Annu. Rev. Astron. Astrophys. 2000. 38: 289-335 Copyright © 2000 by Annual Reviews. All rights reserved

3.3. Spatial Properties of the Intragroup Medium

3.3.1. X-Ray Morphologies     The morphology of the X-ray emission can provide important clues into the nature of the hot gas. There is a considerable range in the observed X-ray morphologies of groups. X-ray luminous (L_X > 10⁴² h^-2₁₀₀ erg s^-1) groups tend to have somewhat regular morphologies (see Figure 1). The total extent of the X-ray emission in these cases is often beyond the optical extent of the group as defined by the galaxies. The peak of the X-ray emission is usually coincident with a luminous elliptical or S0 galaxy, which tends to be the most optically luminous group member (Ebeling et al 1994, Mulchaey et al 1996a, Mulchaey & Zabludoff 1998). The position of the brightest galaxy is also indistinguishable from the center of the group potential, as defined by the mean velocity and projected spatial centroid of the group galaxies (Zabludoff & Mulchaey 1998). Therefore, the brightest elliptical galaxy lies near the dynamical center of the group. There is also a tendency for the diffuse X-ray emission to roughly align with the optical light of the galaxy in many cases (Mulchaey et al 1996a, Mulchaey & Zabludoff 1998). These morphological characteristics are similar to those found for rich clusters containing cD galaxies (e.g. Rhee et al 1992, Sarazin et al 1995, Allen et al 1995).

Figure 1. Contour map of the diffuse X-ray emission as traced by the ROSAT PSPC in HCG 62 (top) and the NGC 2563 group (bottom) overlayed on the STScI Digitized Sky Survey. The X-ray data have been smoothed with a Gaussian profile of width 30". The coordinate scale is for epoch J2000.

At lower luminosities, more irregular X-ray morphologies are often found (see Figure 2). In these cases, the X-ray emission is not centered on one particular galaxy, but rather is distributed around several galaxies. Low X-ray luminosity groups also tend to have lower gas temperatures. Dell'Antonio et al (1994), Mahdavi et al (1997) suggested that the change in X-ray morphologies at low X-ray luminosities indicates a change in the nature of the X-ray emission. They proposed a "mixed-emission" scenario where the observed diffuse X-ray emission originates from both a global group potential and from intragroup gas in the potentials of individual galaxies. In this model, the latter component becomes dominant in low-velocity dispersion systems. This model is consistent with the fact that the X-ray emission is distributed near the luminous galaxies in many of the low-luminosity systems. Another possible source of diffuse X-ray emission in the low-luminosity systems might be gas that is shock-heated to X-ray temperatures by galaxy collisions and encounters within the group environment. This appears to be the case in HCG 92, where the diffuse X-ray emission comes predominantly from an intergalactic feature also detected in radio continuum maps (Pietsch et al 1997). Given that many of the groups with irregular X-ray morphologies are currently experiencing strong galaxy-galaxy interactions (e.g. HCG 16, HCG 90), shocks may be important in many cases. Regardless of the exact origin of the gas, the clumpy X-ray morphologies suggest that the X-ray gas may not be virialized in these cases.

Figure 2. Contour map of the diffuse X-ray emission as traced by the ROSAT PSPC in HCG 16 (top) and HCG 90 (bottom) overlayed on the STScI Digitized Sky Survey. The X-ray data have been smoothed with a Gaussian profile of width 30". The coordinate scale is for epoch J2000.

3.3.2. Spatial Extent     To estimate the extent of the hot gas, the usual method is to construct an azimuthally-averaged surface brightness profile and determine at what radial distance the emission approaches the background value. For most rich clusters, the central surface brightness of the intracluster medium is several orders of magnitude higher than the surface brightness of the X-ray background. Not surprisingly, the central surface brightness of less massive systems like groups tends to be much lower. In fact, in many of the X-ray weakest groups, the central surface brightness of the intragroup gas is just a few times higher than that of the background. Therefore, the measured extent of the X-ray emission in groups is usually much less than that of rich clusters. When comparing groups and clusters, it is useful to normalize the radial extent of the X-ray gas by the mass of the system. Figure 3 plots X-ray extent normalized by the virial radius (R_virial) of each system versus temperature for a sample of groups and clusters. Figure 3 indicates that many rich clusters are currently detected to approximately R_virial, whereas groups are typically detected to a small fraction of R_virial. In some cases, the group X-ray extents are less than 10% of the virial radius. There is also a strong correlation between the radius of detection in virial units and the temperature of the gas in groups: cool groups are detected to a smaller fraction of their virial radius than hot groups. This correlation is important because it suggests that a smaller fraction of the gas mass, and thus, X-ray luminosity, is detected in low temperature systems. Therefore, it is very important to account for this effect when one compares X-ray properties of systems spanning a large range in temperature (i.e. mass). Unfortunately, this has generally not been done in the literature.

