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No subsequent detection of this pulsar has been made exiuuple).. hence we have ouly au approximate period estimate.
No subsequent detection of this pulsar has been made , hence we have only an approximate period estimate.
parameters.
parameters.
Phe values of fh. Oy. and ax are particularly important.
The values of $h$ , $\Omega_{\Lambda}$ , and $\sigma_{8}$ are particularly important.
This spectrum has been previously. calculated in various cases. see. e.g. Llu&Docdelson(2002):Cooray (2002).
This spectrum has been previously calculated in various cases, see, e.g. \citet{hu02, coor02}.
. Llere. it is calculated. for the cosmological moclel ancl parameters fixed in the introduction.
Here, it is calculated for the cosmological model and parameters fixed in the introduction.
The €; quantities of the ISW elleet can be written as follows (Pullana 2000):: where ji being the spherical Bessel function of order £. and where function. {δις} is given by Eqs. (5))
The $C_{\ell} $ quantities of the ISW effect can be written as follows \citep{ful00}: where $j_{\ell}$ being the spherical Bessel function of order $\ell$ , and where function $D_{1}(z)$ is given by Eqs. \ref{ll2}) )
and (6)).
and \ref{ll3}) ).
The integrals in Eqs. (7))
The integrals in Eqs. \ref{isw1}) )
and (8)) have been numerically calculated to get the required spectrum.
and \ref{isw2}) ) have been numerically calculated to get the required spectrum.
Results are presented. in Fig. (2))
Results are presented in Fig. \ref{figu1}) ),
where quantity A,=((6|VC)2a)? in pv. (used. along the paper to describe the angular power spectrum) is clisplaved in the ( interval 2700).
where quantity $\Delta_{_{T}} = [ \ell (\ell +1) C_{\ell} / 2 \pi ]^{1/2} $ in $\mu K$ (used along the paper to describe the angular power spectrum) is displayed in the $\ell $ interval [2,700].
Our estimation. as well as previous ones (see e.g. Llu&Doclelson(2002):CooravPaclmanabhanetal. (2005))). leads to two main conclusions: (1) the most important part of the [SW cllect is produced. by. very large spatial scales (small & values) contributing to small multipoles. and (2) the contribution to this effect strongly decreases as the spatial scale does.
Our estimation, as well as previous ones (see e.g. \citet{hu02, coo02, pad05}) ), leads to two main conclusions: (1) the most important part of the ISW effect is produced by very large spatial scales (small $k$ values) contributing to small multipoles, and (2) the contribution to this effect strongly decreases as the spatial scale does.
For the parameters we have assumed. the A, value corresponding to f=τοῦ is 0.037μὲν and. moreover. quantity AY rapidly decreases as f increases reaching a value close to 0.0045yay for (£~2000.
For the parameters we have assumed, the $\Delta_{_{T}}$ value corresponding to $\ell = 700$ is $ 0.037 \ \mu K$ and, moreover, quantity $\Delta_{_{T}}$ rapidly decreases as $\ell $ increases reaching a value close to $0.0045 \ \mu K$ for $\ell \sim 2000$.
These values are to be compared with those extracted from our numerically simulated maps.
These values are to be compared with those extracted from our numerically simulated maps.
As a technical requirement associated to ray-tracing (see below). our maps are produced bv the total time varving peculiar potential due to all the scales smaller than 60.Ape. which are evolved by N-bocdy simulations from redshift 5.2 to present time: hence. all the ISW ellect. produced. (at 2«3. see Fig. (13)
As a technical requirement associated to ray-tracing (see below), our maps are produced by the total time varying peculiar potential due to all the scales smaller than $60 \ Mpc $, which are evolved by N-body simulations from redshift $5.2$ to present time; hence, all the ISW effect produced (at $z < 3$, see Fig. \ref{figu0}) ))
by these scales is included in the resulting maps.
by these scales is included in the resulting maps.
The elect produced bv scales. greater. than GOAfpe must. be. independently caleulated.
The effect produced by scales greater than $60 \ Mpc$ must be independently calculated.
Is it a pure. TSW elect?
Is it a pure ISW effect?
(X few considerations about linearity are useful to answer this question.
A few considerations about linearity are useful to answer this question.
