Insights into the origin of halo mass profiles from machine learning
Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）；Indian Institute of Science Education and Research（印度科学教育与研究学院）；University of Chicago（芝加哥大学）；Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡夫利宇宙物理研究所）；Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）
Luisa Lucie-Smith, Susmita Adhikari, Risa H. Wechsler
备注：
14 pages, 11 figures. Minor changes to match version accepted for publication in MNRAS
The mass distribution of dark matter haloes is the result of the hierarchical growth of initial density perturbations through mass accretion and mergers. We use an interpretable machine-learning framework to provide physical insights into the origin of the spherically-averaged mass profile of dark matter haloes. We train a gradient-boosted-trees algorithm to predict the final mass profiles of cluster-sized haloes, and measure the importance of the different inputs provided to the algorithm. We find two primary scales in the initial conditions (ICs) that impact the final mass profile: the density at approximately the scale of the haloes' Lagrangian patch $R_L$ ($R\sim 0.7\, R_L$) and that in the large-scale environment ($R\sim 1.7~R_L$). The model also identifies three primary time-scales in the halo assembly history that affect the final profile: (i) the formation time of the virialized, collapsed material inside the halo, (ii) the dynamical time, which captures the dynamically unrelaxed, infalling component of the halo over its first orbit, (iii) a third, most recent time-scale, which captures the impact on the outer profile of recent massive merger events. While the inner profile retains memory of the ICs, this information alone is insufficient to yield accurate predictions for the outer profile. As we add information about the haloes' mass accretion history, we find a significant improvement in the predicted profiles at all radii. Our machine-learning framework provides novel insights into the role of the ICs and the mass assembly history in determining the final mass profile of cluster-sized haloes.
Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）；University College London（伦敦大学学院）；Stockholm University（斯德哥尔摩大学）；Fermi National Accelerator Laboratory（费米国家加速器实验室）；University of Chicago（芝加哥大学）；Science and Technology Facilities Council（科学与技术设施委员会）；Rutherford Appleton Laboratory（卢瑟福·阿普尔顿实验室）
The density profiles of dark matter halos are typically modeled using empirical formulae fitted to the density profiles of relaxed halo populations. We present a neural network model that is trained to learn the mapping from the raw density field containing each halo to the dark matter density profile. We show that the model recovers the widely-used Navarro-Frenk-White (NFW) profile out to the virial radius, and can additionally describe the variability in the outer profile of the halos. The neural network architecture consists of a supervised encoder-decoder framework, which first compresses …
We propose a simple model that elucidates the generation of halo velocity bias. The fluid equation approximation is often adopted in modelling the evolution of the halo density field. In this approach, halos are often taken to be point particles even though in reality they are finite-sized objects. In this paper, we generalize the fluid equation approximation to halos to include the finite extent of halos by taking into account the halo profile. We compute the perturbation of the halo density and velocity field to second order and find that the profile correction gives rise to $k^2$ correction…
Cold dark matter haloes consist of a relatively smooth dark matter component as well as a system of bound subhaloes. It is the prevailing practice to include all halo mass, including mass in subhaloes, in studies of halo density profiles. However, often in observational studies satellites are treated as having their own distinct dark matter density profiles in addition to the profile of the host. This difference makes comparisons between theoretical and observed results difficult. In this work we investigate density profiles of the smooth components of host haloes by excluding mass contained w…
Halos of similar mass and redshift exhibit a large degree of variability in their differential properties, such as dark matter, hot gas, and stellar mass density profiles. This variability is an indicator of diversity in the formation history of these dark matter halos that is reflected in the coupling of scatters about the mean relations. In this work, we show that the strength of this coupling depends on the scale at which halo profiles are measured. By analyzing the outputs of the IllustrisTNG hydrodynamical cosmological simulations we report the radial- and mass-dependent couplings between…
We perform a simple test showing that accreting halos grow inside-out and have density profiles that are statistically indistinguishable from those of halos having undergone major mergers. The test also reveals that the ability for the NFW analytical expression to fit the density profile of halos spoils towards large masses at any redshift. On view of these results, we analyze the M-c relations on extreme mass and redshift domains predicted by usual toy models based on numerical data and one physical model based on the two assumptions above confirmed by the test.
