4.3. X-ray spectra
Observations of the X-ray spectra of clusters of galaxies have played a critical role in establishing the primary emission mechanism (thermal emission from diffuse hot intracluster gas) and in testing models for the origin of this gas. Models in which the emission comes from diffuse thermal gas predict (1) that the spectrum will be roughly exponential (the intensity I (erg / cm2-s-Hz) varies as exp(-h / kTg) where Tg is the gas temperature); (2) that the gas temperature will be such that the thermal velocity of protons in the gas (k Tg / mp)1/2 be comparable to the velocity of the galaxies in the cluster, as both are bound by the same gravitational potential; (3) that there will be no strong low energy photoabsorption; and (4) that emission lines will be present if the gas contains a significant contamination of heavy elements like iron. Alternatively, models in which the emission is due to relativistic nonthermal electrons predict a power-law spectrum I -, which implies an excess at low and high energies when compared to an exponential spectrum; no line emission would be expected for a nonthermal emission process. As another possibility, the emission might be thermal emission from a number of compact sources, such as galactic nuclei or the binary stellar X-ray sources which dominate the X-ray sky within our own galaxy; however, such sources are generally optically thick at low X-ray energies ( 1 keV). The theories for each of these classes of emission processes and the basis for these predictions are discussed in Section 5.1.
The first three of the predictions given above concern the broad-band form of the spectrum (the continuum), while the last prediction concerns lines. Accordingly, the properties of the continuum spectra will first be reviewed, and then those of the line spectra. Reviews devoted primarily to the observations of the X-ray spectra of clusters have been given recently by Canizares (1981) and Mushotzky (1980, 1984, 1985), while Holt and McCray (1982) review all of X-ray spectroscopy.
4.3.1. Continuum features in the spectrum
If the X-ray emission from clusters is due to a diffuse plasma of either thermal or nonthermal electrons, the optical depth of the gas should be quite low. On the other hand, compact X-ray sources (such as galactic nuclei or binary stellar X-ray sources) often contain significant quantities of relatively cool neutral gas, which absorbs soft X-rays through photoionization. Because the fluorescent yield of the light elements is low, the absorbed X-rays are not reemitted and are lost from the spectrum. This low energy photoabsorption occurs in a series of edges which correspond to the absorption edges of cosmically abundant elements. The opacity of a solar abundance, low density, cold neutral gas has been calculated, for example, by Brown and Gould (1970). It is conventional to parametrize the absorption observed in an X-ray spectrum by the column density of hydrogen Nh in a gas with assumed solar abundances required to produce the observed absorption. Typically, compact sources have Nh 1022 cm-2. Even the earliest X-ray spectra of clusters suggested that they had rather weak low energy absorption (Catura et al., 1972; Kellogg, 1973; Davidsen et al., 1975; Kellogg et al., 1975; Margon et al., 1975; Avni, 1976), with column densities Nh 1022 cm-2, which were generally consistent with the amount of neutral hydrogen in our own galaxy along the line of sight to the cluster. This indicated that the emission from clusters comes from a diffuse, ionized plasma.
Initially, there were two competing models for the nature of this ionized plasma (see Section 5.1). It could be a hot, thermal plasma with a temperature Tg 108 K, or it could be a relativistic, nonthermal plasma with a power-law electron energy distribution, such as the plasma responsible for the radio emission observed in clusters (see Section 3.1). In the first case, the X-ray continuum would be primarily due to thermal bremsstrahlung (see Section 5.1.3), with a spectrum given by equation (5.11). If the frequency variation of the Gaunt factor gff(, kTg) is ignored and the gas is all at a single temperature, the spectrum is exponential I exp(-h / kTg). In the second case, the emission is primarily due to the inverse Compton process (the scattering of low energy photons to X-ray energies by the relativistic electrons; see Section 5.1.1), and the expected spectrum is a power-law I -.
Unfortunately, proportional counters have rather poor spectral resolution, and it is therefore difficult to distinguish between thermal and nonthermal spectra. Moreover, any sufficiently smooth and monotonic spectrum can be produced by the combination of the thermal spectra with varying temperatures, or nonthermal spectra with varying spectral indices ; thus the distinction between thermal and nonthermal spectra cannot be made unambiguously. It is not surprising, therefore, that the early proportional counter spectra of clusters could be fit consistently by either thermal (exponential) or nonthermal (power-law) spectra (for example, Kellogg et al., 1975). However, spectra over a large energy range were better fit by the thermal model (Davidsen et al., 1975; Scheepmaker et al., 1976).
The first large surveys of cluster spectra came from observations with OSO-8 and Ariel 5. These satellites observed individual clusters for longer periods of time than had been possible with previous sky survey instruments, and had detectors that were optimized for spectral resolution. The spectra of clusters observed with OSO-8 and Ariel 5 were significantly better fit by the thermal bremsstrahlung model than by the nonthermal model (Mushotzky et al., 1978; Mitchell et al., 1979). The required temperatures for the cluster gas were found to range from about 2 × 107 to 2 × 108 K from cluster to cluster, and some of the clusters required gas at several temperatures to fit the spectrum. Recently, a more extensive survey of X-ray cluster spectra was made with the A-2 experiment on the HEAO-1 satellite (Mushotzky, 1980, 1984, 1985; a href="Sarazin_refs.html#345" target="ads_dw">Henriksen, 1985; a href="Sarazin_refs.html#346" target="ads_dw">Henriksen and Mushotzky, 1985, a href="Sarazin_refs.html#347" target="ads_dw">1986).
