http://www.astro.ubc.ca/people/scott/cmb.html}{D. Scott}, N.G. Turok, and J. Magueijo for comments on a draft of this work. W.H.~was supported by the NSF and WM Keck Foundation. \\vfill \\eject \\appendix" }, "9605/astro-ph9605120_arXiv.txt": { "abstract": "We investigate the dynamical response of stellar orbits in a rotating barred galaxy potential to the perturbation by a nuclear gaseous ring. The change in 3D periodic orbit families is examined as the gas accumulates between the inner Lindblad resonances. It is found that the phase space allowable to the $x_2$ family of orbits is substantially increased and a vertical instability strip appears with the growing mass of the ring. A significant distortion of the $x_1$ orbits is observed in the vicinity of the ring, which leads to the intersection between orbits with different values of the Jacobi integral. We also examine the dependence of the orbital response to the eccentricity and alignment of the ring with the bar. Misalignment between an oval ring and a bar can leave observational footprints in the form of twisted near-infrared isophotes in the vicinity of the ring. It is inferred that a massive nuclear ring acts to weaken and dissolve the stellar bar exterior to the ring, whereas only weakly affecting the orbits interior to the inner Lindblad resonances. Consequences for gas evolution in the circumnuclear regions of barred galaxies are discussed as well. ", "introduction": "It is generally agreed that barred disk galaxies experience radial inflows of the interstellar medium (ISM) (e.g. Kenney \\markcite{ken96} 1996, and refs. therein). These flows are presumably triggered by gravitational torques from non-axisymmetric background potentials, such as stellar bars and ovals. (For a more comprehensive discussion of this phenomenon see review by Shlosman, Begelman \\& Frank \\markcite{shl90} 1990). A large fraction, $\\sim2/3$, of disk galaxies are observed to be barred to various degrees (e.g. de Vaucouleurs \\markcite{dev63} 1963), the remaining 1/3 typically consist of edge-on galaxies where bars would be difficult to detect (e.g. review by Martinet \\markcite{mar95} 1995). In addition, most galactic disks are ovally distorted (Bosma \\markcite{bos81} 1981; Kormendy \\markcite{kor82} 1982; Rix \\& Zaritsky \\markcite{rix95} 1995), especially in the central regions where triaxial stellar bulges are frequent (Kormendy \\markcite{kor93} 1993). Theoretical studies of gaseous inflows confirm that gas can reach the circumnuclear regions of disk galaxies (e.g. Combes and Gerin \\markcite{com85} 1985; Shlosman, Frank \\& Begelman \\markcite{shl89} 1989; Athanassoula \\markcite{ath92} 1992; Friedli and Benz \\markcite{fri93} 1993; Shlosman and Noguchi \\markcite{shl93} 1993) and cause enhanced star formation there, so-called nuclear starbursts (Heller and Shlosman \\markcite{hel94} 1994; Knapen etal. \\markcite{kna95a} 1995a). Indeed, observations of nuclear starburst galaxies reveal ring-like molecular gas accumulations within the central kpc (e.g. Telesco and Decher \\markcite{tel88} 1988; Pogge \\markcite{pog89} 1989; Kenney etal. \\markcite{ken92} 1992; Benedict etal. \\markcite{ben93} 1993; Knapen etal. \\markcite{kna95b} 1995b), where a slowdown of radial inflow is expected in the presence of inner Lindblad resonance(s) (ILRs) (Combes \\& Gerin \\markcite{com85} 1985; Shlosman, Frank \\& Begelman \\markcite{shl89} 1989). Nuclear rings are ovally shaped and their major axes are observed to lead the stellar bars, typically by $\\sim 50\\arcdeg-90\\arcdeg$ in the direction of galactic rotation. Frequently, they are patchy and incomplete (Buta \\& Crocker \\markcite{but93} 1993). A substantial fraction, $\\sim10\\%-30\\%$, of the molecular galactic ISM can accumulate in these rings, which consist of a mixture of neutral and ionized, gas and dust, and is accompanied by massive star formation. Ring masses can be roughly estimated using the axisymmetric rotation curve and/or emission from this gas. Typical masses range from few$\\times 10^8\\,M_{\\sun}$ to few$\\times 10^9\\,M_{\\sun}$, and even higher (Kenney \\markcite{ken96} 1996 and refs. therein). Besides being an active site of star formation, a nuclear ring provides a significant gravitational perturbation to the background galactic potential, and is expected to alter the main stellar and gas orbits in the central regions. Growing molecular rings further contribute to the increased mass concentration in the disk. Because of this we expect them to modify the inner galactic rotation curve and the positions and strength of the ILRs. Previous studies of stellar orbits in a rapidly rotating barred potential focused on the secular effects of a growing {\\it spherically-symmetric} central mass concentration, e.g. massive black hole and/or galactic bulge, exceeding $10^9\\,M_{\\sun}$, or $\\sim1\\%$ of the overall mass of a galaxy (Martinet \\& Pfenniger \\markcite{mar87} 1987; Hasan \\& Norman \\markcite{has90} 1990; Hasan, Pfenniger \\& Norman \\markcite{has93} 1993). In particular, the main 3D periodic orbits in a barred system with a central mass have been identified and their stability analyzed. These studies exposed the crucial role of ILRs and higher-order resonances in increasing the stochasticity in the system, or simply heating it up, which results in the weakening and dissolution of the stellar bar and the buildup of the galactic bulge. This interesting phenomenon has led the authors to argue in favor of galaxy evolution along the Hubble sequence (Pfenniger, Combes and Martinet \\markcite{pfe94} 1994; Martinet \\markcite{mar95} 1995). Implications for gas dynamics have been studied by Pfenniger \\& Norman \\markcite{pfe90} (1990) neglecting the self-gravity in the gas. Although it is possible that all nuclear starburst galaxies (and even all disk galaxies!) harbor central black holes (BHs), it is by no means clear that the masses of these BHs are in the range of $\\gtrsim10^9\\,M_{\\sun}$. It is plausible that typical BHs in disk galaxies, active and normal, are much less massive, and lie in the mass range of $\\sim10^7-10^8\\,M_{\\sun}$ (with the exception of quasar hosts). For example, Emmering, Blandford and Shlosman \\markcite{emm92} (1992) have argued that BHs in Seyfert nuclei may be more efficient in extracting energy and angular momentum from the accreting material than commonly believed, allowing for lower estimates of BH masses there. On the other hand, a buildup of galactic bulges may proceed on a timescale which is a fraction of a Hubble time and cause the same effects on the galactic dynamics within the bar region, as discussed in the previous paragraph. Evidently, the estimated masses of nuclear rings make them competitive with galactic bulges in affecting the structure of disk galaxies. At the same time, their morphology differs quite dramatically from that of nearly spherically-symmetric or weakly triaxial bulges. This motivated us to analyze the main periodic orbits in a barred potential perturbed by a growing nuclear ring. We aim at understanding the gravitational effects of this phenomenon on the stellar orbits, as well as deduce possible implications on the gas evolution in these galaxies. Both circular and oval rings are used, and the results are compared to the previous studies of such orbits, with and without the central mass (e.g. Contopoulos \\& Papayannopoulos \\markcite{con80} 1980; Athanassoula etal. \\markcite{ath83} 1983; Pfenniger \\markcite{pfe84} 1984; Hasan, Pfenniger \\& Norman \\markcite{has93} 1993). We find that in many ways, the dynamical consequences of nuclear rings differ from those of a spherically-symmetric central mass, as addressed so far in the literature. In the next section we describe a model for the background galactic potential, which is perturbed by a massive ring. The potential of an elliptical hoop, representing the ring, is calculated analytically. The third section presents the method we employ to locate the main families of periodic orbits in the phase space. Readers that wish to avoid the technical details may go directly to the fourth section, where the results of the orbital analysis are given for a series of circular and elliptical ring models, with gradually increasing mass and different orientations with respect to the stellar bar. A discussion of the possible effects on the gas flow in a galaxy is given in the last section. ", "conclusions": "We have performed an orbital analysis in a 3D galactic potential perturbed by a growing nuclear ring. The galaxy consisted of a disk, bulge and a bar. We have studied the effects of circular and oval rings positioned in the preexisting double radial ILR region of this system. Different orientations of the oval ring with respect to the stellar bar have been tested as well: aligned, perpendicular, and leading by $60\\arcdeg$ in the direction of galactic rotation. In all cases, both the ring's semi-major axis and the initial outer radial ILR were smaller than the semi-minor axis of the bar by a factor of $\\sim3$. The ring's mass was always negligible compared to the overall mass of the system, but is responsible for a local distortion of the axisymmetric rotation curve. We find that the major periodic orbits within the corotation radius are profoundly affected by the perturbation of the ring. For both circular and oval rings we observe a substantial increase in the phase space allowed by the $x_2$ orbits. If these orbits would be populated, the bar would be weakened. The biggest change comes from the outer radial (and vertical) ILR moving further out to higher energies and increasing its x- and y-extents. The inner ILR moves inwards only slightly. Hence the growing mass in the ring affects mostly the orbits outside the ring (this can be seen even more explicitly in the case of the oblique ring of model F). The only effect the ring has on the inner $x_1$ orbits is the appearance of a shoulder (bump) interior to the inner ILR in the characteristic diagram (Fig. 3). This reflects the fact that the $x_1$ orbits in this region become more rounded. Also, the vertical instability strips of the $x_1$ orbits, $S_1$ and $S_2$, are moving closer to the radial ILRs, i.e. to lower energies. Whereas $S_1$ becomes narrower, $S_2$ widens substantially towards lower energies (Fig.3). The $x_2$ orbits acquire vertical instability strips as well, when the ring becomes massive. This has some similarity to the slowly rotating triaxial models of Udry (1991). Weakening of the bar, when increasing the central mass concentration in a galaxy by adding a massive BH and/or bulge, was reported in all relevant studies (Pfenniger and Norman \\markcite{pfe90} 1990; Hasan and Norman \\markcite{has90} 1990; Hasan, Pfenniger \\& Norman \\markcite{93} 1993). It was associated with the appearance of a single radial (and vertical) ILR due to the altered rotation curve. This ILR moved out rapidly with the growing central mass $M_{\\rm c}$, specifically $R_{\\rm ILR}\\propto M_{\\rm c}^{2.8}$ (e.g. Pfenniger \\markcite{pfe96} 1996). Under these circumstances, chaotic orbits dominate the space between the center and the ILR, which quickly approaches the semi-minor axis of the bar, causing the dissolution of the stellar bar in a secular process. In addition, higher order radial and vertical ILRs contribute to this effect by widening the resonance zone. The growing central mass repells the $x_1$ family of orbits from the central region, i.e. within the ILR, and by doing so it also affects the motion out of the xy-plane. This happens because of two reasons (Hasan, Pfenniger and Norman \\markcite{has93} 1993). First, the vertical bifurcation points which mark the origin of 3D orbits, as described in Section 4, move away from the center as the central mass grows. Second, the stability of the out-of-the-plane orbits is affected, with a region of instability appearing in the innermost family of orbits, which corresponds to our $V_1$ (2:2$_{\\rm s}$:1) orbits. The model presented here differs from the above scenario mainly in two aspects: the preexisting {\\it double} radial (and a single vertical) ILRs, and the differing symmetry in the perturbing potential, which is far from being spherically-symmetric. Consequently, the $x_2$ orbits continue to be limited only to the space between the