N-body simulations predict that dark matter halos with different mass scales are described by a universal model, the Navarro-Frenk-White (NFW) density profiles. As a consequence of baryonic cooling effects, the halos will become more concentrated, and similar to an isothermal sphere over large range in radii ($\sim 300$ $h^{-1}$kpc). The singular isothermal sphere model however has to be truncated artificially at large radii since it extends to infinity. We model a massive galaxy halo as a combination of an isothermal sphere and an NFW density profile. We give an approximation for the mass con…
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…
In this paper, we investigate the dark matter halo density profile of M33. We find that the HI rotation curve of M33 is best described by a NFW dark matter halo density profile model, with a halo concentration of cvir = 4.0\pm1.0 and a virial mass of Mvir = (2.2\pm0.1)\times10^11 Msun. We go on to use the NFW concentration (cvir)of M33, along with the values derived for other galaxies (as found in the literature), to show that cvir correlates with both spiral arm pitch angle and supermassive black hole mass.
While N-body simulations testify for a cuspy profile of the central region of the dark matter haloes, observations favor a shallow, cored density profile of the central region of, at least, some spiral galaxies and dwarf spheroidals. We show that a central profile, very close to the observed one, inevitably forms in the center of dark matter haloes if we make a supposition about a moderate energy relaxation of the system during the halo formation. If we assume the energy exchange between dark matter particles during the halo collapse to be not too intensive, the profile is universal: it depend…
We study the density profile of a dwarf halo in the decaying dark matter (DDM) cosmology, using a new algorithm that resolves halo density profiles down to the innermost $700$ pc robustly with high efficiency. Following Schwarzschild's orbit-based method, we have also developed a simplified model to calculate the DDM halo density profiles, which agree remarkably well with those from N-body simulations. Both zoom-in simulations and the simplified model reveal that dark matter decays lead to the flattening of central density and overall reduction of density in dwarf halos, and the underlying phy…
With help of a set of toy N-body models of dark halo formation we study the impact of small scale initial perturbations on the inner density profiles of haloes. We find a significant flattening of the inner slope $α={d \log ρ\over d \log r}$ to $α=-0.5$ in some range of scales and amplitudes of the perturbations (while in the case of absence of these perturbations the NFW profile with $α=-1$ is reproduced). This effect may be responsible for the formation of cuspless galactic haloes.
We study the impact of primordial non-Gaussianity on the density profile of dark matter halos by using the semi-analytical model introduced recently by Dalal {\it et al.} which relates the peaks of the initial linear density field to the final density profile of dark matter halos. Models with primordial non-Gaussianity typically produce an initial density field that differs from that produced in Gaussian models. We use the path-integral formulation of excursion set theory to calculate the non-Gaussian corrections to the peak profile and derive the statistics of the peaks of non-Gaussian densit…
Large-scale faint structure detected by the recent observations in the halo of the Andromeda galaxy (M31) provides an attractive window to explore the structure of outer cold dark matter (CDM) halo in M31. Using an N-body simulation of the interaction between an accreting satellite galaxy and M31, we investigate the mass density profile of the CDM halo. We find the sufficient condition of the outer density profile of CDM halo in M31 to reproduce the Andromeda giant stream and the shells at the east and west sides of M31. The result indicates that the density profile of the outer dark matter ha…
We calculate the non-linear virialization density, $Δ_c$, of halos under spherical collapse from peaks with an arbitrary initial and final density profile. This is in contrast to the standard calculation of $Δ_c$ which assumes top-hat profiles. Given our formalism, the non-linear halo density can be calculated once the shape of the initial peak's density profile and the shape of the virialized halo's profile are provided. We solve for $Δ_c$ for halos in an Einstein de-Sitter and $Λ$CDM universe. As examples, we consider power-law initial profiles as well as spherically averaged peak profiles c…
I provide notes on the NFW, Einasto, Sersic, and other mass profiles which provide good fits to simulated dark matter halos (S3). I summarize various published c(M) relations: halo concentration as a function of mass (S1). The definition of the virial radius is discussed and relations are given to convert c_vir, M_vir, and r_vir between various defined values of the halo overdensity (S2).
