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What advances can be expected in the near future in the study of X-ray clusters? In this brief look at future prospects, I shall concentrate on new observational opportunities. At present, observational X-ray astronomy is in a rather quiet period. The Einstein X-ray satellite, which revolutionized the study of X-ray astronomy, is no longer operational. As this review was being written, the European Space Agency X-ray satellite EXOSAT was nearing the end of its operational life. EXOSAT is a somewhat less powerful imaging instrument than Einstein. What advances in the technology of X-ray astronomy are needed to answer the major questions we have about X-ray clusters, and what plans are there for the realization of these advances?

The basic data in the X-ray study of clusters consist of the surface brightness of X-rays Inu as a function of the photon frequency nu and the position on the sky. Given these data and a suitable assumption of symmetry for the cluster, the X-ray emissivity epsilonnu(r) as a function of position in the cluster can be derived by deconvolution of the surface brightness (Section 5.5.4). The emissivity varies as the square of the density rhog, and its frequency dependence is determined by the gas temperature Tg and by the abundances of heavy elements (equation 5.19). At the temperatures usually found in the intracluster gas, the heavy element abundances mainly affect the emission in several narrow line features, and the temperature produces an exponential falloff in the intensity for frequencies hnu > kTg. Thus, given suitable observations of the X-ray surface brightness Inu, one can derive the gas density, temperature, and several heavy element abundances, all as a function of position in the cluster.

In relatively nearby clusters, the required instrument for these observations must measure the X-ray surface brightness with at least moderate spatial resolution (< 1 arc minute), and modest spectral resolution (better than about 15%), and must be sensitive to X-rays with photon energies hnu of at least 7 keV. Obviously, it must also have a sufficient sensitivity to detect the clusters. Unfortunately, no past or currently existing satellite has had all these capabilities. Proportional counter systems, such as the Uhuru satellite, have modest spectral resolution out to high X-ray energies, but have very poor spatial resolution. The Einstein satellite had excellent spatial resolution, fairly poor spectral resolution in the imaging detectors, and no sensitivity for photon energies hnu gtapprox 4 keV.

The Advanced X-ray Astronomy Facility (AXAF) would provide the new observational capabilities needed for the further study of X-ray clusters (Giacconi et al., 1980). AXAF is a 1.2 meter diameter X-ray telescope, which would be carried into orbit by the Space Shuttle. As currently planned, AXAF would have roughly 100 times the sensitivity of the Einstein telescope for point sources and a considerably increased sensitivity for extended sources as well. Its mirrors would produce images with a spatial resolution of better than one second of arc, and would be sensitive to X-rays with photon energies of at least 8 keV. At least some of the imaging detectors being considered would have moderate spectral resolution (10-20% or better), and the satellite would have a number of higher resolution spectrometers. With its high spatial resolution, moderate spectral resolution, and sensitivity to harder X-rays, it would provide exactly the data on cluster X-ray surface brightnesses needed to derive their densities, temperatures, and abundances.

Given the run of density and temperature of the gas in a cluster or in an individual galaxy, the hydrostatic equation (5.56) allows one to determine the total mass in the galaxy or cluster as a function of position (Sections 5.5.5 and 5.8.1). These mass determinations are less uncertain than those based on the radial velocities of galaxies in clusters or stars in galaxies because the gas atoms are known to be moving isotropically. These mass distributions would provide very important information on the distribution and nature of the missing mass component in clusters and galaxies.

If measurements of the microwave diminutions of clusters can be made reliably, they can be combined with the determinations of the variation of the gas temperature and density to give distances to clusters that are independent of the Hubble constant (Section 3.5). This will provide a direct determination of the Hubble constant, independent of the usual extragalactic distance scale. If this method could be applied to high redshift clusters, it might allow the determination of the overall structure of the universe.

