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Register a new userClustering in the Phase Space of Dark Matter Haloes. II. Stable Clustering and Dark Matter Annihilation
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Jesus Zavala Franco
Publication date
2013
fields
Physics
and research's language is
English
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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.
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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 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.
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 use a large dark matter simulation of a LambdaCDM model to investigate the clustering and environmental dependence of the number of substructures in a halo. Focusing on redshift z=1, we find that the halo occupation distribution is sensitive at the tens of percent level to the surrounding density and to a lesser extent to asymmetry of the surrounding density distribution. We compute the autocorrelation function of halos as a function of occupation, building on the finding of Wechsler et al. (2006) and Gao and White (2007) that halos (at fixed mass) with more substructure are more clustered. We compute the relative bias as a function of occupation number at fixed mass, finding a strong relationship. At fixed mass, halos in the top 5% of occupation can have an autocorrelation function ~ 1.5-2 times higher than the mean. We also compute the bias as a function of halo mass, for fixed halo occupation. We find that for group and cluster sized halos, when the number of subhalos is held fixed, there is a strong anticorrelation between bias and halo mass. Such a relationship represents an additional challenge to the halo model.
We obtain predictions for the properties of cold dark matter annihilation radiation using high resolution hydrodynamic zoom-in cosmological simulations of Milky Way-like galaxies (APOSTLE project) carried out as part of the Evolution and Assembly of GaLaxies and their Environments (EAGLE) programme. Galactic halos in the simulation have significantly different properties from those assumed in the standard halo model often used in dark matter detection studies. The formation of the galaxy causes a contraction of the dark matter halo, whose density profile develops a steeper slope than the Navarro-Frenk-White (NFW) profile between $rapprox1.5$ kpc and $rapprox10$ kpc. At smaller radii, $rlesssim1.5$ kpc, the halos develop a flatter than NFW slope. This unexpected feature may be specific to our particular choice of subgrid physics model but nevertheless the dark matter density profiles agree within 30% as the mass resolution is increased by a factor 150. The inner regions of the halos are almost perfectly spherical (axis ratios $b/a > 0.97$ within $r=1$ kpc) and there is no offset larger than 45 pc between the centre of the stellar distribution and the centre of the dark halo. The morphology of the predicted dark matter annihilation radiation signal is in broad agreement with $gamma$-ray observations at large Galactic latitudes ($bgtrsim3^circ$). At smaller angles, the inferred signal in one of our four galaxies is similar to that which is observed but it is significantly weaker in the other three.
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