In order to discuss about lincarity in detail. the root mean square (rms) of the relative mass Ductuations inside a sphere having a present raclius of /?AZpe (randomly. placed in our (lat universe) is estimated.
In order to discuss about linearity in detail, the root mean square (rms) of the relative mass fluctuations inside a sphere having a present radius of $R \ Mpc$ (randomly placed in our flat universe) is estimated.
Condition eg=1 implies that number 2 is also the comoving radius of the sphere.
Condition $a_{0}=1$ implies that number $R$ is also the comoving radius of the sphere.
"his rms value is e(/)=(AAL/AL),< ο. with where Wi(Ad) is the window function. of the R-sphere WAR)=PIRE,ycosg) with yo=ABR: see Pechles (1980)]].
This rms value is $\sigma(R) = (\Delta M/M)_{rms} = \langle (\delta M/M)^{2} \rangle^{1/2}$ , with where $W(kR)$ is the window function of the R-sphere $W(kR) = \frac {3}{y^{3}} (\sin y-y \cos y)$ with $y=kR$; see \citet{pee80}] ].
Numerical. calculations based. on. these. formulae lead to the aU?) values presented in. Fig. 3..
Numerical calculations based on these formulae lead to the $\sigma (R) $ values presented in Fig. \ref{figu2}.
From this ligure it follows that. for the chosen normalization of P(&) and the comoving radius 2=15Alpe. the as value is close to 0.7: hence. it can be assumed (standard point. of view) that regions having a comoving diameter greater than 30Ape can be treated as linearly evolving zones.
From this figure it follows that, for the chosen normalization of $P(k)$ and the comoving radius $R = 15 \ Mpc$, the $\sigma_{15}$ value is close to $0.7$; hence, it can be assumed (standard point of view) that regions having a comoving diameter greater than $30 \ Mpc$ can be treated as linearly evolving zones.
The scale L=60Mpe. used along this paper. evolves in the linear regime with e(30)20.4: hence. scales greater than 60ALpe would produce a pure SW ellect to be separately estimated with appropriate linear techniques.
The scale $\hat{L} = 60 \ Mpc$, used along this paper, evolves in the linear regime with $\sigma(30) \simeq 0.4$; hence, scales greater than $60 \ Mpc$ would produce a pure ISW effect to be separately estimated with appropriate linear techniques.
Phe ISW effect produced by all the scales smaller than GOApe is included in our maps and. obviously. it is smaller than the total ISW elfect. (see lig.
The ISW effect produced by all the scales smaller than $60 \ Mpc$ is included in our maps and, obviously, it is smaller than the total ISW effect (see Fig.
2 and previous comments).
\ref{figu1} and previous comments).
RS is a pure gravitational effect ancl. consequently. onlythedominant dark matter component is considered. whereas the sub-clominant barvonie component is neglected.
RS is a pure gravitational effect and, consequently, onlythedominant dark matter component is considered, whereas the sub-dominant baryonic component is neglected.
On account of these facts. the formation and. evolution of non-linear cosmological structures canbe described by using N-body simulations with appropriate boxes andresolutions.
On account of these facts, the formation and evolution of non-linear cosmological structures canbe described by using N-body simulations with appropriate boxes andresolutions.
In the PAL simulations we use here (Llockney&LastwoordLOSS: 1998).. the peculiar potential satisfies the equation (Alartinez-Conzalez.Sanz&Silk 1990):
In the PM simulations we use here \citep{hoc88,qui98}, , the peculiar potential satisfies the equation \citep{mar90}: :
(Caldwell.Dave.&Steinhardt1998:Maetal.1999:Peeblesatra2003).
\citep{caldwell,ma,peebles03}.
. The generalized Chaplvein gas. as a unification of dark matter and dark energy. was recently proposed and can be constrained by observations (Padianabhan&Choudhury2002:Zhi2004).
The generalized Chaplygin gas, as a unification of dark matter and dark energy, was recently proposed and can be constrained by observations \citep{pad,zhu04}.
. In other cosmological models. DE is replaced by certain possible mechanisms. such as brane world cosnmologies (Randall&Sundrum1999a.b) ancl the Carcassian expansion model (Freese&Lewis2002:ZhuFujimoto2002.2003. 2004)..
