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5À.. The spectra covered the wavelength range aat a dispersion of pper pixel. | The spectra covered the wavelength range at a dispersion of per pixel. |
However. we only used the region7000-7590A.. since (his was well corrected for tellure absorption. and contains the TiO band of interest. | However, we only used the region, since this was well corrected for telluric absorption, and contains the TiO band of interest. |
The reduced spectra were shifted so (hat (he spectral lines lav at their rest wavelength and added. using a weighted mean. {ο eive a spectrum with a signal-to-noise of about. 200. | The reduced spectra were shifted so that the spectral lines lay at their rest wavelength and added, using a weighted mean, to give a spectrum with a signal-to-noise of about 200. |
We also observed 35 single IX ancl M stars lo use as template spectra. which were also shifted so that the spectral lines lav at (heir rest wavelength positions. | We also observed 35 single K and M stars to use as template spectra, which were also shifted so that the spectral lines lay at their rest wavelength positions. |
We ensured good relative flux calibration bv observing an O or D-star close to each target. after the target had been observed. | We ensured good relative flux calibration by observing an O or B-star close to each target, after the target had been observed. |
This hot star was itself fluxed (using data from flux stancards). aud (he resulting spectrum (excluding telluric absorption bands) was fitted with a quadratic (a good approximation to the flux distribution of hot stars in (his region of the spectrum). which removed any residual fluxing errors on scales ol less than300A. | This hot star was itself fluxed (using data from flux standards), and the resulting spectrum (excluding telluric absorption bands) was fitted with a quadratic (a good approximation to the flux distribution of hot stars in this region of the spectrum), which removed any residual fluxing errors on scales of less than. |
. We next divided the unlluxed spectrum of the target by the unlluxed spectrum of the O-star. thus removing the telluric absorption lines. | We next divided the unfluxed spectrum of the target by the unfluxed spectrum of the O-star, thus removing the telluric absorption lines. |
Finally we multiplied (his spectrum by the quadratic fit to the hot star spectrum to obtain a fluxed spectrum of the target. | Finally we multiplied this spectrum by the quadratic fit to the hot star spectrum to obtain a fluxed spectrum of the target. |
Our mean 5S (νο spectrum is shown in Figure 1.. | Our mean SS Cyg spectrum is shown in Figure \ref{fig1}. |
There are two strong emission lines αἱ and ((both Hel). whose broadness implies they originale in (he accretion disc. ( | There are two strong emission lines at and (both HeI), whose broadness implies they originate in the accretion disc. ( |
They are broadened both by the rotation of the disc. aud our shifting of the spectra into the rest frame of the secondary star.) | They are broadened both by the rotation of the disc, and our shifting of the spectra into the rest frame of the secondary star.) |
The rest of (he spectrum is a host of weak. rotationally broacdened absorption lines [rom the secondary star. | The rest of the spectrum is a host of weak, rotationally broadened absorption lines from the secondary star. |
It is immediately evident. even without modeling. that there is a broad absorption trough between aand7200A.. which is normally associated with TiO (although the banclheacl itself. al iis obscured by an emission line). | It is immediately evident, even without modeling, that there is a broad absorption trough between and, which is normally associated with TiO (although the bandhead itself, at is obscured by an emission line). |
Llowever. (he secondary star in this CV is of spectral tvpe early IX. (4800-53001Ix). ancl is (hus too hot for TiO (o exist in significant quantity. | However, the secondary star in this CV is of spectral type early K (4800-5300K), and is thus too hot for TiO to exist in significant quantity. |
Indeed TiO only appears in stus of spectral tvpe INT and later. where the temperature is below 43001Ix. It would appear. therefore. that we are observing a Ix-tvpe star. with cooler. M-tvpe | Indeed TiO only appears in stars of spectral type K7 and later, where the temperature is below 4300K. It would appear, therefore, that we are observing a K-type star, with cooler, M-type |
strong perturbation to the nodal evolution of Trojan is from Uranus. | strong perturbation to the nodal evolution of Trojan is from Uranus. |