The two properties that can be derived most easily from the continuum X-ray spectrum are the gas temperature Tg and the emission integral
where np is the proton density, ne is the electron density, and V is the volume of the gas in the cluster. The X-ray luminosity of a cluster is proportional to EI (equation 4.11). The X-ray luminosity (or EI) and gas temperature are found to be strongly correlated (Mitchell et al., 1977, 1979; Mushotzky et al., 1978). The HEAO-1 A-2 sample (Figure 11) gives Lx Tg3 (Mushotzky, 1984). The OSO-8, Ariel 5, and HEAO-1 A-2 spectral surveys established a number of correlations between these X-ray spectral parameters and the optical properties of X-ray clusters, which are discussed in Section 4.6 below.
Figure 11. The correlation between the gas temperatures derived from X-ray spectra with HEAO-1 A-2 and the cluster X-ray luminosities, from Mushotzky (1984).
There was also some evidence from the OSO-8 survey that the gas in clusters was isothermal; that is, the range of temperatures within the gas in a single cluster was relatively small. However, in many cases the OSO-8 and Ariel 5 temperatures were not in agreement within the errors; if these differences are real, they suggest that there are multiple temperature components to the emission. If that were the case, the OSO-8 and Ariel 5 detectors, which have different spectral and spatial sensitivities, might give different weights to the different components, and produce different average temperatures.
The HEAO-1 A-2 detector has provided much more data on the spectra of clusters in the photon energy range 2-60 keV (Mushotzky, 1980, 1984, 1985; Henriksen, 1985; Henriksen and Mushotzky, 1985, 1986). There is now evidence that most clusters contain a range of gas temperatures, with typical values between Tg 2 × 107 and 8 × 107 K. These multiple temperature components appeared to be most significant in clusters with low X-ray luminosities, although it is possible that similar low-luminosity cool components might remain undetected if hidden in the spectrum of clusters with high-luminosity high-temperature emission. The information on the spatial distribution of the X-ray emission in clusters (Section 4.4) suggests two locations for this cool gas. First, in low luminosity clusters, the X-ray emission is often inhomogeneous, with clumps of emission being associated, in some cases, with individual galaxies. These clumps may contain cooler gas. Second, in some clusters there are enhancements in the X-ray surface brightness at the position of the cD or other centrally located dominant galaxy in the cluster. X-ray line observations suggest that these are regions at which the hot intracluster gas is cooling and being accreted by the central dominant galaxy (Section 5.7).
The Einstein X-ray observatory had two instruments capable of providing information on the continuum spectra of clusters. First, there was the Imaging Proportional Counter (IPC), which provided low resolution spatial and spectral information. Initially there were problems with the calibration of the energy scale of the spectra due to gain variations. These problems have now apparently been resolved, and a few cluster spectra from this instrument are available at the present time (Fabricant et al., 1980; Perrenod and Henry, 1981; Fabricant and Gorenstein, 1983; White et al., 1987). The second instrument was the Solid State Spectrometer (SSS), which had considerably better spectral resolution, but had no spatial resolution and less sensitivity than the IPC. Because of its small field of view (6 arc min), it could only observe a small portion of nearby clusters. Thus it was used primarily to determine spectra for the central regions of nearby clusters. It provided strong evidence for the presence of cool gas at the centers of a number of clusters (Mushotzky, 1980, 1984, 1985; Mushotzky et al., 1981; Lea et al., 1982); these observations are discussed further below. One problem with Einstein as an instrument for X-ray cluster spectroscopy is that the telescope was only sensitive to photons with energies of about 0.1 - 4.0 keV. With the typical temperatures of the gas in clusters being kTg 8 keV, observations with Einstein could not determine the thermal structure in this hot gas. However, the Einstein detectors were very sensitive to the presence of low temperature components of the emission.
Detections or limits on the hard X-ray spectrum and flux of clusters have been useful in limiting the contribution of nonthermal processes to their luminosity. As mentioned above, spectra extending into the hard X-ray region (h > 20 keV) gave the first direct, strong indication that the primary emission mechanism was thermal, rather than nonthermal (Davidsen et al., 1975; Scheepmaker et al., 1976). Subsequently, stronger limits on the hard X-ray emission have shown that nonthermal emission makes at most a very small contribution to the X-ray luminosity of clusters (Mushotzky et al., 1977; Lea et al., 1981). When combined with observations of the diffuse radio emission in the cluster (Section 4.4), these hard X-ray limits can be used to give lower limits on the magnetic field in the cluster, because the synchrotron radio emissivity is proportional to the product of the density of relativistic electrons and the magnetic field strength, while the inverse Compton X-ray emission depends only on the density of relativistic particles (see Section 5.1.1 for a more detailed discussion of this point). Typically, these limits are B 10-7G (Lea et al., 1981; Primini et al., 1981; Bazzano et al., 1984).
In the Perseus cluster, a power-law hard X-ray component with 2.25 has been detected; it varies on a time scale of about a year, and the X-ray variations are correlated with variations in the radio flux of the compact radio source at the nucleus of the galaxy NGC1275 (Primini et al., 1981; Rothschild et al., 1981). Much weaker power law sources may also have been detected in the M87/Virgo, A2142, and 3C129 clusters (Lea et al., 1981; Bazzano et al., 1984).