In other cosmological models, DE is replaced by certain possible mechanisms, such as brane world cosmologies \citep{rsa,rsb} and the Cardassian expansion model \citep{freese02,zhu02,zhu03,zhu04a}.
Despite its success. the standard CDM theory of cosmic structure formation has several problems. which exist mostly in the small- regime.
Despite its success, the standard CDM theory of cosmic structure formation has several problems, which exist mostly in the small-scale regime.
For example. the observed. rotation curves of cark-matter-cdominatecl cwarl and low surface brightness (LSB) disk galaxies tend (o favor mass profiles with a flat density core (e.g..Salucci&Burkert2000:Gentileetal. 2004).. unlike the singular profiles of the CDM N-body simulations (e.g.. Navarro. Frenk While 1997. NEW proliles: Moore et al.
For example, the observed rotation curves of dark-matter-dominated dwarf and low surface brightness (LSB) disk galaxies tend to favor mass profiles with a flat density core \citep[e.g.,][]{salucci00,gentile04}, , unlike the singular profiles of the CDM $N$ -body simulations (e.g., Navarro, Frenk White 1997, NFW profiles; Moore et al.
1999: Jing 2000: Jing Suto 2002) and that favored by barvon cooling models (i.e.. singular isothermal sphere. SIS profile).
1999; Jing 2000; Jing Suto 2002) and that favored by baryon cooling models (i.e., singular isothermal sphere, SIS profile).
While there are debates on whether the observed data were resolved well enough to indicate a soft core (vandenBosch&Swatersal. 2002).. quite recent N-body simulations of CDM with higher and higher force and mass resolution still Favor cuspy halo profiles (Diemand.Moore&Stadel2004: 2004).
While there are debates on whether the observed data were resolved well enough to indicate a soft core \citep{van,march}, quite recent $N$ -body simulations of CDM with higher and higher force and mass resolution still favor cuspy halo profiles \citep{diemand,fukushige,navarro04,tasitsiomi,wambs04}.
. Recently. an analvtical model was presented for the post-collapse equilibrium structure ol virialized objects that condense out of a low-density cosmological background universe. with or without a cosmological constant (Shapiro.Liev&Raga1999:HievShapiro2001).
Recently, an analytical model was presented for the post-collapse equilibrium structure of virialized objects that condense out of a low-density cosmological background universe, with or without a cosmological constant \citep{shapiro99,Iliev01}.
. The model is based on (he assumption that cosmological halos form from the collapse ancl virialization of top-hat density perturbations. and are spherical. isotropic and isothermal.
The model is based on the assumption that cosmological halos form from the collapse and virialization of `top-hat' density perturbations, and are spherical, isotropic and isothermal.
According to the authors. this prediets a unique. non-sngular. truncated isothermal sphere (NTIS) and provides a simple physical clue about. the existence of soft cores in. halos of cosmological origin.
According to the authors, this predicts a unique, non-singular, truncated isothermal sphere (NTIS) and provides a simple physical clue about the existence of soft cores in halos of cosmological origin.
This NTIS model is claimed to be in good agreement with observations of ihe internal structure of dark matter dominated halos on scales ranging from cwarl galaxies to X-ray clusters.
This NTIS model is claimed to be in good agreement with observations of the internal structure of dark matter dominated halos on scales ranging from dwarf galaxies to X-ray clusters.
In particular. it matches quite well (he mass profiles of dark matter dominated dwarf galaxies deduced. Grom their observed rotation curves (Shapiroetal. 2004)..
In particular, it matches quite well the mass profiles of dark matter dominated dwarf galaxies deduced from their observed rotation curves \citep{shapiro04}. .
Quite recently. the NTIS model was revisited by using the sell-interacting dark matter (SIDM) hypothesis (Abn&Shapiro2004).
Quite recently, the NTIS model was revisited by using the self-interacting dark matter (SIDM) hypothesis \citep{kyungjin}.
. There are other elforts for analvtical derivations of the density profile: e.g.. Hansen(2004) derived the bound on the central density slope of -1 analviicallv (as found mumerically by. NEW).
There are other efforts for analytical derivations of the density profile; e.g., \citet{hansen04} derived the bound on the central density slope of -1 analytically (as found numerically by NFW).
This is done by a simple solution to the Jeans equation. which is valid under (he assumption (hat both the central density profile and the phase-space-like clensity are exact. power laws.
