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Register a new userCosmic structures from a mathematical perspective 1. Dark matter halo mass density profiles
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Jenny Wagner
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The shapes of individual self-gravitating structures of an ensemble of identical, collisionless particles have remained elusive for decades. In particular, a reason why mass density profiles like the Navarro-Frenk-White or the Einasto profile are good fits to simulation- and observation-based dark matter halos has not been found. Given the class of three dimensional, spherically symmetric power-law probability density distributions to locate individual particles in the ensemble mentioned above, we derive the constraining equation for the power-law index for the most and least likely joint ensemble configurations. We find that any dark matter halo can be partitioned into three regions: a core, an intermediate part, and an outskirts part up to boundary radius $r_mathrm{max}$. The power-law index of the core is determined by the mean radius of the particle distribution within the core. The intermediate region becomes isothermal in the limit of infinitely many particles. The slope of the mass density profile far from the centre is determined by the choice of $r_mathrm{max}$ with respect to the outmost halo particle, such that two typical limiting cases arise that explain the $r^{-3}$-slope for galaxy-cluster outskirts and the $r^{-4}$-slope for galactic outskirts. Hence, we succeed in deriving the mass density profiles of common fitting functions from a general viewpoint. These results also allow to find a simple explanation for the cusp-core-problem and to separate the halo description from its dynamics.
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Although high-resolution N-body simulations make robust empirical predictions for the density distribution within cold dark matter halos, these studies have yielded little physical insight into the origins of the distribution. We investigate the problem using analytic and semi-analytic approaches. Simple analytic considerations suggest that the inner slope of dark matter halos cannot be steeper than alpha=2 (rho ~ r^-alpha), with alpha=1.5-1.7 being a more realistic upper limit. Our analysis suggests that any number of effects, both real (angular momentum from tidal torques, secondary perturbations) and artificial (two-body interactions, the accuracy of the numerical integrator, round-off errors), will result in shallower slopes. We also find that the halos should exhibit a well-defined relation between r_peri/r_apo and j_theta/j_r. We derive this relation analytically and speculate that it may be universal. Using a semi-analytic scheme based on Ryden & Gunn (1987), we further explore the relationship between the specific angular momentum distribution in a halo and its density profile. For now we restrict ourselves to halos that form primarily via nearly-smooth accretion of matter, and only consider the specific angular momentum generated by secondary perturbations associated with the cold dark matter spectrum of density fluctuations. Compared to those formed in N-body simulations, our ``semi-analytic halos are more extended, have flatter rotation curves and have higher specific angular momentum, even though we have not yet taken into account the effects of tidal torques. Whether the density profiles of numerical halos is indeed the result of loss in angular momentum outside the central region, and whether this loss is a feature of hierarchical merging and major mergers in particular, is under investigation.
High-resolution cosmological N-body simulations were performed in order to study the substructure of Milky Way-like galactic halos and the density profiles of halos in a warm dark matter scenario. The results favor this scenario with respect to the cold dark matter one.
Dark matter-dominated cluster-scale halos act as an important cosmological probe and provide a key testing ground for structure formation theory. Focusing on their mass profiles, we have carried out (gravity-only) simulations of the concordance LCDM cosmology, covering a mass range of 2.10^{12}-2.10^{15} solar mass/h and a redshift range of z=0-2, while satisfying the associated requirements of resolution and statistical control. When fitting to the Navarro-Frenk-White profile, our concentration-mass (c-M) relation differs in normalization and shape in comparison to previous studies that have limited statistics in the upper end of the mass range. We show that the flattening of the c-M relation with redshift is naturally expressed if c is viewed as a function of the peak height parameter, u. Unlike the c-M relation, the slope of the c- u relation is effectively constant over the redshift range z=0-2, while the amplitude varies by ~30% for massive clusters. This relation is, however, not universal: Using a simulation suite covering the allowed wCDM parameter space, we show that the c- u relation varies by about +/- 20% as cosmological parameters are varied. At fixed mass, the c(M) distribution is well-fit by a Gaussian with sigma_c/c = 0.33, independent of the radius at which the concentration is defined, the halo dynamical state, and the underlying cosmology. We compare the LCDM predictions with observations of halo concentrations from strong lensing, weak lensing, galaxy kinematics, and X-ray data, finding good agreement for massive clusters (M > 4.10^{14} solar mass/h), but with some disagreements at lower masses. Because of uncertainty in observational systematics and modeling of baryonic physics, the significance of these discrepancies remains unclear.
We explore the cosmological halo-to-halo scatter of the distribution of mass within dark matter halos utilizing a well-resolved statistical sample of clusters from the cosmological Millennium simulation. We find that at any radius, the spherically-averaged dark matter density of a halo (corresponding to the smooth-component) and its logarithmic slope are well-described by a Gaussian probability distribution. At small radii (within the scale radius), the density distribution is fully determined by the measured Gaussian distribution in halo concentrations. The variance in the radial distribution of mass in dark matter halos is important for the interpretation of direct and indirect dark matter detection efforts. The scatter in mass profiles imparts approximately a 25 percent cosmological uncertainty in the dark matter density at the Solar neighborhood and a factor of ~3 uncertainty in the expected Galactic dark matter annihilation flux. The aggregate effect of halo-to-halo profile scatter leads to a small (few percent) enhancement in dark matter annihilation background if the Gaussian concentration distribution holds for all halo masses versus a 10 percent enhancement under the assumption of a log-normal concentration distribution. The Gaussian nature of the cluster profile scatter implies that the technique of stacking halos to improve signal to noise should not suffer from bias.
We present a self-consistent Bayesian formalism to sample the primordial density fields compatible with a set of dark matter density tracers after cosmic evolution observed in redshift space. Previous works on density reconstruction did not self-consistently consider redshift space distortions or included an additional iterative distortion correction step. We present here the analytic solution of coherent flows within a Hamiltonian Monte Carlo posterior sampling of the primordial density field. We test our method within the Zeldovich approximation, presenting also an analytic solution including tidal fields and spherical collapse on small scales using augmented Lagrangian perturbation theory. Our resulting reconstructed fields are isotropic and their power spectra are unbiased compared to the true one defined by our mock observations. Novel algorithmic implementations are introduced regarding the mass assignment kernels when defining the dark matter density field and optimization of the time step in the Hamiltonian equations of motions. Our algorithm, dubbed barcode, promises to be specially suited for analysis of the dark matter cosmic web down to scales of a few Megaparsecs. This large scale structure is implied by the observed spatial distribution of galaxy clusters --- such as obtained from X-ray, SZ or weak lensing surveys --- as well as that of the intergalactic medium sampled by the Lyman alpha forest or perhaps even by deep hydrogen intensity mapping. In these cases, virialized motions are negligible, and the tracers cannot be modeled as point-like objects. It could be used in all of these contexts as a baryon acoustic oscillation reconstruction algorithm.
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