A model for the postcollapse equilibrium of cosmological structure: truncated isothermal spheres from top-hat density perturbations

Shapiro, Paul R.; Iliev, Ilian T.; Raga, Alejandro C.

A model for the postcollapse equilibrium of cosmological structure: truncated isothermal spheres from top-hat density perturbations

Authors

Shapiro, Paul R.

Iliev, Ilian T.

Raga, Alejandro C.

Description

The postcollapse structure of objects which form by gravitational condensation out of the expanding cosmological background universe is a key element in the theory of galaxy formation. Towards this end, we have reconsidered the outcome of the nonlinear growth of a uniform, spherical density perturbation in an unperturbed background universe - the cosmological ``top-hat'' problem. We adopt the usual assumption that the collapse to infinite density at a finite time predicted by the top-hat solution is interrupted by a rapid virialization caused by the growth of small-scale inhomogeneities in the initial perturbation. We replace the standard description of the postcollapse object as a uniform sphere in virial equilibrium by a more self-consistent one as a truncated, nonsingular, isothermal sphere in virial and hydrostatic equilibrium, including for the first time a proper treatment of the finite-pressure boundary condition on the sphere. The results differ significantly from both the uniform sphere and the singular isothermal sphere approximations for the postcollapse objects. These results will have a significant effect on a wide range of applications of the Press-Schechter and other semi-analytical models to cosmology. The truncated isothermal sphere solution presented here predicts the virial temperature and integrated mass distribution of the X-ray clusters formed in the CDM model as found by detailed, 3D, numerical gas and N-body dynamical simulations remarkably well. This solution allows us to derive analytically the numerically-calibrated mass-temperature and radius-temperature scaling laws for X-ray clusters which were derived empirically by Evrard, Metzler and Navarro from simulation results for the CDM model. (Shortened)
29 pages, 7 ps figures, MNRAS-style, LaTeX. Accepted for publication in MNRAS. Minor revisions only (including additional panel in Fig.3 and additional comparison with X-ray cluster simulations)