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Register a new userClustering in the Phase Space of Dark Matter Haloes. I. Results from the Aquarius simulations
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Jesus Zavala Franco
Publication date
2013
fields
Physics
and research's language is
English
Authors
Jesus Zavala
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We present a novel perspective on the clustering of dark matter in phase space by defining the particle phase space average density ($P^2SAD$) as a two-dimensional extension of the two-point correlation function averaged within a certain volume in phase space. This statistics is a sensitive measure of small scale (sub-)structure of dark matter haloes. By analysing the structure of $P^2SAD$ in Milky-Way-size haloes using the Aquarius simulations, we find it to be nearly universal at small scales, i.e. small separations in phase space, where substructures dominate. This remarkable universality occurs across time and in regions of substantially different ambient densities (by nearly four orders of magnitude), with typical variations in $P^2SAD$ of a factor of a few. The maximum variations occur in regions where substructures have been strongly disrupted. The universality is also preserved across haloes of similar mass but diverse mass accretion histories and subhalo distributions. The universality is also broken at large scales, where the smooth dark matter distribution in the halo dominates. Although at small scales the structure of $P^2SAD$ is roughly described by a subhalo model, we argue that the simulation data is better fitted by a family of superellipse contours. This functional shape is inspired by a model that extends the stable clustering hypothesis into phase space. In a companion paper, we refine this model and show its advantages as a method to obtain predictions for non-gravitational signatures of dark matter.
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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.
We use high-resolution Aquarius simulations of Milky Way-sized haloes in the LCDM cosmology to study the effects of dark matter substructures on gravitational lensing. Each halo is resolved with ~ 10^8 particles (at a mass resolution ~ 10^3-4 M_sun/h) within its virial radius. Subhaloes with masses larger than 10^5 M_sun/h are well resolved, an improvement of at least two orders of magnitude over previous lensing studies. We incorporate a baryonic component modelled as a Hernquist profile and account for the response of the dark matter via adiabatic contraction. We focus on the anomalous flux ratio problem, in particular on the violation of the cusp-caustic relation due to substructures. We find that subhaloes with masses less than ~ 10^8 M_sun/h play an important role in causing flux anomalies; such low mass subhaloes have been unresolved in previous studies. There is large scatter in the predicted flux ratios between different haloes and between different projections of the same halo. In some cases, the frequency of predicted anomalous flux ratios is comparable to that observed for the radio lenses, although in most cases it is not. The probability for the simulations to reproduce the observed violations of the cusp lenses is about 0.001. We therefore conclude that the amount of substructure in the central regions of the Aquarius haloes is insufficient to explain the observed frequency of violations of the cusp-caustic relation. These conclusions are based purely on our dark matter simulations which ignore the effect of baryons on subhalo survivability.
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 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.
The mapping of dark matter clustering from real space to redshift space introduces the anisotropic property to the measured density power spectrum in redshift space, known as the redshift space distortion effect. The mapping formula is intrinsically non-linear, which is complicated by the higher order polynomials due to indefinite cross correlations between the density and velocity fields, and the Finger-of-God effect due to the randomness of the peculiar velocity field. Whilst the full higher order polynomials remain unknown, the other systematics can be controlled consistently within the same order truncation in the expansion of the mapping formula, as shown in this paper. The systematic due to the unknown non-linear density and velocity fields is removed by separately measuring all terms in the expansion directly using simulations. The uncertainty caused by the velocity randomness is controlled by splitting the FoG term into two pieces, 1) the one-point FoG term being independent of the separation vector between two different points, and 2) the correlated FoG term appearing as an indefinite polynomials which is expanded in the same order as all other perturbative polynomials. Using 100 realizations of simulations, we find that the Gaussian FoG function with only one scale-independent free parameter works quite well, and that our new mapping formulation accurately reproduces the observed 2-dimensional density power spectrum in redshift space at the smallest scales by far, up to $ksim 0.2h$Mpc, considering the resolution of future experiments.
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