Gravitational potential and X-ray luminosities of early-type galaxies observed with XMM-Newton and Chandra

R. Nagino; K. Matsushita

doi:10.1051/0004-6361/200810978

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Volume 501 / No 1 (July I 2009)

A&A, 501 1 (2009) 157-169

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Issue		A&A Volume 501, Number 1, July I 2009


Page(s)		157 - 169
Section		Extragalactic astronomy
DOI		https://doi.org/10.1051/0004-6361/200810978
Published online		29 April 2009

Gravitational potential and X-ray luminosities of early-type galaxies observed with XMM-Newton and Chandra

R. Nagino - K. Matsushita

Tokyo University of Science, 1-3 Kagurazaka, Shinjyuku-ku, 162-8601 Tokyo, Japan

Received 17 September 2008 / Accepted 25 March 2009

Abstract
Aims. We study the dark matter content in early-type galaxies and investigate whether X-ray luminosities of early-type galaxies are determined by the surrounding gravitational potential.
Methods. We derived gravitational mass profiles of 22 early-type galaxies observed with XMM-Newton and Chandra.
Results. Sixteen galaxies show constant or decreasing radial temperature profiles, and their X-ray luminosities are consistent with kinematical energy input from stellar mass loss. The temperature profiles of the other 6 galaxies increase with radius, and their X-ray luminosities are significantly higher. The integrated mass-to-light ratio of each galaxy is constant at that of stars within 0.5- $1~r_{\rm e}$ , and increases with radius, where $r_{\rm e}$ is the effective radius of a galaxy. The scatter of the central mass-to-light ratio of galaxies was less in K-band light. At $3~r_{\rm e}$ , the integrated mass-to-light ratios of galaxies with flat or decreasing temperature profiles are twice the value at $0.5~r_{\rm e}$ , where the stellar mass dominates, and at $6~r_{\rm e}$ , these increase to three times the value at $0.5~r_{\rm e}$ .
Conclusions. This feature should reflect common dark and stellar mass distributions in early-type galaxies: within $3~r_{\rm e}$ , the mass of dark matter is similar to the stellar mass, while within $6~r_{\rm e}$ , the former is larger than the latter by a factor of two. In contrast, X-ray luminous galaxies have higher gravitational mass in the outer regions than X-ray faint galaxies. We describe these X-ray luminous galaxies as the central objects of large potential structures; the presence or absence of this potential is the main source of the large scatter in the X-ray luminosity.

Key words: galaxies: elliptical and lenticular, cD - galaxies: ISM - X-rays: galaxies - X-rays: ISM

1 Introduction

The bottom-up hierarchical theory of galaxy formation predicts that galaxies should be embedded in massive dark matter halos (e.g. Navarro et al. 1997). The presence of dark matter in spiral galaxies has been revealed through observations of stellar rotation curves (van Albada et al. 1985; Rubin et al. 1978). However, the study of halos in early-type galaxies is limited due to a lack of suitable and easy tracers such as rotation curves. Recently, observations of stellar velocity dispersion of early-type galaxies have reached to 1- $2~r_{\rm e}$ , and a correlation between mass-to-light ratio and optical luminosity was found (e.g., Gerhard et al. 2001; Kronawitter et al. 2000). Here, $r_{\rm e}$ is the effective radius of a galaxy. For a small number of galaxies, mass profiles up to several $r_{\rm e}$ have been obtained using test particles such as globular clusters or planetary nebulae (e.g., Romanowsky et al. 2003; Chakrabarty & Raychaudhury 2008).

Table 1: Galaxy sample in the XMM-Newton archive data.

X-ray observations provide a powerful tool to study the shape of the gravitational potential, and hence dark matter distributions, of early-type galaxies. These galaxies have a hot, X-ray-emitting interstellar medium (ISM), which is considered to be gravitationally confined (e.g., Fukazawa et al. 2006; Matsushita 2001; Forman et al. 1985). The ISM luminosities of early-type galaxies vary by two orders of magnitude for the same optical B-band luminosity (L_B) (e.g., Beuing et al. 1999; Matsushita et al. 2000; Matsushita 2001; Canizares et al. 1987), whereas optical observations indicate that these galaxies are dynamically uniform systems (Bender et al. 1993; Djorgovski & Davis 1987; Kronawitter et al. 2000). A key to solving this discrepancy is the extended X-ray emissions that have been detected around X-ray luminous early-type galaxies (Matsushita 2001; Matsushita et al. 1998). On the basis of ROSAT data, Matsushita (2001) discovered that, for most early-type galaxies, ISM luminosities within the optical radius agree with the kinematical energy input from the stellar mass loss ( $L_\sigma$ ). These galaxies have flat or decreasing temperature profiles against radius. In contrast, galaxies with ISM luminosities much larger than $L_\sigma$ show largely extended emission with a radius of a few tens of $r_{\rm e}$ with positive temperature gradients. XMM-Newton RGS observations provided evidence of a weak positive temperature gradient in the inner region of the ISM in NGC 4636, which has a much higher ISM luminosity than $L_\sigma$ (Xu et al. 2002). The correlation between the temperature gradient and spatial distribution was confirmed with Chandra observations (Fukazawa et al. 2006). These features suggest that X-ray luminous early-type galaxies commonly sit in the center of a large-scale (a few hundred kpc) potential well, which leads to their high luminosities. Other galaxies may lack such a large-scale potential. On the basis of the extent of the ISM brightness, Matsushita (2001) denoted galaxies as either X-ray extended galaxies or X-ray compact galaxies. The gravitational mass profile of cD galaxies also shows two distinct contributions that can be assigned to the gravitational potential of the cD galaxy and that of the cluster (Matsushita et al. 2002). Thus, the only way to measure the gravitational mass profile of pure early-type galaxies is to observe the X-ray compact galaxies.

With ROSAT PSPC observations, O'Sullivan et al. (2003) found that the relation between the central stellar velocity dispersion and the temperature obtained from X-ray emission is similar to that for clusters and the relation between the X-ray luminosity and the temperature has a steep slope comparable to that found for galaxy groups.

Table 2: Observational log of the sample galaxies.

Chandra and XMM-Newton have already observed several tens of early-type galaxies. Most of the analysis was done for X-ray luminous and extended objects, and the number of X-ray compact galaxies with accurately derived gravitational mass profiles is still limited. For X-ray luminous galaxies, mass profiles are easily obtained over $10~r_{\rm e}$ (Fukazawa et al. 2006; Humphrey et al. 2006; Mathews et al. 2006). Using XMM-Newton, even for several X-ray compact galaxies, mass profiles can be derived up to several $r_{\rm e}$ (Fukazawa et al. 2006), and observed gravitational mass profiles of X-ray extended and X-ray compact galaxies are similar when plotted against radius in units of r₂₀₀. The dark matter profiles are well described by the NFW model (Navarro et al. 1996,1997), which is based on numerical simulations assuming cold dark matter (CDM) as well as galaxy clusters (Fukazawa et al. 2006; Zappacosta et al. 2006). Chandra observations suggested that the shape of the X-ray isophotes is unrelated to the shape of the gravitational potential (Diehl & Statler 2008,2007).

In this study, we obtained gravitational mass profiles of 22 early-type galaxies observed with XMM-Newton and Chandra to investigate whether X-ray luminosities of early-type galaxies are determined by the surrounding gravitational potential and to study dark matter content in early-type galaxies. Throughout this paper, we adopt the solar abundances of Anders & Grevesse (1989). Unless otherwise specified, errors are quoted at $1\sigma$ confidence.

