We carry out fully 3-dimensional simulations of evolution from self-similar, spherically symmetric linear perturbations of a Cold Dark Matter dominated Einstein-de Sitter universe. As a result of the radial orbit instability, the haloes which grow from such initial conditions are triaxial with major-to-minor axis ratios of order 3:1. They nevertheless grow approximately self-similarly in time. In all cases they have power-law density profiles and near-constant velocity anisotropy in their inner regions. Both the power-law index and the value of the velocity anisotropy depend on the similarity index of the initial conditions, the former as expected from simple scaling arguments. Halo structure is thus not "universal" but remembers the initial conditions. On larger scales the density and anisotropy profiles show two characteristic scales, corresponding to particles at first pericentre and at first apocentre after infall. They are well approximated by the NFW model only for one value of the similarity index. In contrast, at all radii within the outer caustic the pseudo phase-space density can be fit by a single power law with an index which depends only very weakly on the similarity index of the initial conditions. This behaviour is very similar to that found for haloes formed from LCDM initial conditions and so can be considered approximately universal.
Disk-halo decompositions of galaxy rotation curves are generally performed in a parametric way. We construct self-consistent models of nonspherical isothermal halos embedding a zero-thickness disk, by assuming that the halo distribution function is a Maxwellian. The method developed here can be used to study other physically-based choices for the halo distribution function and the case of a disk accompanied by a bulge. In a preliminary investigation we note the existence of a fine tuning between the scalelengths R_Ω and h, respectively characterizing the rise of the rotation curve and the lumi…
We investigate the splashback features of dark-matter halos based on cosmic density and velocity fields. Besides the density correlation function binned by the halo orientation angle which was used in the literature, we introduce, for the first time, the corresponding velocity statistic, alignment momentum correlation function, to take into account the asphericity of halos. Using large-volume, high-resolution N-body simulations, we measure the alignment statistics of density and velocity. On halo scales, $x\sim R_\mathrm{200m} \sim 1Mpc/h$, we detect a sharp steepening in the momentum correlat…
We investigate nonlocal Lagrangian bias contributions involving gradients of the linear density field, for which we have predictions from the excursion set peak formalism. We begin by writing down a bias expansion which includes all the bias terms, including the nonlocal ones. Having checked that the model furnishes a reasonable fit to the halo mass function, we develop a 1-point cross-correlation technique to measure bias factors associated with 2-distributed quantities. We validate the method with numerical realizations of peaks of Gaussian random fields before we apply it to N-body simulati…
We simulate the growth of isolated dark matter haloes from self-similar and spherically symmetric initial conditions. Our N-body code integrates the geodesic deviation equation in order to track the streams and caustics associated with individual simulation particles. The radial orbit instability causes our haloes to develop major-to-minor axis ratios approaching 10 to 1 in their inner regions. They grow similarly in time and have similar density profiles to the spherical similarity solution, but their detailed structure is very different. The higher dimensionality of the orbits causes their s…
Spherical systems with polytropic equations of state are of great interest in astrophysics. They are widely used to describe neutron stars, red giants, white dwarfs, brown dwarfs, main sequence stars, galactic halos, and globular clusters of diverse sizes. In this paper we construct analytically a family of self-gravitating spherical models in the post-Newtonian approximation of general relativity. These models present interesting cusps in their density profiles which are appropriate for the modeling of galaxies and dark matter halos. The systems described here are anisotropic in the sense tha…
We use self-similarity in N-body simulations of scale-free models to test for resolution dependence in the mass function and two-point correlation functions of dark matter halos. We use 1024$^3$ particle simulations performed with ABACUS, and compare results obtained with two halo finders: friends-of-friends (FOF) and ROCKSTAR. The FOF mass functions show a systematic deviation from self-similarity which is explained by resolution dependence of the FOF mass assignment previously reported in the literature. Weak evidence for convergence is observed only starting from halos of several thousand p…
This papers explores the self similar solutions of the Vlasov-Poisson system and their relation to the gravitational collapse of dynamically cold systems. Analytic solutions are derived for power law potential in one dimension, and extensions of these solutions in three dimensions are proposed. Next the self similarity of the collapse of cold dynamical systems is investigated numerically. The fold system in phase space is consistent with analytic self similar solutions, the solutions present all the proper self-similar scalings. An additional point is the appearance of an $x^{-(1/2)}$ law at t…
