The data gathered by the new generation of X-ray satellites, together with the completion of automated surveys of photographic material covering large regions of the sky, have raised fundamental questions about the origin of galaxy clusters, their clustering properties, and the formation of the intracluster medium (ICM). For example, what is the origin of the scaling laws that relate the X-ray properties of clusters, such as the luminosity-temperature (L_X-T_ X) relation? Is the baryon fraction in clusters representative of the universe as a whole? Why are distant clusters less luminous in X-rays than at present, in contradiction with the naive expectations of hierarchical clustering models? What is the origin of the ICM core radii observed in X-rays? Can the clustering properties of clusters provide significant constraints on cosmological models[17]? The N--body/hydrodynamical code that I have developed is well suited for numerical studies that can address these issues. Its lack of imposed symmetries and large dynamic range make it possible to follow the three-dimensional evolution of the ICM in the dynamically evolving potential well of a cluster.
A few interesting results have emerged from a series of numerical experiments designed specifically to study the structure of X-ray clusters and their evolution in the standard CDM cosmogony. Many of the results are, however, fairly generic and apply to all hierarchical clustering models. We first addressed the process of accretion of baryons into clusters such as Coma[6]. This is an important issue because the baryon mass fraction in Coma appears to exceed by a large factor upper limits derived from nucleosynthesis calculations if, as implied by most inflationary theories, the universe has critical density. It had been suggested that perhaps the effects of cooling and large deviations from sphericity during cluster collapse might be responsible for the large baryon mass fraction of Coma. We were able to prove that the mean baryon fraction within a virial radius (about an Abell radius for a cluster like Coma) cannot exceed the mean baryon fraction of the universe. Since the masses of gas, stars, and dark matter in Coma are relatively well known inside this radius, and given the small uncertainty in the universal baryon abundance from nucleosynthesis constraints, this result forces us to either abandon inflation and accept that we live in a low-density universe (\Omega<1), or else consider the inelegant possibility that the cosmological constant is not zero. Alternatively, we would have to dismiss the primordial nucleosynthesis calculations and with them one of the most important successes of the Big Bang theory.
Other interesting results of the simulations mentioned above concern the process of formation of clusters. As every system in a hierarchical universe, clusters form by the merger of pre-collapsed clumps[1,2,3]. During these mergers, the gaseous component gains energy at the expense of the dark matter. This has two important consequences. (i) Being more energetic, the gas ends up less centrally concentrated than the dark matter. Mergers, therefore, provide a natural explanation for the puzzling ``anti-bias'' or anti-segregation between gas and dark matter found in previous simulations of large scale structure. (ii) The central structure of the gas differs from that of the dark matter. Mergers can thus impose a core radius on the gas component even if no such core radius is present in the dark matter (Figure 7a). This provides a compelling and natural explanation for the X-ray cores observed in many galaxy clusters.
We were also able to show that, if the effects of radiative cooling can be neglected, clusters of widely different masses identified at various redshifts should look remarkably similar when scaled to their virial parameters. All clusters would therefore have similar density profiles, almost isothermal near the center but significantly steeper than isothermal in the outer regions, \rho \propto r^-3. The gas temperature therefore should decrease outwards beyond some radius, to a value of about one half of that at the center near the virial radius (Figure 7b). If clusters are indeed self-similar, a similar temperature drop should be readily observable in other clusters, a prediction that can be tested directly by current X-ray missions. Knowledge of the gas temperature as a function of radius also creates the possibility of determining accurately the mass of a cluster directly from observations. It is therefore crucial to explore possible effects that may lead to systematic biases in the masses determined from X-ray observations. These effects include velocity bias, incomplete gas thermalization, and departures from sphericity. We have recently completed an analysis of a large number of high-resolution numerical simulations devoted to this issue[12,19]. Our main conclusion is that simple estimators of cluster masses based on X-ray information are unbiased and accurate to within 20\%. These results practically rule out the possibility of large systematic errors in the mass determination of galaxy clusters, and emphasize the difficulty of reconciling an \Omega=1 universe with standard primordial nucleosynthesis calculations.
Another consequence of the similarity between clusters is that clusters
of a given mass are expected to be denser and therefore more luminous in
the past, in disagreement with observations. Tight scaling laws are also
predicted between luminosity and temperature, but with a slope, L_ X \propto
T_ X^2, shallower than inferred from observations[16,25].
These discrepancies suggest that non-gravitational processes, such as early
preheating of the ICM or perhaps the effects of cooling or galaxy formation,
are responsible for the structure of the X-ray emitting gas near the center
of clusters. Including these effects self-consistently is one of the challenges
for future simulations of the formation and evolution of X-ray clusters
that I plan to address in future work.
Figure 7a (left):The density profile of an isothermal gas (dotted line) in hydrostatic equilibrium within a cold dark matter halo (solid line). The dashed line shows a fit using a \beta-model. The parameters r_c=0.1 \times r_max and \beta=0.7 give an excellent \beta-model fit to the gas profile.
Figure 7b-right) Gas temperature profiles in clusters spanning a factor of 30 in mass formed in the standard CDM cosmogony. Temperatures are scaled to the mean virial temperature of the system, T_200, and radii are scaled to the virial radius, r_200. Note that scaled this way the temperature profiles of clusters of different mass look remarkably similar. The thick dotted line shows the spherical infall self-similar solution. The thick solid segment indicates T \propto r^-1/2. Vertical segments show the gravitational softening of each simulation. All clusters are nearly isothermal out to r \sim 0.4 r_200. Typical temperatures at the virial radius are about one-half of the values near the center.