The density profiles of dark matter haloes are commonly described by fitting functions such as the NFW or Einasto models, but these approximations break down in the transition region where halos become dominated by newly accreting matter. Here we present a simple, accurate new fitting function that is inspired by the asymptotic shapes of the separate orbiting and infalling halo components. The orbiting term is described as a truncated Einasto profile, $ρ_{\rm orb} \propto \exp \left[-2/α (r / r_{\rm s})^α- 1/β (r / r_{\rm t})^β\right]$, with a five-parameter space of normalization, physically …
Using the model for (bottom-up) hierarchical halo growth recently developed by Salvador-Solé et al. (2012), we derive the typical spherically averaged density profile for haloes with several relevant masses in the concordant warm dark matter (ΛWDM) cosmology with non-thermal sterile neutrinos of two different masses. The predicted density profiles become flat at small radii, as expected from the effects of the spectrum cutoff. The core cannot be resolved, however, because the non-null particle velocity yields the fragmentation of minimum mass protohaloes in small nodes, which invalidates the m…
We use the IllustrisTNG (TNG) cosmological, hydrodynamical simulations of galaxy formation to measure the velocity dispersion profiles of dark matter and star particles in Milky Way-mass, galaxy group, and cluster-scale dark matter halos. The mean profile calculated from both dark and luminous tracers are similar in shape, exhibiting a large degree of halo-to-halo scatter around the average profile. The so-called "splashback" radius demarcates the outer boundary of the halo, and manifests as a kink in the velocity dispersion profile, located on average between $\sim 1.0-1.5r_{200m}$, where $r_…
Accurately predicting structural properties of dark matter halos is one of the fundamental goals of modern cosmology. We use the new suite of MultiDark cosmological simulations to study the evolution of dark matter halo density profiles, concentrations, and velocity anisotropies. The MultiDark simulations cover a large range of masses 1e10-1e15Msun and volumes upto 50Gpc**3. The total number of dark matter halos in all the simulations exceeds 60 billion. We find that in order to understand the structure of dark matter halos and to make ~1% accurate predictions for density profiles, one needs t…
Constraints on dark matter halo masses from weak gravitational lensing can be improved significantly by using additional information about the morphology of their density distribution, leading to tighter cosmological constraints derived from the halo mass function. This work is the first of two in which we investigate the accuracy of halo morphology and mass measurements in 2D and 3D. To this end, we determine several halo physical properties in the MICE-Grand Challenge dark matter only simulation. We present a public catalogue of these properties that includes density profiles and shape param…
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 distributi…
Gravitational redshifts and other relativistic effects are beginning to be studied in the context of galaxy clustering. Distortions consistent with those expected in General Relativity have been measured in galaxy cluster redshift profiles by Wojtak et al. and others and in the the cross-correlation function of galaxy populations by Alam et al. On scales below ~20 Mpc/$h$ simulations have shown that gravitational redshift dominates over other effects. However, this signal is related to the shape and depth of gravitational potentials, and therefore the matter density in galaxies and galaxy clus…
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$. The pseudo-phase-space density (PPSD) profiles of CDM halos also show remarkable regularity, and are well approximated by simple power laws, Q(r)=ρ/σ^3 ~ r^-χ. We show that this is expected from dynamical equilibrium considerations, since Jeans' equations predict that the pseudo-phase-space density profiles of Einasto halos should resemble power laws …
We simulate neutralino dark matter ($χ$DM) haloes from their initial collapse, at $\sim$ earth mass, up to a few percent solar. Our results confirm that the density profiles of the first haloes are described by a $\sim r^{-1.5}$ power-law. As haloes grow in mass, their density profiles evolve significantly. In the central regions, they become shallower and reach on average $\sim r^{-1}$, the asymptotic form of an NFW profile. Using non-cosmological controlled simulations, we observe that temporal variations in the gravitational potential caused by major mergers lead to a shallowing of the inne…