We examine the Velocity Distribution Function (VDF) in dark matter halos from Milky Way to cluster mass scales. We identify an empirical model for the VDF with a wider peak and a steeper tail than a Maxwell--Boltzmann distribution, and discuss physical explanations. We quantify sources of scatter in the VDF of cosmological halos and their implication for direct detection of dark matter. Given modern simulations and observations, we find that the most significant uncertainty in the VDF of the Milky Way arises from the unknown radial position of the solar system relative to the dark matter halo …
The relation between the mass and integrated electron pressure of galaxy group and cluster halos can be probed by stacking maps of the thermal Sunyaev-Zel'dovich (tSZ) effect. Perhaps surprisingly, recent observational results have indicated that the scaling relation between integrated pressure and mass follows the prediction of simple, self-similar models down to halo masses as low as $10^{12.5} \, M_{\odot}$. Hydrodynamical simulations that incorporate energetic feedback processes suggest that gas should be depleted from such low-mass halos, thus decreasing their tSZ signal relative to self-…
We use the $k$-nearest neighbor probability distribution function ($k$NN-PDF, Banerjee & Abel 2021) to assess convergence in a scale-free $N$-body simulation. Compared to our previous two-point analysis, the $k$NN-PDF allows us to quantify our results in the language of halos and numbers of particles, while also incorporating non-Gaussian information. We find good convergence for 32 particles and greater at densities typical of halos, while 16 particles and fewer appears unconverged. Halving the softening length extends convergence to higher densities, but not to fewer particles. Our analysis …
We revisit the non-sphericity of cluster-mass scale halos from cosmological N-body simulation on the basis of triaxial modelling. In order to understand the difference between the simulation results and the conventional ellipsoidal collapse model (EC), we first consider the evolution of individual simulated halos. The major difference between EC and the simulation becomes appreciable after the turn-around epoch. Moreover, it is sensitive to the individual evolution history of each halo. Despite such strong dependence on individual halos, the resulting nonsphericity of halos exhibits weak but r…
We analyzed available observational data of a sample of dark matter (DM) dominated galaxies and clusters of galaxies and we have found correlations between the virial mass, $M_{vir}$, of halos and basic parameters of their cores, namely, the mean DM density, pressure and entropy. These correlations are a natural consequence of similar evolution of all such objects. It is driven mainly by gravitational interactions what implies a high degree of self similarity of both the process of halos formation and their internal structure. We confirmed the CDM--like shape of both the small and large scale …
We apply halo abundance matching to obtain galaxy virial masses, M_h, and radii, Rvir, for the 183 isolated galaxies in the "MgII Absorber-Galaxy Catalog" (MAGIICAT, Nielsen et al.). All galaxies have spectroscopic redshifts (0.1 < z < 1.1) and their circumgalactic medium (CGM) is probed in MgII absorption within projected galactocentric distances D < 200 kpc. We examine the behavior of equivalent width, W(2796), and covering fraction, f_c, as a function of D, D/Rvir, and M_h. We find: [1] systematic segregation of M_h on the W(2796)-D plane (4.0 sigma); high-mass halos are found at higher D w…
We investigate the collapse and internal structure of dark matter halos. We consider halo formation from initially scale-free perturbations, for which gravitational collapse is self-similar. Fillmore and Goldreich (1984) and Bertschinger (1985) solved the one dimensional (i.e. spherically symmetric) case. We generalize their results by formulating the three dimensional self-similar equations. We solve the equations numerically and analyze the similarity solutions in detail, focusing on the internal density profiles of the collapsed halos. By decomposing the total density into subprofiles of pa…
We make use of two suits of ultra high resolution N-body simulations of individual dark matter haloes from the Phoenix and the Aquarius Projects to investigate systematics of assembly history of subhaloes in dark matter haloes differing by a factor of $1000$ in the halo mass. We have found that real progenitors which built up present day subhalo population are relatively more abundant for high mass haloes, in contrast to previous studies claiming a universal form independent of the host halo mass. That is mainly because of repeated counting of the 're-accreted' (progenitors passed through and …
Wave dark matter ($ψ$DM), which satisfies the Schrödinger-Poisson equation, has recently attracted substantial attention as a possible dark matter candidate. Numerical simulations have in the past provided a powerful tool to explore this new territory of possibility. Despite their successes to reveal several key features of $ψ$DM, further progress in simulations is limited, in that cosmological simulations so far can only address formation of halos below $\sim 2\times 10^{11} M_\odot$ and substantially more massive halos have become computationally very challenging to obtain. For this reason, …
