ARlogo Annu. Rev. Astron. Astrophys. 2000. 38: 289-335
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3.4. Spectral Properties

X-ray spectral studies of groups have followed the techniques previously used for other diffuse X-ray sources such as elliptical galaxies and rich clusters. The observed data from X-ray instruments such as ROSAT or ASCA do not give the actual spectrum of the source but a convolution of the source spectrum with the instrument response. In general, it is not possible to uniquely invert the convolution and obtain the input spectrum. The usual solution is to adopt a model spectrum with a few adjustable parameters and to find the best fit to the observed data. By analogy to rich clusters, it has generally been assumed that the dominant emission mechanism in groups is thermal emission from diffuse, low-density gas. Many authors have calculated the spectrum emitted by a hot, optically thin plasma. The most popular models are that of Raymond & Smith (1977) and Mewe and collaborators (the so-called MEKAL model; Mewe et al 1985, Kaastra & Mewe 1993, Liedahl et al 1995). For simplicity, single-temperature (i.e. isothermal) models are usually assumed. The free parameters of interest in the isothermal plasma models include the gas temperature and metal abundance. For very hot systems, such as rich clusters, the X-ray emission in the isothermal model is dominated by the free-free continuum from hydrogen and helium. For the temperatures more typical of groups (~ 107 K), much of the flux is found in line emission and bound-free continuum.

3.4.1. Gas Temperature     In general, isothermal plasma models provide good fits to the ROSAT PSPC spectra of groups. The derived gas temperatures are in the range ~ 0.3-1.8 keV (see Figure 3), which is roughly what is expected given the range of observed velocity dispersions for groups (e.g. Ponman et al 1996, Mulchaey et al 1996a, Mulchaey & Zabludoff 1998, Helsdon & Ponman 2000). There is generally good agreement in the literature on the temperature of the gas; multiple authors have derived temperature values within 10% of each other, even when temperatures were derived over vastly different physical apertures (e.g. Mulchaey et al 1996a). The temperatures derived from the different plasma models (i.e. Raymond-Smith, MekaL) are also fairly consistent with each other (e.g. Mulchaey & Zabludoff 1998). Furthermore, there is very good agreement between gas temperatures determined by the ROSAT PSPC and ASCA for systems with temperatures less than about 2 keV. For higher-temperature gas (i.e. clusters), the ROSAT data appear to underestimate the true gas temperature by approximately 30% (Hwang et al 1999). All these observations suggest that the derived temperatures for the intragroup medium are fairly robust.

For some of the groups observed by ROSAT, it is possible to measure temperature profiles for the hot gas (Ponman & Bertram 1993, David et al 1994, Doe et al 1995, Davis et al 1996, Trinchieri et al 1997, Mulchaey & Zabludoff 1998, Helsdon & Ponman 2000, Buote 2000b). These profiles suggest that the gas is not strictly isothermal, but rather follows a somewhat universal form: the gas temperature is at a minimum at the center of the group, rises to a temperature maximum in the inner ~ 50-75 h-1100 kpc, and drops gradually at large radii. The temperature minimum in the inner regions of the group is coincident with the sharp rise in the X-ray surface brightness profile. This behavior is consistent with that expected from a "cooling flow" (cf Fabian 1994). The temperature drop at larger radii is often based on lower-quality spectra, and in most cases is not statistically significant. Even if this latter effect is present, the gas temperature at large radii is usually within 10-15% of the temperature maximum. Therefore, isothermality is not a bad assumption over most of the group, as long as the central regions are excluded. However, when global gas temperatures are quoted for groups in the literature, the central regions are almost always included. Because the central regions dominate the total counts in the spectrum, the temperatures found in the literature may underestimate the global temperatures in many cases.

3.4.2. betaspec     Although most authors have estimated the ratio of specific energy of the galaxies to the specific energy of the gas (i.e. the beta parameter) from surface brightness profiles (see Section 3.3.3), beta can in principle be determined by directly measuring sigma and Tgas. Unfortunately, because sigma is usually derived from only a few velocity measurements, this method is often not very robust. Detailed membership studies have been made for a few X-ray groups (i.e. Ledlow et al 1996, Zabludoff & Mulchaey 1998, Mahdavi et al 1999), and in these cases the velocity dispersion estimates are more reliable. Using such estimates, Mulchaey & Zabludoff (1998) found betaspec ~ 1 for most of the groups in their sample. Helsdon & Ponman (2000) found a similarly high value for betaspec for groups with temperatures of ~ 1 keV, but noted a trend for betaspec to decrease in the lower-temperature systems. However, almost all of the low-temperture groups in the Helsdon & Ponman (2000) sample have velocity dispersions determined from a small number of galaxies. Thus, while the current data suggest a trend for betaspec to decrease as the temperature of the group decreases, detailed spectroscopy of cool groups will be required to verify this result.