2 Targets and observations

We analyzed archival data of 22 early-type galaxies with distances less than 40 Mpc and B-band luminosities $L_B>10^{10.1}~L_{\odot}$ observed with XMM-Newton. The values of L_B and the distances to the galaxies are taken from Tully (1988). The characteristics and observational log of the sample galaxies are summarized in Tables 1 and 2, respectively. The sample includes 15 elliptical and 7 S0 galaxies. Eight are located in the Virgo Cluster, 2 are in the Fornax Cluster, and the others are either in the field or in small groups. All observations were carried out with MOS1, MOS2, and PN together.

We also used Chandra data for 19 of the sample galaxies with good signal-to-noise ratios to derive the mass profile at their central regions. As summarized in Table 2, 15 galaxies were observed with ACIS-S, and 4 galaxies were observed with ACIS-I.

3 Data reduction

3.1 XMM-Newton

We analyzed MOS1, MOS2, and PN data of 21 galaxies. For NGC 4472, only MOS1 and MOS2 data were used, since PN data for this galaxy did not exist in the archive. We used XMMSAS version 7.0.0 for the data reduction.

We selected events with FLAG = 0 and PATTERN smaller than 4 and 12 for the PN and MOS, respectively. A significant fraction of XMM-Newton observations is contaminated by soft proton flares. To filter the flares, for each observation, we made a count rate histogram of each detector, fitted the histogram with a Gaussian, and selected times within $2.5~\sigma$ of the mean of the histogram. The total exposure times after screening the flare events are summarized in Table 2.

The spectra were accumulated within rings centered on the center of each galaxy. Hereafter, we denote r as the projected radius from the galaxy center. We excluded point sources with the sum of MOS1 and MOS2 count rates larger than 0.01 count/s. The edetect_chain command was used to detect point sources. The response matrix file and the auxiliary response file corresponding to each spectrum were calculated using SAS version 7.0.0.

The background spectrum was calculated for each spectrum by integrating blank sky data in the same detector regions. Among deep sky observations with the XMM, we selected data with the most similar background to that of each galaxy, after screening background flare events in the same way. Each background agrees well with the data at higher energies, as shown in Fig. 1 for NGC 4636.

Table 2 also summarizes total counts of MOS (MOS1 + MOS2) and PN within $4~r_{\rm e}$ centered on each galaxy. Here, an annular region, 10-14 $^{\prime }$ , from the center of each galaxy was used as a background after subtracting a blank sky data. The total counts of sum of those of MOS and PN have a wide range from 1000 to 600 000. We analyzed projected annular spectra of all of the sample galaxies, while fittings of deprojected spectra were performed for thirteen galaxies with the total counts >12 000.

3.2 Chandra

Chandra data analysis was performed with the CIAO software package, version 3.3. We excluded time regions with a high background rate. We also eliminated point sources identified with the tool wavedetect. The outer region of each data set was subtracted as background.

4 Spectral analysis and results

4.1 Spectral fit

4.1.1 Projected annular spectra

To derive the gravitational mass profiles of individual galaxies, we need temperature and density profiles of the ISM. First, we fitted projected annular spectra centered on each galaxy from MOS and PN simultaneously, except NGC 4472. To exclude possible emission from our Galaxy and surrounding clusters, we also subtracted the spectrum in an annular region, 10 $^{\prime }$ -14 $^{\prime }$ , from the annular spectra of each galaxy. The fitting model is a sum of a vAPEC model (Smith et al. 2001) and a power-law model. The vAPEC model represents thin thermal emission from the ISM, and the power-law model represents the contribution from unresolved low-mass X-ray binaries (LMXBs), where we fixed the power-law index at 1.6. Chandra observations found that total spectra of discrete sources in early-type galaxies are well described with this power-law model (Blanton et al. 2001; Randall et al. 2004). The two components were subjected to a common absorption with fixed column density ( $N_{\rm H}$ ) at the Galactic value from Dickey & Lockman (1990). We organized heavy element abundances into three groups: the $\alpha$ -element O group (O, Ne, and Mg), Si group (Si and S), and Fe group (Fe and Ni). The abundances of the three elemental groups were allowed to vary. For the innermost region of IC 1459, we added a power-law model from the central nuclei found by Chandra (Fabbiano et al. 2003).

For the brightest galaxies, NGC 4472, NGC 4636, NGC 4649, and NGC 5044, whose total counts within $4~r_{\rm e}$ are greater than 200 000, we performed spectral fitting on each annular region. In order to derive accurate temperature profiles of the ISM in the other galaxies with lower signal-to-noise ratio, the spectra of all annular regions were fitted simultaneously, where the ISM abundances were assumed to have common values.

Table 3 and Fig. 18 summarize the results of the spectral fitting, ISM temperature, abundance, and ISM luminosity. Figure 2 shows MOS and PN spectra of the innermost regions of several representative galaxies. The spectra of X-ray faint galaxies, whose total counts within $4~r_{\rm e}$ are less than 12 000 counts, provide gradually smaller values of the reduced- $\chi^2$ with this single-temperature model (hereafter 1T model) for the ISM. However, in a representative spectrum of NGC 4382 whose ISM temperature is $\sim$ 0.4 keV, there are residual structures around 0.9 keV. The X-ray brighter galaxies show larger reduced- $\chi^2$ . The spectra of galaxies with $kT \sim 0.6$ keV, NGC 4636, NGC 720 and NGC 3923, show common residuals at 0.7-0.9 keV (Fig. 2). NGC 4649, which is the galaxy with $kT \sim 0.8$ keV, has different residual structures from the other three galaxies.

$\begin{figure} \par\includegraphics[width=9cm,clip]{0978f01.eps} \end{figure}$	Figure 1: Raw MOS (MOS1 + MOS2) spectrum at r=6-14 $^{\prime }$ of NGC 4636 (black), and the adopted background spectrum (red).
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4.1.2 Deprojected spectra

To consider projection effects, we performed spectral fittings of deprojected spectra. For the data with high statistics, for which the total counts of the sum of those of MOS and PN within $4~r_{\rm e}$ are greater than 12 000, deprojected spectra were calculated using ``onion peeling'' methods by subtracting the contribution from the outer shell regions for all spectral components, assuming the ISM is spherically symmetric as described by Takahashi (2004). We then fitted the deprojected spectra with the 1T model in the same way as in Sect. 4.1.1.

Table 4 and Fig. 18 summarize the results. The reduced $\chi^2$ reduced to $\sim$ 1 except at the innermost regions of three brightest galaxies, NGC 4472, NGC 4636, and NGC 4649. However, residual structures around 0.7-0.9 keV in the projected spectra still remain in the deprojected spectra fitted with the 1T model (Fig. 2). We also fitted the spectra of innermost regions of the three brightest galaxies with a two-temperature vAPEC model for the ISM (hereafter 2T model). The results are summarized in Table 4. The reduced $\chi^2$ reduced to 1.2-1.5, and even the 2T model gives similar residual structures (Fig. 2). These discrepancies in the Fe-L energy range are also seen in the RGS spectrum of the X-ray luminous elliptical galaxy, NGC 4636 (Xu et al. 2002). The Suzaku observations of NGC 720 and NGC 1404 whose ISM temperatures are also $\sim$ 0.6 keV also give similar residual structures (Tawara et al. 2008; Matsushita et al. 2007). Therefore, these residual structures are likely to be related to poorly modeled Fe-L lines.

