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Since radial notions are probably driven by energy from star ornation. if is uot necessary for the expansion ceuter to )o comcideut with the geometric ceuter oftle ITI disk. | Since radial motions are probably driven by energy from star formation, it is not necessary for the expansion center to be coincident with the geometric center of the HI disk. |
The expansion Vi, Is assiuned to be aziuithally sviuuuctric. and its variation with ealacto-ceutric distance is as shown iu Fig. S|[ | The expansion $V_{\rm exp}$ is assumed to be azimuthally symmetric, and its variation with galacto-centric distance is as shown in Fig. \ref{fig:model}[ [ |
F|. | F]. |
The rise in the expansion velocity till the radius R1 produces the parallel isovelocity contours iu the central regions of the galaxy. the fall after RL produces he closed οςtours. | The rise in the expansion velocity till the radius R1 produces the parallel isovelocity contours in the central regions of the galaxy, the fall after R1 produces the closed contours. |
The rise in the expansion curve. frou. radius R2 ouwards. produces the kinks seen im the eastern and western edges of the velocity feld. | The rise in the expansion curve, from radius R2 onwards, produces the kinks seen in the eastern and western edges of the velocity field. |
This particular onu of expansion was chosen because it provides a eood natch to the observed velocity field. | This particular form of expansion was chosen because it provides a good match to the observed velocity field. |
While it is possible hat detailed eas dynamic modeling might be able to reproduce this curve. we have uot attempted any such uodeliug in this paper. | While it is possible that detailed gas dynamic modeling might be able to reproduce this curve, we have not attempted any such modeling in this paper. |
While a pure expansion model does produce the closed. coutours aloug the morphological münor axis. it does not produce the uetres iu the velocity field noted iu Sect. 3.2. | While a pure expansion model does produce the closed contours along the morphological minor axis, it does not produce the asymmetries in the velocity field noted in Sect. \ref{ssec:HI_Kin}. |
next qmost natural model to trv is lence one in which here is also some rotation. | The next most natural model to try is hence one in which there is also some rotation. |
A velocity field with the sane Vag, as before. but with non zero Vi is shown in Fig. ΒΙ | A velocity field with the same $V_{\rm exp}$ as before, but with non zero $V_{\rm rot}$ is shown in Fig. \ref{fig:model}[ [ |
ΟΙ. | D]. |
The rotation curve has been axstuned to be near: it rises fo a iuaxinnuu of 6 tat the edge of he ealaxy. | The rotation curve has been assumed to be linear; it rises to a maximum of 6 at the edge of the galaxy. |
A linearly rising rotation curve was chosen because this form of rotation curve is typical of dwart galaxies. | A linearly rising rotation curve was chosen because this form of rotation curve is typical of dwarf galaxies. |
Other types of rotation curves. Le. a coustant rotation curve. a Brandt and an exponential curve Gehiüch are seldom observed for dwarf ealaxies) were also tried. | Other types of rotation curves, i.e. a constant rotation curve, a Brandt and an exponential curve (which are seldom observed for dwarf galaxies) were also tried. |
While a constant rotation curve eives a poor fit to the data. Drandt and exponeutial curves do not provide a better fit to the observed velocity | While a constant rotation curve gives a poor fit to the data, Brandt and exponential curves do not provide a better fit to the observed velocity |
The chromospheric aud coronal activity of coo cava stars like the Sun is thought to arise from the interaction of stellar maguctic fields with differential rotation ane convection. | The chromospheric and coronal activity of cool dwarf stars like the Sun is thought to arise from the interaction of stellar magnetic fields with differential rotation and convection. |
