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. From optical and near-infrared photometry. Puziaetal.(2002.hereafterP02). have suggested that some of the GCs in NGC 4365 might indeed be intermediate-age (2.8 Gyis) and very metal-riceh (Z.— 3Z.). | From optical and near-infrared photometry, \citet[][hereafter P02]{puz02} have suggested that some of the GCs in NGC 4365 might indeed be intermediate-age (2–8 Gyrs) and very metal-rich $Z_{\odot} - 3 Z_{\odot}$ ). |
In this paper we use new spectroscopic data to further investigate the ages and metallicities of GCs in NGC 4365. | In this paper we use new spectroscopic data to further investigate the ages and metallicities of GCs in NGC 4365. |
Spectra for GC candidates in NGC 4365 were obtained in multi-slit mode on 2002 99 and 110 with the LRIS spectrograph (Okeetal.1995). on the Neck I telescope. | Spectra for GC candidates in NGC 4365 were obtained in multi-slit mode on 2002 9 and 10 with the LRIS spectrograph \citep{oke95} on the Keck I telescope. |
Candidate voung clusters were selected [rom the data in P02. but to fill up the slitmask a number of objects without. A-band imaging were also included. | Candidate young clusters were selected from the data in P02, but to fill up the slitmask a number of objects without $K$ -band imaging were also included. |
We obtained 9 exposures with integration times of 30GO min. vielding a total exposure time of 390 min (65 hours). | We obtained 9 exposures with integration times of 30–60 min, yielding a total exposure time of 390 min $\frac{1}{2}$ hours). |
Observations were carried out. simultaneously with the blue ancl red sides on LRIS. using a dichroie splitting al5600AÀ. | Observations were carried out simultaneously with the blue and red sides on LRIS, using a dichroic splitting at. |
On the blue side we used a GOO 1/mm grism. covering AAZ8005600A. while a 600 L/mm erating blazed at wwas used on (he red side. covering the range AASGOO7900À. | On the blue side we used a 600 l/mm grism, covering $\lambda\lambda$, while a 600 l/mm grating blazed at was used on the red side, covering the range $\lambda\lambda$. |
A number of racial velocity and fux standards. as well as Lick/IDS standard stars from: Worthevetal.(1994).. were also observed. | A number of radial velocity and flux standards, as well as Lick/IDS standard stars from \citet{wor94}, were also observed. |
The radial velocity standards were picked [rom (the compilation in Darbier-Drossal(2000) (numbers 9934 and 10927) while the Εις standards were PG0934+554 and Που GOO (Massey.etal.1988). | The radial velocity standards were picked from the compilation in \citet{bar00} (numbers 9934 and 10927) while the flux standards were $+$ 554 and Hiltner 600 \citep{mas88}. |
. Because the spectral range covered in longslit mode is slightly different. [rom the one covered in multislit mode. we observed the fIux standards in multislit mode through one of the slitlets in the NGC 4365 slitmask. (o facilitate flux calibration over the entire spectral range of the science spectra. | Because the spectral range covered in longslit mode is slightly different from the one covered in multislit mode, we observed the flux standards in multislit mode through one of the slitlets in the NGC 4365 slitmask, to facilitate flux calibration over the entire spectral range of the science spectra. |
A slit width of 170 was used for all observations. | A slit width of $1\farcs0$ was used for all observations. |
Initial processing of (he images (bias subtraction. flatfield correction. cosmic rav removal | Initial processing of the images (bias subtraction, flatfield correction, cosmic ray removal |
Note here that the two components of some QSO pairs in KT08 are at similar redshift and therefore the TPE of those fgQSOs may be affected by the bgQSOs. | Note here that the two components of some QSO pairs in KT08 are at similar redshift and therefore the TPE of those fgQSOs may be affected by the bgQSOs. |
The UV light from the bgQSO near a fgQSO may contribute some to the ionization of the near zone of the fgQSO, but this effect should be more significant at the backside than the front side of the fgQSO and lead to a more significant decrease in the DA at Πιν—3 — —5 Mpc. | The UV light from the bgQSO near a fgQSO may contribute some to the ionization of the near zone of the fgQSO, but this effect should be more significant at the backside than the front side of the fgQSO and lead to a more significant decrease in the $DA$ at $R_{\parallel}\sim -3$ – $-5$ Mpc. |
