Peridier Library Abstract Archive

Abstract No. UT 399

Title: A model for the postcollapse equilibrium of cosmological structure: truncated isothermal spheres from top-hat density perturbations
Author(s): Shapiro, Paul R., Iliev, Ilian, and Raga, Alejandro C.
Keywords: cosmology: theory -- dark matter -- galaxies: clusters: general -- galaxies: formation -- galaxies: haloes -- galaxies: kinematics and dynamics
Email: LANL LINK (optional, 7-digit number received after submission to xxx.lanl.gov): http://xxx.lanl.gov/abs/astro-ph/9810164 (to request a full copy of this paper)
Preprint: http://xxx.lanl.gov/abs/astro-ph/9810164 Document source or PostScript
Release date: 10/22/98 08:10:19
Publication status: Submitted to MNRAS
Comments: 28 pages, 7 figures

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 {\it singular} isothermal sphere approximations for the postcollapse objects. The virial temperature which results is more than twice the previously used ``standard value'' of the postcollapse uniform sphere approximation but $1.4$ times smaller than that of the singular, truncated isothermal sphere approximation. The truncation radius is 0.554 times the radius of the top-hat at maximum expansion, and the ratio of the truncation radius to the core radius is 29.4, yielding a central density which is $514$ times greater than at the surface and about $1.8\times10^4$ times greater than that of the unperturbed background density at the epoch of infinite collapse predicted by the top-hat solution. For the top-hat fractional overdensity $\delta_L$ predicted by extrapolating the linear solution into the nonlinear regime, the standard top-hat model assumes that virialization is instantaneous at $\delta_L=\delta_{crit}=1.686$, i.e. the epoch at which the nonlinear top-hat reaches infinite density. The surface of the collapsing sphere meets that of the postcollapse equilibrium sphere slightly earlier, however, when $\delta_L=1.52$. These results will have a significant effect on a wide range of applications of the Press-Schechter and other semi-analytical models to cosmology.

We discuss the density profiles obtained here in relation to the density profiles for a range of cosmic structures, from dwarf galaxies to galaxy clusters, indicated by observation and by N-body simulation of cosmological structure formation, including the recent suggestion of a universal density profile for halos in the Cold Dark Matter (CDM) model. 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.