The beta ~ 1 values derived for hot groups from the direct measurement of temperature and velocity dispersion (betaspec) are significantly higher than the values of beta often derived from surface brightness profile fits (betafit). This so-called beta-discrepancy problem has been discussed extensively for rich clusters (e.g. Mushotzky 1984, Sarazin 1986, Edge & Stewart 1991, Bahcall & Lubin 1994). Based on simulations, Navarro et al (1995) concluded that betafit is biased low in galaxy clusters because of the limited radial range used in the X-ray profiles. This explanation may also explain the discrepancy found for groups, which are typically detected to a much smaller fraction of the virial radius than their rich cluster counterparts. Therefore, the beta-discrepancy in groups may be an indication that the current derived betafit values underestimate the true beta values in many cases.

3.4.3. Gas Metallicity     In addition to measuring gas temperatures, ROSAT PSPC and ASCA observations of groups have been used to estimate the metal content of the intragroup medium. As noted earlier, X-ray spectra of groups are dominated by emission line features. The strongest emission lines are produced when an electron in a highly ionized atom is collisionally excited to a higher level and then radiatively decays to a lower level. The most important features in the X-ray spectra of groups include the K-shell (n = 1) transitions of carbon through sulfur and the L-shell (n = 2) transitions of silicon through iron. Particularly important is the Fe L-shell complex in the spectral range ~ 0.7-2.0 keV (Liedahl et al 1995). The wealth of line features in the soft X-ray band potentially provides powerful diagnostics of the physical conditions of the gas, including the excitation mechanism and the elemental abundance (Mewe 1991, Liedahl et al 1990).

Unfortunately, the X-ray telescopes flown to date have not had high enough spectral resolution to resolve individual line complexes. Still, many attempts have been made to estimate the elemental abundance of the gas. For groups, this method primarily measures the iron abundance in the gas, because lines from this element dominate the spectra. Spectral fits to both ROSAT and ASCA data suggest that the metallicity of the intragroup medium varies significantly from group to group; some systems are very metal-poor (~ 10-20% solar), whereas others are more enriched (~ 50-60% solar; Mulchaey et al 1993, Ponman & Bertram 1993, David et al 1994, Davis et al 1995, Saracco & Ciliegi 1995, Davis et al 1996, Ponman et al 1996, Mulchaey et al 1996a, Fukazawa et al 1996, 1998, Mulchaey & Zabludoff 1998, Davis et al 1999, Finoguenov & Ponman 1999, Hwang et al 1999, Helsdon & Ponman 2000). The low metallicities measured in some groups are surprising because the ratio of stellar mass to gas mass is higher in groups than in clusters. Consequently, one would naively expect the metallicities of the gas to be higher in groups than in rich clusters.

Several potential problems have been noted with the low metallicity measurements for the intragroup medium. Ishimaru & Arimoto (1997) pointed out that most X-ray studies have adopted the old photospheric value for the solar Fe abundance (Fe/H ~ 4.68 × 10-5), whereas the commonly accepted "meteoritic" value is significantly lower (Fe/H ~ 3.24 × 10-5). (Note that more recent estimates of the photospheric Fe abundance in the sun are consistent with the meteoritic value; see McWilliam 1997.) Thus, essentially all the Fe measurements in the X-ray literature should be increased by a factor of ~ 1.44 to renormalize to the meteoritic value. This is particularly important when comparing the X-ray metallicities to chemical-evolution models, which usually adopt the meteoritic Fe solar abundance. The ability of ROSAT data to properly measure the gas abundance has also been questioned. Bauer & Bregman (1996) measured metallicities with the ROSAT PSPC for stars with known metallicities close to the solar value, and found the ROSAT metallicities were typically a factor of five lower than the optical measurements. Bauer & Bregman (1996) suggested several possible explanations for the discrepancy, including instrumental calibration uncertainties, problems with the plasma codes and possible differences in the photospheric and coronal abundances of stars. Instrumental uncertainties with the ROSAT PSPC are unlikely to be the major source of the problem because ASCA spectroscopy of groups also indicates low gas metallicities (Fukazawa et al 1996, 1998, Davis et al 1999, Finoguenov & Ponman 1999, Hwang et al 1999). The possibility that the plasma models are inaccurate or incomplete has been a major concern. While abundance measurements for rich clusters are derived primarily from the well-understood Fe K-alpha line, group measurements rely on the much more complicated Fe L-shell physics. Problems with the plasma models were in fact identified by early ASCA observations of cooling flow clusters (Fabian et al 1994). Liedahl et al's (1995) revision to the standard MEKA thermal emission model likely accounts for the largest problems in the earlier plasma codes. However, fits to ASCA spectra of groups with the revised model still require very low metal abundances. Hwang et al (1997) have shown that for clusters with sufficient Fe L and Fe K emission (i.e. clusters with temperatures in the range ~ 2-4 keV), the metallicities derived from the Fe L line complex are consistent with the values derived from the better understood Fe K complex (see also Arimoto et al's 1997 analysis of the Virgo cluster). Unfortunately, it is not clear that the reliability of the Fe L diagnostics implied from ~ 2-4 keV poor clusters necessarily extends down to lower temperature groups, since other Fe lines dominate the spectrum below ~ 1 keV (Arimoto et al 1997). Therefore, some problems with the plasma models may still exist.