We use the Millennium Simulation series to study the relation between the accretion history (MAH) and mass profile of cold dark matter halos. We find that the mean density within the scale radius, r_{-2} (where the halo density profile has isothermal slope), is directly proportional to the critical density of the Universe at the time when the main progenitor's virial mass equals the mass enclosed within r_{-2}. Scaled to these characteristic values of mass and density, the mean MAH, expressed in terms of the critical density of the Universe, M(ρ_{crit}(z)), resembles that of the enclosed densi…
We present a systematic study of the density profiles of LCDM halos, focusing on the outer regions, 0.1 < r/Rvir < 9. We show that the median and mean profiles of halo samples of a given peak height exhibit significant deviations from the universal analytic profiles discussed previously in the literature, such as the Navarro-Frenk-White and Einasto profiles, at radii r > 0.5 R200m. In particular, at these radii the logarithmic slope of the median density profiles of massive or rapidly accreting halos steepens more sharply than predicted. The steepest slope of the profiles occurs at r ~ R200m, …
We study the mass accretion histories (MAHs) and density profiles of dark matter halos using N-body simulations of self-similar gravitational clustering from scale-free power spectra, $P(k)\propto k^n$. We pay particular attention to the density profile curvature, which we characterize using the shape parameter, $α$, of an Einasto profile. In agreement with previous findings our results suggest that, despite vast differences in their MAHs, the density profiles of virialized halos are remarkably alike. Nonetheless, clear departures from self-similarity are evident: for a given spectral index, $…
Recent advances in observational astronomy allow to study various groups of Dark Matter (DM) dominated objects from the dwarf spheroidal (dSph) galaxies to clusters of galaxies that span the mass range from $10^{6} M_{\odot}$ to $10^{15} M_{\odot}$. To analyze data of this divers collection of objects we used a simple toy model of spherical DM halo formation that was initially proposed by Peebles. This model introduced the concept of the epoch or redshift of halo formation. Using this concept we analyzed selected sample of DM dominated objects and we have found empirical correlations between t…
The cosmological simulations indicates that the dark matter haloes have specific self similar properties. However the halo similarity is affected by the baryonic feedback, the momentum injected by the supernovae re-shape the dark matter core and transform it to a flat density core, with a scale length imposed by the baryonic feedback. Additionally the baryon feedback impose also an equilibrium condition, which when coupled with the imposed baryonic scale length induce a new type of similarity. The new self similar solution implies that the acceleration generated by dark matter is scale free, w…
We investigate the quenching properties of central and satellite galaxies, utilizing the halo masses and central-satellite identifications from the SDSS galaxy group catalog of Yang et al. We find that the quenched fractions of centrals and satellites of similar stellar masses have similar dependence on host halo mass. The similarity of the two populations is also found in terms of specific star formation rate and 4000 Å break. The quenched fractions of centrals and satellites of similar masses show similar dependencies on bulge-to-total light ratio, central velocity dispersion and halo-centri…
Cosmological N-body simulations indicate that the spherically-averaged density profiles of cold dark matter halos are accurately described by Einasto profiles, where the logarithmic slope is a power-law of adjustable exponent, γ=dlnρ/dlnr ~ r^α$. The pseudo-phase-space density (PPSD) profiles of CDM halos also show remarkable regularity, and are well approximated by simple power laws, Q(r)=ρ/σ^3 ~ r^-χ. We show that this is expected from dynamical equilibrium considerations, since Jeans' equations predict that the pseudo-phase-space density profiles of Einasto halos should resemble power laws …
The scaling of observable properties of galaxy clusters with mass evolves with time. Assessing the role of the evolution is crucial to study the formation and evolution of massive halos and to avoid biases in the calibration. We present a general method to infer the mass and the redshift dependence, and the time-evolving intrinsic scatter of the mass-observable relations. The procedure self-calibrates the redshift dependent completeness function of the sample. The intrinsic scatter in the mass estimates used to calibrate the relation is considered too. We apply the method to the scaling of mas…
Ultracompact minihalos (UCMHs) have emerged as a valuable probe of the primordial power spectrum of density fluctuations at small scales. UCMHs are expected to form at early times in regions with ${δρ/ρ\gtrsim 10^{-3}}$, and they are theorized to possess an extremely compact ${ρ\propto r^{-9/4}}$ radial density profile, which enhances their observable signatures. Nonobservation of UCMHs can thus constrain the primordial power spectrum. Using $N$-body simulations to study the collapse of extreme density peaks at ${z \simeq 1000}$, we show that UCMHs forming under realistic conditions do not dev…