Figure 3. Total radius of X-ray extent plotted as a fraction of the virial radius of each system versus the logarithm of the temperature for a sample of groups (circles) and rich clusters (triangles). The groups were taken from Mulchaey et al (1996a), Hwang et al (1999), Helsdon & Ponman (2000). The clusters plotted are a redshift-selected subset of the clusters in White (2000). The virial radius for each system was calculated assuming rvirial(T) = 1.85 (T / 10 keV)0.5 (1 + z)-1.5 h-1100 Mpc (Evrard et al 1996).

3.3.3. The Beta Model     Traditionally, a hydrostatic isothermal model has been used to describe the surface brightness profiles of rich clusters (e.g. Jones & Forman 1984). By analogy to the richer systems, this model is usually adopted for poor groups. The hydrostatic isothermal model assumes that both the hot gas and the galaxies are in hydrostatic equilibrium and isothermal. These assumptions appear to be valid for groups with regular X-ray morphologies, but are likely incorrect for groups with irregular X-ray morphologies (although this model is often applied even in these cases). With King's (1962) analytic approximation to the isothermal sphere, the X-ray surface brightness at a projected radius R is given by:

where r_c is the core radius of the gas distribution. This model is often referred to as the standard beta model in the literature. The parameter is the ratio of the specific energy in galaxies to the specific energy in the hot gas:

where µ is the mean molecular weight, m_p is the mass of the proton, is the one-dimensional velocity dispersion, and T_gas is the temperature of the intragroup medium. For high-temperature systems such as clusters, the X-ray emissivity is fairly independent of temperature over the energy range observed by ROSAT (~ 0.1-2 keV). Therefore, the gas density profile can be derived from the surface brightness profile even if the gas temperature varies somewhat within the cluster. However, at the temperatures more typical of groups, the X-ray emissivity is a strong function of temperature. Thus, to invert the observed surface brightness profiles of groups to a gas density profile, the gas must be fairly isothermal.

Based on fits to ROSAT PSPC data, most authors have derived values of around ~ 0.5 for groups (Ponman & Bertram 1993, David et al 1994, Pildis et al 1995, Henry et al 1995, Davis et al 1995, David et al 1995, Doe et al 1995, Mulchaey et al 1996a). This number is somewhat lower than the typical value found for clusters (e.g. ~ 0.64; Mohr et al 1999). However, simulations of clusters indicate that the value derived from a surface brightness profile depends strongly on the range of radii used in the fit (Navarro et al 1995, Bartelmann & Steinmetz 1996). In particular, values derived on scales much less than the virial radius tend to be systematically low. As most groups are currently detected to a much smaller fraction of the virial radius than rich clusters, a direct comparison between group and cluster values may not be particularly meaningful.

Although the hydrostatic isothermal model has almost universally been used for groups, in most cases it provides a poor fit to the data. In general, the central regions of groups exhibit an excess of emission above the extrapolation of the beta model to small radii. This steepening of the profile is often accompanied by a drop in the gas temperature, which has led some authors to suggest that the central deviations are related to a cooling flow (Ponman & Bertram 1993, David et al 1994, Helsdon & Ponman 2000). Alternatively, the excess flux could be emission associated with the central elliptical galaxy (Doe et al 1995, Ikebe et al 1996, Trinchieri et al 1997, Mulchaey & Zabludoff 1998).

Mulchaey & Zabludoff (1998) have shown that the surface brightness profiles in many groups can be adequately fit using two separate beta models. Although the various parameters are not well-constrained with the two-component models, Mulchaey & Zabludoff (1998) found a systematic trend for the values to be larger with this model than in the case of a single beta model. Similar behavior has been found for rich clusters of galaxies (Ikebe et al 1996, Mohr et al 1999). Mohr et al (1999) suggest that the effect is a consequence of the strong coupling between the core radius (r_c) and in the fitting procedure; a beta model with a large core radius and high value can produce a profile similar to that of a beta model where both parameters are lower. Therefore, the presence of a central excess drives the core radius (and thus ) to lower values in the single beta model fits. While Helsdon & Ponman (2000) verified the need for multiple components in groups, they did not derive systematically higher values. The likely explanation is that the argument in Mohr et al (1999) applies exclusively to systems where the extended component (i.e. the group/cluster gas) dominates the central component. In many of the lower-luminosity systems in Helsdon & Ponman's sample, however, the central component is dominant.

Helsdon & Ponman (2000) also compared the values of groups and rich clusters and found a trend for to decrease as the temperature of the system decreases. A similar trend had previously been found in samples of poor and rich clusters (e.g. David et al 1990, White 1991, Bird et al 1995, Mohr & Evrard 1997, Arnaud & Evrard 1999). Mohr et al (1999) reexamined the effect in clusters and found that it disappears when the surface brightness profiles are properly modeled using the two-component beta models. This explanation does not appear to work for poor groups, however, because Helsdon & Ponman (2000) used two-component beta models in their study. The lower values in groups may be an indication that non-gravitational heating has played a more important role in low-mass systems (David et al 1995, Knight & Ponman 1997, Horner et al 1999, Helsdon & Ponman 2000). However, as noted above, simulations indicate that the derived value depends strongly on the radii over which the surface brightness fit is performed. Thus, given the strong correlation between system temperature and X-ray extent (Figure 3), conclusions about how varies with temperature (i.e. mass) may be premature.