Since significant convection zones make their appearance along the main sequence in late spectral class A. the inch debated turnon of such activity shoul occur at about the same spectral type. althoueh the precise dependence is uot well known. | Since significant convection zones make their appearance along the main sequence in late spectral class A, the much debated turn–on of such activity should occur at about the same spectral type, although the precise dependence is not well known. |
Ou the other hai sjenificautf radiatively driven winds (the imstabilities of which are thought to be responsible for the XNταν emission in O and carly Dtype stars) are not present bevolk spectral tvpe ~ Bl. | On the other hand significant radiatively driven winds (the instabilities of which are thought to be responsible for the X–ray emission in O– and early B–type stars) are not present beyond spectral type $\sim$ B4. |
Thus in the BSAS spectral range a lack ofX.ταν emission is theoretically “expected”. | Thus in the B5–A5 spectral range a lack of X–ray emission is theoretically “expected”. |
In spite of the observational efforts. no conclusive evideuce of Xrav cluission from BSAD type stars has been found: in fact in most of the observed cases the emission is thought to cole not from the carly type star itself. but from a cooler colupalion or from a uearby star (Schutt νήμα 1993: Caené Caillault 1991: Stauffer ot al. | In spite of the observational efforts, no conclusive evidence of X--ray emission from B5–A5 type stars has been found; in fact in most of the observed cases the emission is thought to come not from the early type star itself, but from a cooler companion or from a nearby star (Schmitt Kürrster 1993; Gagné Caillault 1994; Stauffer et al. |
1991: Stern et al. | 1994; Stern et al. |
1995). | 1995). |
Few interesting cases have been found bx Schiuitt et al. ( | Few interesting cases have been found by Schmitt et al. ( |
1993) and Derghóffer Schinitt (1991). which detected N-rav emission from both compoucuts iu sone Visual binaries formed by a BSAS primary star and a cooler compawion. | 1993) and Berghöffer Schmitt (1994), which detected X-ray emission from both components in some visual binaries formed by a B5–A5 primary star and a cooler companion. |
Stimgeut upper limits have been determuned for the Xray cussion of some well studied Atype stars; down to a huuinosity of Ly~3.5«107 | for the prototypical Atype star Vega (Sclunitt 1997). | Stringent upper limits have been determined for the X--ray emission of some well studied A–type stars, down to a luminosity of $L_{X} \sim 3.5 \times 10^{25}$ $^{-1}$ for the prototypical A–type star Vega (Schmitt 1997). |
This secs to indicate that the coronae surrounding these stars (f may exist at all) iuust be very differcut from those surrounding cooler stars. | This seems to indicate that the coronae surrounding these stars (if may exist at all) must be very different from those surrounding cooler stars. |
They do uot have massive winds. ucither have deep chough convective zoue for an effective dyuame activity. | They do not have massive winds, neither have deep enough convective zone for an effective dynamo activity. |
However. in all the cases reported above. onlv siuall suuples of late Bo carly Aotype stars were used. | However, in all the cases reported above, only small samples of late B– early A–type stars were used. |
Recently. Simon et al. ( | Recently, Simon et al. ( |
1995) tried to overcome this problenà bv using pointed ROSAT PSPC observations to study the Nταν properties of a sample of 71 Atype stars. | 1995) tried to overcome this problem by using pointed ROSAT PSPC observations to study the X–ray properties of a sample of 74 A–type stars. |
They detected Norav cussion in 9 late A and 10 carly Atype stars. | They detected X–ray emission in 9 late A– and 10 early A--type stars. |
Of the latter. 5 were confirmed double aud 5 were not known to be double but further optical study are necessary in order to determine if they are really single stars. | Of the latter, 5 were confirmed double and 5 were not known to be double but further optical study are necessary in order to determine if they are really single stars. |