Because of the small value (s<610 '2z/vr) and of the restricted resolution of EET. the precision of s is poorer compared to g and fi. | Because of the small value $s<6\times 10^{-7}\,2\pi$ /yr) and of the restricted resolution of FFT, the precision of $s$ is poorer compared to $g$ and $f_\sigma$. |
In this sense. a longer integration time is needed to give more accurate results about the nodal resonance of Trojan motion. | In this sense, a longer integration time is needed to give more accurate results about the nodal resonance of Trojan motion. |
The dynamical spectrum of the resonant argument σ can also be constructed in a similar wav. | The dynamical spectrum of the resonant argument $\sigma$ can also be constructed in a similar way. |
We do not show them here but. present empirical expressions of the proper frequencies g.5.f£, and construct à resonance map on the initial plane (eo.20) | We do not show them here but present empirical expressions of the proper frequencies $g, s, f_\sigma$ and construct a resonance map on the initial plane $(a_0,i_0)$. |
Ixnowing the values of the proper frequencies g. and. f; on the initial plane (e.790). we obtain empirical expressions5 through numerical fitting. | Knowing the values of the proper frequencies $g, s$ and $f_\sigma$ on the initial plane $(a_0,i_0)$, we obtain empirical expressions through numerical fitting. |
Set c=ay30.2194sin/o ancl adopt the quaclratic formula used in references (Milani1904:Alarzari.‘Tricarico&Scholl2003b).. the best Gt of these proper frequencies from our calculations are: About one thousand orbits have been used to caleulate the coefficients andthe precision of the fitting is guaranteed by the reduced 47=9.570.10.193,799.1 and 10.7 for g.s and. f, respectively. | Set $x=a_0-30.219, y=\sin i_0$ and adopt the quadratic formula used in references \citep{mil94,mar03b}, the best fit of these proper frequencies from our calculations are: About one thousand orbits have been used to calculate the coefficients andthe precision of the fitting is guaranteed by the reduced $\chi^2=9.570\times 10^{-16}, 3.799\times 10^{-16}$ and $3.646\times 10^{-13}$ for $g, s$ and $f_\sigma$ respectively. |
The value 30.219 in ris assumed to be the semimajor axis at the center of tadpole orbits around the £- point. | The value $30.219$ in $x$ is assumed to be the semimajor axis at the center of tadpole orbits around the $L_5$ point. |
The analytical formulas are svmametric with respect to his center. | The analytical formulas are symmetric with respect to this center. |
As we have mentioned at the end. of 33.1. this svmmectry is not "exactly conserved actually. | As we have mentioned at the end of 3.1, this symmetry is not “exactly” conserved actually. |
In addition. one should note that the analytical expressions are more accurate and reliable in the central part of he (e65./9) plane where the proper frequencies are more accurately determined. | In addition, one should note that the analytical expressions are more accurate and reliable in the central part of the $(a_0,i_0)$ plane where the proper frequencies are more accurately determined. |
Near the border between the stable and unstable region. the motion is more chaotic and the »ecision of the frequencies is relatively poor. | Near the border between the stable and unstable region, the motion is more chaotic and the precision of the frequencies is relatively poor. |
Given the analytical expressions of the proper frequencies. we can identifv the main secular resonances on the initial lane (eo.£9). | Given the analytical expressions of the proper frequencies, we can identify the main secular resonances on the initial plane $(a_0,i_0)$. |
For example. a Ixozai resonance happens when Q—s (since w=ασ O.g=s infers i= 0). so that he position where the Ixozai resonance may arise can be calculated: by solving the equation gGr.gj)—sGr.=0. | For example, a Kozai resonance happens when $g=s$ (since $\omega=\varpi - \Omega$, $g=s$ infers $\dot\omega=0$ ), so that the position where the Kozai resonance may arise can be calculated by solving the equation $g(x,y)-s(x,y)=0$. |
In 111. we plot the major secular resonances on g)the initial dane. | In 11, we plot the major secular resonances on the initial plane. |
The dynamical map is plotted: as the background simultaneously. providing a convenient comparison between he secular resonances and the dynamical stability. | The dynamical map is plotted as the background simultaneously, providing a convenient comparison between the secular resonances and the dynamical stability. |
The very good. agreement. between the fine structures in dynamical map and the locations of clifferent secular resonances. is obvious. | The very good agreement, between the fine structures in dynamical map and the locations of different secular resonances, is obvious. |