This is done by a simple solution to the Jeans equation, which is valid under the assumption that both the central density profile and the phase-space-like density are exact power laws.
However. (his work did not clearly give a density core.
However, this work did not clearly give a density core.
Toinvestigate whether (here is a soft core atthe center of each CDM halo. we use another
Toinvestigate whether there is a soft core atthe center of each CDM halo, we use another
A shell or bubble within a gas cloud can be generated through a variety of mechanisms.
A shell or bubble within a gas cloud can be generated through a variety of mechanisms.
Currently. one of the most popular theories involves a voung energetic star or cluster. which ionises the surrounding gas into a hot. high pressure region and. produces a spherical. high-density shockwave which propagates into the ambient neutral eas (Shu 1992).
Currently, one of the most popular theories involves a young energetic star or cluster, which ionises the surrounding gas into a hot, high pressure region and produces a spherical, high-density shockwave which propagates into the ambient neutral gas (Shu 1992).
In addition to ionisation. the voung star constantly sheds mass in a stellar wind which impinges on the local gas.
In addition to ionisation, the young star constantly sheds mass in a stellar wind which impinges on the local gas.
The result is a relatively low density sphere. enclosed by a higher density hydrogen shell. the outer edge of which is neutral and moves at supersonic velocities into the ambient eas (AleCray Snow 1979).
The result is a relatively low density sphere, enclosed by a higher density hydrogen shell, the outer edge of which is neutral and moves at supersonic velocities into the ambient gas (McCray Snow 1979).
Supernova events will alsodeposit energy into the medium (Cox 1972) and alternative mechanisms such as Gamma rav bursts (Efremov. Elmegreen and Hodge. 19938) and LIVC-disk. collisions Clenorio-lagle 1951 and "Tenorio-‘Tagle et al.
Supernova events will also deposit energy into the medium (Cox 1972) and alternative mechanisms such as Gamma ray bursts (Efremov, Elmegreen and Hodge, 1998) and HVC-disk collisions (Tenorio-Tagle 1981 and Tenorio-Tagle et al.
1987) max. also produce. elliptical structures with similar appearance.
1987) may also produce elliptical structures with similar appearance.
Lo general. it is very dillicult to determine the process by which a particular shell has been formecl.
In general, it is very difficult to determine the process by which a particular shell has been formed.
The QSO optical luminosity function (OLE) ancl its evolution with recshift has been studied extensively for over three decades (see e.g. Schmidt 1968. Marshall et 11983. Jovle οἱ 11988. Llewett. Foltz Challee 1993. La Franca Cristiani 1997).
The QSO optical luminosity function (OLF) and its evolution with redshift has been studied extensively for over three decades (see e.g. Schmidt 1968, Marshall et 1983, Boyle et 1988, Hewett, Foltz Chaffee 1993, La Franca Cristiani 1997).
This has led to a detailed. picture of the QSO OLE over à wide range in redshift from z0.3 to 2d.
This has led to a detailed picture of the QSO OLF over a wide range in redshift from $z\sim 0.3$ to $z>4$.
In contrast. the local ές< 0.15) QSO OLF is actually much more poorly determined. frustrating attempts to link QSO evolution at moderate to high redshifts with nuclear activity in galaxies at the present epoch.
In contrast, the local $z<0.15$ ) QSO OLF is actually much more poorly determined, frustrating attempts to link QSO evolution at moderate to high redshifts with nuclear activity in galaxies at the present epoch.
This is due to a number of factors associated with the compilation of a suitable sample of local active galactic nuclei (AGN) with which to derive the local OLE.
This is due to a number of factors associated with the compilation of a suitable sample of local active galactic nuclei (AGN) with which to derive the local OLF.
First. local AGN are relatively rare.
First, local AGN are relatively rare.
Their space density is approximately LOO times less than that of normal galaxies. and large area surveys are required. to vield a statistically useful sample.
Their space density is approximately 100 times less than that of normal galaxies, and large area surveys are required to yield a statistically useful sample.
Secondly. many selection techniques for local AGN sulfer (rom morphological biases.
Secondly, many selection techniques for local AGN suffer from morphological biases.
While surveys for stellar-like objects are clearly biased against resolved AG ealaxy-based surveys are equally biased against objects with a dominant nuclear component.
