3 Mass profilesWe use the temperature and gas density values obtained by fits to the spectra extracted in concentric annuli to calculate the gravitating mass distribution, solving the equation of hydrostatic equilibrium assuming spherical symmetry. We assume parametrizations for the temperature and mass profiles to calculate the gas density (G07). The mass profiles are well described by a two component model: an NFW for the DM and a de Vaucoleurs stellar mass model (see Fig.1) for eight objects. Reasonable stellar mass-to-light ratios are obtained for these detections. For the remaining objects a pure NFW is a good fit of the data. Failure to detect stellar mass is due either to poor sampling of the inner 20 kpc or localized disturbance in the core. The measured c-M relation agrees with the prediction of ΛCDM and in particular in the mass range of our group sample has been detected for the first time (see Fig.2). There is a trend, common to all X-ray observations, toward more concentrated halos which can be understood in terms of a selection bias toward relaxed, earlier forming systems. The cosmological implications are discussed in Buote et. al. (2007).

The mean gas fraction (see Fig. 3) measured at an overdensity of 2500 (0.053 0.012) is significantly smaller than he one obtained for hot, massive clusters (0.092 0.04, V06). The fractional scatter obtained for groups (0.2) exceeds the values for clusters (e.g., 0.04 V06). There is a clear mass dependence on gas fraction (mean and factional scatter), not surprising if feedback energy injection is more severe at the group scale.

Mass and Entropy Profiles of X-ray Galaxy Groups

F. Gastaldello1,2, D. Buote1, P. Humphrey1, L. Zappacosta1,3, J. Bullock1, F. Brighenti2,4, W. Mathews4

1University of California Irvine,2University of Bologna,3Trieste Observatory,4University of California Santa Cruz

AbstractWe present mass and entropy profiles for a sample of 16 relaxed groups/poor clusters, observed with Chandra and XMM, covering the temperature range 1-3 keV and selected to have the best available data for hydrostatic mass analysis.

After accounting for the mass of the hot gas, the mass profiles within 0.3 rvir are well described by a model consisting of dark matter, represented by an NFW, and stars from the central galaxy. In contrast to results for local massive clusters, the NFW concentration parameter (cvir) for groups decreases with increasing Mvir. The mean gas fraction (0.05 0.01) measured within an overdensity of 2500 is lower than for massive clusters, but the fractional scatter is larger, implying a greater impact of feedback processes on groups.

This is reflected also on the entropy profiles, in particular for objects with Mvir<1014 solar masses, which show a large scatter, a stronger deviation form the adiabatic prediction and they are consistent with an increasing broken power law with steeper inner slope and flatter outer slope, at odd with the single power law found for massive clusters.

4 Entropy profiles

The entropy profiles for groups (Mvir<1014 solar masses) and poor clusters (Mvir in the range 1-2 1014 solar masses) are shown in Fig.4, scaled by the virial radius and the natural entropy scale for a non-radiative ICM (Svir following the definition of Voit et al. 2005a and scaling for our virial overdensity of 101).

Entropy profiles of groups show a large scatter and they are consistent with an increasing broken power law with steeper inner slope (0.8-1.3) and flatter outer slope (0.4-0.6). A similar behaviour has been noticed for a sample of 8 groups by Mahdavi et al. 2005. Some objects show a central flattening in the very inner core, a behaviour seen in more massive clusters (e.g. Donahue et al. 2006). The origin can be attributed to AGN heating or merging in the case of RGH 80 (the only object in our sample which has two dominant elliptical galaxy in the center). NGC 2563 is showing an entropy plateau at 0.1-0.2 rvir, most likely a fossil of an extreme heating episode which has deeply affected its core, explaining the low central gas density of this object.

Entropy profiles for poor clusters show less scatter like the ones observed in more massive objects. Local entropy modification, as the core flattening of AWM 4, may be due to AGN heating (details about this fascinating object can be found in Gastaldello et al. 2008).

We compared the entropy profiles of the objects in the sample with the baseline entropy profile due to gravitational effects alone, derived from adiabatic simulations (Voit et al. 2005b): in Fig. 5 we show the ratio of the observed profiles and the baseline predictions and compare it with the equivalent plot shown for a sample of nearby clusters in the temperature range 2-9 keV (P06). The trend of increasing deviation from the pure gravitational adiabatic prediction with decreasing mass (temperature) is confirmed by our data.