As shown in 111. it is clear that the unstable eap. around.)44° is determined. by. the vs resonance. the Wozai resonance can be found at high inclination. and the nodal resonance ix takes place at. low inclination. | As shown in 11, it is clear that the unstable gap around $i_0\sim 44^\circ$ is determined by the $\nu_8$ resonance, the Kozai resonance can be found at high inclination, and the nodal resonance $\nu_{18}$ takes place at low inclination. |
On one hand. around the exact location. every resonance has a "width in which the resonance happens and the corresponding resonant argument oscillates with a definite amplitude. | On one hand, around the exact location, every resonance has a “width” in which the resonance happens and the corresponding resonant argument oscillates with a definite amplitude. |
On the other hand. 111 gives only the location in the phase space where the secular resonance possibly occurs. | On the other hand, 11 gives only the location in the phase space where the secular resonance possibly occurs. |
Whether a resonance actually happens depends on whether the motion is strongly. influenced. by other mechanisms than the resonance itself. | Whether a resonance actually happens depends on whether the motion is strongly influenced by other mechanisms than the resonance itself. |
For example. the V-shape curves in 111 indicate the position where the vis secular resonance may happen. but in fact. we only observed. this resonance at low inclination with /y«1.5 | For example, the V-shape curves in 11 indicate the position where the $\nu_{18}$ secular resonance may happen, but in fact, we only observed this resonance at low inclination with $i_0<1.5^\circ$ . |
At higher inclination this resonance is hidden by other mechanisms. | At higher inclination this resonance is hidden by other mechanisms. |
From the dynamical spectrum of g in 09. we have | From the dynamical spectrum of $g$ in 9, we have |
the Newtonian component ancl the observed. velocities. | the Newtonian component and the observed velocities. |
The velocity e. profiles agree very well with the observed velocity v4; profiles. for high as well as low vj. aud especially so in view of observational complications and the simplicity of our model. | The velocity $v_c$ profiles agree very well with the observed velocity $v_{obs}$ profiles, for high as well as low $v_{obs}$, and especially so in view of observational complications and the simplicity of our model. |
Also. our fits indicate that there is a smooth transition between the small and large disks. with the m, potential becoming progressively more important as (he radial dimensions of (he galaxies increase. | Also, our fits indicate that there is a smooth transition between the small and large disks, with the $m_g$ potential becoming progressively more important as the radial dimensions of the galaxies increase. |
For comparisons with Figures 1 απα 2.. dark matter halo fits are shown by dDETAL or Ohοἱal.(2008) aud. except for NGC 925 and IC 2574. the MOND fits are shown by (2011). | For comparisons with Figures \ref{fig-res} and \ref{fig-res2}, dark matter halo fits are shown by dBETAL or \cite{Oetal:08} and, except for NGC 925 and IC 2574, the MOND fits are shown by \cite{GFdB:11}. |
. Note Chat each dark matter halo fit requires a pair of parameters that is idiosvneratic to the particular galaxy. being modeled. 2x12=24 parameters in all. and that the MOND fits require recurrent (weakines of both the "universal constant αμ ancl the galaxy distances (Bottemaetal.2002). | Note that each dark matter halo fit requires a pair of parameters that is idiosyncratic to the particular galaxy being modeled, $2\times 12=24$ parameters in all, and that the MOND fits require recurrent tweakings of both the “universal constant” $a_0$ and the galaxy distances \citep{Betal:02}. |
. By contrast. all of our fits are for the same two constants. 4, and 46. and the galaxy distances are not modified. | By contrast, all of our fits are for the same two constants, $\gamma_g$ and $\mu_g$, and the galaxy distances are not modified. |
All the dynamically determined M/L ratios in Table 2. are unambiguous and. with one exception (DDO 154). they are consistent with stellar population svuthesis models. | All the dynamically determined M/L ratios in Table \ref{tbl-res} are unambiguous and, with one exception (DDO 154), they are consistent with stellar population synthesis models. |