The spectral fittings of the deprojected spectra mostly give the same temperatures as those of the projected ones (Fig. 18). Therefore, for the fainter galaxies for which the deprojected analysis were not performed, we used the temperature profiles derived from the projected spectra to derive gravitational mass profiles.

$\begin{figure} \par\includegraphics[width=13.6cm,clip]{0978f02.eps} \end{figure}$

Figure 2:

a) Innermost projected spectra observed with MOS (black) and PN (red), and innermost deprojected spectra with MOS (blue) and PN (magenta). These spectra are fitted with a vAPEC model plus power-law multiplied by the Galactic absorption (solid line). Dashed lines correspond to the contribution from each component. b), c) The actual data to model ratio from the fit in panel a). The meanings of colors correspond to that in panel a). d) The same as panel b) and c), but using the vAPEC + vAPEC model plus power-law multiplied by the Galactic absorption as the fitting model.

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4.2 Results

4.2.1 ISM luminosities within $4~r_{\rm e}$

We derived the absorption-corrected ISM luminosities ( $L_{\rm ISM}$ ) and the luminosities of the power-law component ( $L_{\rm hard}$ ) in the energy band of 0.3-2.0 keV within $4~r_{\rm e}$ (Table 5). The values of $L_{\rm ISM}$ derived from the deprojected spectra are close to those from projected annular spectra. Hereafter, we use $L_{\rm ISM}$ from the deprojected analysis. For the X-ray fainter galaxies without deprojected analysis, we use the values derived from the projected analysis.

The relationship of $L_{\rm ISM}$ to L_B is shown in the left panel of Fig. 3. The sample galaxies have L_Bfrom 10^10.1 to $10^{10.9}~{L_\odot}$ . On the other hand, $L_{\rm ISM}$ scatters from 10^39.4 erg/s to 10^42.4 erg/s.

The right panel of Fig. 3 shows the correlation between $L_{\rm ISM}$ within $4~r_{\rm e}$ and $L_B\sigma ^2$ , with $\sigma$ denoting the central stellar velocity dispersion in each galaxy. If stellar motion is the main heat source for the hot ISM, its X-ray luminosity should be approximated by the input rate of the kinetic energy of the gas from stellar mass loss. This is proportional to $L_B\sigma ^2$ , because the mass-loss rate is thought to be proportional to L_B (e.g., Ciotti et al. 1991). Figure 3 also shows the expected energy input from stellar mass loss ( $L_\sigma$ ) assuming a mass-loss rate of $1.5 \times 10^{-11} (L_B/L_{\odot})~ t_{15}^{-1.3}~M_{\odot}~{\rm yr}^{-1}$ (Ciotti et al. 1991). Here, t₁₅ is the stellar age in units of 15 Gyr, and we assumed a stellar age of 12 Gyr. Several galaxies have larger $L_{\rm ISM}$ than $L_\sigma$ , while $L_{\rm ISM}$ values of the other galaxies are similar to or smaller than $L_\sigma$ .

$\begin{figure} \par\includegraphics[width=13.0cm,clip]{0978f03.eps} \end{figure}$

Figure 3:

$L_{\rm ISM}(<$ $4~r_{\rm e})$ of galaxies plotted against L_B ( left panel) and $L_B\sigma ^2$ ( right panel). Symbols indicate galaxy categories defined in Sect. 4.2.2 for $X_{\rm E}$ galaxies (red crosses), field $X_{\rm C}$ galaxies (filled blue circles), and $X_{\rm C}$ galaxies in the clusters (open blue circles). The solid line represents the kinetic heating rate by stellar mass loss ( $L_\sigma$ ).

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Table 5: X-ray luminosities within $4~r_{\rm e}$ of each sample galaxy.

4.2.2 Temperature profiles of the ISM and classification with X-ray extended and X-ray compact galaxies

Figure 4 shows the derived radial temperature profiles of the ISM. Some galaxies have gradually increasing temperature profiles toward the outer radius. In contrast, other galaxies have flat or decreasing radial temperature profiles. The galaxies with positive temperature gradients have high ISM temperatures of 0.8-1.5 keV at a radius of several times $r_{\rm e}$ , which are comparable to those of galaxy groups. On the other hand, the temperatures of the other galaxies are systematically lower at 0.2-0.6 keV. The derived temperature profiles were fitted with the sum of a constant and single- or double- $\beta$ functions.

The derived temperature profiles are mostly consistent with previous results from ROSAT (Matsushita 2001) and Chandra (Fukazawa et al. 2006; Athey 2007), except central regions of several brightest galaxies with positive temperature gradients, due to the higher angular resolution of Chandra.

In Fig. 5, we plotted kT(1- $~4r_{\rm e})/kT(<$ $1~r_{\rm e})$ and kT(4- $8~r_{\rm e})/kT(<$ $1~r_{\rm e})$ against $L_{\rm ISM}/L_B\sigma ^2$ . Here, kT(< $1~r_{\rm e})$ , kT(1- $4~r_{\rm e})$ , and kT(4- $8~r_{\rm e})$ correspond to the emission-weighted ISM temperatures of regions in $R< 1~r_{\rm e}$ , $1~r_{\rm e}<R<4~r_{\rm e}$ and $4~r_{\rm e}<R<8~r_{\rm e}$ , respectively. Here, R is the deprojected radius from the galaxy center. In general, the temperature profiles of galaxies with $L_{\rm ISM} \lesssim L_\sigma$ have smaller kT(1- $4~r_{\rm e})$ and kT(4- $8~r_{\rm e})$ than kT(< $1~r_{\rm e})$ . In contrast, $L_{\rm ISM}$ of galaxies with kT(4- $8~r_{\rm e})/kT(<$ $1~r_{\rm e})>1.3$ are systematically larger than $L_\sigma$ .

Our sample galaxies are divided into two types: X-ray faint galaxies with flat or negative temperature gradients and X-ray luminous galaxies with positive temperature gradients. The ISM luminosities in the former type are consistent with heating by stellar motion, while galaxies of the latter type need additional sources of heating. Hereafter, we denote galaxies with kT(4- $8~r_{\rm e})/kT(<$ $1~r_{\rm e})>1.3$ as X-ray extended ( $X_{\rm E}$ ) galaxies and others as X-ray compact ( $X_{\rm C}$ ) galaxies. The classification of each galaxy is summarized in Table 1.

5 Spatial analysis and results

5.1 X-ray surface brightness and gas density profiles

We derived radial profiles of X-ray surface brightness from background-subtracted and vignetting-corrected X-ray images from MOS1 and MOS2. We considered only photons in the energy band 0.8-2.0 keV, where the ISM emission dominates. PN data were not used for this analysis because of gaps between CCD chips. Figure 6 shows two representative X-ray surface brightness profiles, those of an $X_{\rm E}$ galaxy, NGC 4636, and an $X_{\rm C}$ galaxy, NGC 720.

Assuming circular symmetry, we deprojected the X-ray surface brightness profiles to derive gas density profiles. In order to subtract emission from outside the field of view, we first fitted the radial surface brightness profile within $8~r_{\rm e}$ of each galaxy and assumed that the profile extends outside the field of view. The radial profiles of most of the galaxies were fitted with a $\beta$ -model. The brightness of several galaxies in clusters are clearly constant at the outer regions because of the surrounding intra-cluster medium (ICM). Therefore, we fitted these profiles with the sum of a $\beta$ model and a constant. Several X-ray luminous galaxies need a double- $\beta$ model to fit the surface brightness profiles. Because at > $5~r_{\rm e}$ , one of the $\beta$ models dominates, the profiles at r> $5~r_{\rm e}$ are fitted with a single- $\beta$ model. The derived density profiles are summarized in Fig. 7. Since we need only the gradient of a density profile to derive a gravitational mass profile, the plotted density profiles were arbitrarily normalized.