This effect cannot explain the significant excess of DA at ~—3 — —5 Mpc but rather require a more significantlyRy enhanced density in the fgQSO near zone. | This effect cannot explain the significant excess of $DA$ at $R_{\parallel}\sim -3$ – $-5$ Mpc but rather require a more significantly enhanced density in the fgQSO near zone. |
In addition, if the density is also enhanced in the near zone of the bgQSOs, a more significant excess of the absorption at Ry~—5 Mpc can be expected, which might bring the observed DA at Rj——5 Mpc in better consistency and strengthen the above conclusions. | In addition, if the density is also enhanced in the near zone of the bgQSOs, a more significant excess of the absorption at $R_{\parallel}\sim -5$ Mpc can be expected, which might bring the observed $DA$ at $R_{\parallel}=-5$ Mpc in better consistency and strengthen the above conclusions. |
In order to check the significance of the sample variance on the TPE obtained by KT08, we again generate 100 realizations of mock samples, each with 130 synthetic Lya spectra. | In order to check the significance of the sample variance on the TPE obtained by KT08, we again generate 100 realizations of mock samples, each with 130 synthetic $\alpha$ spectra. |
Figure 4 shows the expected TPE for those mock samples with similar settings to that shown in Figure 3dd. According to this Figure, the KT08 results are still consistent with that the QSO lifetime is as long as a few 10” yr and the torus half opening angle Oo~60°. | Figure \ref{fig:f4} shows the expected TPE for those mock samples with similar settings to that shown in Figure \ref{fig:f3}d d. According to this Figure, the KT08 results are still consistent with that the QSO lifetime is as long as a few $10^7$ yr and the torus half opening angle $\Theta_0\sim 60\arcdeg$. |
For the cases of πι€10° yr, the probability that the inconsistency between the KT08 TPE results and the expected TPE are simply due to sample variance is low. | For the cases of $\tau_{\rm lt} \la 10^6$ yr, the probability that the inconsistency between the KT08 TPE results and the expected TPE are simply due to sample variance is low. |
There are still some uncertainties in the current estimation of UVB which may affect the simulation results. | There are still some uncertainties in the current estimation of UVB which may affect the simulation results. |
In our calculations, we set the UVB as l'uyg= 10-7?s-1, which might be somewhat large as the latest estimation of is only 0.5x10-??s-!. | In our calculations, we set the UVB as $\Gamma_{\rm UVB} =10^{-12}{\rm s}^{-1}$ , which might be somewhat large as the latest estimation of is only $0.5\times
10^{-12}{\rm s}^{-1}$. |
If the UVB is set to be (2008a)this smaller value, a more significant LOSPE would be expected, and the effective density enhancement factor (A(R)) should be slightly larger compared to that in Section ?? in order to fit the LOSPE estimated by KT08. | If the UVB is set to be this smaller value, a more significant LOSPE would be expected, and the effective density enhancement factor $\left<\Delta(R)\right>$ should be slightly larger compared to that in Section \ref{sec:low} in order to fit the LOSPE estimated by KT08. |
Therefore, the QSO lifetime τι and/or the torus opening angle Qo are required to be even larger than that given in Section ?? in order to reproduce the TPE. | Therefore, the QSO lifetime $\tau_{\rm lt}$ and/or the torus opening angle $\Theta_0$ are required to be even larger than that given in Section \ref{sec:low} in order to reproduce the TPE. |
But if the UVB is unreasonably much larger than 1071271, the excess of absorption at the transverse direction detected by KT08 cannot be explained by simply changing Τι, Oo and (A(R)). | But if the UVB is unreasonably much larger than $10^{-12}{\rm s}^{-1}$, the excess of absorption at the transverse direction detected by KT08 cannot be explained by simply changing $\tau_{\rm lt}$, $\Theta_0$ and $\left<\Delta(R)\right>$. |
We caution here that other uncertainties could also affect the results presented here quantitatively. | We caution here that other uncertainties could also affect the results presented here quantitatively. |