The same exception was noted by dBETAL in their dark halo modeling: we refer the reader to their paper lor a discussion of possible explanations. | The same exception was noted by dBETAL in their dark halo modeling; we refer the reader to their paper for a discussion of possible explanations. |
Also. the inner M/L ratios lor NGC 7331 and NGC 2903 appear odd. | Also, the inner M/L ratios for NGC 7331 and NGC 2903 appear odd. |
However. possible explanations could be the presence of a strong dust ring in the inner disk of NGC 7331. and the presence of the bar and a very dense molecular disk in the inner disk of NGC 2903. | However, possible explanations could be the presence of a strong dust ring in the inner disk of NGC 7331, and the presence of the bar and a very dense molecular disk in the inner disk of NGC 2903. |
In fact. both dBETAL and also get unrealistic M/L ratios For these (wo galaxies. | In fact, both dBETAL and \cite{GFdB:11} also get unrealistic M/L ratios for these two galaxies. |
The essential result. of this work is that the in, exponential potential can account [or the magnitude of the cliscrepancy ancl reproduces the general shapes of the rotation curves of these 12 THINGS spiral galaxies. | The essential result of this work is that the $m_g$ exponential potential can account for the magnitude of the discrepancy and reproduces the general shapes of the rotation curves of these 12 THINGS spiral galaxies. |
Iivoking dark matter halos to reproduce the observed shapes requires 24 additional free parameters which have no unclerlving physical significance: they are chosen just to get satisfactory fits. | Invoking dark matter halos to reproduce the observed shapes requires 24 additional free parameters which have no underlying physical significance; they are chosen just to get satisfactory fits. |
And. although MOND purportedly involves only one universal constant. eg. iis actually a parameter that does not remain precisely the same for all fits. and the galaxy. distances and the exact functional Forms of F (see Eq. 3)) | And, although MOND purportedly involves only one universal constant, $a_0$, it is actually a parameter that does not remain precisely the same for all fits, and the galaxy distances and the exact functional forms of ${\mathcal F}$ (see Eq. \ref{MF}) ) |
are also sometimes modified. | are also sometimes modified. |
By contrast. the mi, exponential potential is determined by only two fixed and physically significant parameters: 4/4. which is proportional to the exchange boson mass. and 5,. which is proportional to the square of the coupling constant. | By contrast, the $m_g$ exponential potential is determined by only two fixed and physically significant parameters: $\mu_g$ which is proportional to the exchange boson mass, and $\gamma_g$, which is proportional to the square of the coupling constant. |
The inequality 2«24 provides a compelling argument for the superiority of the m, exponential potential overhoc dark matter halos for modeling spiral galaxy rotation profiles. | The inequality $2<24$ provides a compelling argument for the superiority of the $m_g$ exponential potential over dark matter halos for modeling spiral galaxy rotation profiles. |
A similar. although nol so lopsided.inequality applies on contrasting the my potential fits with those of MOND | A similar, although not so lopsided,inequality applies on contrasting the $m_g$ potential fits with those of MOND |
Brinkmann et al. (1996)) | Brinkmann et al. \cite{wpb96}) ) |
analyzed the ASCA observation of aand found distinct. changes in the spectral parameters compared to the earlier ROSAT data. | analyzed the ASCA observation of and found distinct changes in the spectral parameters compared to the earlier ROSAT data. |
These findings were confirmed by Brandt et al. (1997)) | These findings were confirmed by Brandt et al. \cite{brandt97}) ) |
in an independent analysis of the data. | in an independent analysis of the data. |
In particular. the strong aabsorption edge found in the PSPC observation was not detected anymore. | In particular, the strong absorption edge found in the PSPC observation was not detected anymore. |
Instead. both analyses find a spectral feature around ~0.65 keV. which ts interpreted as an emission line by Brinkmann et al. (1996)) | Instead, both analyses find a spectral feature around $\sim 0.65$ keV, which is interpreted as an emission line by Brinkmann et al. \cite{wpb96}) ) |
and a weak aabsorption edge by Brandt et al. (1997)). | and a weak absorption edge by Brandt et al. \cite{brandt97}) ). |
Besides a successful spectral fit. a key argument for invoking the presence of warm absorbers is the apparent discrepancy between the column densities of cold material derived from the optical reddening and the absence of excess soft X-ray absorption. | Besides a successful spectral fit, a key argument for invoking the presence of warm absorbers is the apparent discrepancy between the column densities of cold material derived from the optical reddening and the absence of excess soft X-ray absorption. |