radial ILRs, whereas the $x_1$ orbits still support the bar between the center and the inner ILR, and between the outer ILR and corotation. This is true irrespective of the ring's mass, shape or inclination to the bar. The radius of the outer ILR grows approximately {\\it linearly} with the mass in the ring, slower than in the case of the central mass increase. In addition, an oval ring, oblique to the bar, further degrades the symmetry in the galactic plane, which is otherwise dominated by the $m=2$ mode due to the stellar bar. As a result the $x_1$ orbits within $\\sim2-3$ semimajor axes outside the ring, and at the position of the ring, are significantly distorted. We note, that such shapes and inclinations of a ring are not merely of a theoretical possibility, but are in fact supported by observations of molecular gas distributions in nuclear starburst galaxies. The above differences, between the dynamical effects of a central mass and of a ring, create interesting possibilities for bar evolution in response to the growing mass in the ring. In both cases the stellar bar should weaken as the supporting $x_1$ family of orbits are destroyed or depopulated. However, the ring has a relatively small effect on the interior orbits, and so we expect that the dissolution of the bar should mainly proceed at and exterior to the ILR resonance region. We speculate, that the observed difference between stellar bars in early and late-type disk galaxies (Elmegreen and Elmegreen 1989) may have its origin in the secular dissolution of the $x_1$ family of orbits beyond the ILR(s). Another example which is relevant to this discussion and was studied by us in detail using high-resolution NIR imaging is M100 (=NGC~4321), a nuclear starburst galaxy of intermediate type SABbc (Knapen etal. \\markcite{kna95a}\\markcite{kna95b} 1995a,b). This galaxy exhibits all the virtues of a double ILR with a nuclear ring. It possesses a 6 kpc semimajor axis stellar bar, bissected by a weakly oval NIR nuclear ring whose inner boundary, at the inferred position of the inner ILR, is clearly delineated by an incomplete ring of star formation. If NIR isophote ellipse fitting provides a reliable measure of the strength of the barred potential, we measure the maximal ellipticity exterior to the ring to be approximately 20\\% lower than the maximal ellipticity interior to the ring. It is very interesting, that its NIR isophote twist is similar to that of Fig. 10 (see also Fig. 11). Two more examples supporting our conjecture that nuclear rings weaken mainly the large-scale bars are NGC~4274 and NGC~4643 (Shaw etal. \\markcite{sha95} 1995), whose nuclear barlike features have higher ellipticities than their primary bars. A crude estimate from our model shows that the linearly growing radius of the outer radial ILR will reach the size of the semi-minor axis of the bar when the mass in the ring is approaching $\\sim10^{10}\\,M_{\\sun}$, a value which is comparable to typical masses of galactic bulges. Evidently, the stellar bar cannot extend to the corotation in this case. Of course, the above model lacks self-consistency in the sense that the orbit analysis is performed in the static potentials of a galaxy and stellar bar. In reality, the stellar bar potential would adjust itself to the loss of the main supporting orbits and the dissolution process would be accelerated, lowering the mass required for bar destruction between the ILRs and the corotation. How relevant is the above analysis for the gas evolution in the barred region? Periodic orbits do not exactly correspond to the gas orbits in a galactic potential, mainly due to our neglect of pressure forces. However, by virtue of being the most stable orbits, they can trap gas if the latter is only weakly dissipative. We find that the $x_1$ periodic orbits of different Jacobi energy in our models begin to intersect in the vicinity of a ring when its mass provides a sufficient perturbation to the background potential. The $x_2$ orbits start to intersect later-on, when the ring becomes even more massive. This difference in the behavior of $x_1$ and $x_2$ orbits happens because the latter are more rounded than the $x_1$ orbits (see Section 4.1) and must be perturbed stronger in order to overlap. We estimate roughly that this occurs when the mass in the ring approaches $\\sim10\\%- 20\\%$ of the mass interior to the ring, and so the self-gravity in the gas cannot be neglected. The above estimate agrees favorably with the results of $N$-body simulations (Wada and Habe \\markcite{wad92} 1992; Heller and Shlosman \\markcite{hel94} 1994; Knapen etal. \\markcite{kna95a} 1995a). Such intersecting orbits will be quickly depopulated by the gas in a steady state flow which can only move to orbits deeper in the potential well. An even stronger effect on the gas is expected in the model with an oblique ring (model F). Here the $x_1$ orbits experience a large-angle rotation with respect to the bar due to the double forcing from the bar and the ring. Such rotations would almost certainly lead to the intersection between $x_1$ orbits, which exterior to the ring, have fairly eccentric shapes. Stars populating these orbits would contribute to the twisting of isophotes, such as observed in the NIR, in a number of nuclear starburst galaxies (Shaw etal. 1993; Knapen etal. 1995b). If the gas populates these orbits, it will quickly lose angular momentum in shocks and will fall through towards the nonintersecting $x_2$ orbits (if such exist), where it is expected to accumulate. Knapen etal. \\markcite{kna95a}(1995a) found that subsequent evolution of this gas depends crucially on its self-gravity, which acts roughly as a surface tension. It causes the gaseous ring to contract by shifting to lower energy $x_2$ orbits and ultimately shrinking across the inner ILR towards the interior non-intersecting $x_1$ orbits. Hence, oblique nuclear rings represent transient phenomena. Their characteristic time scales of $\\sim10^8-10^9$ yrs and their potentially recurrent nature make them important when studying gas and stellar dynamics of galactic interiors. Stability of accumulating gas in the ring, with its self-gravity increasingly dominating the local dynamics, is an important issue. Simulations of such gaseous rings support the above arguments and are capable of following the gas evolution into the nonlinear regime. Knapen etal. \\markcite{kna95a} (1995a) observed the accumulation of gas at the inner ILR and the beginning of its subsequent collapse to the center. This instability is clearly dynamical, but its growth and the final outcome depends on the efficiency of star formation and the fraction of the released stellar energy (winds and supernovae) which is radiated away by the ISM. Clearly, this phase of evolution in barred galaxies is closely related to their circumnuclear activity and deserves further study. An intriguing possibility is that the gas accumulated in the nuclear rings becomes dynamically unstable by decoupling from the background gravitational potential, leading to a runaway instability and dumping some of this material much closer to the center (Shlosman, Frank and Begelman \\markcite{shl89} 1989). In summary, we have analyzed the main periodic orbits in a barred galaxy perturbed by a massive ring positioned in the inner resonance region, in the vicinity of a double ILR. In some respects, the effect of the ring is similar to that of a central spherically-symmetric mass concentration studied earlier in the literature, such as the secular evolution of the stellar bar. However, a number of profound differences exist. In particular, we find that the orbits affected most are those exterior to the ring, leading to the weakening and ultimate dissolution of the large-scale bar, while the part of the bar interior to the ring and to the ILRs remain stable. It remains to be seen how the proposed evolution of bar length fits the observed difference in bar properties between early and late-type disk galaxies. We also find that oblique rings are capable of inducing an azimuthal twist in the main periodic orbits supporting the stellar bar, similar to that observed in the NIR in some nuclear starburst galaxies. Overall, gas evolution in the vicinity of nuclear rings is accelerated due an increasing number of intersecting orbits there. This underlines the crucial role that self-gravity in the gas plays in driving the circumnuclear activity in barred galaxies." }, "9605/astro-ph9605066_arXiv.txt": { "abstract": "We calculate the ``seeing'' effect on distant sources due to a gravitational wave background. We derive the limit in strain and energy density of the gravitational wave based on the limit of detectability of this effect with the present day telescope resolution. We also compare our detection limit to those obtained from existing methods. ", "introduction": "The generation of gravitational waves is believed to be an ongoing process in the evolution of the universe. Presently, aspherical supernovae and the merger of compact binaries are probably the two most common (or at least prosaic) important sources of gravitational waves. Gravity waves may also have been copiously produced in the early universe and would probably have led to a nearly homogeneous and isotropic background of gravity waves. The most well-motivated model predicting a gravitational wave background from the early universe is inflation (Grishchuk; Ford and Parker; Starobinsky; Rubakov, Sahin and Veryaskin; Fabbri and Pollock; Abbot and Wise; Starobinsky; Abbot and Shaefer; Abbot and Harari; Allen; Ressel and Turner; Sahni; Souradeep and Sahni; Liddle and Lyth; Davis et al.; Salopek; Lucchin, Matarrese and Mollerach; Dolgov and Silk; Turner; Crittenden et. al.; Harari and Zaldarriaga; Crittenden, Davis and Steinhardt; Ng and Ng; Krauss \\& White; White; White, Krauss and Silk; Bond et. al.; Grischuk; Falk, Rangaranjan and Srednicki; Luo and Schramm; Srednicki). The effect of this gravitational wave background on pulsar timing measurements has already been investigated (Bertotti {\\it et al.} 1983). It has been also been studied in the context of the cosmic microwave background radiation when computing the Sachs-Wolfe contribution (Krauss \\& White 1992; Davis {\\it et al.} 1992) and the polarization of the radiation (Polnarev 1985; Crittenden {\\it et al.} 1993). Fakir (1993) has shown how individual gravity waves bend lightlike geodesics. For distant objects such as quasars, one therefore expects the gravitational wave background to perturb the light coming to us and distort the image, creating a ``seeing'' effect. The detection (or non-detection) of this effect provides us with an important additional constraint on models predicting the existence of a gravitational wave background. We present in the following sections a calculation of the expected deviation of light rays due to a gravitational wave background. We begin by recalculating the null geodesic deviation due to a single gravitational wave. We proceed to derive the expected RMS deviation, with the deviation modeled as a random walk in three-dimensional space. We use that to put an upper limit on the dimensionless strain, $h$, and on the ratio, $\\Omega_g$, of energy density in the gravitational wave background to the critical energy density required to close the universe. This calculation is valid only if the dimension of the source is larger than the wavelength of the gravitational wave. ", "conclusions": "" }, "9605/astro-ph9605030_arXiv.txt": { "abstract": "The microlensing probability (optical depth $\\tau$) toward the Galactic center carries information about the mass distribution of the Galactic bulge/bar, so can be used to constrain the very uncertain shape parameters of the Galactic bar. In this paper we study a family of bar models with tunable triaxiality, boxyness and radial profile to span the range of plausible density models of the Galactic bar. It also includes four models that were used to fit to the COBE maps by Dwek et al (1995). We find the optical depth on the minor axis of the whole family of models and in special cases the whole microlensing map of the bulge/bar are given by simple analytical formulae. The formulae show the following dependence of the optical depth on the bar mass, radial profile, angle, axis scale