While surveys for stellar-like objects are clearly biased against resolved AGN, galaxy-based surveys are equally biased against objects with a dominant nuclear component.
Finally. accurate knowledge of the nuclear OLE requires accurate subtraction of the light from the host galaxy.
Finally, accurate knowledge of the nuclear OLF requires accurate subtraction of the light from the host galaxy.
In the low luminosity AGN (Ale 23) that constitute the vast majority of the low redshift population. the light from the host galaxy may dominate the nuclear luminosity.
In the low luminosity AGN $M_B>-23$ ) that constitute the vast majority of the low redshift population, the light from the host galaxy may dominate the nuclear luminosity.
Even at relatively low redshifts (27 0.1). secing limitations imposed by ground. based: observations limit accurate modelling of the luminosity profiles of the central regions of ACN host. galaxies to scales typically leger than Lh. kpe.
Even at relatively low redshifts $z \simeq 0.1$ ), seeing limitations imposed by ground based observations limit accurate modelling of the luminosity profiles of the central regions of AGN host galaxies to scales typically larger than $_{50}^{-1}$ kpc.
A recent attempt to estimate the local AG:N OLE has been carried out by Ixóhhler et (C1997). hereinafter KOT.
A recent attempt to estimate the local AGN OLF has been carried out by Köhhler et (1997), hereinafter K97.
Using a sample of 27 candidates selected from. the Iamburg/I2SO objective prism survey. WOT derived a local AGN LE that exhibited a featureless power law form over a wide range in absolute magnitudes 24«Alp15.
Using a sample of 27 candidates selected from the Hamburg/ESO objective prism survey, K97 derived a local AGN LF that exhibited a featureless power law form over a wide range in absolute magnitudes $-24<M_B<-18$.
The form of the low redshift ACGN LE is thus very dillerent from. the two-power-law luminosity function at. higher redshifts (2> 0.5).
The form of the low redshift AGN LF is thus very different from the two-power-law luminosity function at higher redshifts $z\ge0.5$ ).
This is a significant challenge for anv theoretical model which seeks to connect the evolution of QSOs at high redshift with the local AGN population.
This is a significant challenge for any theoretical model which seeks to connect the evolution of QSOs at high redshift with the local AGN population.
The Hamburg/ESO survey covers an extensive area (Glldeg: now extended to 3700deg?. see Wisotzki 2000) ancl is free of morphological bias.
The Hamburg/ESO survey covers an extensive area $^{2}$; now extended to $^2$, see Wisotzki 2000) and is free of morphological bias.
Unfortunately the spatial resolution (12 aresec) of the survey is not. sulliciently good to permit an accurate deconvolution of the galaxy and nuclear light even for the lowest redshift AGN 0.1) in the sample.
Unfortunately the spatial resolution (1–2 arcsec) of the survey is not sufficiently good to permit an accurate deconvolution of the galaxy and nuclear light even for the lowest redshift AGN $z<0.1$ ) in the sample.
For the 0.07 <2« 0.3 sample KOT used: small-aperture. zero-point corrected 2 band CCD magnitudes which were subsequently: corrected. to. reflect nuclear luminosities by subtracting a template host galaxy value of Ade=21: for the AGN with z«0.07 corrections were caleulatec individually and ranged from 0.21 to 1.61 mag.
For the 0.07 $< z <$ 0.3 sample K97 used small-aperture, zero-point corrected $B$ band CCD magnitudes which were subsequently corrected to reflect nuclear luminosities by subtracting a template host galaxy value of $M_B = -21$; for the AGN with $z<0.07$ corrections were calculated individually and ranged from 0.21 to 1.61 mag.
Until recently. AGN cata sets studied with LST were either too small or the samples on which they were based were too heterogeneous to construct a reliable estimate of
Until recently, AGN data sets studied with HST were either too small or the samples on which they were based were too heterogeneous to construct a reliable estimate of
logio(o) and (0, is found to be fogis(a)=(4.9440.75)—(0.16+0.02)tj. with the correlation coefficient of -0.66.
$log_{10}(\sigma)$ and $\langle \mu \rangle_e$ is found to be $log_{10}(\sigma)=(4.94\pm0.75)-(0.16\pm0.02)\langle \mu \rangle_e$ with the correlation coefficient of -0.66.