Ou the other haud convincing evidence of chromospheric and Xrav cussion has been detected iu stars as early as spectral type AT (Schinitt et al. | On the other hand convincing evidence of chromospheric and X–ray emission has been detected in stars as early as spectral type A7 (Schmitt et al. |
1985: Simon Landsman 19901). | 1985; Simon Landsman 1991). |
Recently Simou Landsman (1997) reported the detection of claomospheric emission iu IIST/GIRS spectra of the Al star 7° Exi that secus to be the hottest main sequence star known to have a chromosphere and thus an outer convection zone. | Recently Simon Landsman (1997) reported the detection of chromospheric emission in HST/GHRS spectra of the A4 star $\tau^{3}$ Eri that seems to be the hottest main sequence star known to have a chromosphere and thus an outer convection zone. |
Activity indicators in ATF5 type stars seem to be independent ou rotation. while the coronal Nrav cussion. as measured relatively το chromospleric cussion. ids deficient 1 colmpared with latertype stars (Pallavicini et al. | Activity indicators in A7–F5 type stars seem to be independent on rotation, while the coronal X–ray emission, as measured relatively to chromospheric emission, is deficient if compared with later–type stars (Pallavicini et al. |
1981: Scehuutt et al. | 1981; Schmitt et al. |
1985: Sinon Landsman 1991). | 1985; Simon Landsman 1991). |
The | The |
given the model parameters fy. e. (M,/L)g and dlogM/L)/dz which we abbreviate as £. | given the model parameters $f_*$ , $c$ , $(M_*/L)_0$ and $d\log(M/L)/dz$ which we abbreviate as $\bfxi$. |
Combining the (wo terms. we have the probability of the model filling the data D; for galaxy 7 In addition to the measurement errors listed in Table L.. we should also consider sources of svsteniatic errors. | Combining the two terms, we have the probability of the model fitting the data $D_i$ for galaxy $i$ In addition to the measurement errors listed in Table \ref{tab:tab1}, we should also consider sources of systematic errors. |
The essence of the method is to compare the mass inside (he Einstein ving M(«R,) toa virial mass estimate from the velocity dispersion o2/2/G. | The essence of the method is to compare the mass inside the Einstein ring $M(<R_e)$ to a virial mass estimate from the velocity dispersion ${\sigma}_v^2R/G$. |
We can identify five sources of svstematic errors. | We can identify five sources of systematic errors. |
First. while there is little uncertainty in Mp. some of the mass may be projected surface density from either a parent group halo to which the lens belongs. or [rom another along the line of sight. | First, while there is little uncertainty in $M_E$, some of the mass may be projected surface density from either a parent group halo to which the lens belongs, or from another along the line of sight. |
The extra density. &=X/X,. in dimensionless units. modifies (he mass inside the Einstein radius by weREM... so we can think of its effects as a svstematic error in interpreting o, of e,=6,/2. | The extra density, $\kappa=\Sigma/\Sigma_c$ in dimensionless units, modifies the mass inside the Einstein radius by $\pi\kappa R_E^2 \Sigma_c$, so we can think of its effects as a systematic error in interpreting $\sigma_v$ of $\rm e_\sigma=\sigma_{\kappa}/2$. |
The Full probability distribution ol & is skewed to positive values (e.g. Takada&Ilamana 2003)). bul we will ignore this problem and assume 6,20.05 since the positive tail of the distribution is associated with detectable objects (galaxies and clusters). | The full probability distribution of $\kappa$ is skewed to positive values (e.g. \citealt{th03}) ), but we will ignore this problem and assume $\sigma_{\kappa}\backsimeq 0.05$ since the positive tail of the distribution is associated with detectable objects (galaxies and clusters). |
This svstematic error also affects. estimates of the mass-to-light ratios. | This systematic error also affects estimates of the mass-to-light ratios. |
Second. there are 1—10 uncertainties in the galaxy effective radius measurements which contribute uncertainties of 0.5% to 5% to our interpretation of the velocity dispersion. | Second, there are $1-10\%$ uncertainties in the galaxy effective radius measurements which contribute uncertainties of $0.5\%$ to $5\%$ to our interpretation of the velocity dispersion. |