First, the DA estimated from observations may be affected by the continuum fitting. | First, the $DA$ estimated from observations may be affected by the continuum fitting. |
However, the error in the continuum fitting is typically on the percentage level depending on the signal-to-noise ratio of the QSO spectrum2007),, which is not likely to change the observational results by KT08 on PE qualitatively. | However, the error in the continuum fitting is typically on the percentage level depending on the signal-to-noise ratio of the QSO spectrum, which is not likely to change the observational results by KT08 on PE qualitatively. |
Second, the combined sample in KT08 are obtained from several different instruments and is highly heterogeneous. | Second, the combined sample in KT08 are obtained from several different instruments and is highly heterogeneous. |
The ignoring of the detailed exact redshift and luminosity distributions of the QSO pairs in our simulations is sufficient for the demonstration purpose in this paper, but it may introduce some uncertainties to the resulted PE. | The ignoring of the detailed exact redshift and luminosity distributions of the QSO pairs in our simulations is sufficient for the demonstration purpose in this paper, but it may introduce some uncertainties to the resulted PE. |
Future works on extracting QSO properties from the PEs should consider the uncertainties. | Future works on extracting QSO properties from the PEs should consider the uncertainties. |
In addition, the luminosity of QSOs may evolve or fluctuate on timescales 10° yr, which may lead to more significant excess of absorption in the transverse directions | In addition, the luminosity of QSOs may evolve or fluctuate on timescales $10^6$ yr, which may lead to more significant excess of absorption in the transverse directions. |
However, such a luminosity variation of QSOs is2004).. not required according to our simulations. | However, such a luminosity variation of QSOs is not required according to our simulations. |
Figure 5. shows the expected DA obtained from the mock samples by assuming that both the systematic and random errors in the estimates of the fgQSO systemic redshifts through CIV are the same as those adopted in KTO08. | Figure \ref{fig:f5} shows the expected $DA$ obtained from the mock samples by assuming that both the systematic and random errors in the estimates of the fgQSO systemic redshifts through CIV are the same as those adopted in KT08. |
Compared to the density enhancement used in Figure 2,, here a larger value of it is used so that the LOSPE of fgQSOs obtained by KT08 can also be produced well (see the red line and points in Figure 5aa). | Compared to the density enhancement used in Figure \ref{fig:f2}, here a larger value of it is used so that the LOSPE of fgQSOs obtained by KT08 can also be re-produced well (see the red line and points in Figure \ref{fig:f5}a a). |
With the density enhancement required by the LOSPE, the DA distribution near thefgQSOs indicated by the bgQSO spectra (i.e., the TPE) is also calculated as shown in Figure 5bb. We find that the observational asymmetric distribution of the excess in DA near ~0, i.e., the lack of excess in DA at Ry~2.5 Mpc andRy the significant excess of DA at Ry~—5 Mpc, cannot be simultaneously re-produced for any given Τι and Qo, in contrast to the results in Figures 3dd and 4.. | With the density enhancement required by the LOSPE, the $DA$ distribution near thefgQSOs indicated by the bgQSO spectra (i.e., the TPE) is also calculated as shown in Figure \ref{fig:f5}b b. We find that the observational asymmetric distribution of the excess in $DA$ near $R_{\parallel}\sim 0$, i.e., the lack of excess in $DA$ at $R_{\parallel}\sim 2.5$ Mpc and the significant excess of $DA$ at $R_{\parallel}\sim -5$ Mpc, cannot be simultaneously re-produced for any given $\tau_{\rm lt}$ and $\Theta_0$ , in contrast to the results in Figures \ref{fig:f3}d d and \ref{fig:f4}. |
Assuming that the effect of the density enhancement near type 2 fgQSOs is the same as that of type 1 fgQSOs with similar intrinsic L,, constrained by the LOSPE Figure we generate synthetic Lya forest spectra of (seetype 1 bgQSOs2)), whose light passed by the proximity region of type 2 fgQSOs to study the TPE of type 2 fgQSOs. | Assuming that the effect of the density enhancement near type 2 fgQSOs is the same as that of type 1 fgQSOs with similar intrinsic $L_{\nu_0}$ constrained by the LOSPE (see Figure \ref{fig:f2}) ), we generate synthetic $\alpha$ forest spectra of type 1 bgQSOs whose light passed by the proximity region of type 2 fgQSOs to study the TPE of type 2 fgQSOs. |