This relation is translated to {ο-xστ2OuEU.5 where /, is effective surface brightness in flux units. in FSI4W-band.
This relation is translated to $I_e \propto \sigma^{2.5\pm 0.3}$, where $I_e$ is effective surface brightness in flux units, in F814W-band.
Using the results of Binggeli. Sandage Tarenghi (1984). we expect {οxc>" for elliptical galaxies.
Using the results of Binggeli, Sandage Tarenghi (1984), we expect $I_e \propto \sigma^{-2.5}$ for elliptical galaxies.
Using the virial theorem for spherical systems. 07xGAL4T. and the relation between luminosity and effective surface brightness. L=24,7. the Al/L ratio is obtained as AL/Lxo/VIL (Co09).
Using the virial theorem for spherical systems, $\sigma^2 \propto GM_e/R_e$, and the relation between luminosity and effective surface brightness, $L=2\pi I_eR_e^2$, the $M/L$ ratio is obtained as $M/L \propto {\sigma^2}/{\sqrt{I_eL}}$ (Co09).
Substituting our derived Faber-Jackson relation (Paper D. £x1.99+0.14. and the dependency of /, upon o we obtain AJ/LxσOLSEUXLο...AlU.l5czu.22 ‘or all galaxies in our sample.
Substituting our derived Faber-Jackson relation (Paper I), $L\propto{1.99\pm0.14}$, and the dependency of $I_e$ upon $\sigma$, we obtain $M/L \propto \sigma^{-0.25\pm0.33} \propto L^{-0.13\pm0.17}\propto M^{-0.15\pm0.22}$ for all galaxies in our sample.
Our result is more consistent with Co09 who found the Alyy.7LxAL’5 for a sample with almost the same luminosity range as ours.
Our result is more consistent with Co09 who found the $M_{dyn}/L \propto M^{0.09\pm0.06}$ for a sample with almost the same luminosity range as ours.
As seen in panels CA) (B) of Figure 12.. for Maj>> 17.5. some galaxies have larger ÀA7/L ratios with respect to the faintward extrapolation of the linear trend of brighter galaxies. while few faint galaxies follow the ΑΙ—A relation of bright galaxies.
As seen in panels (A) (B) of Figure \ref{fig:mtolratio}, for $M_{814}>-17.5$ , some galaxies have larger $M/L$ ratios with respect to the faintward extrapolation of the linear trend of brighter galaxies, while few faint galaxies follow the $M/L-M$ relation of bright galaxies.
The most deviant galaxies in AL—M diagram (see Figure 129) are the bluer galaxies. too.
The most deviant galaxies in $M/L-M$ diagram (see Figure \ref{fig:mtolratio}) ) are the bluer galaxies, too.
This suggests that the formation of the most deviant dwarf galaxies and those which are following the trend of bright ellipticals can be explained by different scenarios.
This suggests that the formation of the most deviant dwarf galaxies and those which are following the trend of bright ellipticals can be explained by different scenarios.
Nevertheless. we still need more data point to study the scatter of faint dEs about the trends of brighterellipticals and to examine different formation mechanisms at the faint regime.
Nevertheless, we still need more data point to study the scatter of faint dEs about the trends of brighterellipticals and to examine different formation mechanisms at the faint regime.
In agreement with our results (see Figure 125. studying the dwarf galaxies with 16<Ady«ς12 in the core of Perseus cluster. Penny et al. (
In agreement with our results (see Figure \ref{fig:mtolratio}) ), studying the dwarf galaxies with $-16<M_V<-12$ in the core of Perseus cluster, Penny et al. (
2009) found that fainter dwarfs have larger AZ/£ ratios.
2009) found that fainter dwarfs have larger $M/L$ ratios.
In addition. Geha et al. (
In addition, Geha et al. (
2002) showed that fainter galaxies have larger Al/£ ratios compared to their brighter counterparts We have also investigated the waveband dependency of CAL/L)-AL relation. to explore whether it is governed by the change in metalicity of galaxies and/or their stellar population.
2002) showed that fainter galaxies have larger $M/L$ ratios compared to their brighter counterparts We have also investigated the waveband dependency of $M/L$ $M$ relation, to explore whether it is governed by the change in metalicity of galaxies and/or their stellar population.