Third. the measured velocity dispersion is a Gaussian fit to the specirum. which is not identical to the rms velocity appearing in the Jeans equation (e.g. Dinnev&Tremaine 1957)). | Third, the measured velocity dispersion is a Gaussian fit to the spectrum, which is not identical to the rms velocity appearing in the Jeans equation (e.g. \citealt{bs87}) ). |
The difference can be estimated from the (vpical Gaussian-Hermite coefficients |;|=0.02 (Bender.Saglia&GerhardL994) as a fractional error in σι ol order νο=0.05 in (he velocity dispersion (e.g. vanderMarel.Dokkum 2003)). | The difference can be estimated from the typical Gaussian-Hermite coefficients $|h_4|\backsimeq0.02$ \citep{bsg94} as a fractional error in $\sigma_v$ of order $\sqrt{6}|h_4|\backsimeq0.05$ in the velocity dispersion (e.g. \citealt{vf03}) ). |
Fourth. non-sphericitv. (somewhat to our surprise) leads (o negligible svstematic errors provided we use the intermediate scale length (the geometric mean of the semi-major and minor axes). al least in the limit of the tensor virial theorem. | Fourth, non-sphericity, (somewhat to our surprise) leads to negligible systematic errors provided we use the intermediate scale length (the geometric mean of the semi-major and minor axes), at least in the limit of the tensor virial theorem. |
It leads (ο large errors if any other scale length is used. | It leads to large errors if any other scale length is used. |
Barnabe&Koopmans(2007) have taken the first steps towards removing these (wo dynamical problems. although they ave restricted to oblate Gwo-integral models which may not be appropriate for massive elliptical galaxies. | \citet{Barnabe07} have taken the first steps towards removing these two dynamical problems, although they are restricted to oblate two-integral models which may not be appropriate for massive elliptical galaxies. |
Finally. calibration errors in the velocity dispersions contribute Iractional errors of order 0.03 (see Dernardi 2003a)). | Finally, calibration errors in the velocity dispersions contribute fractional errors of order 0.03 (see \citealt{bernardi03a}) ). |
Combining all these contributions in quadrature. which corresponds (ο assuming a Gaussian model for each svstematic error. we estimate that the (wpical systematic uncertainty to interpreting the velocity dispersions is approximately 8% with the exact value depending on the uncertainties in (he effective radius. | Combining all these contributions in quadrature, which corresponds to assuming a Gaussian model for each systematic error, we estimate that the typical systematic uncertainty to interpreting the velocity dispersions is approximately $8\%$ with the exact value depending on the uncertainties in the effective radius. |
Our statistical methods are chosen so that we can understandthe homogeneityof the lens galaxies in either (heir evolution or their cdvnamical properties and estimate (heir average properties in the presence of inhomogeneities. | Our statistical methods are chosen so that we can understandthe homogeneityof the lens galaxies in either their evolution or their dynamical properties and estimate their average properties in the presence of inhomogeneities. |
We will analvze (he results using two Davesian | We will analyze the results using two Bayesian |
Ever since the discovery that only a small minority of selected quasars are also luminous radio sources (e.g. LocHy107 !sr 4). many studies have attempted to isolate the physical mechanism underlying this so-called) quasar radio-loudness dichotomy. | Ever since the discovery that only a small minority of optically-selected quasars are also luminous radio sources (e.g. $L_{\rm{5GHz}}>10^{24}$ $^{-1}$ $^{-1}$ ), many studies have attempted to isolate the physical mechanism underlying this so-called quasar radio-loudness dichotomy. |
Although previous studies found a clear bimodality in the radio luminosities of optically-selected quasars (eg. | Although previous studies found a clear bimodality in the radio luminosities of optically-selected quasars (eg. |
Kellermann et al. | Kellermann et al. |