Another potentially important problem is that the usually assumed isothermal model may be inappropriate for groups (Trinchieri et al 1997, Buote 1999, 2000a). There is clear evidence for temperature gradients in groups, particularly in the inner ~ 50 h-1100 kpc. In fact, the surface brightness profiles of ROSAT PSPC data suggest the presence of at least two distinct components in groups (Mulchaey & Zabludoff 1998). Mixing of multiple-temperature components is particularly an issue for ASCA data because separating out the central component from more extended emission is not possible with the ASCA point spread function. Buote (1999, 2000a) has studied this problem in detail for both elliptical galaxies and groups, and finds that in general single-temperature models provide poor fits to the ASCA spectra. By adopting a two-temperature model, one can obtain better fits, and the metallicities derived are substantially higher. For a sample of 12 groups, Buote (2000a) derives an average metallicity of Z = 0.29 ± 0.12 Zodot for the isothermal model and Z = 0.75 ± 0.24 Zodot for the two-temperature model (a single metallicity is assumed for the gas in these models). Buote (2000a) also finds that a multiphase cooling flow model provides a good description of the data. This model also requires higher metallicities (Z = 0.65 ± 0.17 Zodot). Buote (2000a) finds a trend for the metallicities to be lowest in those groups for which the largest extraction apertures were used. This result is consistent with metallicity gradients in groups (see also Buote 2000c). Alternatively, it may simply reflect that the relative contribution of the "group" gas component increases as one adopts a larger aperture. In fact, given the results of the ROSAT surface brightness profile fits, emission from the central elliptical galaxy may dominate the flux in the typical ASCA aperture and thus likely dominates the metallicity measurement. Therefore, the ASCA measurements may not be providing an accurate gauge of the global metal content of the group gas. Regardless, the work of Buote (1999, 2000a) is an important reminder that the properties derived from X-ray spectroscopy are very sensitive to the choice of the input model.

Matsushita et al (2000) also considered multi-temperature models for a large sample of early-type galaxies observed with ASCA. In contrast to Buote (1999, 2000a), Matsushita et al (2000) concluded that the poor spectral fits to ASCA data were not caused by incorrect modeling of multi-temperature emission. Furthermore, the multi-temperature models used by Matsushita et al (2000) produced relatively small increases in the overall abundance in many cases. Matsushita et al (2000) suggested that the strong coupling between the abundance of the so-called alpha-elements (i.e. O, Ne, Mg, Si, S) and the abundance of Fe hampers a unique determination of the overall metallicity. By fixing the abundance of the alpha-elements, Matsushita et al (2000) found that the derived metallicities are approximately solar. Although Matsushita et al (2000) restricted their analysis to early-type galaxies, these results may be applicable to groups, which have X-ray properties very similar to those of X-ray luminous ellipticals.

Although the dominant line features for the intragroup medium are produced by iron, strong lines are also expected from elements such as oxygen, neon, magnesium, silicon, and sulfur. The relative abundance of these various elements provides strong constraints on the star formation history of the gas. Some authors have attempted to fit the ASCA spectra with an isothermal model where the alpha-elements are varied together and separately from the iron abundance (Fukazawa et al 1996, 1998; Davis et al 1999; Finoguenov & Ponman 1999; Hwang et al 1999). In general, these studies find that the alpha-element to iron ratio is approximately solar in groups. Unfortunately, the determination of this ratio is very sensitive to the spectral model adopted (Buote 2000a) and if the isothermal assumption is not valid, these determinations are not particularly meaningful.