We also used Chandra data for 19 galaxies with sufficiently high signal-to-noise ratios to derive accurate X-ray surface brightness profiles within 1- $2~r_{\rm e}$ . Radial profiles of X-ray surface brightness were derived from ACIS X-ray images in the energy band 0.3-2.0 keV. Then, we deprojected the X-ray surface brightness profiles and derived gas density profiles in the same way as for the XMM-Newton data. As summarized in Fig. 7, normalized density profiles of the ISM derived from XMM-Newton and Chandra are mostly consistent with each other from $0.5~r_{\rm e}$ to $2~r_{\rm e}$ .

We then fitted the derived gas density profiles of XMM-Newton at $R>0.5~r_{\rm e}$ and that of Chandra within $R<2~r_{\rm e}$ of each galaxy simultaneously with a $\beta$ model, as $f(R)=S_0(1+(R/R_{\rm c})^{2})^{-{\rm IN}}$ . Most of the density profiles were well fitted with this single- $\beta$ model (Fig. 7). The derived $R_{\rm c}$ values of galaxies with Chandra data are almost about $0.05~r_{\rm e}$ . Therefore, we fixed the $R_{\rm c}$ value to $0.05~r_{\rm e}$ to fit the gas density profiles of galaxies without Chandra data. For NGC 4552 we also fixed the $R_{\rm c}$ value to $0.05~r_{\rm e}$ , because of an edge-like structure at 0.4- $0.6~r_{\rm e}$ observed with Chandra (Machacek et al. 2006). Several X-ray luminous galaxies need a double- $\beta$ model to fit the density profiles.

$\begin{figure} \par\includegraphics[width=12.5cm,clip]{0978f04.eps} \end{figure}$	Figure 4: The derived temperature profiles of the ISM. The $X_{\rm E}$ galaxies are plotted in the top left panel, the $X_{\rm C}$ galaxies in clusters are in the top right, and the field $X_{\rm C}$ galaxies are in the bottom panels. Colors indicate individual galaxies. The solid lines represent the best-fit function.
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$\begin{figure} \par\includegraphics[width=12.5cm,clip]{0978f05.eps} \end{figure}$

Figure 5:

The ISM temperature gradients parametrized by kT(1- $4~r_{\rm e})/kT(<$ $1~r_{\rm e})$ ( left panel) and kT(4- $8~r_{\rm e})/kT(<$ $1~r_{\rm e})$ ( right panel) plotted against $L_{\rm ISM}/L_B\sigma ^2$ . Meanings of the symbols are the same as those in Fig. 3. The dotted line represents the rate of kinetic heating by stellar mass loss. The dashed lines indicate that kT(1- $4~r_{\rm e})$ (or kT(4- $8~r_{\rm e})$ ) is 1 or 1.3 times higher than kT(< $1~r_{\rm e})$ .

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The ISM and the hard component may have different surface brightness profiles. Therefore, we also derived gas density profiles of galaxies whose $L_{\rm ISM}$ is less than 80% of the total luminosity within $4~r_{\rm e}$ , directly from the normalization of the ISM component derived from spectral fittings. The best-fit $\beta$ -model of the density profile of each galaxy is plotted in Fig. 18. The best-fit values of $\beta$ derived in this way are mostly consistent with those derived from surface brightness profiles, although several galaxies show discrepancies of a few tens of %.

$\begin{figure} \par\includegraphics[width=7cm,clip]{0978f06.eps} \end{figure}$	Figure 6: X-ray surface brightness profiles derived from MOS images of NGC 720 (blue) and NGC 4636 (red).
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6 Mass profiles

We then calculated the total mass profile M(R) within a three-dimensional radius R from the obtained best-fit functions of ISM temperature T(R) and gas density n(R) profiles from the surface brightness, assuming hydrostatic equilibrium and circular symmetry, by the equation

$\displaystyle M(R)=-\frac{kT(R)\cdot R}{G\mu m_{\rm p}} \left(\frac{{\rm d}\ln n(R)}{{\rm d}\ln R}+\frac{{\rm d}\ln T(R)}{{\rm d}\ln R}\right),$

(1)

where $m_{\rm p}$ is the proton mass, k is the Boltzmann constant, G is the constant of gravity, and $\mu \sim 0.62$ is the mean particle mass in units of $m_{\rm p}$ . Figure 8 summarizes the derived mass profiles. For NGC 1549, NGC 4477, and NGC 5322, the mass profiles within $0.5~r_{\rm e}$ were not plotted in the figure, since we used only XMM-Newton data for those galaxies.

$\begin{figure} \par\includegraphics[width=13cm,clip]{0978f07.eps} \end{figure}$

Figure 7:

ISM density profiles. The $X_{\rm E}$ galaxies are plotted in the top left panel, the $X_{\rm C}$ galaxies in clusters are in the top right, and the field $X_{\rm C}$ galaxies are in the bottom panels. These profiles are arbitrarily normalized. Colors indicate individual galaxies. Solid lines represent the best-fit function. Crosses and diamonds correspond to Chandra and XMM-Newton data, respectively.

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$\begin{figure} \mbox{\includegraphics[width=4.5cm,clip]{0978f08a.eps} \includeg... ...includegraphics[width=4.5cm,clip]{0978f08k.eps}\hspace*{2.25cm}} \end{figure}$	Figure 8: Integrated mass profiles of galaxies. The solid lines are total gravitational mass obtained from the best-fit functions of temperature and ISM density profiles. The dashed lines correspond to the upper and lower limits derived from the local gradients of temperature and density. We also plotted the stellar mass profiles assuming stellar M/L_B to be 3 and 8 (dotted lines).
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$\begin{figure} \par\mbox{\includegraphics[width=4.5cm]{0978f08l.eps} \includegra... ...ps} \includegraphics[width=4.5cm]{0978f08v.eps}\hspace*{2.25cm}} \end{figure}$	Figure 8: continued.
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In addition, the upper and lower limits of the mass profiles were calculated considering the errors in the temperature and the temperature and density gradients of each data bin. The upper and lower limits of the temperature and density gradients of the ith shell were obtained from the ratio of the value within i+1th shell to that within i-1th shell. Here, we used the temperature profiles derived from XMM-Newton. At $R< 1~r_{\rm e}$ and $R>1~r_{\rm e}$ , density profiles derived from Chandra and XMM-Newton, respectively, were used. For NGC 4636, the density at 0.3- $0.4~r_{\rm e}$ is significantly smaller than the best-fit function, due to the existence of complicated structure discovered by Chandra (Jones et al. 2002). Therefore, we ignored this shell when deriving the mass profiles. As summarized in Fig. 8, the total masses derived in this way are mostly consistent with those using the best-fit functions.

We also derived stellar mass profiles, using the deprojected de Vaucouleurs profile of Mellier & Mathez (1987), assuming stellar M/L_Bis in the range from 3 to 8 in solar units. We plotted these profiles in Fig. 8. Within $1~r_{\rm e}$ , the gravitational mass is consistent with the stellar mass. Further, the gradients of the gravitational mass are similar to those of the stellar mass. In contrast, outside the radius of a few $r_{\rm e}$ , the derived gravitational mass becomes much larger than the stellar mass. These results indicate the existence of dark matter in the outer regions of early-type galaxies.