A crucial assumption for this argument is that both. the optical and the X-ray continua. are seen along the same line of sight. | A crucial assumption for this argument is that both, the optical and the X-ray continua, are seen along the same line of sight. |
The necessity of warm material would be alleviated if the X-ray emission were spatially extended. te. if the X-rays would not pass through the material causing the optical extinction. | The necessity of warm material would be alleviated if the X-ray emission were spatially extended, i.e. if the X-rays would not pass through the material causing the optical extinction. |
Observations with the ROSAT HRI allow to set limits on the contribution of an extended component to the X-ray emission by its improved spatial resolution and the confirmation of the rapid X-ray variability observed with ASCA (Brinkmann et al. 1996)). | Observations with the ROSAT HRI allow to set limits on the contribution of an extended component to the X-ray emission by its improved spatial resolution and the confirmation of the rapid X-ray variability observed with ASCA (Brinkmann et al. \cite{wpb96}) ). |
We note that wwas also considered as anarrow-line Seyfert |. galaxy (Osterbrock Pogge 1985). due to some of its. optical (permitted emission line widths. III]/H./ ratio) and X-ray properties (steep spectrum. rapid variability). which are typical for this class of AGN. | We note that was also considered as anarrow-line Seyfert 1 galaxy (Osterbrock Pogge \cite{osterbrock}) ), due to some of its optical (permitted emission line widths, $\beta$ ratio) and X-ray properties (steep spectrum, rapid variability), which are typical for this class of AGN. |
We will discuss some of our results in view of this hypothesis. | We will discuss some of our results in view of this hypothesis. |
Wwwas observed twice with the ROSAT HRI. | was observed twice with the ROSAT HRI. |
The first observation (hereafter H1) took place in 1996 from July 16 to July 21 and resulted in an effective exposure of 6209 s. The second observation (H2) was conducted roughly one year later. from June 15 to June 24 1997. and resulted in 24748 s of good exposure. | The first observation (hereafter H1) took place in 1996 from July 16 to July 21 and resulted in an effective exposure of 6209 s. The second observation (H2) was conducted roughly one year later, from June 15 to June 24 1997, and resulted in 24748 s of good exposure. |
wwas observed on-axis in both observations with an average count rate of =0.3 cts/s. The high spatial resolution of the ROSAT HRI provides tight constraints on any extended emission component in. | was observed on-axis in both observations with an average count rate of $\approx 0.3$ cts/s. The high spatial resolution of the ROSAT HRI provides tight constraints on any extended emission component in. |
334942438... The HRI point spread function (PSF) can be approximated by two Gaussians with σιz2.2 aresee and σο7|.U aresec and an exponential term. which is relevant for large radit (z30 aresec) and bright sources (David et al. 1997)). | The HRI point spread function (PSF) can be approximated by two Gaussians with $\sigma_{\rm 1}\approx 2.2$ arcsec and $\sigma_{\rm 2}\approx 4.0$ arcsec and an exponential term, which is relevant for large radii $\approx 30$ arcsec) and bright sources (David et al. \cite{david}) ). |
The inner core of the PSF corresponds to a projected linear size of ~5.7 kpe at the redshift of13349-2438. | The inner core of the PSF corresponds to a projected linear size of $\approx 5.7$ kpc at the redshift of. |
Due to random errors in the aspect solution. the values of σι and o» vary from 1.9 to 2.5 aresee and from 3.3 to 4.1 aresec. respectively. between individual observations of point sources. | Due to random errors in the aspect solution, the values of $\sigma_{\rm 1}$ and $\sigma_{\rm 2}$ vary from 1.9 to 2.5 arcsec and from 3.3 to 4.1 arcsec, respectively, between individual observations of point sources. |
Further. elongations of the PSF by uncorrected residual wobble motion have been reported for à number of sources (Morse 1994:: W.Pietsch. priv. | Further, elongations of the PSF by uncorrected residual wobble motion have been reported for a number of sources (Morse \cite{morse}; W.Pietsch, priv. |
com.). | com.). |