The Gaia HR diagram shows the presence of apparently young stars at high tangential velocities. Using a simple analytical model I show that these stars are likely to be blue stragglers. Once normalized to red giant stars, the fraction of nearby halo blue stragglers is of order 20 percent, and remarkably close to that measured in dwarf galaxies. Motivated by this similarity, I apply to field blue stragglers scaling relations inferred from blue stragglers in dwarf galaxies. Doing this for the Milky Way halo returns an average stellar density of 3.4 x 10^-5 Msun/pc^3 and a dark matter density of …
The phase-space structure of primordial dark matter halos is revisited using cosmological simulations with three sine waves and Cold Dark Matter (CDM) initial conditions. The simulations are performed with the tessellation based Vlasov solver ColDICE and a Particle-Mesh (PM) $N$-body code. The analyses include projected density, phase-space diagrams, radial density and pseudo-phase space density. Particular attention is paid to force and mass resolution. Because the phase-space sheet complexity, estimated in terms of total volume and simplices count, increases very quickly, ColDICE can follow …
We present a new catalogue of 55,121 groups and clusters centred on Luminous Red Galaxies from SDSS DR7 in the redshift range 0.15<z<0.4. We provide halo mass estimates for each of these groups derived from a calibration between the optical richness of bright galaxies (M_r<-20.5) within 1 Mpc, and X-ray-derived mass for a small subset of 129 groups and clusters with X-ray measurements. We derive the mean (stacked) surface number density profiles of galaxies as a function of total halo mass in different mass bins. We find that derived profiles can be well-described by a projected NFW profile wi…
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, …
The similarity between the distributions of spins for galaxies ($λ_{\rm g}$) and for dark-matter haloes ($λ_{\rm h}$), indicated both by simulations and observations, is naively interpreted as a one-to-one correlation between the spins of a galaxy and its host halo. This is used to predict galaxy sizes in semi-analytic models via $R_{\rm e}\simeqλ_{\rm h} R_{\rm v}$, with $R_{\rm e}$ the half-mass radius of the galaxy and $R_{\rm v}$ the halo radius. Utilizing two different suites of zoom-in cosmological simulations, we find that $λ_{\rm g}$ and $λ_{\rm h}$ are in fact only barely correlated, …
We use numerical simulations to explore whether direct collapse can lead to the formation of SMBH seeds at high-z. We follow the evolution of gas within DM halos of 2 x 10^8 Mo and 1 kpc. We adopt cosmological density profiles and j-distributions. Our goal is to understand how the collapsing flow overcomes the centrifugal barrier and whether it is subject to fragmentation. We find that the collapse leads either to a central runaway or to off-center fragmentation. A disk-like configuration is formed inside the centrifugal barrier. For more cuspy DM distribution, the gas collapses more and exper…
Satellite galaxies in rich clusters are subject to numerous physical processes that can significantly influence their evolution. However, the typical L* satellite galaxy resides in much lower mass galaxy groups, where the processes capable of altering their evolution are generally weaker and have had less time to operate. To investigate the extent to which satellite and central galaxy evolution differs, we separately model the stellar mass - halo mass (M* -Mh) relation for these two populations over the redshift interval 0 < z < 1. This relation for central galaxies is constrained by the galax…
According to the standard cold dark matter (CDM) cosmology, the structure of dark halos including those of galaxy clusters reflects their mass accretion history. Older clusters tend to be more concentrated than younger clusters. Their structure, represented by the characteristic radius $r_s$ and mass $M_s$ of the Navarro--Frenk--White (NFW) density profile, is related to their formation time. In~this study, we showed that $r_s$, $M_s$, and the X-ray temperature of the intracluster medium (ICM), $T_X$, form a thin plane in the space of $(\log r_s, \log M_s, \log T_X)$. This tight correlation in…
A decade ago cosmological simulations of increasingly higher resolution were used to demonstrate that virialized regions of Cold Dark Matter (CDM) halos are filled with a multitude of dense, gravitationally-bound clumps. These dark matter subhalos are central regions of halos that survived strong gravitational tidal forces and dynamical friction during the hierarchical sequence of merging and accretion via which the CDM halos form. Comparisons with observations revealed that there is a glaring discrepancy between abundance of subhalos and luminous satellites of the Milky Way and Andromeda as a…
We use analytic computations to predict the power spectrum as well as the bispectrum of Cosmic Infrared Background (CIB) anisotropies. Our approach is based on the halo model and takes into account the mean luminosity-mass relation. The model is used to forecast the possibility to simultaneously constrain cosmological, CIB and halo occupation distribution (HOD) parameters in the presence of foregrounds. For the analysis we use wavelengths in eight frequency channels between 200 and 900$\;\mathrm{GHz}$ with survey specifications given by Planck and LiteBird. We explore the sensitivity to the mo…