From the variation of the gas temperature with density and with position in a cluster, the influence of the various heating, cooling, and energy transport processes (Sections 5.3, 5.4) can be deduced. As discussed in Section 5.5.1, the surface brightness distributions in nearby clusters from the Einstein satellite are consistent with isothermal gas distributions, although temperatures could not be determined directly. Unfortunately, the temperatures required by the surface brightness fits are generally not consistent with temperatures derived from the integrated spectra of the clusters. Given this discrepancy, we cannot claim to have any real understanding of the thermal processes in intracluster gas. Direct measurements of the temperature profiles of clusters are needed to resolve this problem.

The moderate spectral resolution of AXAF's imaging detectors and sensitivity to 7 keV X-rays will allow this instrument to map out the abundance of iron and possibly other heavy elements in clusters. The distribution of heavy elements in clusters must be known if accurate abundances are to be derived for them. As noted in Sections 5.4.5 and 5.5.6, if the iron in clusters is concentrated in the core, the iron abundances may have been significantly overestimated. These abundances are used to determine the amount of gas that must have been ejected from stars in galaxies, and affect models for the origin and early evolution of galaxies (Section 5.10.2). Moreover, the distributions of heavy elements provide information on the relative proportions of ejected galactic gas and primordial intergalactic gas in clusters.

The higher resolution spectrometers on AXAF can be used to determine the abundances of additional elements and give more precise information on the temperature structure. It is particularly useful that the 7 keV iron lines will be observable, as these are the strongest lines in the intracluster gas and have many fine structure components whose intensities are sensitive to temperature. High resolution line studies will be particularly useful in studying the physical conditions in cooling flows (Section 5.7). They may also permit the determination of redshifts for X-ray clusters for which optical data are not available, and will certainly resolve any ambiguities when several clusters at different redshifts are seen along the same line-of-sight. At the highest spectral resolution, it may be possible to determine directly the flow velocities in clusters, particularly those with cooling flows.

The high spatial resolution of AXAF will be very important to the study of cooling flows and of other gas associated with individual galaxies (Sections 5.7 and 5.1). The increased sensitivity and enhanced spectral response of AXAF should make it possible to get spectra of the gas in these individual galaxy sources, in order to test the hypothesis that the emission is from hot gas. Gas in individual galaxies in clusters has so far been studied only in relatively nearby clusters. Of particular interest is the interaction of this gas with the intracluster medium.

AXAF should detect X-ray clusters out to very high redshifts, z approx 1 - 4. From the study of these clusters, we shall learn directly about the origin of the intracluster gas and its evolution in clusters. We may actually see the gas being ejected from galaxies. If galaxy morphologies are altered by the galaxy's environment, and the main mechanism is gas stripping by intracluster gas, the buildup of the intracluster gas should be related to the evolution of galaxy morphologies. With the Hubble Space Telescope (Hall, 1982), it should be possible to classify galaxies out to at least moderate redshifts. The variation in the heavy element abundances in clusters as a function of redshift should constrain models for the chemical evolution of galaxies. The variations in the temperature of the gas will allow us to assess the effects of heating and cooling.

It will also be interesting to see if there is any relationship between the evolution of X-ray clusters and that of quasars and other active galactic nuclei.

One problem with these studies of high redshift clusters is that few are currently known. Because AXAF is not primarily a survey instrument, it might not detect a very large number of previously unknown clusters. It is possible that deeper ground based optical surveys or studies with the Hubble Space Telescope will provide longer lists of cosmological clusters. It is also possible they may be found by studying high redshift radio galaxies and quasars with the morphological distortions normally associated with sources in clusters (Section 3.3). Another exciting possibility involves the Roentgen Satellite (ROSAT). This instrument will perform an all-sky soft X-ray survey, with a spatial resolution of about 1 minute of arc and a sensitivity limit similar to that of the Einstein satellite. A luminous X-ray cluster at a redshift of 1 might possibly be detected in this survey. Because an X-ray cluster at a redshift of 1 would have an angular size of about 1 minute of arc, it might appear as a resolved source. The most common extragalactic X-ray sources found in deep surveys are quasars, which are point sources. Thus most of the resolved high galactic latitude sources in the ROSAT survey should be clusters, and some of those should be at high redshifts. This survey may provide a valuable list of X-ray clusters for further study.

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