lengths and boxyness. (1) $\\tau$ is proportional to the mass of the bar, $M$. (2) $\\tau$ falls along the minor axis with a gradient determined by the density profile and boxyness of the bar. (3) Going from an oblate bulge to a triaxial bar, the optical depth increases only if $\\alpha<45^\\circ$, where $\\alpha$ is the angle between the bar's major axis and our line of sight to the center. (4) Among bars with different degree of triaxiality, $\\tau$ is the largest when the bar axis ratio ${y_0 \\over x_0} =\\tan \\alpha$, where $y_0, x_0$ are the bar scale lengthes on the short and long axes in the Galactic plane respectively. (5) At a fixed field on the minor axis but away from the center, boxy bars with a flat density profile tend to give a larger optical depth than ellipsoidal bars with a steep profile. (6) Main sequence sources should have a significantly lower (20-50\\% lower) optical depth than red clump giants if main sequence stars are not observed as deep as the bright clump giants. For the four COBE-constrained models, the optical depths contributed by the bar is in the range of $\\approx (0.3-2.2) \\times 10^{-6} M/(2 \\times 10^{10} M_\\odot)$ at Baade window. Out of the four models, only the model with a Gaussian profile and ellipsoidal shape satisfies the observational constraint, the other three models produce optical depths which are inconsistent or marginally consistent with the $2\\sigma$ lower limit of the observed optical depths, even if we adopt both a massive bar $2.8\\times 10^{10} M_\\odot$ and a full disk. Independent of the COBE map, we find that the microlensing models can potentially provide constraints on the mass distribution. If increasing microlensing statistics confirm the high optical depth, $\\approx 3\\times 10^{-6}$, presently observed by the MACHO and OGLE collaborations, then the observation argues for a massive ($\\ge 2\\times 10^{10}M_\\odot$) boxy bar with axis ratio ${y_0 \\over x_0} \\approx \\tan(\\alpha)$ and $\\alpha \\le 20^\\circ$ and with a flat radial profile up to corotation. Stronger limits on the bar parameters can be derived within two years when the sample is increased from the current fifty events to about two hundred events. ", "introduction": "Microlensing surveys such as the MACHO (Alcock et al. 1993, 1995a, b), OGLE (Udalski et al. 1993, 1994), EROS (Aubourg et al. 1993) and DUO (Alard et al. 1995) collaborations have discovered more than 100 microlensing events toward the Galactic bulge and about 10 events toward the LMC. One of the many exciting discoveries (see Paczy\\'nski 1996 for a review) is the surprisingly high optical depth, $\\tau$, i.e., microlensing probability, toward the Galactic centre (Udalski et al. 1994; Alcock et al. 1995b). The OGLE collaboration found $\\tau_{-6} \\equiv \\tau/10^{-6}=(3.3 \\pm 2.4)$ ($2\\sigma$ error bar) based on 9 events and the MACHO collaboration found $\\tau_{-6}=2.43 ^{+0.9}_{-0.74}$ ($2\\sigma$) based on the full sample of 41 events and $\\tau_{-6} = 6.32^{+6}_{-3.57}$ ($2\\sigma$) for 10 low latitude clump giants. This is clearly in excess of all the predictions prior to the discovery of microlensing events (Kiraga \\& Paczy\\'nski 1994a). Both a maximum disk (Gould 1994a, Alcock et al. 1995b) and a Galactic bar oriented roughly toward us (Paczy\\'nski et al. 1994a; Zhao, Spergel \\& Rich 1995, Zhao, Rich \\& Spergel 1996, hereafter ZSR95, ZRS96) have been proposed as an explanation. The latter interpretation is favored by other lines of evidence, such as the non-circular motion of gas in the inner Galaxy (Binney et al. 1991; Blitz \\& Spergel 1991), the asymmetric and boxy COBE map (Weiland et al. 1995) and that the clump giants appear brighter at one side ($l>0^\\circ$) than the other side ($l<0^\\circ$) of the bulge (Stanek et al. 1994). A Galactic bar, together with a normal disk, can produce an optical depth $\\tau_{-6} \\approx 2.5$ (ZSR95, ZRS96). This value is in good agreement with the OGLE and the MACHO full sample values, but seems to be at the $2\\sigma$ lower limit of that for the 10 low latitude clump giants in the MACHO sample. The theoretical prediction depends on the still uncertain bar axial ratio, orientation and mass profile; Dwek et al. (1995) found that several bar volume density models are consistent with the COBE map. Given these uncertainties, what is the range of the predicted optical depth? What are the optimal bar configurations that can produce an optical depth as high as $\\tau_{-6}=6$? Can the Galactic microlensing observations put constraints on the bar parameters? These are the main questions we want to address in the paper. We demonstrate that the published optical depth based on about 10 microlensing events with red clump giants as sources already put interesting constraints on the orientation, axial ratio and boxyness of the bar. With steadily increasing number of events and decreasing error bar for the optical depth, microlensing will become a very powerful tool to probe the Galactic structure. The outline of the paper is as follows. In \\S 2, we study a family of models for the bar density distribution, which includes many models used in the literature. We derive an analytical expression of their optical depths on the minor axis and for ellipsoidal bars the whole microlensing map on the sky as well. In \\S 3, we apply our formalism to the Galactic bar, and compare the results with the observations. We summarize our results and discuss the implications in \\S 4. More mathematical details are given in the appendices and at the end of Appendix C some instructions of using our formulae. ", "conclusions": "We have evaluated the optical depths for a family of bar models. The analytical formulae developed are applicable to both the bulge clump giants and the main sequence stars. We have studied the dependence of the optical depth on the bar parameters. With about 50 microlensing events, we have demonstrated that microlensing already provides interesting constraints on the bar models. For example, the COBE constrained power-law ellipsoidal (PE) model produces an optical depth just too small to be consistent with the observed optical depths, primarily due to the large bar angle, $\\alpha \\approx 45^\\circ$. The axisymmetric oblate bulge model is also only marginally compatible with the observation. The Gaussian ellipsoidal (GE) model clearly best reproduces the observation. It can produce $\\tau_{-6}=6$ if the Galactic bar is very massive ($M=2.8\\times 10^{10} M_\\odot$) and the disk contribution is $\\tau_{\\mathrm{disk},-6}=1$. We believe that the truncated boxy (TB) model is also a viable model. It is therefore desirable to constrain the parameters for this kind of finite truncated bar using the COBE map. From our comparison of the optimal optical depths with the observations, we found the high optical depth already suggests a less than $20^\\circ$ angle between the long axis of the bar and our line of sight to the Galactic centre, and that the axis ratio of the bar is close to the optimal (cf. Fig. 5 and 6). In our comparison between the prediction and the observation, we have neglected a central nucleus and the dependence of $\\tau$ on the longitude. The longitude dependence in general reduces the optical depth. But as the mean longitude of the MACHO and OGLE fields are quite small, $l \\le 2.5^\\circ$, which corresponds to approximately 375 pc, the reduction is about 20\\% for the power-law ellipsoidal (PE) model and only about 10\\% for all the other models. In our Galactic bar models, the density profiles are flat near the Galactic centre, while a nucleus has long been observed in the infrared (Becklin \\& Neugebauer 1968). But since the MACHO and OGLE fields are all offset by more than $2^\\circ$ from the centre, a nucleus within $2^\\circ-3^\\circ$ of the Galactic centre does not affect the microlensing prediction directly except that the nucleus contributes to the dynamical mass within 3 kpc. Including a nucleus would reduce the predicted optical depth outside the nucleus. But we estimate that the mass of the nucleus inside $2^\\circ$ is only about 5\\% of the total bar mass, much smaller than the uncertainty in the bar and disk mass. So the nucleus can be neglected for predicting optical depth at any field a few degrees ($\\ga 3^\\circ$) away from the Galactic centre. In this study, we have used the MACHO and OGLE samples (Alcock et al. 1995b; Udalski et al. 1994). The number of analysed events (50) is still very limited, therefore the errorbars of the inferred optical depths are still quite large. The subsample of (13) clump giant events that we used has even larger errorbars. In addition, some of the long events in the MACHO sample are not well understood and these contribute about 1/3 of the optical depth (Han \\& Gould 1996). Therefore the current limits on the optical depth have to be interpreted with some caution. Fortunately, the number of events detected toward the Galactic bulge is increasing rapidly with time. In two years, the number of (analysed) microlensing events is likely to increase by four-fold. It will then become feasible to analyse the whole microlensing map of a large fraction of the bulge. If on the order of one hundred events are obtained at two or three low extinction fields close to the minor axis, e.g., the Sgr I field $(1.4^\\circ, -2.6^\\circ)$ and Baade window $(1^\\circ, -3.9^\\circ)$, then we can measure the gradient for the optical depth, which we can use to distinguish bar models with different minor axis profile and boxyness (cf. Fig. 3). If the optical depth remains high, then tighter limits on the bar parameters can be derived (cf. Figs. 5 and 6). By combining the microlensing map with the event duration distributions, it seems possible to disentangle the relative contributions of the disk and the bar. Furthermore, a comprehensive study combining the information in the gas, stellar kinematics, COBE map and microlensing surveys should provide precise values on all the bar parameters. We conclude that microlensing has become a promising and unique tool in probing the Galactic structures. This project is partly supported by the ``Sonderforschungsbereich 375-95 f\\\"ur Astro-Teilchenphysik'' der Deutschen Forschungsgemeinschaft. We thank Peter Schneider for comments on the paper. \\appendix" }, "9605/hep-ph9605325_arXiv.txt": { "abstract": "{\\rm We investigate the cosmological constraints on exotic stable matter states which arise in realistic free fermionic superstring models. These states appear in the superstring models due to a ``Wilson--line'' breaking of the unifying non--Abelian gauge symmetry. In the models that we consider the unifying $SO(10)$ gauge symmetry is broken at the string level to $SO(6)\\times SO(4)$, $SU(5)\\times U(1)$ or $SU(3)\\times SU(2)\\times U(1)^2$. The exotic matter states are classified according to the patterns of the $SO(10)$ symmetry breaking. In $SO(6)\\times SO(4)$ and $SU(5)\\times U(1)$ type models one obtains fractionally charged states with $Q_{\\rm e.m.