When $L_{\rm ISM}$ is less than 80% of the total luminosity within $4~r_{\rm e}$ , the total mass profile is calculated using the best-fit $\beta$ -model of the density profile from the spectral fitting. The results are compared with those from the surface brightness in Fig. 18. The two methods give similar total mass profiles within 10-20%. For NGC 3585 and NGC 5322, these discrepancies are $\sim$ 30%, but within the large errors of the mass profiles of the two galaxies. Thus, the mass profiles of these galaxies obtained from two methods are consistent within the error. Hereafter, we use the total mass profiles derived from the surface brightness profiles.

$\begin{figure} \par\includegraphics[width=9cm,clip]{0978f09.eps} \end{figure}$

Figure 9:

Central ISM temperatures plotted against central stellar velocity dispersion, $\sigma$ . Colors indicate galaxy categories for $X_{\rm E}$ galaxies (red crosses), field $X_{\rm C}$ galaxies (filled blue symbols), and $X_{\rm C}$ galaxies in clusters (open blue symbols). For $X_{\rm C}$ galaxies, the temperatures within $0.5~r_{\rm e}$ (circles) and $1~r_{\rm e}$ (triangles) are plotted for the data with high and poor statistics, respectively. The dotted lines correspond to $\beta _{\rm spec}$ of 0.25, 0.5, and 1.0 from the top to bottom.

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7 Discussion

The observed temperature profiles and X-ray luminosities of the ISM lead to a division of early-type galaxies into two categories: $X_{\rm E}$ galaxies and $X_{\rm C}$ galaxies. The $X_{\rm E}$ galaxies have increasing temperature profiles and $L_{\rm ISM}/L_{\sigma}>1$ , whereas the $X_{\rm C}$ galaxies have flat or negative temperature gradients and $L_{\rm ISM}/L_{\sigma}\lesssim 1$ . Here, $L_\sigma$ represents the expected energy input from stellar mass loss (Matsushita 2001). In Sect. 7.1, the derived ISM temperatures are compared with the stellar velocity dispersions. In Sects. 7.2 and 7.3, we derive gravitational mass-to-light ratios in the B- and K-band, respectively, and constrain contributions from stellar mass and differences in dark mass between the $X_{\rm C}$ and $X_{\rm E}$ galaxies. Finally, in Sect. 7.4, we discuss dark matter distribution in early-type galaxies themselves and their luminosity.

Table 6: Integrated M/L_B and M/L_K at 0.5, 3 and $6~r_{\rm e}$ .

7.1 ISM temperature vs. stellar velocity dispersion

Figure 9 shows the correlation between central ISM temperature and central stellar velocity dispersion $\sigma^2$ (Table 1). The temperature roughly correlates with the stellar velocity dispersion. The parameter $\beta _{\rm spec}$ denotes the ratio of stellar velocity dispersion to ISM temperature with $\beta_{\rm spec}=\mu m_{\rm p} \sigma^2/kT$ , with $\mu$ indicating the mean molecular weight in terms of proton mass $m_{\rm p}$ . For $X_{\rm C}$ galaxies, $\beta _{\rm spec}$ is about $\beta_{\rm spec}=0.5$ -1.0, which indicates that the ISM temperatures are consistent with heating due to stellar motion (Matsushita 2001). The galaxies with low $\sigma$ tend to have low $\beta$ values. This may be due to a selection effect, since brighter galaxies with higher ISM temperatures were the first proposed for observation.

In Fig. 10, we plotted the temperature profiles of the sample galaxies scaled with central stellar velocity dispersion. There is no significant difference in the ISM temperature between the $X_{\rm C}$ and $X_{\rm E}$ galaxies at the central regions. Therefore, the ISM temperatures of the $X_{\rm C}$ and $X_{\rm E}$ galaxies would reflect the same potential. However, in the outer regions the $X_{\rm E}$ galaxies have higher ISM temperatures than the $X_{\rm C}$ galaxies for the same stellar velocity dispersion. This is due to the difference in potential due to the hot intra-group medium around the $X_{\rm E}$ galaxies.

$\begin{figure} \par\includegraphics[width=9cm,clip]{0978f10.eps} \end{figure}$	Figure 10: Temperature profiles of the ISM scaled with central stellar velocity dispersion. The solid red, solid blue, and dashed blue lines represent the $X_{\rm E}$ galaxies, field $X_{\rm C}$ galaxies, and $X_{\rm C}$ galaxies in clusters, respectively.
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7.2 Mass-to-light ratio in B-band

$\begin{figure} \par\includegraphics[width=13.7cm,clip]{0978f11.eps} \end{figure}$	Figure 11: Profiles of integrated M/L_B ( left) and M/L_K ( right). The meanings of colors and lines are the same as those in Fig. 10.
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$\begin{figure} \par\includegraphics[width=18cm,clip]{0978f12.eps} \end{figure}$	Figure 12: M/L_B(< $0.5~r_{\rm e})$ ( left), M/L_B(< $3~r_{\rm e})$ ( center), and M/L_B(< $6~r_{\rm e})$ ( right) against L_B. The quadrangle represents the value of M87 by Matsushita et al. (2002). Meanings of other symbols are the same as those in Fig. 3. The solid line represents the correlation derived from the stellar velocity dispersion by Gerhard et al. (2001).
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In order to compare the difference in dark matter profiles between the $X_{\rm C}$ and $X_{\rm E}$ galaxies, we used the mass-to-light ratio (M/L_B). We assumed the de Vaucouleurs law for the stellar distribution. Figure 11 summarizes the integrated M/L_B profiles. For NGC 1549, NGC 4477, and NGC 5322, profiles within $0.5~r_{\rm e}$ were not plotted in the figure, since we used only XMM-Newton data for those galaxies. From $0.2~r_{\rm e}$ to $1~r_{\rm e}$ , M/L_B of each $X_{\rm C}$ galaxy is nearly constant at 3-10, which is consistent with typical values of stellar M/L_B. Even in the $X_{\rm E}$ galaxies, M/L_B values within 0.5- $1~r_{\rm e}$ are also flat. These results suggest that stellar mass dominates within R < 0.5- $1~r_{\rm e}$ . In NGC 4636, a wavy M/L_B profile is seen at $R<0.3~r_{\rm e}$ , which is artificially caused by the complicated X-ray structures in the central regions discovered by Chandra (Jones et al. 2002). Hereafter, we denote integrated M/L_B within $s~r_{\rm e}$ as M/L_B(< $s~r_{\rm e})$ , where s is a constant.

The top left panel of Fig. 12 shows the relationship of M/L_B(< $0.5~r_{\rm e})$ to total B-band luminosity, L_B. In this plot, we add M/L_B of the cD galaxy of the Virgo cluster, M 87, obtained from XMM-Newton observations (Matsushita et al. 2002). M/L_B(< $0.5~r_{\rm e})$ of the $X_{\rm E}$ and $X_{\rm C}$ galaxies is about 10, with significant scatter. A correlation between M/L_B and L_B elliptical galaxies was found by optical measurements (Gerhard et al. 2001), where gravitational mass was derived from stellar velocity dispersion in the central region of elliptical galaxies. Our M/L_B and L_B relation is scattered around the relation found by Gerhard et al. (2001).

