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Register a new userThe phase-space density distribution of dark matter halos
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Liliya L. R. Williams
Publication date
2004
fields
Physics
and research's language is
English
Authors
Liliya L.R. Williams
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High resolution N-body simulations have all but converged on a common empirical form for the shape of the density profiles of halos, but the full understanding of the underlying physics of halo formation has eluded them so far. We investigate the formation and structure of dark matter halos using analytical and semi-analytical techniques. Our halos are formed via an extended secondary infall model (ESIM); they contain secondary perturbations and hence random tangential and radial motions which affect the halos evolution at it undergoes shell-crossing and virialization. Even though the density profiles of NFW and ESIM halos are different their phase-space density distributions are the same: rho/sigma^3 ~ r^{-alpha}, with alpha=1.875 over ~3 decades in radius. We use two approaches to try to explain this ``universal slope: (1) The Jeans equation analysis yields many insights, however, does not answer why alpha=1.875. (2) The secondary infall model of the 1960s and 1970s, augmented by ``thermal motions of particles does predict that halos should have alpha=1.875. However, this relies on assumptions of spherical symmetry and slow accretion. While for ESIM halos these assumptions are justified, they most certainly break down for simulated halos which forms hierarchically. We speculate that our argument may apply to an ``on-average formation scenario of halos within merger-driven numerical simulations, and thereby explain why alpha=1.875 for NFW halos. Thus, rho/sigma^3 ~ r^{-1.875} may be a generic feature of violent relaxation.
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We study the evolution of phase-space density during the hierarchical structure formation of LCDM halos. We compute both a spherically-averaged surrogate for phase-space density (Q) and the coarse-grained distribution function f(x,v) for dark matter particles that lie within~2 virial radii of four Milky-Way-sized dark matter halos. The estimated f(x,v) spans over four decades at any radius. Dark matter particles that end up within two virial radii of a Milky-Way-sized DM halo at $z=0$ have an approximately Gaussian distribution in log(f) at early redshifts, but the distribution becomes increasingly skewed at lower redshifts. The value corresponding to the peak of the Gaussian decreases as the evolution progresses and is well described by a power-law in (1+z). The highest values of f are found at the centers of dark matter halos and subhalos, where f can be an order of magnitude higher than in the center of the main halo. The power-law Q(r) profile likely reflects the distribution of entropy (K = sigma^2/rho^{2/3} propto r^{1.2}), which dark matter acquires as it is accreted onto a growing halo. The estimated f(x, v), on the other hand, exhibits a more complicated behavior. Although the median coarse-grained phase-space density profile F(r) can be approximated by a power-law in the inner regions of halos and at larger radii the profile flattens significantly. This is because phase-space density averaged on small scales is sensitive to the high-f material associated with surviving subhalos, as well as relatively unmixed material (probably in streams) resulting from disrupted subhalos, which contribute a sizable fraction of matter at large radii. (ABRIDGED)
We use N-body simulations to investigate the radial dependence of the density and velocity dispersion in cold dark matter (CDM) halos. In particular, we explore how closely Q rho/sigma^3, a surrogate measure of the phase-space density, follows a power-law in radius. Our study extends earlier work by considering, in addition to spherically-averaged profiles, local Q-estimates for individual particles, Q_i; profiles based on the ellipsoidal radius dictated by the triaxial structure of the halo, Q_i(r); and by carefully removing substructures in order to focus on the profile of the smooth halo, Q^s. The resulting Q_i^s(r) profiles follow closely a power law near the center, but show a clear upturn from this trend near the virial radius, r_{200}. The location and magnitude of the deviations are in excellent agreement with the predictions from Bertschingers spherical secondary-infall similarity solution. In this model, Q propto r^{-1.875} in the inner, virialized regions, but departures from a power-law occur near r_{200} because of the proximity of this radius to the location of the first shell crossing - the shock radius in the case of a collisional fluid. Particles there have not yet fully virialized, and so Q departs from the inner power-law profile. Our results imply that the power-law nature of $Q$ profiles only applies to the inner regions and cannot be used to predict accurately the structure of CDM halos beyond their characteristic scale radius.
