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Register a new userThe spherical collapse model with shell crossing
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Added by
Miguel Angel Sanchez-Conde
Publication date
2006
fields
Physics
and research's language is
English
Authors
M.A. Sanchez-Conde
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In this work, we study the formation and evolution of dark matter halos by means of the spherical infall model with shell-crossing. We present a framework to tackle this effect properly based on the numerical follow-up, with time, of that individual shell of matter that contains always the same fraction of mass with respect to the total mass. In this first step, we do not include angular momentum, velocity dispersion or triaxiality. Within this framework - named as the Spherical Shell Tracker (SST) - we investigate the dependence of the evolution of the halo with virial mass, with the adopted mass fraction of the shell, and for different cosmologies. We find that our results are very sensitive to a variation of the halo virial mass or the mass fraction of the shell that we consider. However, we obtain a negligible dependence on cosmology. Furthermore, we show that the effect of shell-crossing plays a crucial role in the way that the halo reaches the stabilization in radius and the virial equilibrium. We find that the values currently adopted in the literature for the actual density contrast at the moment of virialization, delta_vir, may not be accurate enough. In this context, we stress the problems related to the definition of a virial mass and a virial radius for the halo. The question of whether the results found here may be obtained by tracking the shells with an analytic approximation remains to be explored.
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We develop a new perturbation theory (PT) treatment that can describe gravitational dynamics of large-scale structure after shell-crossing in the one-dimensional cosmological case. Starting with cold initial conditions, the motion of matter distribution follows at early stages the single-stream regime, which can, in one dimension, be described exactly by the first-order Lagrangian perturbation, i.e. the Zeldovich solution. However, the single-stream flow no longer holds after shell-crossing and a proper account of the multi-stream flow is essential for post-collapse dynamics. In this paper, extending previous work by Colombi (2015, MNRAS 446, 2902), we present a perturbative description for the multi-stream flow after shell-crossing in a cosmological setup. In addition, we introduce an adaptive smoothing scheme to deal with the bulk properties of phase-space structures. The filtering scales in this scheme are linked to the next-crossing time in the post-collapse region, estimated from our PT calculations. Our PT treatment combined with adaptive smoothing is illustrated in several cases. Predictions are compared to simulations and we find that post-collapse PT with adaptive smoothing reproduces the power spectrum and phase-space structures remarkably well even at small scales, where Zeldovich solution substantially deviates from simulations.
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-? 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 study, for the first time, how shear and angular momentum modify typical parameters of the spherical collapse model, in dark energy dominated universes. In particular, we study the linear density threshold for collapse $delta_mathrm{c}$ and the virial overdensity $Delta_mathrm{V}$, for several dark-energy models and its influence on the cumulative mass function. The equations of the spherical collapse are those obtained in Pace et al. (2010), who used the fully nonlinear differential equation for the evolution of the density contrast derived from Newtonian hydrodynamics, and assumed that dark energy is present only at the background level. With the introduction of the shear and rotation terms, the parameters of the spherical collapse model are now mass-dependant. The results of the paper show, as expected, that the new terms considered in the spherical collapse model oppose the collapse of perturbations on galactic scale giving rise to higher values of the linear overdensity parameter with respect to the non-rotating case. We find a similar effect also for the virial overdensity parameter. For what concerns the mass function, we find that its high mass tail is suppressed, while the low mass tail is slightly affected except in some cases, e.g. the Chaplygin gas case.
Spherical vacuum and scalar collapse for the Starobinsky R^2 model is simulated. Obtained by considering the quantum-gravitational effects, this model would admit some cases of singularity-free cosmological spacetimes. It is found, however, that in vacuum and scalar collapse, when f or the physical scalar field is strong enough, a black hole including a central singularity can be formed. In addition, near the central singularity, gravity dominates the repulsion from the potential, so that in some circumstances the Ricci scalar is pushed to infinity by gravity. Therefore, the semiclassical effects as included here do not avoid the singularity problem in general relativity. A strong physical scalar field can prevent the Ricci scalar from growing to infinity. Vacuum collapse for the RlnR model is explored, and it is observed that for this model the Ricci scalar can also go to infinity as the central singularity is approached. Therefore, this feature seems universal in vacuum and scalar collapse in f(R) gravity.
In the Elliott SU(3) symmetry scheme the single particle basis is derived from the isotropic harmonic oscillator Hamiltonian in the Cartesian coordinate system. These states are transformed into the solutions of the same Hamiltonian within the spherical coordinate system. Then the spin-orbit coupling can be added in a straightforward way. The outcome is a transformation between the Elliott single particle basis and the spherical shell model space.
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