On the other hand, at $R>1~r_{\rm e}$ , the derived M/L_B starts to increase (Fig. 11). The $X_{\rm C}$ galaxies have similarly shaped M/L_Bprofiles. M/L_B(< $3~r_{\rm e})$ and M/L_B(< $6~r_{\rm e})$ of the $X_{\rm C}$ galaxies are about 6- $25~M_{\odot}/L_{\odot}$ . The $X_{\rm E}$ galaxies have systematically higher M/L_B values than the $X_{\rm C}$ galaxies at > $3~r_{\rm e}$ . (Fig. 12). The $X_{\rm E}$ galaxies have M/L_B(< $3~r_{\rm e})$ and M/L_B(< $6~r_{\rm e})$ of 25- $40~M_{\odot}/L_{\odot}$ and 40- $100~M_{\odot}/L_{\odot}$ , respectively. These results indicate that dark matter is common in early-type galaxies. In addition, the $X_{\rm E}$ galaxies have more dark matter than the $X_{\rm C}$ galaxies.

$\begin{figure} \par\includegraphics[width=7cm,clip]{0978f13.eps} \end{figure}$	Figure 13: Relationship between B-band and K-band luminosity of the sample galaxies. Meanings of the symbols are the same as those in Fig. 3. The dotted line corresponds to the appropriate color B-K=4.2 for early-type galaxies (Lin & Mohr 2004).
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7.3 Mass-to-light ratios in K-band

Historically, the B-band mass-to-light ratio has been used in such studies. However, K-band luminosity well describes the stellar mass. Thus, we also derived the K-band mass-to-light ratio to study the dark matter profiles. We calculated the K-band luminosity L_K from the Two Micron All Sky Survey (2MASS). The effect of Galactic extinction was corrected using the NASA/IPAC Extragalactic Database (NED). The relationship between L_B and L_K is close to that of B-K=4.2, which is the appropriate color of stars in early-type galaxies (Lin & Mohr 2004), with some scatter (Fig. 13).

The right panel of Fig. 11 shows the integrated profiles of the K-band mass-to-light ratio, M/L_K, of the sample galaxies. At the central region, the $X_{\rm E}$ and $X_{\rm C}$ galaxies have similar M/L_K at $\sim$ 1.

In Fig. 14, we compared the relationship of M/L_K(< $0.5~r_{\rm e})$ , M/L_K(< $3~r_{\rm e})$ , and M/L_K(< $6~r_{\rm e})$ with L_K except M 87. For early-type galaxies, the stellar K-band mass-to-light ratio, M/L_K, is about $1~M_{\odot}/L_{\odot}$ . The scatter of M/L_K(< $0.5~r_{\rm e})$ values becomes smaller than that of M/L_B(< $0.5~r_{\rm e})$ values (Fig. 14). Both the $X_{\rm E}$ and $X_{\rm C}$ galaxies have M/L_K values of $\sim 1~M_{\odot}/L_{\odot}$ , and no correlation with L_K. This result indicates that stars dominate the mass within $0.5~r_{\rm e}$ , and we observed the stellar M/L_K in these region, except the cD galaxy M 87. M 87 may contain a similar amount of dark matter with stellar mass within $0.5~r_{\rm e}$ , since M/L_K is a factor of 2 larger than those of $X_{\rm E}$ and $X_{\rm C}$ galaxies. On the other hand, the M/L_K(< $3~r_{\rm e})$ values of the $X_{\rm E}$ and $X_{\rm C}$ galaxies are 4-10 and 1- $4~M_{\odot}/L_{\odot}$ , respectively (Fig. 14). The M/L_K(< $6~r_{\rm e})$ values of the $X_{\rm E}$ and $X_{\rm C}$ galaxies are $\sim$ 10 and 2- $6~M_{\odot}/L_{\odot}$ , respectively (Fig. 14).

$\begin{figure} \par\includegraphics[width=18cm,clip]{0978f14.eps} \end{figure}$	Figure 14: Integrated M/L_K(< $0.5~r_{\rm e})$ ( left), M/L_K(< $3~r_{\rm e})$ ( center), and M/L_K(< $6~r_{\rm e})$ ( right) against L_K. Meanings of the symbols are the same as those in Fig. 12.
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$\begin{figure} \par\includegraphics[width=9cm,clip]{0978f15.eps} \end{figure}$	Figure 15: of M/L_K normalized by M/L_K(< $0.5~r_{\rm e})$ . We also plotted the M/L_K profile of M 87 by Matsushita et al. (2002) (orange solid line). The meanings of other colors and lines are the same as those in Fig. 10.
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7.4 Dark matter in early-type galaxies

We normalized the M/L_K profile with M/L_K(< $0.5~r_{\rm e})$ for each galaxy (Fig. 15). Then, the profiles of mass-to-light ratios of $X_{\rm C}$ galaxies have similarities. We also derived the ratio of M/L_K(< $3~r_{\rm e})$ and M/L_K(< $6~r_{\rm e})$ to M/L_K(< $0.5~r_{\rm e})$ for each galaxy. The ratios of M/L_K(< $3~r_{\rm e})$ and M/L_K(< $6~r_{\rm e})$ to M/L_K(< $0.5~r_{\rm e})$ are similar among the $X_{\rm C}$ galaxies at 2 and 3-4, respectively (Fig. 16). Considering that stellar mass dominates within $1~r_{\rm e}$ , and assuming that the stellar M/L_K is nearly constant within a galaxy, the $X_{\rm C}$ galaxies contain similar amounts of dark matter. Within $3~r_{\rm e}$ , the mass of dark matter is similar to the stellar mass, while within $6~r_{\rm e}$ , the former is 2-3 times larger than the latter. These ratios should reflect the potential of early-type galaxies themselves. Thus, the dark mass distribution in early-type galaxies is slightly more extended than that of stars. It is thought that early-type galaxies have 10 times more dark mass than stellar mass as in spiral galaxies (e.g., Ciotti et al. 1991). However, the galaxies themselves may not contain such large amounts of mass, at least within several times $r_{\rm e}$ . This result is important for the study of the origin of the dark matter content in early-type galaxies and for the study of the formation and evolution of these galaxies.

$\begin{figure} \par\includegraphics[width=13cm,clip]{0978f16.eps} \end{figure}$	Figure 16: Ratio of the integrated M/L_K(< $3~r_{\rm e})$ and M/L_K(< $6~r_{\rm e})$ to M/L_K(< $0.5~r_{\rm e})$ plotted against L_K. Meanings of the symbols are the same as those in Fig. 12.
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$\begin{figure} \par\includegraphics[width=13cm,clip]{0978f17.eps} \end{figure}$	Figure 17: Ratio of the integrated M/L_K(< $3~r_{\rm e})$ and M/L_K(< $6~r_{\rm e})$ to M/L_K(< $0.5~r_{\rm e})$ plotted against $L_{\rm ISM}/L_B\sigma ^2$ . Meanings of the symbols are the same as those in Fig. 12. The dotted line represents the kinetic heating rate by stellar mass loss.
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In contrast, the $X_{\rm E}$ galaxies have systematically larger ratios; i.e., they have more dark matter in their outer regions. Figure 17 shows that the galaxies with a larger $L_{\rm ISM}/L_B\sigma ^2$ have more dark matter at $R>1~r_{\rm e}$ . The ratio of M 87 may also lie in the relation between $L_{\rm ISM}/L_B\sigma ^2$ and dark to stellar mass ratio, considering that M 87 may contain a similar amount of dark mass to stellar mass within $0.5~r_{\rm e}$ . In other words, the X-ray luminosity of the $X_{\rm E}$ galaxies may be determined in relation to their potential structure, as indicated by Matsushita (2001) and Matsushita et al. (2002). The difference in temperature profiles between the $X_{\rm E}$ and $X_{\rm C}$ galaxies would be due to differences in the surrounding gravitational potential. These results suggest that the X-ray luminous early-type galaxies commonly sit in the center of a large-scale (a few hundred kpc) potential well, which leads to their high luminosities. Other galaxies may lack such a large-scale potential well and contain their own dark matter.