Figure 6 shows our simulation results on their DA distribution near the fgQSOs. | Figure \ref{fig:f6} shows our simulation results on their $DA$ distribution near the fgQSOs. |
Figure 6aa shows the dependence of the TPE on the half opening angle of the torus Og for the mock samples of type 2 fgQSOs, given the QSO lifetime. | Figure \ref{fig:f6}a a shows the dependence of the TPE on the half opening angle of the torus $\Theta_0$ for the mock samples of type 2 fgQSOs, given the QSO lifetime. |
As seen from the panel, generally the larger the Oo, the less the excess of the absorption near Ry~0 Mpc. | As seen from the panel, generally the larger the $\Theta_0$, the less the excess of the absorption near $R_{\parallel}\sim 0$ Mpc. |
Figure 6bb shows the dependence of the TPE on the QSO lifetime, given the half opening angle Og= 60°. | Figure \ref{fig:f6}b b shows the dependence of the TPE on the QSO lifetime, given the half opening angle $\Theta_0=60\degr $ . |
As seen from the panel, the differencesin DA are relatively small among the cases with large Ty (~10°—1077 yr). | As seen from the panel, the differencesin $DA$ are relatively small among the cases with large $\tau_{\rm
lt}$ $\sim 10^7-10^{7.7}$ yr). |
If πι~10° yr, the absorption at Ry0 Mpc is larger than those cases with large τι | If $\tau_{\rm lt}\sim 10^6$ yr, the absorption at $R_{\parallel}\sim 0$ Mpc is larger than those cases with large $\tau_{\rm
lt}$ |
with higher IC fluxes. | with higher IC fluxes. |
When the source brightens. the svuehrotron fluxes increase. while the 1C fluxes decrease. | When the source brightens, the synchrotron fluxes increase, while the IC fluxes decrease. |
The svnchirotron fIuxes also show larger variations than the IC: [hixes. | The synchrotron fluxes also show larger variations than the IC fluxes. |
The X-ray SEDs convolved with the svnchrotron and IC components exhibit significant concave shapes. | The X-ray SEDs convolved with the synchrotron and IC components exhibit significant concave shapes. |
The crossing energies and (he SED trough energies increase with (he increasing total fluxes. | The crossing energies and the SED trough energies increase with the increasing total fluxes. |
The flux dependence of the crossing energies and the SED trough energies is consistent with that of the first oobservation (FEOG). | The flux dependence of the crossing energies and the SED trough energies is consistent with that of the first observation (FE06). |
We further notice that the SED trough energies are smaller than the crossing energies in most cases. indicating that they are not the exact energies αἱ which the svuchrotron component transits to the IC component in terms of the equal contributions of the two components to the total fluxes. | We further notice that the SED trough energies are smaller than the crossing energies in most cases, indicating that they are not the exact energies at which the synchrotron component transits to the IC component in terms of the equal contributions of the two components to the total fluxes. |
The SED evolution. characterized by (he shifts of the SED troughs to higher energies with higher flixes. might be mainly caused by the changes of the synehrotron normalization. | The SED evolution, characterized by the shifts of the SED troughs to higher energies with higher fluxes, might be mainly caused by the changes of the synchrotron normalization. |
The changes of the svnchrotron and IC photon indices aud ol the IC normalization may affect the SED evolution in a weaker was. | The changes of the synchrotron and IC photon indices and of the IC normalization may affect the SED evolution in a weaker way. |
The spectral and temporal behaviors of $5 0716-714 and its svuchrotron and IC enission are just the consequence of the peaks of both the svnchrotron and IC SEDs shilting to higher energies with increasing fluxes. | The spectral and temporal behaviors of S5 0716+714 and its synchrotron and IC emission are just the consequence of the peaks of both the synchrotron and IC SEDs shifting to higher energies with increasing fluxes. |