We construct two linear filtering techniques based on weak gravitational lensing to constrain the inner slope $α$ of the density profile of dark-matter halos. Both methods combine all available information into an estimate of this single number. Under idealised assumptions, $α$ is constrained to ~15% if the halo concentration c is known, and to < 30% if not. We argue that the inevitable degeneracy between density-profile slope and halo concentration cannot be lifted under realistic conditions, and show by means of Fisher-matrix methods which linear combination of $α$ and c is best constrained …
The near universality of DM halo density profiles provided by N-body simulations has proven to be robust against changes in total mass density, power spectrum, and some forms of initial velocity dispersion. In this letter we study the effects of coherently spinning up an isolated DM-only progenitor on halo structure. Halos with spins within several standard deviations of the simulated mean ($λ\lesssim 0.20$) produce profiles with negligible deviations from the universal form. Only when the spin becomes quite large ($λ\gtrsim 0.20$) do departures become evident. The angular momentum distributio…
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, …
With SDSS galaxy data and halo data from up-to-date N-body simulations we construct a semi-empirical catalog (SEC) of early-type systems by making a self-consistent bivariate statistical match of stellar mass (M_star) and velocity dispersion (sigma) with halo virial mass (M_vir). We then assign stellar mass profile and velocity dispersion profile parameters to each system in the SEC using their observed correlations with M_star and sigma. Simultaneously, we solve for dark matter density profile of each halo using the spherical Jeans equation. The resulting dark matter density profiles deviate …
Some observations of galaxies, and in particular dwarf galaxies, indicate a presence of cored density profiles in apparent contradiction with cusp profiles predicted by dark matter N-body simulations. We constructed an analytical model, using particle distribution functions (DFs), to show how a supernova (SN) explosion can transform a cusp density profile in a small-mass dark matter halo into a cored one. Considering the fact that a SN efficiently removes matter from the centre of the first haloes, we study the effect of mass removal through a SN perturbation in the DFs. We found that the tran…
We present the evolution of the structure of relaxed cold dark matter haloes in the cosmology from the Planck satellite. Our simulations cover 5 decades in halo mass, from dwarf galaxies to galaxy clusters. Due to the increased matter density and power spectrum normalization the concentration mass relation in the Planck cosmology has a 20 percent higher normalization at redshift z=0 compared to WMAP cosmology. We confirm that CDM haloes are better described by the Einasto profile; for example, at scales near galaxy half-light radii CDM haloes have significantly steeper density profiles than im…
We use N-body simulations to quantify how the escape velocity in cluster-sized halos maps to the gravitational potential in a LambdaCDM universe. Using spherical density-potential pairs and the Poisson equation, we find that the matter density inferred gravitational potential profile predicts the escape velocity profile to within a few percent accuracy for group and cluster-sized halos (10^13 < M_200 < 10^15 M_sun, with respect to the critical density). The accuracy holds from just outside the core to beyond the virial radius. We show the importance of explicitly incorporating a cosmological c…
We study the imprint of Dark Energy on the density profile of Dark Matter halos using a set of high-resolution large volume cosmological N-body simulations from the Dark Energy Universe Simulation Series (DEUSS). We first focus on the analysis of the goodness-of-fit of the Navarro-Frenk-White (NFW) profile which we find to vary with halo mass and redshift. We also find that the fraction of halos ill-fitted by NFW varies with cosmology, thus indicating that the mass assembly of halos with perturbed density profiles carries a characteristic signature of Dark Energy. To access this information in…
We define and study statistical ensembles of matter density profiles describing spherically symmetric, virialized dark matter haloes of finite extent with a given mass and total gravitational potential energy. Our ensembles include spatial degrees of freedom only, a microstate being a spherically symmetric matter density function. We provide an exact solution for the grand canonical partition functional, and show its equivalence to that of the microcanonical ensemble. We obtain analytically the mean profiles that correspond to an overwhelming majority of microstates. All such profiles have an …
A longstanding puzzle of fundamental importance in modern cosmology has been the origin of the nearly universal density profiles of dark matter halos found in N-body simulations -- the so-called NFW profile. We show how this behavior may be understood, simply, by applying adiabatic contraction to peaks of Gaussian random fields. We argue that dynamical friction acts to reduce enormously the effect of random scatter in the properties of initial peaks, providing a key simplification. We compare our model predictions with results of the ultra-high resolution Via Lactea-II N-body simulation, and f…