In à practical. approach. the observation dependent uncertainties were modeled by smearing the theoretical PSF with an additional Gaussian characterized by σι. | In a practical approach, the observation dependent uncertainties were modeled by smearing the theoretical PSF with an additional Gaussian characterized by $\sigma_+$ . |
We searched | We searched |
is the ratio of the MHD Poynting flux to the kinetic energy flux measured at the disk surface. | is the ratio of the MHD Poynting flux to the kinetic energy flux measured at the disk surface. |
This quantity is sometimes referred to as the (initial) jet magnetization. | This quantity is sometimes referred to as the (initial) jet magnetization. |
A cold jet requires therefore o* larger than unity. | A cold jet requires therefore $\sigma^+$ larger than unity. |
We plotted in Fig. | We plotted in Fig. |
15 (top) the jet magnetization as function of the disk launching radius for our reference simulation. | \ref{sigmu} (top) the jet magnetization as function of the disk launching radius for our reference simulation. |
Beyond a radius of about 5, this quantity becomes indeed smaller than unity, corresponding nicely to the end of zone I (super-FM jet). | Beyond a radius of about 5, this quantity becomes indeed smaller than unity, corresponding nicely to the end of zone I (super-FM jet). |
A super-A outflow is nevertheless launched at larger radii, but this is a matter dominated flow that never reaches a steady-state. | A super-A outflow is nevertheless launched at larger radii, but this is a matter dominated flow that never reaches a steady-state. |
The overall picture is therefore consistent. | The overall picture is therefore consistent. |
But what determines the radial distribution o(r)? | But what determines the radial distribution $\sigma^+(r)$? |
Another way to write the initial jet magnetization is | Another way to write the initial jet magnetization is |
We beein by splitting the integral ou the rielthaucl side of equation (57)) into two parts: Iu these equations. we have used the fact that aud 0)=Al (eq. 12)). | We begin by splitting the integral on the righthand side of equation \ref{eqn:friction}) ) into two parts: In these equations, we have used the fact that and $f_0(0)=\dot{M}$ (eq. \ref{eqn:mdotf0}) ). |
We have further defined We uext show that 7 vanishes. | We have further defined We next show that $\cal I$ vanishes. |
First recall that our flow is irrotational. | First recall that our flow is irrotational. |
Specifically. the ó-componeut of the vorticity vanislies. so that Expressing both velocity components in terms of the stream function through equations (1)) aud (5)). we have We substitute the series expansions lor z aud p into this last equation ancl set the coefficients oln all powers ofa r to zero. | Specifically, the $\phi$ -component of the vorticity vanishes, so that Expressing both velocity components in terms of the stream function through equations \ref{eqn:ur}) ) and \ref{eqn:ut}) ), we have We substitute the series expansions for $\psi$ and $\rho$ into this last equation and set the coefficients of all powers of $r$ to zero. |
Following4n thisn procedure forHJ 77L7 aud 1rt. aud usingn the kuown expressionsn [or fa. fy. aud g4. vielcls kleutities. | Following this procedure for $r^2$ and $r^1$, and using the known expressions for $f_2$, $f_1$, and $g_{-1}$, yields identities. |
However. setting the r-independent terius to zero leads to a uoutrivial result: We acd this last equation to the second-order equation (35)). obtaiuiue Multiplying through by gives | However, setting the $r$ -independent terms to zero leads to a nontrivial result: We add this last equation to the second-order equation \ref{eqn:secondr2}) ), obtaining Multiplying through by gives |
reler to a formal correction to a new data set that is obtained by comparing it to an extrinsic data set. | refer to a formal correction to a new data set that is obtained by comparing it to an extrinsic data set. |
In the contributing papers. values of A tend to be reported in groups. | In the contributing papers, values of $M$ tend to be reported in groups. |
To summarize results for a given group. one procedure adopted here is (o state a value of This practice is based on the following lemma: if there are V=4 or more values of Af in a eiven group. and id<2.5 lor all eroup members. it is fair to conclude that none of them differ [rom zero with a confidence level C>0.95. | To summarize results for a given group, one procedure adopted here is to state a value of This practice is based on the following lemma: if there are $N = 4$ or more values of $M$ in a given group, and if $t < 2.5$ for all group members, it is fair to conclude that none of them differ from zero with a confidence level $C \geq 0.95$. |
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