}=\\pm1/2$. In $SU(3)\\times SU(2)\\times U(1)^2$ type models one also obtains states with the regular charges under the Standard Model gauge group but with ``fractional'' charges under the $U(1)_{Z^\\prime}$ symmetry. These states include down--like color triplets and electroweak doublets, as well as states which are Standard Model singlets. By analyzing the renormalizable and nonrenormalizable terms of the superpotential in a specific superstring model, we show that these exotic states can be stable. We investigate the cosmological constraints on the masses and relic density of the exotic states. We propose that, while the abundance and the masses of the fractionally charged states are highly constrained, the Standard Model -- like states, and in particular the Standard Model singlet, are good dark matter candidates. } ", "introduction": "Superstring theories \\cite{Sreviews} are believed to provide a consistent framework for the unification of gravity with the gauge interactions. An important task is to connect superstring theory with the Standard Model \\cite{heterotic,CHSW}. Several approaches may be pursued to derive the Standard Model from superstring theory. One possibility is to go through a simple \\cite{simple} or a semi--simple \\cite{semisimple,revamp,ALR,FSU,LNY} unifying gauge group at intermediate energy scale. Another is to derive the Standard Model directly from superstring theory \\cite{ssm,fny,eu,SLM,custodial}. Proton lifetime considerations motivate the hypothesis that the Standard Model must be obtained directly from superstring theory \\cite{DTSMo,DTSMm}. A second important question is whether there exist some property of superstring models that will distinguish them from other attempts to understand the origin of the Standard Model. If such a property exists it may result in an experimental signal that can prove or disprove the validity of superstring unification. In this paper we explore one such possible signature of superstring unification. We argue that realistic superstring models produce additional heavy stable matter, beyond the spectrum of the Standard Model. The specific matter states and their properties vary between models. However, the existence of additional stable matter, beyond the observed spectrum of the Standard Model, is generic. One type of such generic states in superstring models are of course the moduli fields. Indeed, it as been argued that because of the absence of superpotential for the moduli fields, they will decouple at a very early stage in the evolution of the universe and will overclose the universe \\cite{modcos}. However, in the class of models that we study, it has been suggested that all the moduli (except, of course, the dilaton) are projected out by the GSO projections \\cite{halyo}. Thus, these models the cosmological moduli problem can be resolved. The matter states that we study in this paper arise due to the superstringy breaking of the unifying gauge symmetry. We investigate the possibility that these stringy stable matter states can be the dark matter and can perhaps be detected. In the attempts to derive the Standard Model from superstring theory one traditionally starts with a larger, unifying, gauge symmetry $G$. The gauge symmetry is then broken to the Standard Model by means of Wilson lines. In many respects the unifying gauge symmetry $G$ is similar to the gauge group of four dimensional grand unification and the Wilson lines are similar to the Higgs bosons in the adjoint representation. However, there are some notable differences. The eigenvalues of the Wilson lines are quantized while the eigenvalues of the Higgs in the adjoint representation are continuous. Another important difference is that the breaking of the gauge symmetries by Wilson lines results in massless states that do not fit into multiplets of the original unbroken gauge symmetry. We refer to such states generically as exotic ``Wilsonian'' matter states. This is an important property as it may result in conserved quantum numbers that will indicate the stability of these massless ``Wilsonian'' states. The simplest example of this phenomenon is the existence of states with fractional electric charge in the massless spectrum of superstring models \\cite{ww,eln,huet,fcp}. Such states are stable due to electric charge conservation. As there exist strong constraints on their masses and abundance, states with fractional electric charge must be diluted away or extremely massive. Remarkably, however, the same ``Wilson line'' breaking mechanism, which produces matter with fractional electric charge, is also responsible for the existence of states which carry the ``standard'' charges under the Standard Model gauge group but which carry fractional charges under a different subgroup of the unifying gauge group. For example, if the group $G$ is $SO(10)$ then the ``Wilsonian'' states carry non--standard charges under the $U(1)_{Z^\\prime}$ symmetry, which is embedded in $SO(10)$ and is orthogonal to $U(1)_Y$. Such states can therefore be stable if the $U(1)_{Z^\\prime}$ gauge symmetry remains unbroken down to low energies, or if some residual local discrete symmetry is left unbroken after the $U(1)_{Z^\\prime}$ symmetry breaking. In this paper we propose that the existence of heavy stable ``Wilsonian'' matter may be the ``smoking gun'' of string unification. The existence of stable ``Wilsonian'' states at intermediate energy scale have important cosmological implications. In a previous letter \\cite{letter} we examined the possibility that one type of the extra ``Wilsonian'' states constitute the dark matter of the universe. These states consist of heavy down--like quark with the standard down--like charge assignment. Due to its role in the string unification we referred to this type of particle as the {\\it uniton}. We proposed that because of its ``fractional'' charge under the $U(1)_{Z^\\prime}$ symmetry, the uniton may be stable. In this paper we extend the analysis of ref. \\cite{letter}. We discuss in detail the cosmological constraints on the existence of heavy ``Wilsonian'' states. We provide the details of the analysis of ref. \\cite{letter} and extend our investigation to other exotic matter states which appear in the realistic superstring derived models. In the superstring models that we consider the unifying gauge symmetry is $SO(10)$. The $SO(10)$ symmetry is broken at the string level to $SO(6)\\times SO(4)$, $SU(5)\\times U(1)$ or $SU(3)\\times SU(2)\\times U(1)^2$. We classify the exotic ``Wilsonian'' matter states according to the pattern of the $SO(10)$ symmetry breaking. The $SO(6)\\times SO(4)$ and $SU(5)\\times U(1)$ type models give rise to fractionally charged states with $Q_{\\rm e.m.}=\\pm1/2$. On the other hand, the $SU(3)\\times SU(2)\\times U(1)^2$ type models produce in addition states with the regular charges under the Standard Model gauge group but with ``fractional'' charges under the $U(1)_{Z^\\prime}$ gauge group. These states include down--like color triplets and electroweak doublets, as well as states which are Standard Model singlets. We show, by analyzing the renormalizable and nonrenormalizable terms of the superpotential in a specific superstring model, that these exotic states can be stable. We investigate the cosmological constraints on the masses and relic density of the exotic states. We propose that, while the abundance and the masses of the fractionally charged states are highly constrained, the Standard Model -- like states, and in particular the Standard Model singlet, are possible candidates for the dark matter. The exotic ``Wilsonian'' matter states that we study in this paper are divided into three distinct classes: The first class consists of down--like color triplets with ``fractional'' charge under the $U(1)_{Z^\\prime}$ symmetry. The existence of such a heavy colored state is motivated from the constraints arising from string gauge coupling unification \\cite{DF}. In a specific superstring model we analyze the interaction terms of this colored triplets with the Standard Model states. In that model we show that if we assume that an hidden $SU(3)_H$ gauge group remains unbroken then all the interaction terms in the superpotential vanish to any order of nonrenormalizable terms. This result arises due to the fractional $U(1)_{Z^\\prime}$ of the color ``Wilsonian'' triplets and because in the specific string model which we analyze in detail the only other Standard Model singlet states which carry fractional $U(1)_{Z^\\prime}$ charge are triplets of $SU(3)_H$. Thus, we argue that the ``Wilsonian'' states can arise as stable states. We then proceed to analyze the constraints on the relic density of stable heavy color triplets. The heavy color triplets can annihilate into quarks, squarks, gluons and gluinos. We examine the possibility that the heavy color down--like triplets are the dark matter. The heavy stable down--like states form charged and neutral meson bound states with the up and down quarks, respectively. An important issue in this regard is the mass splitting between the charged and neutral meson states. We argue that with our present understanding of QCD, and the experimental determination of the light quark masses, there exists a region in the parameter space in which the neutral heavy meson state is the neutral one. Next we examine the constraints on the relic density of fractionally charged states, with electric charge $\\pm1/2$. We show that generically these states either have to be super massive or have to be inflated away. We demonstrate in one specific model that all the fractionally charged states have a cubic level mass term. Thus, all the fractionally charged states can decouple from the massless spectrum by some choices of flat directions. An alternative is that all the fractionally charged states are confined by some non--Abelian gauge group in the hidden sector. Another novel feature that arises in some string models is the appearance of fractionally charged baryons and fractionally charged leptons. Thus, one can speculate that the these baryons and leptons will continue to scatter in the early universe until they coalesce to form neutral heavy hydrogen--like atoms. The final class of ``Wilsonian'' states that we consider are Standard Model singlets with fractional $U(1)_{Z^\\prime}$ charge. These type of states arise in the superstring derived standard--like models and interact with the Standard Model states only via the $U(1)_{Z^\\prime}$ gauge boson and are candidates for weakly interacting dark matter (WIMPs). We examine four possible scenarios: with and without inflation and with the $U(1)_{Z^\\prime}$ gauge boson being heavier or lighter than the ``Wilsonian''--singlet states. We propose that this Standard Model singlet states is the most likely candidate for the dark matter in the superstring models. Our paper is organized as follows. In section two we review the realistic free fermionic superstring models. In section three we describe the exotic ``Wilsonian'' states and classify them according to the patterns of the $SO(10)$ symmetry breaking. In section four we examine the cosmological constraints on the different classes of ``Wilsonian'' matter states which are obtained from the superstring models. In section five we present our conclusions. Our discussion of the mass difference in the heavy meson system are given in appendix A. The details of the calculation of the annihilation cross sections are give in appendix B. \\setcounter{footnote}{0} ", "conclusions": "In this paper we studied the cosmological constraints on the exotic matter states that appear in the massless spectrum of realistic free fermionic superstring models. The free fermionic superstring models are among the most realistic string models constructed to date, and reproduce many of the observed properties of the Standard Model. Among those, the replication of three and only three families and the qualitative spectrum of fermion masses \\cite{TOP,CKM}. The realistic nature of the free fermionic models is perhaps not accidental but may reflect deeper properties of string compactification, which are at present unknown. Indeed, the free fermionic models are constructed at a highly symmetric point in the moduli space and the appearance of three generations is deeply rooted in the underlying $Z_2\\times Z_2$ orbifold structure \\cite{foc}. In the derivation of the Standard Model from superstring theory we start with some larger symmetry which is subsequently broken to the Standard Model. Absence of adjoint representations in the massless spectrum of level one Kac--Moody algebras restricts the possible gauge groups in the effective low energy field theory. Furthermore, proton lifetime constraints motivate the hypothesis that the Standard Model must be derived directly from string theory, without an intermediate non--Abelian gauge symmetry. Within the free fermionic construction the breaking is achieved by constructing boundary condition basis vectors which are equivalent to Wilson lines in the geometrical formulation. The use of Wilson lines to break the non--Abelian gauge symmetries is quite generic in superstring theory. The breaking of the non--Abelian gauge symmetries by Wilson lines has an important feature: it produces matter representations that do not fit into multiplets of the original unbroken gauge symmetry. This is an important feature as it may result in local discrete symmetries that forbid the decay of the ``Wilsonian'' matter states into the lighter Standard Model particles. Superstring models thus provide an intrinsic mechanism that produces heavy stable states. The ``Wilsonian'' matter states are classified by the patterns of symmetry breaking, induced by the ``Wilson'' lines. In the free fermionic models the underlying $SO(10)$ gauge symmetry is broken to $SO(6)\\times SO(4)$, $SU(5)\\times U(1)$ or $SU(3)\\times SU(2)\\times U(1)^2$. All three cases give rise to fractionally charged states with $Q_{\\rm e.m.