5.8. X-ray emission from individual galaxies
A number of topics concerning the X-ray emission from hot gas associated with individual galaxies in clusters will now be discussed. Material on the accretion of gas by central galaxies in clusters with cooling flows was reviewed in the previous section.
5.8.1. Massive haloes around M87 and other central galaxies
The X-ray emission from the M87/Virgo cluster is considerably different from the emission from richer and more regular clusters (Section 4.5.3). The gas is much cooler and less extended, and the X-ray luminosity is rather small. Initially, this was explained by noting that the X-ray luminosity and temperature of clusters appeared to correlate with the cluster velocity dispersion (equations 4.8 and 4.10), although this argument was somewhat circular, since M87/Virgo was one of the strongest pieces of evidence in favor of these correlations.
Bahcall and Sarazin (1977) and Mathews (1978b) suggested an alternative; the gas in M87/Virgo might be hydrostatic and bound to the galaxy M87, rather than to the cluster as a whole. To bind the gas, the galaxy would have to have a much deeper gravitational potential well than it would appear to have from its optical emission. Based on the best observations at that time, Bahcall and Sarazin showed that M87 must have a massive halo, with a total mass of 3 × 1013 M extending out to 100 kpc from the galaxy center. Bahcall and Sarazin assumed a number of reasonable equations of state for the gas (adiabatic, polytropic, etc.; see Section 5.5). Mathews (1978b) reached a similar conclusion, although he assumed that the gas was exactly isothermal and that the mass distribution was the King analytic form for an isothermal distribution (5.57). Because such isothermal gas models diverge unless the gas is cool compared to the potential (equations 5.65 and 5.66), Mathews required much more mass, 1014 M. This high mass limit is very sensitive to the assumption that the gas is exactly isothermal (Bahcall and Sarazin, 1978; Fabricant et al., 1980).
There is considerable evidence that M87/Virgo has a cooling flow (Section 5.7). However, at large distances from the galaxy center the flow is highly subsonic, and the hydrostatic equation applies. Thus the cooling flow does not alter the requirement that the mass be large.
Binney and Cowie (1981) suggested that the mass of M87 might be much lower ( 3 × 1011 M). They argued that the gas around M87 is bound by the pressure of surrounding, hotter gas, rather than by the gravity of M87. This hotter gas was in turn assumed to be extended and bound by the cluster gravitation potential of Virgo. The hot, diffuse, confining, intracluster gas is required to have a density and temperature of np 10-3 cm-3 and Tg 108 K. The cool gas is produced by a cooling flow, which is drawn from the hot gas.
A key point in the Binney and Cowie model is that there must be enough hot, diffuse gas to provide a pressure that confines the cool gas around M87. Because this gas would be less dense than the cooler gas, it would have a lower surface brightness, but it should be detectable in hard X-rays. Davison (1978) and Lawrence (1978) found a hard X-ray component from M87/Virgo, which they suggested was extended. However, more recent observations indicate that this hard component is not extended, has a power-law spectrum, and is centered on M87 (Lea et al., 1981, 1982). This hard source is probably nonthermal emission from the nucleus of M87. The present limits on the amount of extended hard X-ray emission are, at best, marginally consistent with the Binney and Cowie model (Fabricant and Gorenstein, 1983).
The Einstein satellite observations of the X-ray emission from M87 have been analyzed in detail by Fabricant et al. (1980), Fabricant and Gorenstein (1983), and Stewart et al. (1984a). All of these papers used basically the method of analysis outlined in Sections 5.5.4 and 5.5.5; that is, the observed surface brightness was deconvolved to give the variation of emissivity with radius from the galaxy center. At the time of the first paper, the spectral response of the IPC on Einstein was poorly calibrated, and the density was derived from the emissivity assuming that the gas was isothermal.
From the hydrostatic equation, the total mass M(r) interior to a radius r is
Beyond 3 arc min from the center of M87, the surface brightness is well represented as a power-law r-1.62 (Fabricant and Gorenstein, 1983). Thus, as long as the temperature gradient is not significant, the density derivative in this equation is a constant, and the mass increases with the radius. Fabricant et al. (1980) found a total mass of 2 - 4 × 1013 M within a radius of 230 kpc.
Binney and Cowie (1981) analyzed the same Einstein data and found consistency with their low mass model for M87. They argued that the disparity between their conclusion and that of Fabricant et al. (1980) was due to two differences. First, Fabricant et al. assumed that the surface brightness approached zero far from M87, whereas Binney and Cowie invoke extended intracluster gas. More importantly, in the Binney and Cowie cooling flow model the gas temperature decreases rapidly towards the center, d log Tg / d log r 0.8. This large temperature gradient nearly cancels the density gradient (i.e., the pressure is nearly constant), and the resulting mass is significantly reduced.
The Einstein data were reanalyzed by Fabricant and Gorenstein (1983) and Stewart et al. (1984a), who found that the mass of M87 is 3 - 6 × 1013 M within a radius of 260 kpc. By this time, the spectral response of the IPC had been calibrated and the temperature gradient could be derived directly from the data, albeit with large errors. (Note that this is possible for M87/Virgo and not for most cluster sources because the temperature in M87/Virgo is low enough to be measured with the soft X-ray sensitivity of Einstein). In addition, the temperature gradient was constrained by the wide field proportional counter observations from previous satellites, and by data from the SSS and FPCS X-ray spectrometers on Einstein. The observed temperature gradient appears to be inconsistent with that required by Binney and Cowie. These data appear to rule out the Binney and Cowie model.
Thus M87 appears to have a very massive halo, which extends well beyond the region where the galaxy is luminous. Like the massive haloes around spiral galaxies (Section 2.8), the mass appears to increase roughly in proportion to the radius in the outer portions of M87. However, spiral galaxies have rotation velocities nearly independent of radius, on the order of 300 km/s (Faber and Gallagher, 1979). The inferred circular orbital velocity in the halo of M87 is much higher, about 750 km/s. This is also much higher than the orbital velocities of stars in the visible portion of M87, and thus the orbital velocities in M87 are not independent of radius over the span from the luminous portions of the galaxy to the outer halo.
One important question is whether other elliptical galaxies have massive dark haloes. This question will be addressed in Section 5.8.3.