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Register a new userTracing the Dark Matter Sheet in Phase Space
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The primordial velocity dispersion of dark matter is small compared to the velocities attained during structure formation. The initial density distribution is close to uniform and it occupies an initial sheet in phase space that is single valued in velocity space. Because of gravitational forces this three dimensional manifold evolves in phase space without ever tearing, conserving phase-space volume and preserving the connectivity of nearby points. N-body simulations already follow the motion of this sheet in phase space. This fact can be used to extract full fine-grained phase-space-structure information from existing cosmological N-body simulations. Particles are considered as the vertices of an unstructured three dimensional mesh, moving in six dimensional phase-space. On this mesh, mass density and momentum are uniquely defined. We show how to obtain the space density of the fluid, detect caustics, and count the number of streams as well as their individual contributions to any point in configuration-space. We calculate the bulk velocity, local velocity dispersions, and densities from the sheet - all without averaging over control volumes. This gives a wealth of new information about dark matter fluid flow which had previously been thought of as inaccessible to N-body simulations. We outline how this mapping may be used to create new accurate collisionless fluid simulation codes that may be able to overcome the sparse sampling and unphysical two-body effects that plague current N-body techniques.
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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.
We summarize recent developments in the use of spectral methods for analyzing large numbers of orbits in N-body simulations to obtain insights into the global phase space structure of dark matter halos. The fundamental frequencies of oscillation of orbits can be used to understand the physical mechanism by which the shapes of dark matter halos evolve in response to the growth of central baryonic components. Halos change shape primarily because individual orbits change their shapes adiabatically in response to the growth of a baryonic component, with those at small radii become preferentially rounder. Chaotic scattering of orbits occurs only when the central point mass is very compact and is equally effective for centrophobic long-axis tube orbits as it is for centrophilic box orbits.
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 have recently introduced a novel statistical measure of dark matter clustering in phase space, the particle phase space average density ($P^2SAD$). In a two-paper series, we studied the structure of $P^2SAD$ in the Milky-Way-size Aquarius haloes, constructed a physically motivated model to describe it, and illustrated its potential as a powerful tool to predict signals sensitive to the nanostructure of dark matter haloes. In this letter, we report a remarkable universality of the clustering of dark matter in phase space as measured by $P^2SAD$ within the subhaloes of host haloes across different environments covering a range from dwarf-size to cluster-size haloes ($10^{10}-10^{15}$ M$_odot$). Simulations show that the universality of $P^2SAD$ holds for more than 7 orders of magnitude, over a 2D phase space, covering over 3 orders of magnitude in distance/velocity, with a simple functional form that can be described by our model. Invoking the universality of $P^2SAD$, we can accurately predict the non-linear power spectrum of dark matter at small scales all the way down to the decoupling mass limit of cold dark matter particles. As an application, we compute the subhalo boost to the annihilation of dark matter in a wide range of host halo masses.
We present a model for the structure of the particle phase space average density ($P^2SAD$) in galactic haloes, introduced recently as a novel measure of the clustering of dark matter. Our model is based on the stable clustering hypothesis in phase space, the spherical collapse model, and tidal disruption of substructures, which is calibrated against the Aquarius simulations. Using this model, we can predict the behaviour of $P^2SAD$ in the numerically unresolved regime, down to the decoupling mass limit of generic WIMP models. This prediction can be used to estimate signals sensitive to the small scale structure of dark matter. For example, the dark matter annihilation rate can be estimated for arbitrary velocity-dependent cross sections in a convenient way using a limit of $P^2SAD$ to zero separation in physical space. We illustrate our method by computing the global and local subhalo annihilation boost to that of the smooth dark matter distribution in a Milky-Way-size halo. Two cases are considered, one where the cross section is velocity independent and one that approximates Sommerfeld-enhanced models. We find that the global boost is $sim10-30$, which is at the low end of current estimates (weakening expectations of large extragalactic signals), while the boost at the solar radius is below the percent level. We make our code to compute $P^2SAD$ publicly available, which can be used to estimate various observables that probe the nanostructure of dark matter haloes.
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