}$. These states may all be confined, they may all be superheavy, or they may diluted by inflation. Nevertheless, it may be worthwhile to search for such states in experimental searches for rare matter. Of further interests are the exotic states which appear specifically when the symmetry is broken directly to the Standard Model. The ``Wilsonian'' sectors then contain also states which carry the Standard Model charges, but with fractional charge under the $U(1)_{Z^\\prime}$ symmetry. We have shown, in a specific model, that these states can, in fact, be stable. This is an exciting observation, for then the stable ``Wilsonian'' matter states can be natural dark matter candidates. Furthermore, their stability arises due to a well motivated local discrete symmetry \\cite{KW}. The superstring derived standard--like models give rise to ``Wilsonian'' color triplets, electroweak doublets with the standard charge assignment, and to Standard Model singlets. Of those the Standard Model singlets are the most suited to be the dark matter. The appearance of a good dark matter candidate in the superstring derived standard--like models provides further motivation to focus on the phenomenology of this class of models. Although our analysis and results are limited to the models in the free fermionic formulation, the mechanism which gives rise to the ``Wilsonian'' matter states is generic in superstring models. Thus, exotic ``Wilsonian'' matter states may be the generic, long--sought, signature of string unification. It is of further interest to study other phenomenological properties of these states. Such questions are currently under investigation and will be reported in future publications." }, "9605/hep-ph9605277_arXiv.txt": { "abstract": "We study the full out-of-thermal-equilibrium dynamics of a relativistic classical scalar field through a symmetry breaking phase transition. In these circumstances we determine the evolution of the ensemble averages of the correlation length and topological defect densities. This clarifies many aspects of the non-perturbative dynamics of fields in symmetry breaking phase transitions and allows us to comment on a quantitative basis on the canonical pictures for topological defect formation and evolution. We also compare these results to those obtained from the field evolution in the Hartree approximation or using the linearized theory. By doing so we conclude about the regimes of validity of these approximations. ", "introduction": "\\label{s1} The formation of topological defects is a general consequence of symmetry breaking phase transitions in field theories with a topologically non-trivial vacuum manifold, both in the early Universe \\cite{Kib,Book}, and in a number of materials in the laboratory \\cite{ZurekReview,Helium4,Helium3,liqcrys}. To date predictions of the number and distributions of defects formed in these circumstances has relied on very simplistic heuristic models where some qualitative aspects of the phase transition are invoked but where all dynamics is sacrificed \\cite{VV}. These are at the basis of large scale simulations of defect networks subsequently used to generate the energy density perturbations responsible for the formation of structure in the Universe \\cite{Struc}. Recently, considerable effort has been devoted to the development of more realistic methods to follow the approximate evolution of relativistic field theories in out of equilibrium settings \\cite{quench,non-eq,LA} and, in this context, to account for the number of defects formed \\cite{Ray} at a symmetry breaking transition. In this paper we perform the first complete fully non-linear dynamical study of a relativistic classical theory out of thermal equilibrium in a symmetry breaking phase transition. We compute the time evolution of many quantities of interest, such as the correlation length and the defect densities as well as their dependence on the choice of initial conditions and on the presence of external dissipation. We then compare these results to other approaches found recently in the literature. We will show by explicit computation of the time evolution for the zero densities of our field in well specified and illustrative circumstances that both the Hartree approximation and the linearized theory have different merits in approximating the full classical evolution. By virtue of this comparison we also learn, in a quantitave manner, when they fail and consequently about the regimes of their applicability. The results of this paper raise many extremely interesting new questions concerning the non-perturbative dynamics of relativistic fields away from thermal equilibrium. Our present methods rely heavily on the usage of extensive computational facilities. Rather than openly trying to tackle some of these new issues the intention of the presentation below will be a more modest one, openly restricted in its character to that of reporting on the finds of a numerical experiment. A more analytical approach must be sought in order to complete our understanding, though, and it is our intention to expand on our attempts in forthcoming publications. Nevertheless, we believe the present results constitute considerable quantitave progress on the usual canonical qualitative pictures of defect formation and evolution. This paper is organized as follows. In section \\ref{s2} we describe the theoretical background for the field evolution. We discuss the field equations for the full classical evolution, in the presence of external dissipation, and our choice of initial conditions, which for consistency we choose to follow a classical Boltzmann distribution. We then describe two approximation schemes to the classical evolution, namely the Hartree approximation and the linearized theory. In the latter case we present the exact analytical evolution and Halperin's formula for the zero densities of the scalar field in a Gaussian theory. We finish this section by briefly describing our numerical procedure for the full classical evolution and the computation of approximate statistical ensemble-averaged quantities. In section \\ref{s3} we present our results. We show the fully non-equilibrium evolution of the scalar field correlation length as well as its zero and defect densities. We show explicitly that the latter can be counted at a given sensible field coarse-graining scale, independently of the necessary ultra-violet cut-off of our implementation. We also discuss the dependence of these results on our choice of initial conditions. We then proceed to compare these zero densities to those obtained from the Hartree approximation and the linearized theory, and to draw conclusions about the regimes of their applicability. Finally we present the evolution of the defect densities per correlation volume and seek to relate our results to the qualitative canonical arguments for defect formation and long time evolution: the Kibble mechanism and scaling conjectures. In section \\ref{s4} we summarize our most important results, present our conclusions and point to questions raised by the present work we intend to study in the near future. ", "conclusions": "\\label{s4} We presented a detailed study of the non-equilibrium dynamics of a classical scalar field theory in a symmetry breaking phase transition. In doing so we were able to probe regimes of field evolution where perturbation theory breaks down and extract conclusions about the detailed correlation length and topological defect density evolution. We showed that after an instantaneous quench a field develops momentary instabilities responsible for the growth of its amplitude during which the evolution is approximately linear, and on a later stage when stability around the true minimum is found evolves, in a period of re-heating very similar to that of inflationary scenarios. During this later stage the evolution proceeds in a strongly non-linear fashion so as to redistribute energy among all scales. We showed the effect of external dissipation in the evolution and established evidence for the independence of defect densities per correlation length on the choice of initial conditions as well as their approach to a scaling regime for large times. In passing we confronted the predictions of the Kibble mechanism to our results and discussed the effect of the external dissipation on the asymptotic defect densities. We have also shown the comparison between the zero densities given by the full classical evolution and the predictions from the linearized theory and the Hartree approximations thus clarifying when these approximate schemes are valid. Finally we believe that the present work raises many new important questions about the evolution of relativistic fields away from thermal equilibrium. We are presently investigating the effect of an expanding background on topological defect production and evolution, in higher spatial dimensions, and studying the details of the energy redistribution during the phase transition. Both these subjects have important cosmological applications to the role of topological defects as the seeding mechanism for the formation of structure in the Universe and the theory of re-heating after a period of inflationary expansion." }, "9605/astro-ph9605097_arXiv.txt": { "abstract": "} \\newcommand{\\eab}{ ", "introduction": " ", "conclusions": "" }, "9605/hep-ph9605382_arXiv.txt": { "abstract": "We investigate the cosmological consequences of particle physics theories that admit stable loops of superconducting cosmic string - {\\it vortons}. General symmetry breaking schemes are considered, in which strings are formed at one energy scale and subsequently become superconducting in a secondary phase transition at what may be a considerably lower energy scale. We estimate the abundances of the ensuing vortons, and thereby derive constraints on the relevant particle physics models from cosmological observations. These constraints significantly restrict the category of admissible Grand Unified theories, but are quite compatible with recently proposed effects whereby superconducting strings may have been formed close to the electroweak phase transition. ", "introduction": "\\label{sec:1} In the past few years it has become clear that topological defects produced in the early universe may have a considerably richer microstructure than had previously been imagined\\cite{sym rest}. In particular, the core of a defect acquires additional features at each subsequent symmetry breaking which preserves the topology of the object. The new microphysics associated with additional core structure has been exploited by several authors to provide a new, defect-based scenario for electroweak baryogenesis\\cite{{BDT},{DMEWBG}}. The purpose of the present paper is to constrain general particle physics theories by demanding that the microphysics of defects in these models be consistent with the requirements of the standard cosmology. The basic idea, due originally to Davis and Shellard\\cite{{D&S},{D&S 89},{V&S}}, is as follows. If a spontaneously broken field theory admits linear topological defects - {\\it cosmic strings} - which subsequently become superconducting, then an initially weak current on a closed string loop will automatically tend to amplify as the loop undergoes dissipative contraction. This current may become sufficiently strong to modify the dynamics and halt the contraction so that the loop settles down in an equilibrium state known as a {\\it vorton}. The population of vorton states produced by such a mechanism is tightly constrained by empirical cosmological considerations. It was first pointed out by Davis and Shellard that to avoid obtaining a present day cosmological closure factor $\\Om$ greatly exceeding unity, any theory giving rise to stable vorton creation by superconductivity that sets in during string formation is ruled out if the symmetry breaking scale is above some critical value. One of