8 Conclusion

We analyzed 22 early-type galaxies using XMM-Newton and Chandra data. To derive the gravitational mass profiles, we obtained the temperature and ISM density profiles through spectral fitting and spatial analysis, respectively. We classified the galaxies into two categories, $X_{\rm E}$ and $X_{\rm C}$ galaxies, on the basis of whether the temperature gradient is positive or negative toward the outer radius. The ISM luminosity of the $X_{\rm C}$ galaxies is consistent with the energy input from stellar mass loss. In contrast, the $X_{\rm E}$ galaxies have higher ISM luminosity.

At the central regions, R < 0.5- $1~r_{\rm e}$ , the derived integrated M/L_Kof both of the $X_{\rm C}$ and $X_{\rm E}$ galaxies are about 1 and have smaller scatter than M/L_B. The values and profiles of M/L_K indicate that stellar mass dominates the total mass in these regions. In the outer regions, M/L_Band M/L_K of the $X_{\rm E}$ galaxies are higher than those of the $X_{\rm C}$ galaxies.

On the basis of these results, we can conclude the following. The normal early-type galaxies, $X_{\rm C}$ galaxies, contain their own dark matter at amounts that are 1.5-2 times larger than the stellar mass within $5~r_{\rm e}$ . The $X_{\rm E}$ galaxies are located as the central galaxy in a larger scale potential structure, such as a galaxy group. This fact directly affects the gravitational potential profile of the galaxy itself, and causes it to contain significantly higher amounts of dark matter than that in the $X_{\rm C}$ galaxies. This difference in the gravitational potential leads to the difference in the temperature profile and X-ray ISM luminosity between the $X_{\rm E}$ and $X_{\rm C}$ galaxies.

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Online Material

Table 3: Spectral fitting results of the projected annular spectra.

Table 4: Spectral fitting results of the deprojected annular spectra.

$\begin{figure} \par\includegraphics[width=16cm,clip]{0978fA1a.eps}\\ \includeg... ...8fA1d.eps}\\ \includegraphics[width=16cm,clip]{0978fA1e.eps}\\ \end{figure}$

Figure 18:

( Left) The ISM temperature profiles of sample galaxies. The cross data points represent temperature profile derived from projected spectra, and the diamond data points are from deprojected spectra. The solid lines represent each best-fit function. ( Center) The ISM density profiles. The diamond data points represent XMM-Newton data, and the cross data points are Chandra data obtained from spatial analysis. The solid lines represent each best-fit function. The black data points are used to fit the function, but the gray data points are not. The dot-dashed lines show best-fit function of the ISM density profile obtained from the spectral fit. These ISM density profiles are normalized by the value at $1~r_{\rm e}$ . ( Right) The integrated mass profiles. The solid and dot-dashed lines are total mass obtained from ISM density profiles from the surface brightness and spectral fit, respectively. The dashed lines are upper and lower limit. We also plotted the stellar mass profiles assuming stellar M/L_B to be 3 and 8 (dotted lines).

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$\begin{figure}\par\includegraphics[width=18cm]{0978fA1f.eps}\\ \includegraphic... ...]{0978fA1i.eps}\\ \includegraphics[width=18cm]{0978fA1j.eps}\\ \end{figure}$	Figure 18: continued.
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$\begin{figure}\par\includegraphics[width=18cm]{0978fA1k.eps}\\ \includegraphic... ...]{0978fA1n.eps}\\ \includegraphics[width=18cm]{0978fA1o.eps}\\ \end{figure}$	Figure 18: continued.
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$\begin{figure}\par\includegraphics[width=18cm]{0978fA1p.eps}\\ \includegraphic... ...]{0978fA1s.eps}\\ \includegraphics[width=18cm]{0978fA1t.eps}\\ \end{figure}$	Figure 18: continued.
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$\begin{figure}\par\includegraphics[width=18cm]{0978fA1u.eps}\\ \includegraphics[width=18cm]{0978fA1v.eps}\\ \end{figure}$	Figure 18: continued.
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Footnotes

... Chandra: Tables 3, 4 and Fig. 18 are only available in electronic form at: http://www.aanda.org

All Tables

Table 1: Galaxy sample in the XMM-Newton archive data.

Table 2: Observational log of the sample galaxies.

Table 5: X-ray luminosities within $4~r_{\rm e}$ of each sample galaxy.

Table 6: Integrated M/L_B and M/L_K at 0.5, 3 and $6~r_{\rm e}$ .

Table 3: Spectral fitting results of the projected annular spectra.

Table 4: Spectral fitting results of the deprojected annular spectra.

All Figures

$\begin{figure} \par\includegraphics[width=9cm,clip]{0978f01.eps} \end{figure}$	Figure 1: Raw MOS (MOS1 + MOS2) spectrum at r=6-14 $^{\prime }$ of NGC 4636 (black), and the adopted background spectrum (red).
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In the text

$\begin{figure} \par\includegraphics[width=13.6cm,clip]{0978f02.eps} \end{figure}$	Figure 2: a) Innermost projected spectra observed with MOS (black) and PN (red), and innermost deprojected spectra with MOS (blue) and PN (magenta). These spectra are fitted with a vAPEC model plus power-law multiplied by the Galactic absorption (solid line). Dashed lines correspond to the contribution from each component. b), c) The actual data to model ratio from the fit in panel a). The meanings of colors correspond to that in panel a). d) The same as panel b) and c), but using the vAPEC + vAPEC model plus power-law multiplied by the Galactic absorption as the fitting model.
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In the text

$\begin{figure} \par\includegraphics[width=13.0cm,clip]{0978f03.eps} \end{figure}$	Figure 3: $L_{\rm ISM}(<$ $4~r_{\rm e})$ of galaxies plotted against L_B ( left panel) and $L_B\sigma ^2$ ( right panel). Symbols indicate galaxy categories defined in Sect. 4.2.2 for $X_{\rm E}$ galaxies (red crosses), field $X_{\rm C}$ galaxies (filled blue circles), and $X_{\rm C}$ galaxies in the clusters (open blue circles). The solid line represents the kinetic heating rate by stellar mass loss ( $L_\sigma$ ).
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In the text

$\begin{figure} \par\includegraphics[width=12.5cm,clip]{0978f04.eps} \end{figure}$	Figure 4: The derived temperature profiles of the ISM. The $X_{\rm E}$ galaxies are plotted in the top left panel, the $X_{\rm C}$ galaxies in clusters are in the top right, and the field $X_{\rm C}$ galaxies are in the bottom panels. Colors indicate individual galaxies. The solid lines represent the best-fit function.
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In the text

$\begin{figure} \par\includegraphics[width=12.5cm,clip]{0978f05.eps} \end{figure}$	Figure 5: The ISM temperature gradients parametrized by kT(1- $4~r_{\rm e})/kT(<$ $1~r_{\rm e})$ ( left panel) and kT(4- $8~r_{\rm e})/kT(<$ $1~r_{\rm e})$ ( right panel) plotted against $L_{\rm ISM}/L_B\sigma ^2$ . Meanings of the symbols are the same as those in Fig. 3. The dotted line represents the rate of kinetic heating by stellar mass loss. The dashed lines indicate that kT(1- $4~r_{\rm e})$ (or kT(4- $8~r_{\rm e})$ ) is 1 or 1.3 times higher than kT(< $1~r_{\rm e})$ .
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0978f06.eps} \end{figure}$	Figure 6: X-ray surface brightness profiles derived from MOS images of NGC 720 (blue) and NGC 4636 (red).
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In the text

