Ilian T. Iliev

A model for the post‐collapse equilibrium of cosmological structure: truncated isothermal spheres from top‐hat density perturbations

ABSTRA C T The post-collapse structure of objects that 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 non-linear 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 post-collapse object as a uniform sphere in virial equilibrium by a more self-consistent one as a truncated, non-singular, 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 post-collapse objects. The virial temperature that results is more than twice the previously used ‘standard value’ of the post-collapse 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 that is 514 times greater than at the surface and 1:8 10 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 d L predicted by extrapolating the linear solution into the non-linear regime, the standard top-hat model assumes that virialization is instantaneous at dLa dca 1:686 i.e. the epoch at which the non-linear top-hat reaches infinite density. The surface of the collapsing sphere meets that of the post-collapse equilibrium sphere slightly earlier, however, when dLa 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 haloes in the cold dark matter (CDM) model. The non-singular 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 & Navarro from simulation results for the CDM model.

The post-collapse equilibrium structure of cosmological haloes in a low-density universe

An analytical model is presented for the postcollapse equilibrium structure of virialized objects which condense out of a low-density cosmological background universe, either matter-dominated or flat with a cosmological constant. This generalizes the model we derived previously for an Einstein-de Sitter (EdS) universe. The model is based upon the assumption that cosmological haloes form from the collapse and virialization of top-hat density perturbations and are spherical, isotropic, and isothermal. This leads to the prediction of a unique, nonsingular, truncated isothermal sphere (TIS), a particular solution of the Lane-Emden equation (modified for nonzero cosmological constant). The size and virial temperature are unique functions of the mass and redshift of formation of the object for a given background universe. The central density is roughly proportional to the critical density of the universe at the epoch of collapse. This TIS model is in good agreement with observations of the internal structure of dark matter--dominated haloes on scales ranging from dwarf galaxies to X-ray clusters. It also reproduces many of the average properties of haloes in simulations of the Cold Dark Matter (CDM) model to good accuracy, suggesting that it is a useful analytical approximation for haloes which form from realistic initial conditions. Our TIS model matches the density profiles of haloes in CDM N-body simulations outside the innermost region, while avoiding the steep central cusp of the latter which is in apparent conflict with observations. The TIS model may also be relevant to nonstandard CDM models, like self-interacting dark matter, recently proposed to resolve this conflict.

On the Mass Profile of Galaxy Cluster CL 0024+1654 Inferred from Strong Lensing

Observations of a flat-density profile in the cores of dark matter-dominated halos on the two extremes of mass for virialized objects in the universe, dwarf galaxies and galaxy clusters, present a serious challenge to the current standard theory of structure formation involving cold dark matter (CDM). By contrast, N-body simulations of halo formation in the latter indicate density profiles that are singular and steeply rising toward the center. A flat-density core on the cluster scale is indicated by gravitational lensing observations, most significantly by the strong-lensing measurements of Cl 0024+1654 by the Hubble Space Telescope. A recent reanalysis of this cluster has suggested that a uniform-density core is not demanded by the data, thereby eliminating a significant piece of the conflict between the observations and the CDM theoretical predictions. We show here, however, that the singular mass profile that that analysis reports as consistent with the lensing measurements of Cl 0024+1654 implies a velocity dispersion that is much higher than the measured value for this cluster.

ON THE ORIGIN OF THE ROTATION CURVES OF DARK MATTER-DOMINATED GALAXIES

Rotation curves of dark matter-dominated galaxies measure the mass profiles of galactic halos and thereby test theories of their cosmological origin. While attention has focused lately on the possible discrepancy at small galactocentric radii between observed rotation curves and the singular density profiles predicted by N-body simulations of the cold dark matter (CDM) model, the observed rotation curves nevertheless contain valuable additional information with which to test the theory and constrain the fundamental cosmological parameters, despite this uncertainty at small radii. An analytical model we derived elsewhere for the postcollapse equilibrium of cosmological halos as truncated, nonsingular, isothermal spheres (TISs) reproduces many of the average properties of halos in CDM simulations to good accuracy, including the density profiles outside the central region. The circular velocity profile of this TIS model, moreover, is in excellent agreement with the observed ones and yields the mass and formation epoch of an observed halo from the parameters of its rotation curve. This allows us to predict correlations among rotation curve parameters, such as the maximum velocity and the radius at which it occurs, for different mass halos forming at different epochs in the CDM model. As an example, we derive the observed vmax-rmax relation analytically, with preference for the flat ΛCDM model.

The Inhomogeneous Background of H2 Dissociating Radiation During Cosmic Reionization

The first, self‐consistent calculations of the cosmological H2 dissociating UV background produced during the epoch of reionization by the sources of reionization are presented. Large‐scale radiative transfer simulations of reionization trace the impact of all the ionizing starlight on the IGM from all sources in our simulation volume down to dwarf galaxies of mass ∼108 M⊙, identified by very high‐resolution N‐body simulations, including the self‐regulating effect of IGM photoheating on dwarf galaxy formation. The UV continuum emitted below 13.6 eV by each source is then transferred through the same IGM, attenuated by atomic H Lyman series resonance lines, to predict the evolution of the inhomogeneous background in the Lyman‐Werner band of H2 between 11 and 13.6 eV.

Using the cosmic infrared background to deduce properties of high redshift stars

Properties of high redshift (z > 6) star formation are very difficult to constrain observationally. Further complicating the problem, the majority of sources are very faint, making direct detections extremely rare. Therefore, we discuss ways to constrain properties of star formation using the cumulative light from these high redshift sources, seen in the Cosmic Infrared Background. This background can constrain many properties of these high redshift stars, such as the properties of the stars themselves, but also of their host galaxies - such as their mass, escape fraction, and dust content. I will discuss the implications of some of the newest observations, and what they can mean for our knowledge of high redshift star formation.

On the Detectability of the Cosmic Dark Ages: 21‐cm Lines from Minihalos

In the standard Cold Dark Matter (CDM) theory of structure formation, virialized minihalos (with Tvir ⩽ 10,000K) form in abundance at high redshift (z > 6), during the cosmic “dark ages.” The hydrogen in these minihalos, the first nonlinear baryonic structures to form in the universe, is mostly neutral and sufficiently hot and dense to emit strongly at the 21‐cm line. We calculate the emission from individual minihalos and the radiation background contributed by their combined effect. Minihalos create a “21‐cm forest” of emission lines. We predict that the angular fluctuations in this 21‐cm background should be detectable with the planned LOFAR and SKA radio arrays, thus providing a direct probe of structure formation during the “dark ages.” Such a detection will serve to confirm the basic CDM paradigm while constraining the background cosmology parameters, the shape of the power‐spectrum of primordial density fluctuations, the onset and duration of the reionization epoch, and the conditions which led to ...

The equilibrium structure of cosmological halos

We have derived an analytical model for the postcollapse equilibrium structure of cosmological halos as nonsingular truncated isothermal spheres (TIS) and compared this model with observations and simulations of cosmological halos on all scales. Our model is in good agreement with the observations of the internal structure of dark-matter-dominated halos from dwarf galaxies to X-ray clusters. It reproduces many of the average properties of halos in CDM simulations to good accuracy, including the density profiles outside the central region, while avoiding the possible discrepancy at small radii between observed galaxy and cluster density profiles and the singular density profiles predicted by N-body simulations of the CDM model. While much attention has been focused lately on this possible discrepancy, we show that the observed galaxy rotation curves and correlations of halo properties nevertheless contain valuable additional information with which to test the theory, despite this uncertainty at small radii...