When the source brightens. the svnchrotron peak moves to higher energy. | When the source brightens, the synchrotron peak moves to higher energy. |
In. turn. the high energv tail of the svichrotron emission extends to higher energv. | In turn, the high energy tail of the synchrotron emission extends to higher energy. |
The svnchrotron peak is therefore more close to the observed X-ray. baud. bring on that the svnchrotron flux increases and the svnchrotron spectrum hardens. | The synchrotron peak is therefore more close to the observed X-ray band, bring on that the synchrotron flux increases and the synchrotron spectrum hardens. |
At the same (me. the IC peak also shilts to higher enerev. incurring (hat the low enerev end of the IC emission recedes [rom lower energv (o the observed. X-ray bad. | At the same time, the IC peak also shifts to higher energy, incurring that the low energy end of the IC emission recedes from lower energy to the observed X-ray band. |
The IC peak is thus more far from the observed. X-ray band. | The IC peak is thus more far from the observed X-ray band. |
As a result. the IC! flix decreases and the IC spectrum hardens. | As a result, the IC flux decreases and the IC spectrum hardens. |
Accordingly. the svncehrotron flux anti-correlates with the IC {Inxs when the source brightens. | Accordingly, the synchrotron flux anti-correlates with the IC flux when the source brightens. |
The series of changes make the SED trough move to higher energy with higher total flux. | The series of changes make the SED trough move to higher energy with higher total flux. |
The high energy tail of the svnehrotvon emission originates [rom the hieh energv electrons. showing strong and rapid variations. | The high energy tail of the synchrotron emission originates from the high energy electrons, showing strong and rapid variations. |
The low energv end of the IC emission comes [rom the low energv electrons. exhibiting small ancl slow variations. | The low energy end of the IC emission comes from the low energy electrons, exhibiting small and slow variations. |
Soft lag is expected if both the soft and hard N-ray. variations are caused by the cooling of the hieh energv electrons. | Soft lag is expected if both the soft and hard X-ray variations are caused by the cooling of the high energy electrons. |
In conclusions. 55 07162114 exhibits different X-ray. variability. properties between the ivo oobservations. | In conclusions, S5 0716+714 exhibits different X-ray variability properties between the two observations. |
During the second observation. it shows harder svnchrotron and IC spectra and lower variability amplitude. | During the second observation, it shows harder synchrotron and IC spectra and lower variability amplitude. |
Even though the low energy end of the IC emission contributes more to the hard X-ray [hixes than the high energy (ail of the svnchrotron emission does. the energy dependence of the variability amplitude suggests that the hard. X-ray variations might be dominated by the svnchrotron tail. | Even though the low energy end of the IC emission contributes more to the hard X-ray fluxes than the high energy tail of the synchrotron emission does, the energy dependence of the variability amplitude suggests that the hard X-ray variations might be dominated by the synchrotron tail. |
The large hard. X-ray. variability. amplitude | The large hard X-ray variability amplitude |
where c is a parameter of magnitude 1.10. the emission timescale of gravitational waves can be estimated as La }) EET, — 6.1 alpha,.: ) 1n) where we set Lo—agJAIT fog. and oo is à constant which depends on the value of E but very weakly on sh: for ISOL ay~ 08.0.9. and. 1.2 for D—2. 5/3. and 7/5. respectively. within ~LOM error. | where $\epsilon$ is a parameter of magnitude 1–10, the emission timescale of gravitational waves can be estimated as = 100 _0 ) )^4 M = 6.1 _0 ) )^4, where we set $T = \alpha_0 \beta M^2/R_{\rm eq}$ , and $\alpha_0$ is a constant which depends on the value of $\Gamma$ but very weakly on $\hat A$; for $\beta \alt 0.1$ , $\alpha_0 \sim 0.8$, 0.9, and 1.2 for $\Gamma=2$, 5/3, and 7/5, respectively, within $\sim 10\%$ error. |
The characteristic frequency. of gravitational waves is denoted as — [—⋅⋅ -790¢ MP | The characteristic frequency of gravitational waves is denoted as f = f_r 790 ). |