$\begin{figure} \par\includegraphics[width=13cm,clip]{0978f07.eps} \end{figure}$	Figure 7: ISM density profiles. The $X_{\rm E}$ galaxies are plotted in the top left panel, the $X_{\rm C}$ galaxies in clusters are in the top right, and the field $X_{\rm C}$ galaxies are in the bottom panels. These profiles are arbitrarily normalized. Colors indicate individual galaxies. Solid lines represent the best-fit function. Crosses and diamonds correspond to Chandra and XMM-Newton data, respectively.
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In the text

$\begin{figure} \mbox{\includegraphics[width=4.5cm,clip]{0978f08a.eps} \includeg... ...includegraphics[width=4.5cm,clip]{0978f08k.eps}\hspace*{2.25cm}} \end{figure}$	Figure 8: Integrated mass profiles of galaxies. The solid lines are total gravitational mass obtained from the best-fit functions of temperature and ISM density profiles. The dashed lines correspond to the upper and lower limits derived from the local gradients of temperature and density. We also plotted the stellar mass profiles assuming stellar M/L_B to be 3 and 8 (dotted lines).
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=4.5cm]{0978f08l.eps} \includegra... ...ps} \includegraphics[width=4.5cm]{0978f08v.eps}\hspace*{2.25cm}} \end{figure}$	Figure 8: continued.
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In the text

$\begin{figure} \par\includegraphics[width=9cm,clip]{0978f09.eps} \end{figure}$	Figure 9: Central ISM temperatures plotted against central stellar velocity dispersion, $\sigma$ . Colors indicate galaxy categories for $X_{\rm E}$ galaxies (red crosses), field $X_{\rm C}$ galaxies (filled blue symbols), and $X_{\rm C}$ galaxies in clusters (open blue symbols). For $X_{\rm C}$ galaxies, the temperatures within $0.5~r_{\rm e}$ (circles) and $1~r_{\rm e}$ (triangles) are plotted for the data with high and poor statistics, respectively. The dotted lines correspond to $\beta _{\rm spec}$ of 0.25, 0.5, and 1.0 from the top to bottom.
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[width=9cm,clip]{0978f10.eps} \end{figure}$	Figure 10: Temperature profiles of the ISM scaled with central stellar velocity dispersion. The solid red, solid blue, and dashed blue lines represent the $X_{\rm E}$ galaxies, field $X_{\rm C}$ galaxies, and $X_{\rm C}$ galaxies in clusters, respectively.
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[width=13.7cm,clip]{0978f11.eps} \end{figure}$	Figure 11: Profiles of integrated M/L_B ( left) and M/L_K ( right). The meanings of colors and lines are the same as those in Fig. 10.
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[width=18cm,clip]{0978f12.eps} \end{figure}$	Figure 12: M/L_B(< $0.5~r_{\rm e})$ ( left), M/L_B(< $3~r_{\rm e})$ ( center), and M/L_B(< $6~r_{\rm e})$ ( right) against L_B. The quadrangle represents the value of M87 by Matsushita et al. (2002). Meanings of other symbols are the same as those in Fig. 3. The solid line represents the correlation derived from the stellar velocity dispersion by Gerhard et al. (2001).
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0978f13.eps} \end{figure}$	Figure 13: Relationship between B-band and K-band luminosity of the sample galaxies. Meanings of the symbols are the same as those in Fig. 3. The dotted line corresponds to the appropriate color B-K=4.2 for early-type galaxies (Lin & Mohr 2004).
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[width=18cm,clip]{0978f14.eps} \end{figure}$	Figure 14: Integrated M/L_K(< $0.5~r_{\rm e})$ ( left), M/L_K(< $3~r_{\rm e})$ ( center), and M/L_K(< $6~r_{\rm e})$ ( right) against L_K. Meanings of the symbols are the same as those in Fig. 12.
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[width=9cm,clip]{0978f15.eps} \end{figure}$	Figure 15: of M/L_K normalized by M/L_K(< $0.5~r_{\rm e})$ . We also plotted the M/L_K profile of M 87 by Matsushita et al. (2002) (orange solid line). The meanings of other colors and lines are the same as those in Fig. 10.
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[width=13cm,clip]{0978f16.eps} \end{figure}$	Figure 16: Ratio of the integrated M/L_K(< $3~r_{\rm e})$ and M/L_K(< $6~r_{\rm e})$ to M/L_K(< $0.5~r_{\rm e})$ plotted against L_K. Meanings of the symbols are the same as those in Fig. 12.
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[width=13cm,clip]{0978f17.eps} \end{figure}$	Figure 17: Ratio of the integrated M/L_K(< $3~r_{\rm e})$ and M/L_K(< $6~r_{\rm e})$ to M/L_K(< $0.5~r_{\rm e})$ plotted against $L_{\rm ISM}/L_B\sigma ^2$ . Meanings of the symbols are the same as those in Fig. 12. The dotted line represents the kinetic heating rate by stellar mass loss.
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[width=16cm,clip]{0978fA1a.eps}\\ \includeg... ...8fA1d.eps}\\ \includegraphics[width=16cm,clip]{0978fA1e.eps}\\ \end{figure}$	Figure 18: ( Left) The ISM temperature profiles of sample galaxies. The cross data points represent temperature profile derived from projected spectra, and the diamond data points are from deprojected spectra. The solid lines represent each best-fit function. ( Center) The ISM density profiles. The diamond data points represent XMM-Newton data, and the cross data points are Chandra data obtained from spatial analysis. The solid lines represent each best-fit function. The black data points are used to fit the function, but the gray data points are not. The dot-dashed lines show best-fit function of the ISM density profile obtained from the spectral fit. These ISM density profiles are normalized by the value at $1~r_{\rm e}$ . ( Right) The integrated mass profiles. The solid and dot-dashed lines are total mass obtained from ISM density profiles from the surface brightness and spectral fit, respectively. The dashed lines are upper and lower limit. We also plotted the stellar mass profiles assuming stellar M/L_B to be 3 and 8 (dotted lines).
Open with DEXTER
In the text

$\begin{figure}\par\includegraphics[width=18cm]{0978fA1f.eps}\\ \includegraphic... ...]{0978fA1i.eps}\\ \includegraphics[width=18cm]{0978fA1j.eps}\\ \end{figure}$	Figure 18: continued.
Open with DEXTER
In the text

$\begin{figure}\par\includegraphics[width=18cm]{0978fA1k.eps}\\ \includegraphic... ...]{0978fA1n.eps}\\ \includegraphics[width=18cm]{0978fA1o.eps}\\ \end{figure}$	Figure 18: continued.
Open with DEXTER
In the text

$\begin{figure}\par\includegraphics[width=18cm]{0978fA1p.eps}\\ \includegraphic... ...]{0978fA1s.eps}\\ \includegraphics[width=18cm]{0978fA1t.eps}\\ \end{figure}$	Figure 18: continued.
Open with DEXTER
In the text

$\begin{figure}\par\includegraphics[width=18cm]{0978fA1u.eps}\\ \includegraphics[width=18cm]{0978fA1v.eps}\\ \end{figure}$	Figure 18: continued.
Open with DEXTER
In the text

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