the first attempts to estimate this critical scale\\cite{C} indicated that it probably could not exceed that of electroweak symmetry breaking at about $10^2 \\GeV$ by more than a few orders of magnitude. Such strong limits are of course dependent on the supposition that the vortons are absolutely stable on timescales as long as the present age of the universe. However, even if the vortons only survive for a few minutes, this would be sufficient to significantly affect primordial nucleosynthesis and hence provide limits of a weaker but nevertheless still interesting kind\\cite{vorton papers}. In all previous work it was supposed that the relevant superconductivity sets in during or very soon after the primary phase transition in which the strings are formed. What is new in the present work is an examination of the extent to which the limits discussed above are weakened if it is supposed that superconductivity sets in during a distinct secondary phase transition occurring at what may be a very much lower temperature than the string formation scale\\cite{DPWP}. The structure of the paper is as follows. In Section IIA we shall, for completeness, give a brief introductory review of string superconductivity. In Section IIB we describe the mechanism of formation of a vorton from an originally distended string loop and in Section IIC we summarize the basic properties of vorton equilibrium states. In Section IIIA we first comment on how it can be that the formation scale and the superconductivity scale can be separated by many orders of magnitude. We then demonstrate, using a suitably simplified statistical description of the string network, how to estimate the vorton abundance for a generic theory as a function of the temperature and the symmetry breaking scales. In Section IIIB we apply this procedure to the relatively simple case when the superconductivity develops during the early period when dissipation is mainly due to the friction of the ambient medium. In Section IIIC we go on to treat the more complicated situation that arises if the superconductivity does not develop until the much later stage in which dissipation is mainly due to gravitational radiation and in Section IIID we briefly comment on stability issues. In Section IV we consider the comparitively weak bounds that are obtained if it is supposed that the vortons are stable only for a few minutes. Finally, in Section V we consider the rather stronger bounds that are obtained if the vortons are of a kind that is sufficiently stable to survive as a constituent of the dark matter in the universe at the present epoch. We conclude in Section VI. ", "conclusions": "We have explored the constraints and implications both for particle physics and cosmology arising from the existence of populations of remnant vortons of more general types than have previously been considered. Specifically, we have envisaged the possibility of cosmic string superconductivity by condensation of the relevant carrier field at energy scales significantly below that of the string formation. We have seen that there are two qualitatively very different possibilities. In scenarios for which the carrier condensation occurs at comparitively high energy, during the friction damping regime, a substantial majority of the superconducting string loops will ultimately survive as vortons. Such scenarios are more easily excluded on observational grounds than the alternative possibility, which is that superconductivity does not set in until a later stage, in which case only a minority of the loops initially present ultimately become vortons. We have shown that large classes of particle physics models can provisionally be ruled out as incompatible by these cosmological considerations, and in particular we have shown that models admitting GUT strings must not allow any string superconductivity giving stable vortons to set in much above $10^{9}$ GeV. The excluded regions of parameter space are shown in figure~2. Our conclusions are, however, dependent on a number of more or less ``conventional\" assumptions, whose validity will need to be systematically scrutinised in future work. Invalidation of these conventional assumptions, particularly those concerning the long term stability of the vortons, in specific theoretical contexts would mean that in such circumstances the constraints given here might need to be considerably relaxed. On the other hand, our constraints may be considerably tightened by the use of more detailed observational data and the ensuing limits on the populations of various kinds of vortons that can exist today. On the constructive side, we have shown that it is possible for various conceivable symmetry breaking schemes to give rise to a remnant vorton density sufficient to make up a significant portion of the dark matter in the universe." }, "9605/astro-ph9605024_arXiv.txt": { "abstract": "Angular and spatial correlations are measured for $K$-band--selected galaxies, 248 having redshifts, 54 with $z>1$, in two patches of combined area $\\simeq27$~arcmin$^2$. The angular correlation for $K\\le21.5$ mag is $\\omega(\\theta)\\simeq (\\theta/1.4\\pm0.19^{\\prime\\prime}e^{\\pm0.1})^{-0.8}$. From the redshift sample we find that the real-space correlation, calculated with $q_0=0.1$, of $M_K\\le-23.5$ mag galaxies (k-corrected) is $\\xi(r) = (r/2.9e^{\\pm0.12}\\hmpc)^{-1.8}$ at a mean $z\\simeq 0.34$, $(r/2.0e^{\\pm0.15}\\hmpc)^{-1.8}$ at $z\\simeq 0.62$, $(r/1.4e^{\\pm0.15}\\hmpc)^{-1.8}$ at $z\\simeq 0.97$, and $(r/1.0e^{\\pm0.2}\\hmpc)^{-1.8}$ at $z\\simeq 1.39$, the last being a formal upper limit for a blue-biased sample. In general, these are more correlated than optically selected samples in the same redshift ranges. Over the interval $0.3\\le z\\le0.9$ galaxies with red rest-frame colors, $(U-K)_0>2$ $AB$ mag, have $\\xi(r)\\simeq(r/2.4e^{\\pm0.14}\\hmpc)^{-1.8}$ whereas bluer galaxies, which have a mean $B$ of 23.7 mag and mean \\oii\\ equivalent width $W_{eq} = 41$~\\AA, are very weakly correlated, with $\\xi(r)\\simeq(r/0.9e^{\\pm0.22}\\hmpc)^{-1.8}$. For our measured growth rate of clustering, this blue population, if non-merging, can grow only into a low-redshift population less luminous than $0.4L_\\ast$. The cross-correlation of low- and high-luminosity galaxies at $z\\simeq0.6$ appears to have an excess in the correlation amplitude within 100 \\hkpc. The slow redshift evolution is consistent with these galaxies tracing the mass clustering in low density, $\\Omega\\simeq 0.2$, relatively unbiased, $\\sigma_8\\simeq0.8$, universe, but cannot yet exclude other possibilities. ", "introduction": "N-body simulations give reliable predictions for the redshift dependence of the two-point correlation function of the density field, $\\xi(r|z)$, as a function of $\\Omega$. A convenient power-law parameterization to describe the evolving correlation function of galaxies is (\\cite{gp,ks}) \\begin{equation} \\xi(r|z)=\\left({r\\over r_0}\\right)^{-\\gamma} (1+z)^{-(3+\\epsilon)}, \\label{eq:def} \\end{equation} where the lengths $r$ are measured in physical (proper) co-ordinates. For this double power-law approximation the predicted evolution of clustering in the mass field is faster for $\\Omega=1$ ($\\epsilon=1.0\\pm0.1$) than it is for low-$\\Omega$ values, for instance $\\epsilon=0.2\\pm0.1$ for $\\Omega=0.2$ (\\cite{ccc}). Therefore, measurement of the redshift evolution of clustering can be used to test the gravitational instability theory of structure formation and the relation of galaxy clustering to dark matter clustering, and provides a constraint on $\\Omega$. Knowledge of these quantities enables predictions of the distribution of assembly times of dark halos, which on the relatively small scales investigated here is of great interest for the mass evolution of galaxies. At present, observational measures of clustering evolution are uncertain simply due to the difficulties of assembling large samples of faint galaxies with sufficient sky coverage to give a statistically representative sample. At low redshift the form of nonlinear galaxy clustering is accurately established (\\eg\\ \\cite{dp,apm,lcrs_lin,lcrs_tucker}), with a basic characterization of its dependencies on galaxy color, luminosity, and morphology. At higher redshifts the clustering is only now being directly measured (\\cite{cfrs,chuck}), although the small fields leave concerns that field-to-field variations are not yet well controlled. The galaxy luminosity function and its color dependence evolve substantially over the redshift 0 to 1 interval (\\cite{cfrs_lf,autofib,cshc,cnoc_lf}). Differential luminosity evolution of blue and red galaxies, in which the blue galaxies are less correlated at low redshift, can cause the apparent correlation of a magnitude-limited sample to change faster than either of the two underlying populations are changing. In this paper we report the clustering properties of a very deep redshift survey selected in the $K$ band. A near-IR selected survey has the enormous advantage that both k-corrections and the evolutionary corrections are small, allowing galaxy luminosities to be identified with total stellar mass with reasonable confidence. The Hawaii $K$-band survey (\\cite{cshc}) with a couple hundred galaxy redshifts, is large enough to be useful for correlation studies. Furthermore this survey contains galaxies up to a redshift of 2.19, which provides a fairly large redshift baseline over which correlation changes can be measured. The next section summarizes the sample properties. Measures of the angular correlation are given in Section 3 and of the real space correlation function in Section 4. In Section 5 the correlations of red and blue galaxies and of low- and high-luminosity galaxies are compared. Section 6 discusses the redshift evolution of galaxy correlations and compares the available data to various model predictions. Section 7 summarizes our results. All measurements in this paper assume $H_0=100\\ h^{-1} \\kmsm$ and $q_0=0.1$. It should be noted that correlation amplitudes at $z\\simeq 1$ are reduced by about 30\\% for $q_0=0.5$. ", "conclusions": "The fitted correlation length of luminous $K$-selected galaxies over the redshift range 0.2 to 1.2 is substantially stronger than that found for optically selected samples, about a factor of two in the amplitude, $r_0^\\gamma$. The galaxy correlation amplitude is measured at a mean $z\\simeq1.39$ as $r_0=1.0e^{\\pm0.2}\\hmpc$ (formally an upper limit, but deficient in the more strongly clustered faint red galaxies), $r_0=1.4e^{\\pm0.15}\\hmpc$ at $z\\simeq0.97$, $2.0e^{\\pm0.15}\\hmpc$ at $z\\simeq0.62$, and $2.9e^{\\pm0.12}\\hmpc$ at $z\\simeq 0.34$. Together these give a clustering $\\epsilon\\simeq0.2\\pm0.5$. The red galaxies are about a factor of 5 more correlated than the blue galaxies, which have $r_0\\simeq0.9e^{\\pm0.22}\\hmpc$. These blue galaxies have a mean equivalent width in the \\oii\\ line of 41\\AA. Together this can be taken as strong evidence that the faint blue galaxies are an intrinsically weakly correlated population (therefore likely low mass) with a high star formation rate that brightens them into the range of much more strongly correlated red galaxies. These galaxies are so weakly correlated that for our measured growth of correlations, $\\epsilon\\simeq0.2\\pm0.5$, they would grow to a current epoch correlation length of $r_0\\simeq 2\\hmpc$. This correlation length is less than that measured in any galaxy population at low redshift (\\cite{apm}), so these faint blue galaxies cannot by themselves make a significant contribution to the current epoch galaxy population. Overall the $K$ selected galaxy correlation evolution is somewhat too slow with redshift to be easily consistent with the evolution of the matter correlation function for $\\Omega_0\\simeq1$. A $\\sigma_8\\simeq 0.8$ and $\\Omega\\simeq0.2-0.3$ would describe both the amplitude and its evolution, if these galaxies are tracing the matter clustering. To further test models of correlation evolution requires large datasets of precision comparable to that available in current low redshift surveys with good control over population changes with redshift." }, "9605/astro-ph9605162_arXiv.txt": { "abstract": "The color-magnitude diagrams of $\\sim 7 \\times 10^5$ stars obtained