We develop a new method to reconstruct the cosmic density field from the distribution of dark matter haloes above a certain mass threshold. Our motivation is that well-defined samples of galaxy groups/clusters, which can be used to represent the dark halo population, can now be selected from large redshift surveys of galaxies, and our ultimate goal is to use such data to reconstruct the cosmic density field in the local universe. Our reconstruction method starts with a sample of dark matter haloes above a given mass threshold. Each volume element in space is assigned to the domain of the nearest halo according to a distance measure that is scaled by the virial radius of the halo. The distribution of the mass in and around dark matter haloes of a given mass is modelled using the cross-correlation function between dark matter haloes and the mass distribution within their domains. We use N-body cosmological simulations to show that the density profiles required in our reconstruction scheme can be determined reliably from large cosmological simulations, and that our method can reconstruct the density field accurately using haloes with masses down to $sim 10^{12}msun$ (above which samples of galaxy groups can be constructed from current large redshift surveys of galaxies). Working in redshift space, we demonstrate that the redshift distortions due to the peculiar velocities of haloes can be corrected in an iterative way. We also describe some applications of our method.
We have performed a series of numerical experiments to investigate how the primordial thermal velocities of fermionic dark matter particles affect the physical and phase space density profiles of the dark matter haloes into which they collect. The initial particle velocities induce central cores in both profiles, which can be understood in the framework of phase space density theory. We find that the maximum coarse-grained phase space density of the simulated haloes (computed in 6 dimensional phase space using the EnBid code) is very close to the theoretical fine-grained upper bound, while the pseudo phase space density, Q ~ {rho}/{sigma}^3, overestimates the maximum phase space density by up to an order of magnitude. The density in the inner regions of the simulated haloes is well described by a pseudo-isothermal profile with a core. We have developed a simple model based on this profile which, given the observed surface brightness profile of a galaxy and its central velocity dispersion, accurately predicts its central phase space density. Applying this model to the dwarf spheroidal satellites of the Milky Way yields values close to 0.5 keV for the mass of a hypothetical thermal warm dark matter particle, assuming the satellite haloes have cores produced by warm dark matter free streaming. Such a small value is in conflict with the lower limit of 1.2 keV set by observations of the Lyman-{alpha} forest. Thus, if the Milky Way dwarf spheroidal satellites have cores, these are likely due to baryonic processes associated with the forming galaxy, perhaps of the kind proposed by Navarro, Eke and Frenk and seen in recent simulations of galaxy formation in the cold dark matter model.
(Abridged) We apply a very general statistical theorem introduced by Cramer (1936) to study the origin of the deviations of the halo spin PDF from the reference lognormal shape. We find that these deviations originate from correlations between two quantities entering the definition of spin, namely the ratio $J/M^{5/2}$ (which depends only on mass) and the total gravitational binding energy $E$. To reach this conclusion, we have made usage of the results deduced from two high spatial- and mass resolution simulations. Our simulations cover a relatively small volume and produce a sample of more than 16.000 gravitationally bound halos, each traced by at least 300 particles. We verify that our results are stable to different systematics, by comparing our results with those derived by the GIF2 and by a more recent simulation performed by Maccio et al. We find that the spin probability distribution function shows systematic deviations from a lognormal, at all redshifts z <= 1. These deviations depend on mass and redshift: at small masses they change little with redshift, and also the best lognormal fits are more stable. The J-M relationship is well described by a power law of exponent $alpha$ very near to the linear theory prediction (alpha=5/3), but systematically lower than this at z<= 0.3. We argue that the fact that deviations from a lognormal PDF are present only for high-spin halos could point to a role of large-scale tidal fields in the evolution of the spin PDF.
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