We present rotation curve fits to 175 late-type galaxies from the Spitzer Photometry & Accurate Rotation Curves (SPARC) database using seven dark matter (DM) halo profiles: pseudo-isothermal (pISO), Burkert, Navarro-Frenk-White (NFW), Einasto, Di Cintio (2014, DC14), coreNFW, and a new semi-empirical profile named Lucky13. We marginalize over stellar mass-to-light ratio, galaxy distance, disk inclination, halo concentration and halo mass (and an additional shape parameter for Einasto) using a Markov Chain Monte Carlo method. We find that cored halo models such as the DC14 and Burkert profiles …
We study the dependence of surface mass density profiles, which can be directly measured by weak gravitational lensing, on the orientation of haloes with respect to the line-of-sight direction, using a suite of $N$-body simulations. We find that, when major axes of haloes are aligned with the line-of-sight direction, surface mass density profiles have higher amplitudes than those averaged over all halo orientations, over all scales from $0.1$ to $100\,\mathrm{Mpc}/h$ we studied. While the orientation dependence at small scales is ascribed to the halo triaxiality, our results indicate even stro…
A steepening feature in the outer density profiles of dark matter halos indicating the splashback radius has drawn much attention recently. Possible observational detections have even been made for galaxy clusters. Theoretically, Adhikari et al. have estimated the location of the splashback radius by computing the secondary infall trajectory of a dark matter shell through a growing dark matter halo with an NFW profile. However, since they imposed a shape of the halo profile rather than computing it consistently from the trajectories of the dark matter shells, they could not provide the full sh…
We derive the density profile for collisionless dissipationless dark matter haloes in hierarchical cosmologies making use of the Secondary Infall (SI) model. The novelties are: i) we deal with triaxial virialised objects; ii) their seeds in the linear regime are peaks endowed with {\it unconvolved} spherically averaged density profiles according to the peak formalism; iii) the initial peculiar velocities are taken into account; and iv) accreting haloes are assumed to develop from the inside out, keeping the instantaneous inner system unaltered. The validity of this latter assumption is accurat…
Secondary Dependence of Baryonic Effects on the Density Profile of Dark Matter Halos
Case Western Reserve University（凯斯西储大学）；Universidad de Sevilla（塞维利亚大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Bologna（意大利国家核物理研究所博洛尼分所）；Durham University（杜伦大学）；Harvard–Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）
In this series of papers we present an emulator-based halo model for the non-linear clustering of galaxies in modified gravity cosmologies. In the first paper, we present emulators for the following halo properties: the halo mass function, concentration-mass relation and halo-matter cross-correlation function. The emulators are trained on data extracted from the \textsc{FORGE} and \textsc{BRIDGE} suites of $N$-body simulations, respectively for two modified gravity (MG) theories: $f(R)$ gravity and the DGP model, varying three standard cosmological parameters $Ω_{\mathrm{m0}}, H_0, σ_8$, and o…
Using SDSS Stripe82 data we have obtained deep radial surface brightness profiles of 7 face-on to intermediate inclined late-type spirals down to \sim 30 mag arcsec^-2 in the r'-band. We do not find any evidence for a sharp cut-off of the light distribution of the disks but a smooth continuation into the stellar halos of galaxies. Stellar halos start to affect the surface brightness profiles of the galaxies at \sim 28 mag arcsec^-2, and at a radial distance of \sim 4-10 inner scale-lengths. We find that the light contribution from the stellar halo could be responsible of previous classificatio…
Dark matter haloes from cosmological N-body simulations typically have triaxial shapes and anisotropic velocity distributions. Recently it has been shown that the velocity anisotropy, beta, of cosmological haloes and major merger remnants depends on direction in such a way that beta is largest along the major axis and smallest along the minor axis. In this work we use a wide range of non-cosmological N-body simulations to examine halo shapes and direction-dependence of velocity anisotropy profiles. For each of our simulated haloes we define 48 cones pointing in different directions, and from t…
Novel density profile for isothermal cores of dark matter halos
