ELLIPSOIDAL COLLAPSE AND PREVIRIALIZATION

Open Astronomy, 2001

In this paper, we study the role of shear fields on the evolution of density perturbations embedded in a Friedmann flat background universe, by studying the evolution of a homogeneous ellipsoid model. In this context, we show that while the effect of the shear is that of increasing the growth rate of the density contrast of a mass element, the angular momentum acquired by the ellipsoid has the right magnitude to counterbalance the shear. Finally, our result show that initial asphericities and tidal interaction induce a slowing down of the collapse after the system has broken away from the general expansion, in perfect agreement with the previrialization conjecture (Peebles & Groth 1976; Davis & Peebles 1977).

I study the role of shear fields on the evolution of density perturbations by using an analytical approximate solution for the equations of motion of homogeneous ellipsoids embedded in a homogeneous background. The equations of motion of a homogeneous ellipsoid (Icke 1973; White & Silk 1979, hereafter WS) are modified in order to take account of the tidal field, as done in Watanabe (1993) and then are integrated analytically, similar to what was done in WS. The comparison of the analytical solution with numerical simulations shows that it is a good approximation of the numerical one. This solution is used to study the evolution of the configuration of the ellipsoids, to calculate the evolution of the density contrast and that of the axial peculiar velocity of the ellipsoids for several values of the amplitude of the external tidal field, and is compared again with numerical simulations. In order to calculate the evolution of the density contrast at turnaround and collapse velocity at the epoch of collapse, as a function of the ratio of the initial value of the semi-axes, I use the previously-obtained approximate solution to modify the analytical model proposed by Barrow & Silk (1981) for the ellipsoid evolution in the non-linear regime. The density contrast at turnaround and the collapse velocity are found to be reduced with respect to that found by means of the spherical model. The reduction increases with increasing strength of the external tidal field and with increasing initial asymmetry of the ellipsoids. These last calculations are also compared with numerical solutions and they are again in good agreement with the numerical ones.

I study the joint effect of dynamical friction, tidal torques and cosmological constant on clusters of galaxies formation. I show that within high-density environments, such as rich clusters of galaxies, both dynamical friction and tidal torques slows down the collapse of low-ν peaks producing an observable variation in the time of collapse of the perturbation and, as a consequence, a reduction in the mass bound to the collapsed perturbation. Moreover, the delay of the collapse produces a tendency for less dense regions to accrete less mass, with respect to a classical spherical model, inducing a biasing of over-dense regions toward higher mass. I show how the threshold of collapse is modified if dynamical friction, tidal torques and a non-zero cosmological constant are taken into account and I use the Extended Press Schecter (EPS) approach to calculate the effects on the mass function. Then, I compare the numerical mass function given in Reed et al. (2003) with the theoretical mass function obtained in the present paper. I show that the barrier obtained in the present paper gives rise to a better description of the mass function evolution with respect to other previous models (Sheth & Tormen 1999, MNRAS, 308, 119 (hereafter ST); Sheth & Tormen 2002, MNRAS, 329, 61 (hereafter ST1)).

We investigate here how the shearing effects present within a collapsing matter cloud influence the outcome of gravitational collapse in terms of formation of either a black hole or a naked singularity as the final end state. For collapse of practically all physically reasonable matter fields, we prove that it would always end up in a black hole if it is either shear-free or has homogeneous density. Thus it follows that whenever a naked singularity forms as end product, the collapsing cloud must necessarily be shearing with inhomogeneous density. Our consideration brings out the physical forces at work which could cause a naked singularity to result as collapse end state, rather than a black hole.

Nuclear Physics A, 1992

Celestial Mechanics, 1987

A brief review of previous work and the present situation in the problem of formation of elliptical galaxies via dissipationless collapse are presented, as well as the results of a new set of numerical experiments. It is shown that collapses started from cold initial conditions are different from warmer collapses, due to the presence of a dynamical instability associated with radial orbits. This instability leads to triaxial final configurations, regardless of the initial amount of random kinetic energy, rotational kinetic energy, or shape of the initial conditions, as long as 2T/W < 0.1, where T is the total (rotational plus thermal) kinetic energy and W is the potential energy of the initial conditions. Warmer initial conditions preserve their initial shape, or become oblate if initially rotating. Cold initial conditions produce equilibrium systems with realistic density profiles, as opposed to collapses from warmer conditions that result in core-halo profiles, unlike the observed surface brightness profiles of elliptical galaxies. Although the same cold collapses that result in triaxial shapes produce realistic density profiles, it is shown that these two effects are not directly connected: cold collapses simulated with an N-body code that enforces spherical symmetry result in realistic density profiles too.

Classical and Quantum Gravity, 2007

We explore the effects of background cosmology on large scale structures with non-spherical symmetry by using the concept of quasi-equilibrium which allows certain internal properties (e.g. angular velocity) of the bodies to change with time. In accordance with the discovery of the accelerated phase of the universe we model the cosmological background by two representative models: the ΛCDM Model and the Chaplygin Gas Model. We compare the effects of the two models on various properties of large astrophysical objects. Different equations of state are also invoked in the investigation.

New Astronomy, 2012

The effect of background dynamics of the universe on formation of large scale structures in the framework of Modified Newtonian Dynamics (MOND) is investigated. A spherical collapse model is used for modeling the formation of the structures. This study is done in two extreme cases: (i) assuming a universe with a low-density baryonic matter without any cold dark matter and dark energy; (ii) a dark energy dominated universe with baryonic matter, without cold dark matter. We show that for the case (ii) the structures virialize at lower redshifts with larger radii compared to the low-density background universe. The dark energy slow downs the collapse of the structures. We show that our results are compatible with recent simulations of the structure formation in MOND.

International Journal of Modern Physics D, 2013

The influence of the shear stress and angular momentum on the nonlinear spherical collapse model is discussed in the framework of the Einstein-de Sitter (EdS) and ΛCDM models. By assuming that the vacuum component is not clustering within the homogeneous nonspherical overdensities, we show how the local rotation and shear affects the linear density threshold for collapse of the nonrelativistic component (δc) and its virial overdensity (∆V). It is also found that the net effect of shear and rotation in galactic scale is responsible for higher values of the linear overdensity parameter as compared with the standard spherical collapse model (no shear and rotation).

Classical and Quantum Gravity, 1996

Further to results in [9], pointing out the role of initial density and velocity distributions towards determining the final outcome of spherical dust collapse, the causal structure of singularity is examined here in terms of evolution of the apparent horizon. We also bring out several related features which throw some useful light towards understanding the nature of this singularity, including the behaviour of geodesic families coming out and some aspects related to the stability of singularity.