In summary, despite the great potential of X-ray spectroscopy to provide clues into the enrichment history of the intragroup medium, it is not possible at the present time to make strong conclusions about the metal content of the hot gas. Until we have higher resolution X-ray spectra and more complete plasma codes, the metallicity of the intragroup medium will remain an open issue.

3.4.4. Absorbing Column     The soft X-ray band is sensitive to low-energy photoabsorption by gas both within the source and along the line of sight. This absorption must be included in the X-ray spectral fits. It is usually assumed that the X-ray flux is diminished by:

Equation 3

where NH is the hydrogen column density and sigma(E) is the photo-electric cross section (solar abundances are almost universally assumed for the absorbing gas). The cross sections in Morrison & McCammon (1983) are commonly adopted for X-ray analysis. The standard procedure is to allow NH to be a free parameter in the spectral fit. If the best-fit spectral model returns a value of NH significantly higher than the Galactic value, this is taken as evidence for excess absorption intrinsic to the group or central galaxy. The ROSAT and ASCA spectra of groups are often not of high enough quality to adequately constrain the absorbing column. Therefore, many authors have chosen to fix NH to the Galactic value for spectral fits. For a few groups, however, column densities above the Galactic value have been inferred (Fukazawa et al 1996; Davis et al 1999; Buote 2000a, b). Buote (2000b) undertook the most ambitious study of absorption in groups, measuring NH as a function of radius in a sample of 10 luminous systems observed by the ROSAT PSPC. Buote (2000b) found that the value of NH derived depends strongly on the bandpass used in the X-ray analysis and suggested the bandpass-dependent NH values are consistent with additional absorption in the group from a collisionally ionized gas. This excess absorption manifests itself primarily as a strong oxygen edge feature at ~ 0.5 keV. Buote (2000b) found that within the central regions of the groups, the estimated masses of the absorbers are consistent with the matter deposited by a cooling flow over the lifetime of the flow. If a warm absorber exists in groups, as suggested by Buote (2000b), it should be verified by the next generation of X-ray telescopes.

3.4.5. X-Ray Luminosity     For a thermal plasma, the X-ray luminosity is a rough measure of the total mass in gas. Therefore, the total X-ray luminosity of a group provides a potentially interesting probe of a group's properties. In almost all cases in the literature, the total flux or luminosity quoted is out to the radius to which X-ray emission is detected. In this sense, quoted X-ray luminosities should be thought of as "isophotal luminosities." The measured luminosity is also sensitive to the exact techniques used in the X-ray analysis. For example, the total radial extent of the X-ray emission (and thus the total X-ray luminosity) is strongly dependent on the assumed background level (Henriksen & Mamon 1994, Davis et al 1996). Because of this, different authors often derive vastly different X-ray luminosities for the same group using the same ROSAT observation (Mulchaey et al 1996a).

It is a common practice to quote bolometric luminosities in the literature. The bolometric correction is estimated by extrapolating the spectral model for the gas beyond the limited bandpass of the particular telescope and by making a correction for any absorption along the line of sight. In the case of ROSAT observations, these corrections can easily double the luminosity of the source. The bolometric correction is also somewhat sensitive to uncertainties in the spectral model such as gas metallicity. For very shallow observations, such as those based on ROSAT All-Sky Survey data, a spectral model must usually be assumed to estimate the total X-ray luminosity. The bolometric luminosities of groups are typically in the range several times 1040 h-2100 to nearly 1043 h-2100 (Mulchaey et al 1996a, Ponman et al 1996, Helsdon & Ponman 2000). Thus, the X-ray luminosities of groups can be several orders of magnitude lower than the X-ray luminosities of rich clusters (cf Forman & Jones 1982).

Finally, it is worth noting that because X-ray emission is usually traced only to a fraction of the virial radius in groups, it is likely that the isophotal measurements significantly underestimate the true luminosities of the hot gas. This is particularly true for the coolest groups. Helsdon & Ponman (2000) have attempted to account for the missing luminosity by extrapolating the gas density profile models out to the virial radius. A comparison of the observed isophotal luminosities to the corrected virial luminosities in the Helsdon & Ponman sample indicate that in many cases, over half of the luminosity could occur beyond the radius to which X-ray emission is currently detected.

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