Massachusetts Institute of Technology（麻省理工学院）；University of Chicago（芝加哥大学）；University of Pennsylvania（宾夕法尼亚大学）；Princeton University（普林斯顿大学）；Center for Astrophysics, Harvard & Smithsonian（哈佛-史密松天体物理中心）；University of Rochester（罗切斯特大学）
Dark matter (DM) haloes forming near the thermal cut-off scale of the density perturbations are unique, since they are the smallest objects and form through monolithic gravitational collapse, while larger haloes contrastingly have experienced mergers. While standard cold dark matter (CDM) simulations readily produce haloes that follow the universal Navarro-Frenk-White (NFW) density profile with an inner slope, $ρ\propto r^{-α}$, with $α=1$, recent simulations have found that when the free-streaming cut-off expected for the CDM model is resolved, the resulting haloes follow nearly power-law den…
We explore the possibility that the density profiles of elliptical galaxies and cold dark matter (CDM) halos found in cosmological simulations can be understood in terms of the same physical process, collisionless gravitational collapse. To investigate this, we study a simplified model, the collapse of a perfectly cold Plummer sphere. First, we examine an N-body simulation of this model with particles constrained to purely radial orbits. This results in a final state characterized by a profile slightly steeper than ρ\propto r^{-2} at small radii and behaving as ρ\propto r^{-4} at large radii, …
The splashback radius, $R_{\rm sp}$, is a physically motivated halo boundary that separates infalling and collapsed matter of haloes. We study $R_{\rm sp}$ in the hydrodynamic and dark matter only IllustrisTNG simulations. The most commonly adopted signature of $R_{\rm sp}$ is the radius at which the radial density profiles are steepest. Therefore, we explicitly optimise our density profile fit to the profile slope and find that this leads to a $\sim5\%$ larger radius compared to other optimisations. We calculate $R_{\rm sp}$ for haloes with masses between $10^{13-15}{\rm M}_{\odot}$ as a func…
The dark matter halo sparsity, i.e. the ratio between spherical halo masses enclosing two different overdensities, provides a non-parametric proxy of the halo mass distribution which has been shown to be a sensitive probe of the cosmological imprint encoded in the mass profile of haloes hosting galaxy clusters. Mass estimations at several overdensities would allow for multiple sparsity measurements, that can potentially retrieve the entirety of the cosmological information imprinted on the halo profile. Here, we investigate the impact of multiple sparsity measurements on the cosmological model…
We introduce a mass dependent density profile to describe the distribution of dark matter within galaxies, which takes into account the stellar-to-halo mass dependence of the response of dark matter to baryonic processes. The study is based on the analysis of hydrodynamically simulated galaxies from dwarf to Milky Way mass, drawn from the MaGICC project, which have been shown to match a wide range of disk scaling relationships. We find that the best fit parameters of a generic double power-law density profile vary in a systematic manner that depends on the stellar-to-halo mass ratio of each ga…
We present the observational evidence of the 2-halo term in the stacked shear profile of a sample of about 1200 optically selected galaxy clusters based on imaging data and the public shear catalog from the CFHTLenS. We find that the halo bias, a measure of the correlated distribution of matter around galaxy clusters, has amplitude and correlation with galaxy cluster mass in very good agreement with the predictions based on the LCDM standard cosmological model. The mass-concentration relation is flat but higher than theoretical predictions. We also confirm the close scaling relation between th…
We use the secondary infall model described in Del Popolo (2009), which takes into account the effect of dynamical friction, ordered and random angular momentum, baryons adiabatic contraction and dark matter baryons interplay, to study how in- ner slopes of relaxed LCDM dark matter (DM) halos with and without baryons (baryons+DM, and pure DM) depend on redshift and on halo mass. We apply the quoted method to structures on galactic scales and clusters of galaxies scales. We find that the inner logarithmic density slope, of dark matter halos with baryons has a significant dependence on halo mass…
We study the pseudo phase-space density, $ρ(r)/σ^3(r)$, of $Λ$CDM dark matter halos with and without baryons (baryons+DM, and pure DM), by using the model introduced in Del Popolo (2009), which takes into account the effect of dynamical friction, ordered and random angular momentum, baryons adiabatic contraction and dark matter baryons interplay. We examine the radial dependence of $ρ(r)/σ^3(r)$ over 9 orders of magnitude in radius for structures on galactic and cluster of galaxies scales. We find that $ρ(r)/σ^3(r)$ is approximately a power-law only in the range of halo radius resolved by curr…