Comparing panels (A) and (CB). which are based on ACS FSIJW and F475W-band photometry. we find the same behaviour of ΛΙ, ratio in different wavebands.
Comparing panels (A) and (B), which are based on ACS F814W and F475W-band photometry, we find the same behaviour of $M/L$ ratio in different wavebands.
We noted that. the CA//£)-Al relation of galaxies fainter than Aij;=—17.5 is also independent of the passband.
We noted that, the $M/L$ $M$ relation of galaxies fainter than $M_{814}=-17.5$ is also independent of the passband.
Therefore. the stellar population is not the only parameter responsible for the change of A7/L ratios (Mo99).
Therefore, the stellar population is not the only parameter responsible for the change of $M/L$ ratios (Mo99).
As a conclusion. we found that the 17/£L ratio is not constant over all of our sample dEs and varies with the mass and the luminosity of the galaxies.
As a conclusion, we found that the $M/L$ ratio is not constant over all of our sample dEs and varies with the mass and the luminosity of the galaxies.
The variation in A7L ratio is responsible for the deviation of our fainter dEs from the FP.
The variation in $M/L$ ratio is responsible for the deviation of our fainter dEs from the FP.
Since the fainter galaxies in our sample are bluer than the other galaxies and have larger A//£ ratios. we attribute their deviation from the FP to their recent star formation activities (see also $4.39).
Since the fainter galaxies in our sample are bluer than the other galaxies and have larger $M/L$ ratios, we attribute their deviation from the FP to their recent star formation activities (see also \ref{sec:devcol}) ).
In this paper. we studied the fundamental and photometric planes of a sample of 71 dEs in the core of Coma cluster. the nearest massive elliptical-rich cluster down to luminosity of Maaos15.3.
In this paper, we studied the fundamental and photometric planes of a sample of 71 dEs in the core of Coma cluster, the nearest massive elliptical-rich cluster down to luminosity of $M_{814}<-15.3$.
Taking advantage of the DEIMOS high resolution spectrograph. which enables us to measure the internal velocity dispersion of dwarf ellipticals. and high resolution imaging of HST/ACS which allows an accurate surface brightness modelling. we were able to extend the FP of galaxies to —1 magnitude fainter than the previous studies.
Taking advantage of the DEIMOS high resolution spectrograph, which enables us to measure the internal velocity dispersion of dwarf ellipticals, and high resolution imaging of HST/ACS which allows an accurate surface brightness modelling, we were able to extend the FP of galaxies to $\sim$ 1 magnitude fainter than the previous studies.
We obtained the FP for a subsample of 12 galaxies brighter than Au; —20 as 4jx hich is consistent with the previous studies of bright galaxies in Coma (JFK96: Mo99).
We obtained the FP for a subsample of 12 galaxies brighter than $M_{814}=-20$ as $R_e \propto \sigma^{1.33\pm0.02} \langle I\rangle_e^{-0.80\pm0.01} $ which is consistent with the previous studies of bright galaxies in Coma (JFK96; Mo99).
Studying the FP of 141 early-type galaxies in the Shapley super cluster at 2—0.049. Gargiulo et al. (
Studying the FP of 141 early-type galaxies in the Shapley super cluster at $z$ =0.049, Gargiulo et al. (
2009: Ga09) found that the FP follows the relation BR.xots7 for galaxies with ao>»100Anis and Mg<—18.7.
2009: Ga09) found that the FP follows the relation $R_e \propto \sigma^{1.35} \langle I\rangle_e^{-0.81}$ for galaxies with $\sigma>100~km~s^{-1}$ and $M_R<-18.7$.
When including all galaxies in their sample. including low-mass galaxies down to σ 50 Kins.+. Ga09 found a shallower exponent for o.
When including all galaxies in their sample, including low-mass galaxies down to $\sigma \sim$ 50 $km~s^{-1}$, Ga09 found a shallower exponent for $\sigma$.
The FP relation of our dEs displays even shallower exponents for σ and ¢/),. than in Ga09. due to further extension to fainter galaxies.
The FP relation of our dEs displays even shallower exponents for $\sigma$ and $\langle I \rangle_e$ than in Ga09, due to further extension to fainter galaxies.