1989: Miller. Peacock Mead 1990). more recently the very existence of the radio-loudness dichotomy has been questioned (Lacy et al. | 1989; Miller, Peacock Mead 1990), more recently the very existence of the radio-loudness dichotomy has been questioned (Lacy et al. |
2001: Cirasuolo et al. | 2001; Cirasuolo et al. |
2003: although see Ivezié et al. | 2003; although see Ivezić et al. |
2002 for an alternative viewpoint). | 2002 for an alternative viewpoint). |
The principal reason. behind this renewed interest in the radio properties of optically selected quasars is the ability to combine the large SDSS and 2dF optical quasar samples with wide-area radio surveys such as the Faint Images of the Radio Sky at Twenty-cm (FIRST) and the NRAO VLA Sky Survey (NVSS). | The principal reason behind this renewed interest in the radio properties of optically selected quasars is the ability to combine the large SDSS and 2dF optical quasar samples with wide-area radio surveys such as the Faint Images of the Radio Sky at Twenty-cm (FIRST) and the NRAO VLA Sky Survey (NVSS). |
The FIRST survey (Becker. White Helfand 1995) in particular has identified large numbers of so-called radio-intermediate quasars which have largely tilled-in the apparent gap in radio luminosities between the RLQ and RQO populations teg. | The FIRST survey (Becker, White Helfand 1995) in particular has identified large numbers of so-called radio-intermediate quasars which have largely filled-in the apparent gap in radio luminosities between the RLQ and RQQ populations (eg. |
Lacy et al. | Lacy et al. |
2001). | 2001). |
Consequently. the distribution of optically-selected quasars on the optical-radio luminosity plane is undoubtedly more continuous than was previously thought. | Consequently, the distribution of optically-selected quasars on the optical-radio luminosity plane is undoubtedly more continuous than was previously thought. |
Irrespective of this. the fundamental question of what causes luminous quasars with seemingly identical optical properties to differ in their radio luminosities by several orders of magnitude remains unanswered. | Irrespective of this, the fundamental question of what causes luminous quasars with seemingly identical optical properties to differ in their radio luminosities by several orders of magnitude remains unanswered. |
Recent progress has been made in largely eliminating two parameters which were originally suspected of influencing the radio-loudness dichotomy: host-galaxy morphology and cluster environment. | Recent progress has been made in largely eliminating two parameters which were originally suspected of influencing the radio-loudness dichotomy; host-galaxy morphology and cluster environment. |
Thanks largely to the Hubble Space Telescope (HST). quasar host-galaxy morphologies have now been investigated out to intermediate redshifts. 0.1.<20.5 teg. | Thanks largely to the Hubble Space Telescope (HST), quasar host-galaxy morphologies have now been investigated out to intermediate redshifts, $0.1<z<0.5$ (eg. |
Dunlop et al. | Dunlop et al. |
2003: Schade et al 2000: MeLure et al. | 2003; Schade et al 2000; McLure et al. |
1999: Disney et al. | 1999; Disney et al. |
1996). | 1996). |
Drawing together the results of these studies. it is clear that the hosts of optically luminous quasars (Le. Mj< 24) are bulge-dominated. spheroidal galaxies irrespective of radio luminosity (Dunlop et al. | Drawing together the results of these studies, it is clear that the hosts of optically luminous quasars (i.e. $M_{R}<-24$ ) are bulge-dominated, spheroidal galaxies irrespective of radio luminosity (Dunlop et al. |
2003: Schade et al. | 2003; Schade et al. |
2000). | 2000). |
In the light of the discovery of the correlation between black-hole and bulge mass (Magorrian et al. | In the light of the discovery of the correlation between black-hole and bulge mass (Magorrian et al. |
1998: Gebhardt et al. | 1998; Gebhardt et al. |
2000: Ferrarese Merritt 2000). this result is perhaps not surprising. | 2000; Ferrarese Merritt 2000), this result is perhaps not surprising. |
However. it should also be remembered that in the optical the hosts of RLQs are consistently found to be 0.5 magnitudes brighter than their RQQ counterparts (eg. | However, it should also be remembered that in the optical the hosts of RLQs are consistently found to be $\simeq 0.5$ magnitudes brighter than their RQQ counterparts (eg. |