ON) Assuming that the nonasxisvnimetric perturbation would not be dissipated by viscosities or magnetic fields on the emission timescale of gravitational waves (e.g..Daunm-earteetal. 2000).. the accumulated. eveles of gravitational wave-train AV are estimated as 2[((19) | Assuming that the nonaxisymmetric perturbation would not be dissipated by viscosities or magnetic fields on the emission timescale of gravitational waves \cite{BSS}, the accumulated cycles of gravitational wave-train $N$ are estimated as N 10^3 _0 ) ) . |
The etfective amplitude of gravitational waves is defined bv hup=NUT where denotes the characteristic amplitude οἱ periodic eravitational waves. | The effective amplitude of gravitational waves is defined by $h_{\rm eff} \equiv N^{1/2}h$ where $h$ denotes the characteristic amplitude of periodic gravitational waves. |
Using this relation. we find )(20) (Thorne1987:Lai&Shapiro1995:LiuLinclblom where f=frkegAIT. | Using this relation, we find 3.2 ) ) \cite{Kip,LS,LL1,LL2} where $\bar h\equiv h r R_{\rm eq}/M^2$. |
Since fo h.c and j depend on the values of D. ot. and ἐν. har can vary bv a factor of ~3. | Since $\bar f_r$ , $\bar h$, $\epsilon$ and $\beta$ depend on the values of $\Gamma$, $\hat A$, and $C_a$ , $h_{\rm eff}$ can vary by a factor of $\sim 3$. |
However. for all the rotating stars that we studied. in this paper. fay is always [larger than 1077; at a distance x~100 Mpe with Aa,~30 km and AoLA... | However, for all the rotating stars that we studied in this paper, $h_{\rm eff}$ is always larger than $10^{-22}$ at a distance $r \sim 100$ Mpc with $R_{\rm eq} \sim 30$ km and $M \sim 1.4M_{\odot}$. |
Furthermore. the requency of gravitational waves is about 1 kllz for Ray~30 km and AlzLAAL.. | Furthermore, the frequency of gravitational waves is about 1 kHz for $R_{\rm eq} \sim 30$ km and $M \approx 1.4M_{\odot}$. |
‘Thus. gravitational waves from proto-neutron stars of a high degree of dillerential rotation. of mass LAA.. and. of radius z30 km at a distance of 100 Alpe are Likely to be sources for laser interferometric detectors such as LIGO (Thorne1995).. if the other dissipation processes are neeligible. | Thus, gravitational waves from proto-neutron stars of a high degree of differential rotation, of mass $\sim 1.4 M_{\odot}$, and of radius $\agt 30$ km at a distance of $\sim 100$ Mpc are likely to be sources for laser interferometric detectors such as LIGO \cite{Kip2}, if the other dissipation processes are negligible. |
We have studied the dynamical bar-mocde instability of cillerenially rotating stars of polvtropic equations of state. | We have studied the dynamical bar-mode instability of differentially rotating stars of polytropic equations of state. |
We chose three polvtropic indices and two angular velocity profiles in this study. | We chose three polytropic indices and two angular velocity profiles in this study. |
We found that rotating stars of a high5 cegree5 of dillerential rotation are dynamically unstable against the nonaxisvounetric bar-mocde deformation. even with 3«0.27. irrespective of the polvtropic indices ane angular velocity profile. | We found that rotating stars of a high degree of differential rotation are dynamically unstable against the nonaxisymmetric bar-mode deformation even with $\beta \ll 0.27$, irrespective of the polytropic indices and angular velocity profile. |
Phe criterion of the value of 3 for onset of the instability depends on the rotational profile anc the equations of state. but the dependence is very weak if the degree ofdillerential rotation is high enough as vi0.1. | The criterion of the value of $\beta$ for onset of the instability depends on the rotational profile and the equations of state, but the dependence is very weak if the degree of differential rotation is high enough as $\hat A \sim 0.1$. |
We estimated. the effective amplitude of gravitationa waves [rom nonaxisvmametrie objects formed after onset of the dynamical instability. | We estimated the effective amplitude of gravitational waves from nonaxisymmetric objects formed after onset of the dynamical instability. |
For typical proto-neutron stars of mass LAAL. and radius several 10. km. the effective amplitude of gravitational waves at a distance of 100 Alpe is larger than 10 and the frequency ~ 1 ΚΣ. | For typical proto-neutron stars of mass $\sim 1.4 M_{\odot}$ and radius several $10$ km, the effective amplitude of gravitational waves at a distance of $\sim 100$ Mpc is larger than $10^{-22}$, and the frequency $\sim$ 1 kHz. |
