Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSemi-analytical dark matter halos and the Jeans equation
344
0
0.0
(
0
)
Authors
Crystal G. Austin
Ask ChatGPT about the research
No Arabic abstract
Although N-body studies of dark matter halos show that the density profiles, rho(r), are not simple power-laws, the quantity rho/sigma^3, where sigma(r) is the velocity dispersion, is in fact a featureless power-law over ~3 decades in radius. In the first part of the paper we demonstrate, using the semi-analytic Extended Secondary Infall Model (ESIM), that the nearly scale-free nature of rho/sigma^3 is a robust feature of virialized halos in equilibrium. By examining the processes in common between numerical N-body and semi-analytic approaches, we argue that the scale-free nature of rho/sigma^3 cannot be the result of hierarchical merging, rather it must be an outcome of violent relaxation. The empirical results of the first part of the paper motivate the analytical work of the second part of the paper, where we use rho/sigma^3 proportional to r^{-alpha} as an additional constraint in the isotropic Jeans equation of hydrostatic equilibrium. Our analysis shows that the constrained Jeans equation has different types of solutions, and in particular, it admits a unique ``periodic solution with alpha=1.9444. We derive the analytic expression for this density profile, which asymptotes to inner and outer profiles of rho ~ r^{-0.78}, and rho ~ r^{-3.44}, respectively.
rate research
Read More
We present a wave generalization of the classic Schwarzschild method for constructing self-consistent halos -- such a halo consists of a suitable superposition of waves instead of particle orbits, chosen to yield a desired mean density profile. As an illustration, the method is applied to spherically symmetric halos. We derive an analytic relation between the particle distribution function and the wave superposition amplitudes, and show how it simplifies in the high energy (WKB) limit. We verify the stability of such constructed halos by numerically evolving the Schrodinger-Poisson system. The algorithm provides an efficient and accurate way to simulate the time-dependent halo substructures from wave interference. We use this method to construct halos with a variety of density profiles, all of which have a core from the ground-state wave function, though the core-halo relation need not be the standard one.
The velocity distribution of dark matter near the Earth is important for an accurate analysis of the signals in terrestrial detectors. This distribution is typically extracted from numerical simulations. Here we address the possibility of deriving the velocity distribution function analytically. We derive a differential equation which is a function of radius and the radial component of the velocity. Under various assumptions this can be solved, and we compare the solution with the results from controlled numerical simulations. Our findings complement the previously derived tangential velocity distribution. We hereby demonstrate that the entire distribution function, below 0.7 v_esc, can be derived analytically for spherical and equilibrated dark matter structures.
We investigate the effect of dark energy on the density profiles of dark matter haloes with a suite of cosmological N-body simulations and use our results to test analytic models. We consider constant equation of state models, and allow both w>-1 and w<-1. Using five simulations with w ranging from -1.5 to -0.5, and with more than ~1600 well-resolved haloes each, we show that the halo concentration model of Bullock et al. (2001) accurately predicts the median concentrations of haloes over the range of w, halo masses, and redshifts that we are capable of probing. We find that the Bullock et al. (2001) model works best when halo masses and concentrations are defined relative to an outer radius set by a cosmology-dependent virial overdensity. For a fixed power spectrum normalization and fixed-mass haloes, larger values of w lead to higher concentrations and higher halo central densities, both because collapse occurs earlier and because haloes have higher virial densities. While precise predictions of halo densities are quite sensitive to various uncertainties, we make broad comparisons to galaxy rotation curve data. At fixed power spectrum normalization (fixed sigma_8), w>-1 quintessence models seem to exacerbate the central density problem relative to the standard w=-1 model. Meanwhile w<-1 models help to reduce the apparent discrepancy. We confirm that the Jenkins et al. (2001) halo mass function provides an excellent approximation to the abundance of haloes in our simulations and extend its region of validity to include models with w<-1.
We study properties of dark matter halos at high redshifts z=2-10 for a vast range of masses with the emphasis on dwarf halos with masses 10^7-10^9 Msun/h. We find that the density profiles of relaxed dwarf halos are well fitted by the NFW profile and do not have cores. We compute the halo mass function and the halo spin parameter distribution and find that the former is very well reproduced by the Sheth & Tormen model while the latter is well fitted by a lognormal distribution with lambda_0 = 0.042 and sigma_lambda = 0.63. We estimate the distribution of concentrations for halos in mass range that covers six orders of magnitude from 10^7 Msun/h to 10^13} Msun/h, and find that the data are well reproduced by the model of Bullock et al. The extrapolation of our results to z = 0 predicts that present-day isolated dwarf halos should have a very large median concentration of ~ 35. We measure the subhalo circular velocity functions for halos with masses that range from 4.6 x 10^9 Msun/h to 10^13 Msun/h and find that they are similar when normalized to the circular velocity of the parent halo. Dwarf halos studied in this paper are many orders of magnitude smaller than well-studied cluster- and Milky Way-sized halos. Yet, in all respects the dwarfs are just down-scal
This papers explores the self similar solutions of the Vlasov-Poisson system and their relation to the gravitational collapse of dynamically cold systems. Analytic solutions are derived for power law potential in one dimension, and extensions of these solutions in three dimensions are proposed. Next the self similarity of the collapse of cold dynamical systems is investigated numerically. The fold system in phase space is consistent with analytic self similar solutions, the solutions present all the proper self-similar scalings. An additional point is the appearance of an $x^{-(1/2)}$ law at the center of the system for initial conditions with power law index larger than $-(1/2)$. It is found that the first appearance of the $x^{-(1/2)}$ law corresponds to the formation of a singularity very close to the center. Finally the general properties of self similar multi dimensional solutions near equilibrium are investigated. Smooth and continuous self similar solutions have power law behavior at equilibrium. However cold initial conditions result in discontinuous phase space solutions, and the smoothed phase space density looses its auto similar properties. This problem is easily solved by observing that the probability distribution of the phase space density $P$ is identical except for scaling parameters to the probability distribution of the smoothed phase space density $P_S$. As a consequence $P_S$ inherit the self similar properties of $P$. This particular property is at the origin of the universal power law observed in numerical simulation for ${rho}/{sigma^3}$. The self similar properties of $P_S$ implies that other quantities should have also an universal power law behavior with predictable exponents. This hypothesis is tested using a numerical model of the phase space density of cold dark matter halos, an excellent agreement is obtained.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