for 12 fields across the Galactic bulge with the OGLE project reveal a well-defined population of bulge red clump giants. We find that the distributions of the apparent magnitudes of the red clump stars are systematically fainter when moving towards lower galactic $l$ fields. The most plausible explanation of this distinct trend is that the Galactic bulge is a bar, whose nearest end lies at positive galactic longitude. We model this Galactic bar by fitting for all fields the observed luminosity functions in the red clump region of the color-magnitude diagram. We find that almost regardless of the analytical function used to describe the 3-D stars distribution of the Galactic bar, the resulting models have the major axis inclined to the line of sight by $20-30\\deg$, with axis ratios corresponding to $x_0\\!:\\!y_0\\!:\\!z_0=3.5\\!:\\!1.5\\!:\\!1$. This puts a strong constraint on the possible range of the Galactic bar models. Gravitational microlensing can provide us with additional constrains on the structure of the Galactic bar. ", "introduction": "There is a mounting evidence that the Galactic bulge is a triaxial structure, or a bar. This was first postulated by de Vaucouleurs~(1964), based on similarities between the kinematics of the gas observed towards the Galactic center and in other barred galaxies. However, the hypothesis that our Galaxy is a barred galaxy was for a long time overshadowed by ``$3\\; kpc$ expanding arm'' hypothesis, despite a number of papers arguing for bar's presence (e.g. Peters 1975; Liszt \\& Burton 1980; Gerhard \\& Vietri 1986). Only recently has the view of our Galaxy as a barred spiral gained momentum, mostly due to the work of Blitz \\& Spergel (1991). They analyzed $2.4\\;\\mu m$ observations of the Galactic center and showed convincingly that the observed asymmetry in the galactic longitude distribution of surface brightness is naturally explained by the bar with the near side in the first Galactic quadrant. Binney et al.~(1991) have constructed a dynamical model for gas in the inner Galaxy, and their resulting bar has the same orientation as that suggested by Blitz \\& Spergel~(1991) in the sense that the closer part of the bar is at positive galactic longitudes. COBE-DIRBE multiwavelength observations of the Galactic center (Weiland et al.~1994) confirmed the existence of the longitudinal asymmetry discussed by Blitz \\& Spergel~(1991). This data was used by Dwek et al.~(1995) to constrain a number of analytical bar models existing in the literature. Star counts have also shown evidence for triaxial structure in the center of the Galaxy. Nakada et al.~(1991) analyzed the distribution of IRAS Galactic bulge stars and found asymmetry in the same sense as Blitz \\& Spergel~(1991). Whitelock \\& Catchpole~(1992) analyzed the number distribution of Mira variables in the bulge as a function of distance modulus and found that the half of the bulge which is at positive galactic longitude is closer to us than the other half. The observed stellar distribution could be modelled with a bar inclined at roughly $45\\deg$ to the line of sight. Weinberg~(1992) used AGB stars as star tracers and mapped the Galaxy inside the solar circle. He found evidence for a large stellar bar with semimajor axis of $\\approx\\;5\\;kpc$ and inclination placing the nearer side of the bar at positive galactic longitudes. A third thread of evidence comes from the gravitational microlensing towards the Galactic bulge (Udalski et al.~1994; Alcock et al.~1995; Alard et al. 1995). Observed high microlensing rate can be accounted for by stars placed in the near part of the Galactic bar microlensing the stars from the far side of the bar (Kiraga \\& Paczy\\'nski 1994; Paczy\\'nski et al.~1994b; Zhao, Spergel \\& Rich 1995). There are many implications if this scenario is correct, discussed latter in this paper. For recent reviews on the Galactic bar see Gerhard (1996) and Kuijken (1996). In this paper we use a color-magnitude data obtained by the Optical Gravitational Lensing Experiment collaboration for 12 fields scattered across the galactic bulge to construct the three-dimensional model of the mass distribution in the Galactic bar. The Optical Gravitational Lensing Experiment (OGLE, Udalski et al.~1993; 1994) is an extensive photometric search for the rare cases of gravitational microlensing of Galactic bulge stars by foreground stars, brown dwarfs and planets. It provides a huge database (Szyma\\'nski \\& Udalski 1993), from which color-magnitude diagrams have been compiled (Udalski et al.~1993). Stanek et al.~(1994; 1996) used the well-defined population of bulge red clump stars to investigate the presence of the bar in our Galaxy. Comparing extinction-adjusted apparent magnitudes of the red clump giants observed at fields lying at $l=\\pm5\\deg$, we found that the red clump stars lying at the positive Galactic longitudes are systematically brighter by $\\sim0.4\\;mag$ than the stars lying at negative $l$. A bar-shaped bulge whose nearer side is at the positive Galactic longitude most easily explains this offset. This agrees with Blitz \\& Spergel~(1991) and other works. The paper is organized as follows. In Section 2 we discuss the basis for using the red clump stars as a distance indicator. In Section 3 we discuss the data used for the bar modelling. In Section 4 we discuss various analytical models of the bar. In Section 5 we constrain these models using our data. In Section 6 we discuss various factors which might affect the fits. In Section 7 we discuss some astrophysical implications of the constructed models, among the others for the gravitational microlensing optical depth. ", "conclusions": "In this paper we have used color-magnitude data obtained by the OGLE collaboration for 12 fields scattered across the galactic bulge (Fig.\\ref{fig3}) to construct the three-dimensional model of the mass distribution in the Galactic bar. We model the Galactic bar by fitting for all fields the observed luminosity functions in the red clump region of the color-magnitude diagram (Fig.\\ref{fig4}, \\ref{fig5}). We find that almost regardless of the analytical function used to describe the 3-D stars distribution of the Galactic bar, the resulting models are inclined to the line of sight by $20-30\\deg$ (Fig.\\ref{fig7}), with axis ratios corresponding to $x_0\\!:\\!y_0\\!:\\!z_0=3.5\\!:\\!1.5\\!:\\!1$ (Fig.\\ref{fig8}). This puts a strong constraint on the possible range of the Galactic bar models. Comparing our result with the results of Dwek et al. (1995), we find a good agreement between the derived parameters of the models (Fig.\\ref{fig9}), but we constrain the bar parameters much tighter. We recommend as a model which fits well both COBE-DIRBE and our data the E2 model (Eq.9) with the values for the bar parameters: $\\alpha=24\\deg; x_0=900\\;pc; y_0=385\\;pc; z_0=250\\;pc$. We show various properties of this model in Fig.ref{fig6}, \\ref{fig10}, \\ref{fig11}. Gravitational microlensing can provide us with additional constrains on the structure of the Galactic bar. The text of this paper along with the figures in PostScript format is available using anonymous {\\tt ftp} on {\\tt astro.princeton.edu}, in {\\tt stanek/Barmodel} directory." }, "9605/astro-ph9605005_arXiv.txt": { "abstract": "A leading mechanism for producing cosmological gamma-ray bursts (GRBs) is via ultra-relativistic particles in an expanding fireball. The kinetic energy of the particles is converted into thermal energy in two shocks, a forward shock and a reverse shock, when the outward flowing particles encounter the interstellar medium. The thermal energy is then radiated via synchrotron emission and Comptonization. We estimate the synchrotron cooling time scale of the shocked material in the forward and reverse shocks for electrons of various Lorentz factors, focusing in particular on those electrons whose radiation falls within the energy detection range of the BATSE detectors. We find that in order to produce the rapid variability observed in most bursts the energy density of the magnetic field in the shocked material must be greater than about 1\\% of the thermal energy density. Additionally, the electrons must be nearly in equipartition with the protons, since otherwise we do not have reasonable radiative efficiencies of GRBs. Inverse Compton scattering can increase the cooling rate of the relevant electrons but the Comptonized emission itself is never within the BATSE range. These arguments allow us to pinpoint the conditions within the radiating regions in GRBs and to determine the important radiation processes. In addition, they provide a plausible explanation for several observations. The model predicts that the duty cycle of intensity variations in GRB light curves should be nearly independent of burst duration, and should scale inversely as the square root of the observed photon energy. Both correlations are in agreement with observations. The model also provides a plausible explanation for the bimodal distribution of burst durations. There is no explanation, however, for the presence of a characteristic break energy in GRB spectra. ", "introduction": "A cosmological gamma-ray burst (GRB) occurs, most likely, in the deceleration of a shell of ultra-relativistic particles encountering a surrounding interstellar medium (ISM) (M\\'esz\\'aros \\& Rees 1992). This process is believed to be essential for the production of a GRB regardless of the specific nature of the original source of relativistic particles (see e.g. Piran 1995 for a discussion). In a recent paper, Sari and Piran (1995, denoted SP hereafter) estimated the hydrodynamical time scales that arise in the interaction of an ultra-relativistic shell with the ISM. They showed that the observed durations of GRBs impose a direct limit on the Lorentz factors of the relativistic particles, namely $\\gamma >100$ for most bursts and $\\gamma$ even larger in a few cases. SP also worked out the hydrodynamical conditions in the various fluid zones of the expanding shell. They calculated the bulk velocity, thermal energy and particle density in the shocked material behind the forward and reverse shocks, as well as the velocities of the two shock fronts. The radiation we observe in a GRB is produced when the shock-heated gas loses its thermal energy through various radiation processes. In this paper we consider the cooling of the shocked material via Comptonized synchrotron emission. In developing a radiation model for GRBs, we can consider two distinct possibilities, depending on the relative magnitudes of the cooling time scale of the thermal electrons, $t_{cool}$, and the hydrodynamical time scale of the expanding shell, $t_{hyd}$. The case we focus on in this paper is similar to that assumed by SP, namely that $t_{hyd}>t_{cool}$. This assumption finds strong support in the fact that most bursts have complicated temporal structure with multiple peaks. A natural explanation is that the total duration of a burst is due to $t_{hyd}$, the time needed to convert the bulk of the kinetic energy of the expanding shell into thermal energy via the two shocks, while the individual peaks within the profile arise because of shot-like thermalization events in the shocks. In this picture, the individual sub-peaks within a burst represent the cooling curves of episodically heated electrons. The width of an individual sub-peak then represents the cooling time scale $t_{cool}$, and the ``duty cycle'' of the burst, which we define to be the ratio of the observed width of an individual peak to the total duration of the burst, is given by the ratio $D=t_{cool}/t_{hyd}$. The second case, which we do not consider in this paper, is when $t_{hyd}t_{cool}$, we make the further assumption that the hydrodynamical conditions do not change significantly during the cooling of the electrons. In other words, we assume that the rapid cooling does not drastically modify the adiabatic shock structure calculated by SP. This is a reasonable approximation if the thermalization in the shocks transfers half or more of the energy to the protons and only the remainder to the electrons. While the electrons cool rapidly, the proton energy remains locked up in the gas, leaving the hydrodynamical conditions relatively unaffected. The true conditions will thus