References

Bullock, J. et al., 2001, MNRAS, 321, 559Buote, D.A. et al., 2007, ApJ, 664, 123Donahue, M. et al., 2006, ApJ, 643, 730 Gastaldello, F. et al., 2007 (G07), ApJ, 669, 158Gastaldello, F. et al., 2008, ApJ, 673, L17Mahdavi, A. et al., 2005, ApJ, 622, 187Navarro et al., 1997 (NFW), ApJ, 490, 413Ponman, T. et al., 2003, MNRAS, 343, 331Pratt, G.W. et al., 2006 (P06), A&A, 446, 429Vikhlinin, A. et al., 2006 (V06), ApJ, 640, 691Voit, M. 2005a, Rev. Mod. Phys., 77, 207Voit, M. et al. 2005b, MNRAS, 364, 909

Fig.1 Temperature profile of the group NGC 533 derived from XMM (black) and from Chandra (red) data.

Fig.4 Scaled entropy profiles for group scale objects (left panel) and for poor cluster scale objects (right panel).

1 IntroductionThe properties of dark matter (DM) halos are a powerful discriminator between different cosmological scenarios of structure formation. Simulations have shown that the radial density profile of DM halos are fairly well described by the two parameter NFW model (Navarro et al. 1997). These two parameters can be cast in the form of a concentration cvir (the ratio between the virial radius rvir and the characteristic scale of the density profile rs) and the virial mass Mvir. These two parameters are inversely correlated because they reflect the mass-dependence of halo assembly times.

High quality X-ray observations from Chandra and XMM indicate that NFW is a remarkably good description for massive clusters mass profiles (e.g., Vikhlinin et al. 2006, V06 hereafter). The slope for the c-M relation at this scale is consistent with a constant.

Very few constraints exist on the group scale, where detailed mass profiles can be obtained with the high quality data provided by the new generation of X-ray satellites. In this contribution we present measurements of mass profiles of a sample of 16 groups with the best available XMM and Chandra data, selected for optimal mass determination (see details in Gastaldello et al. 2007, G07 hereafter).

X-ray observations have shown that the structure of the Intracluster medium (ICM) departs from the self-similarity expected if only gravitational processes are shaping its properties (e.g. Ponman et al. 2003). Investigation of the entropy profiles is of fundamental importance because entropy records the thermodynamic history of the ICM, reflecting cooling and feedback heating from supernovae and AGN (Voit 2005a). High quality XMM and Chandra cluster observations are showing that ICM entropy profiles have the S(r) r1.1 shape characteristic of gravitational structure formation outside of the core, but the overall normalization of these profiles scales as T2/3 instead of T as in the self-similar prediction (e.g. Pratt et al. 2006, P06 hereafter). It is important to extend these studies to groups/poor clusters with temperatures less than 2 keV. At this scale the effects of feedback are more severe and should have a more dramatic impact on entropy profiles.

2 Data analysisChandra + XMMThe use of both Chandra and XMM data is essential. The better Chandra PSF allows the use of annuli with the smallest possible radial width, avoiding departures from single-temperature emission which stem primarily from a steep temperature gradient (see Fig.1). Furthermore point sources are better resolved, in particular X-ray binaries in the central galaxy. For this reason, when available, we use only Chandra data in the core. At large radii the better effective area of XMM is crucial to detect the low surface brightness emission of groups.

MKW 4

NGC 533

Fig.1 Emission weighted projection of the gas density squared (left), emission weighted projected temperature (middle) and total gravitating mass (right) for two representative objects of the sample. Red symbols corresponds to Chandra data while black symbols corresponds to XMM data. Residuals from the best-fit model are also shown. When Chandra data are present in the core, XMM data are only shown for comparison but not fitted. In the mass plot the different mass components are shown: DM with the blue dash-dotted line, gas mass with the green dashed line and stellar mass with the red dotted line.

Fig.2 Concentration parameters cvir (corrected for redshift evolution with the term 1+z) vs. the group mass, Mvir. The black solid line represent the median c-M relation and the outer dotted lines the 1σ scatter from the model of Bullock et al. (2001). The red solid line represents the best fit power law relation to the data.

Fig.3 Observed gas fractions within r2500 as a function of virial mass. Error bars are on the virial mass have not been shown for clarity of the plot. The red solid line represents the mean value for the group sample, whereas the dashed blue line represents the mean fgas,2500 for the sample of massive clusters of V06.

Fig.5 Ratio between the observed entropy profiles and the best fitting power law relation found by Voit et al. (2005b) for the sample of groups (left panel) and the sample of clusters of P06. The colour coding from blue-magenta to red represents in both panels an increase in temperature (mass) of the objects.