Therefore. the gravitational waves can be sources for laser interferometric detectors. such as advanced LIGO (ο... Vhorne 1995). | Therefore, the gravitational waves can be sources for laser interferometric detectors such as advanced LIGO (e.g., Thorne 1995). |
As we mentioned above. this conclusion is. drawn under the assumption that dissipation of nonaxisymmoetric perturbations by viscosity ancl magnetic fields is negligible. | As we mentioned above, this conclusion is drawn under the assumption that dissipation of nonaxisymmetric perturbations by viscosity and magnetic fields is negligible. |
The dissipation timescale due to molecular viscosities ancl magnetic braking is likely to be longer than LO see (e.g.Baumearteetal. 2000). | The dissipation timescale due to molecular viscosities and magnetic braking is likely to be longer than 10 sec \cite{BSS}. |
. Phus. these cllects can be safely neglected. | Thus, these effects can be safely neglected. |
However. turbulent magnetic viscosity (Balbus&Lawley1998) may be relevant lor redistribution of the angular momentum profile. | However, turbulent magnetic viscosity \cite{BH} may be relevant for redistribution of the angular momentum profile. |
This implies that a cillercntially rotatingstar might be enforced toa rigidly rotating stateon a dvnamical timescale and.hence.thenonaxisvmamoetric structure might.disappear. | This implies that a differentially rotatingstar might be enforced toa rigidly rotating stateon a dynamical timescale and,hence,thenonaxisymmetric structure mightdisappear. |
Many.theoretical works have clarified that the magnetic viscous ellect can redistribute the angular momentum distribution of accretion disks around central objects on a dynamical timescale | Manytheoretical works have clarified that the magnetic viscous effect can redistribute the angular momentum distribution of accretion disks around central objects on a dynamical timescale |
Pecuhar velocities for cach galaxy are deteriuned frou the N-body simulations. | Peculiar velocities for each galaxy are determined from the N-body simulations. |
As a result. these velocities have the full structure we might expect to find in the data. | As a result, these velocities have the full structure we might expect to find in the data. |
The most miportaut limitation of the GIF simulations for this conparison is them relatively low mass resolution. | The most important limitation of the GIF simulations for this comparison is their relatively low mass resolution. |
Thev resolve ouly the most massive aud Iunimous host ealaxics. | They resolve only the most massive and luminous host galaxies. |
To test our analysis of SDSS satellite inotions. we conduct a parallel analysis within the GIE sunulatious. | To test our analysis of SDSS satellite motions, we conduct a parallel analysis within the GIF simulations. |
We define as isolated all galaxies which are at least two times brighter than anv other galaxy within their halo. | We define as isolated all galaxies which are at least two times brighter than any other galaxy within their halo. |
We then search these for cases with satellites at least four times fainter. | We then search these for cases with satellites at least four times fainter. |
We use the velocity differences between hosts aud satellites to populate velocity difference listoerams. aud sort these bv host hpuuinositv. iu the same meamner used in the SDSS satellite studs; | We use the velocity differences between hosts and satellites to populate velocity difference histograms, and sort these by host luminosity, in the same manner used in the SDSS satellite study. |
As a first check of Equation 3.0 we use the simulations to check our asstuuptions about {j and the relationship between σᾷ aud lation.(2. | As a first check of Equation \ref{m260_def}, we use the simulations to check our assumptions about $\beta$ and the relationship between $\sigma_{r}^{2}$ and $\overline{v_{r}^{2}}$. |
We calculate the velocity anisotropy from the sinn and fud P=0.06+0.05. | We calculate the velocity anisotropy from the simulation, and find $\beta = 0.06 \pm 0.03$. |
We also find the LOS velocity dispersion σὲ=1.0340.03«(c2, | We also find the LOS velocity dispersion $\sigma_{r}^{2} = 1.03 \pm
0.03 \times \overline{v_{r}^{2}}$. |
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