differ from the idealized adiabatic shocks considered by SP by only factors of order unity which we ignore. In this paper, we use two pieces of information from observations to constrain the parameters of our model of the radiating regions of GRBs. First, we note that the vast majority of GRBs have complex time profiles where individual sub-peaks are significantly narrower than the overall duration of a burst. Roughly, the observations give a mean duty cycle of about 5\\%. As we show, this provides a significant constraint on the model. Second, we demand efficient conversion of thermal energy into radiation at the two shocks since we feel that low efficiency burst models are implausible. The observations show that the net energy emitted by cosmological bursts just within the BATSE band is $\\sim10^{51}~{\\rm ergs}$ (Cohen \\& Piran 1995, Fenimore et. al. 1993). In the most popular models of bursts, namely merging neutron star binaries (Narayan, Paczy\\'nski \\& Piran 1993) and failed supernovae (Woosley 1993), the total energy budget is only $\\sim10^{53.5}~{\\rm ergs}$, and there are some difficulties in converting even 1\\% of the initial explosion energy into kinetic energy of the expanding shell. Any further inefficiency in the conversion of shock thermal energy into radiation would be catastrophic. We show in this paper that to produce the rapid variability observed in many bursts the magnetic energy density in the shocked region must be at least 1\\% of the random thermal energy density of the gas. Additionally, we show that in order to have a reasonable radiative efficiency, the electrons must be nearly in equipartition with the protons. Thus, the observational data on GRBs restrict directly the conditions in the emitting region of these sources. We begin the paper with a brief summary in section 2 of the main results from SP, namely the hydrodynamical time scale of the shell and the characteristics of the forward and reverse shocks. We continue with an estimate of the synchrotron cooling time scale in section 3, and establish a lower limit for the magnetic field strength in the shocked material. In section 4 we examine the role of inverse Compton (IC) emission. We show that this process is irrelevant in the forward shock since the electrons there are too energetic and the scattering cross section is reduced considerably according to the Klein-Nishina formula. IC can be important in the reverse shock and can increase the cooling rate there. However, the IC photons themselves will generally be outside the energy range of the BATSE detector and therefore are not relevant for understanding the BATSE data. In section 5 we discuss the distribution of electron energy and the effect this has on the ``efficiency'' of a burst, namely the fraction of the initial kinetic energy in the shell which finally appears as radiation in the BATSE energy window. We show that the forward shock often produces nearly all its radiation at energies above the BATSE range, especially for short duration bursts. In contrast, the reverse shock is always visible to BATSE. However, the efficiency of the reverse shock is usually somewhat low, whereas the forward shock, when it radiates within the BATSE window, always has a high efficiency. We show in section 6 that these characteristics of the two shocks provide a plausible explanation for the bimodal distribution of GRB durations observed by BATSE (Kouveliotou et. al. 1993, Lamb, Graziani and Smith, 1993). We suggest that short bursts originate from the reverse shocks of fireballs which expand with high Lorentz factor $\\gamma$, while long bursts originate from the forward shock of low $\\gamma$ events. This simple model is also in agreement with the relative luminosities of short and long bursts as estimated by Mao, Narayan \\& Piran (1994). ", "conclusions": "Our basic picture follows the scenario proposed by M\\'esz\\'aros \\& Rees (1992), namely that a GRB is produced when a relativistic outflow of particles from a central explosion is slowed down by interaction with an external ISM. The interaction takes place in the form of two shocks---a forward shock which propagates into the ISM and a reverse shock which propagates into the relativistic shell. We have used the results of Sari \\& Piran (1995) to express the density, velocity, and thermal energy of the gas in the shocked regions in terms of physical parameters such as the Lorentz factor $\\gamma$ of the relativistic flow and the density of the external medium. Some properties of the shocked medium are, however, impossible to estimate from first principles. One such is the energy density of the magnetic field, which we write as a fraction $\\epsilon_B$ of the total energy. Another is the fraction of the thermal energy which goes into electrons, which we write as $\\epsilon_e$. We consider $\\epsilon_B$ and $\\epsilon_e$ to be free parameters (though constrained to be less than unity) which we adjust by comparing the predictions of the model with observations. We calculate the radiation emitted by the shocked gas via synchrotron emission and also consider modifications introduced by inverse Compton (IC) scattering. In comparing the predictions of the model to observations, we use two important constraints. First, we know that most GRBs have complex time structure with a duty cycle (defined to be the duration of the sharpest feature divided by the overall duration of the burst) of a few percent. We therefore require the cooling time of the shock-heated electrons in our model to be short enough to satisfy this constraint. Second, we impose the requirement that a reasonably large fraction of the shock-generated thermal energy should ultimately be visible as radiation within the BATSE window, 25 KeV to 1 MeV. Most proposed models of GRBs have a limited overall energy budget $\\sim10^{53}-10^{54}$ ergs and convert only a percent or so of this energy into kinetic energy of the expanding shell. If there were any further inefficiency in converting the kinetic energy into BATSE-visible radiation then it would be very hard to match the observed fluences of GRBs, which correspond to a $\\gamma$-ray energy output $\\sim10^{51}$ ergs per burst. One of the primary results of this paper is that we have calculated the cooling time of the shock-heated electrons via synchrotron emission and IC scattering. We reach several interesting conclusions. \\noindent 1. For photons detected by BATSE, say of energy 100 KeV, there is a very well-defined relation between the synchrotron cooling time $\\tau_{\\rm syn}$ of the electrons and the observed duration of a GRB $t_{\\rm dur}$. The relation is given in equation (\\ref{tausyn2}) and is the same for both the forward and reverse shocks, and is independent of whether the reverse shock is Newtonian or relativistic. Equation (\\ref{dutycyclesyn}) gives a formula for the duty cycle of a burst and predicts that the duty cycle should be nearly independent of burst duration. This prediction appears to be supported by observations but needs to be checked against the data in more detail. \\noindent 2. If we require the duty cycle to be no more than a few percent, as suggested by the observations, then we find that the magnetic field parameter $\\epsilon_B$ must be greater than about $10^{-2}$ (assuming $\\epsilon_e\\sim1$, see below). Such strong fields are not expected merely from flux-freezing, especially in the forward shock where the field in the external ISM is likely to be very low. We conclude, therefore, that the ultra-relativistic shocks in GRBs must have some mechanism to build up the magnetic field to near-equipartition strength in the post-shock gas. \\noindent 3. We find that the duty cycle should decrease with increasing photon energy as $(h\\nu_{\\rm obs})^{-1/2}$. Such a variation in the widths of features in GRB light curves has been reported by Fenimore et al. (1995). These authors find a variation of the form $(h\\nu_{\\rm obs})^{-0.4}$, which is reassuringly close to our predicted scaling. \\noindent 4. IC scattering does not modify the results for the forward shock because the scattering cross-section is strongly suppressed by the Klein-Nishina effect. For the reverse shock, IC can be important in some cases. While the IC radiation never falls within the BATSE window, the electrons which produce the BATSE-visible synchrotron radiation can be significantly cooled by IC if $\\epsilon_B < \\epsilon_e$. In addition to the cooling time scale, we also calculate the efficiency of a burst. The efficiency depends on the parameter $\\epsilon_e$, which determines how much energy is available in the electrons, but also on exactly how much of the energy is actually radiated within the BATSE range. Our analysis leads to the following conclusions. \\noindent 1. We find that the radiation from the forward shock is visible to BATSE only for bursts with long durations, $t_{\\rm dur}>10$ s. In shorter bursts, the radiation from the forward shock is too hard and falls in the MeV range. This implies that there is a populations of MeV bursts to which BATSE is not sensitive and which may be worth searching for in future missions (see Piran \\& Narayan 1995). \\noindent 2. The radiation from the reverse shock falls within the BATSE window for all bursts. However, the amount of radiation received is maximum for very short duration bursts and decreases with increasing burst duration. \\noindent 3. Combining the above two results, and imposing the requirement of reasonable burst efficiency, we conclude that $\\epsilon_e$ must be large. This means that ultra-relativistic shocks must be able to accelerate electrons almost as effectively as they accelerate ions. For quantitative estimates, we choose $\\epsilon_e=0.5$, which corresponds to the shock thermal energy going into ions and electrons in equal amounts. Even with this choice, we find that the reverse shock is fairly inefficient, with efficiencies as low as 1\\% for $\\epsilon_B=10^{-2}$ and $t_{\\rm dur}>1$ s. If we give up burst efficiency as a criterion, then some of the constraints stated earlier become looser. For instance, it may be possible to accept values of $\\epsilon_B$ as low as $10^{-5}$ (as in M\\'esz\\'aros, Laguna \\& Rees 1993). \\noindent 4. For the particular choice of parameters we favor, $\\epsilon_B=10^{-2}$, $\\epsilon_e=0.5$, the model provides a natural explanation for the bimodal distribution of burst durations. Long bursts are produced by the forward shock from fireball shells with somewhat low values of $\\gamma\\sim100$. These bursts are efficient. Short bursts, on the other hand, are produced by the reverse shock from higher $\\gamma$ events. These are generally much less efficient. The model even explains the curious feature noted by Mao et al. (1994) that the {\\it luminosities} of short and long bursts are similar even though their fluences differ by a large factor. This results naturally in our model from the different efficiencies of the two shocks. We conclude with two caveats. First, our model in its present form does not have an explanation for the break seen by BATSE in many GRB spectra at around a few hundred KeV. In the present paper we merely required that the model should be able to produce photons visible to BATSE and we calculated the properties of these photons and the electrons which produce them. An additional requirement we could have imposed, but did not, is a low energy cut-off so that the model does not produce an excess of X-ray photons. The forward shock in our model does naturally have a low energy cutoff, and is possibly consistent with measured constraints in the X-ray band, but the reverse shock in our model produces too much low energy radiation. It is possible that IC cooling suppresses the lower energy radiation. To investigate this, the IC interactions will need to be calculated in greater detail than we have done in this paper. The second point is that we have assumed that the overall duration of a burst $t_{\\rm dur}$ is given by the hydrodynamical time $t_{\\rm hyd}$, and that this time is greater than the cooling time $t_{\\rm cool}$ of the electrons. We associate the widths of individual features in burst profiles with $t_{\\rm cool}$. We find this choice natural. However, it is possible to consider the oposite case in which $t_{\\rm hyd}