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

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dc.creatorShapiro, Paul R.
dc.creatorIliev, Ilian T.
dc.creatorRaga, Alejandro C.
dc.date1998-10-09
dc.date1999-03-28
dc.date.accessioned2026-07-07T06:24:51Z
dc.date.available2026-07-07T06:24:51Z
dc.descriptionThe 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)
dc.description29 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)
dc.identifierhttps://arxiv.org/abs/astro-ph/9810164
dc.identifierhttp://arxiv.org/abs/astro-ph/9810164
dc.identifierMon.Not.Roy.Astron.Soc. 307 (1999) 203
dc.identifierdoi:10.1046/j.1365-8711.1999.02609.x
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96684
dc.subjectAstrophysics
dc.titleA model for the postcollapse equilibrium of cosmological structure: truncated isothermal spheres from top-hat density perturbations
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