Dunlop et | Dunlop et |
1 Introduction Open svstems tvpicallygive rise toresonances. Aresonance Is along-living quasi- stationarystate. | on an analogy with Thouless' arguments concerning the sensitivity of eigenstates to the boundary conditions in Hermitian localization theory \cite{Thouless,gang4}. |
which eventually decavs into thecontimuum. Physically. it maybe thought infinity.of asaparticle. | Indeed, the coupling of the disordered system to the external world plays in our case a role similar to changing the boundary conditions in Thouless' picture. |
initiallytrapped inside (hesvstem. which eventually escapes to One common approach to studying resonances isbased onthe analytic properties ofthe scattering matrix 5(£) poles labelpoles E,bk, (10! 5(£) thenon-physical sheet|1. | Namely, the width of a typical resonance in the insulating regime should be exponentially small, $\Gamma_{typ}\sim \exp -L/\xi(E)$ $L$ being the size of the system), whereas in the metallic regime the typical width is $\Gamma_{typ}\sim {\cal D}/L^2$, namely, the inverse Thouless time scale ${\cal D}$ is the diffusion coefficient in the disordered metal). |
2].. In alternative = 5b on an equivalent approach. | Thus, $\Gamma_{typ}$, measured in units of level spacing $\Delta$, is analogous to the Thouless conductance. |
whichweshall follow here.onesolves | This picture was already pursued numerically in \cite{Kot3}. |
theSchrodeinger equation subjected to the boundary | The continuum limit of the disordered chain was studied in \cite{mumbai}. |
condition of purely outgoing wave | For simplicity, a chain opened only at one end was studied. |
ejectedfrom the svstem. renders the problem non-IHermitian. The Sehiróddinger equation will this boundary condition leads | The spectral determinant for the problem was derived, and the averaged DOR was expressed in terms of a certain integral over the solution of a certain singular two-dimensional Fokker-Planck equation. ( |
tocomplexeigenvalues €,which correspond Lo resonances[1.2].. Fora recentlucid | That Fokker-Planck equation determined the probability distribution of the logarithmic derivative of the outgoing wave at the open end of the chain.) |
discussionofresonances in quantunsvstems. with | The present work was motivated in part by \cite{ks1,ks2}. |
particular emphasis onthelatter approach. see3.4].. The outgoing-wave approach leads. inanatural way.to non-Hermitian effective 5. hamiltonians0]. whose c | In particular, an analytical approach was developed in \cite{ks2} for studying resonances, which is based on counting poles of the resolvent of the non-Hermitian tight-binding effective hamiltonian of the open chain. |
omplex eigenvaluesare the resonances ofthe studied system 6. Such effective hamiltonians arevery use | In the case of a semi-infinite disordered chain, coupled to a semi-infinite perfect lead, these authors have derived an exact integral representation for the DOR, valid for arbitrary disorder and chain-lead coupling strength. |
ful forstudying resonances in scattering theory.including scattering inchaotic anddisordered svstenms[0. 0. 0. 0. 0].. There are many | In the limit of weak chain-lead coupling (in which resonances are typically narrow) they were able to rigorously derive a universal scaling formula for the DOR, valid for any degree of disorder and everywhere inside the unperturbed energy band of the closed chain. |
examplesof resonancesin atom | The $1/\Gamma$ behavior of the DOR follows from that formula. |
ic andnuclear plivsies. Recently. {herehasbeen considerable interestin resonances whicharise | In this paper we shall review and explain how to construct energy dependent non-hermitian hamiltonians for studying resonance statistics in open systems. |
in chaotic anddisordered systems. See [0] fora recent review. One ofthe main goals inthese studies | While many (but by no means all) of the results presented in this paper are known, we believe our presentation offers a somewhat fresh look at these issues. |
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