A numerical fit of analytical to simulated density profiles in dark matter haloes

Analytical and geometrical properties of generalized power-law (GPL) density profiles are investigated in detail. In particular, a one-to-one correspondence is found between mathematical parameters and geometrical parameters. Then GPL density profiles are compared with simulated dark haloes (SDH) density profiles, and nonlinear least-absolute values and least-squares fits involving the above mentioned five parameters (RFSM5 method) are prescribed. More specifically, the sum of absolute values or squares of absolute logarithmic residuals is evaluated on a large number of points making a 5-dimension hypergrid, through a few iterations. The size is progressively reduced around a fiducial minimum, and superpositions on nodes of earlier hypergrids are avoided. An application is made to a sample of 17 SDHs on the scale of cluster of galaxies, within a flat $\Lambda$CDM cosmological model (Rasia et al. 2004). In dealing with the mean SDH density profile, a virial radius, averaged over the whole sample, is assigned, which allows the calculation of the remaining parameters. Using a RFSM5 method provides a better fit with respect to other methods. No evident correlation is found between SDH dynamical state (relaxed or merging) and asymptotic inner slope of the logarithmic density profile or (for SDH comparable virial masses) scaled radius. Mean values and standard deviations of some parameters are calculated, and a comparison with previous results is made with regard to the scaled radius. A certain degree of degeneracy is found in fitting GPL to SDH density profiles. If it is intrinsic to the RFSM5 method or it could be reduced by the next generation of high-resolution simulations, still remains an open question.Comment: 44 pages, 6 figures, updated version with recent results from high-resolution simulations (Diemand et al. 2004; Reed et al. 2005) included in the discussion; accepted for publication on SAJ (Serbian Astronomical Journal

Halo Mass Profiles and Low Surface Brightness Galaxies Rotation Curves

A recent study has claimed that the rotation curve shapes and mass densities of Low Surface Brightness (LSB) galaxies are largely consistent with $\Lambda$CDM predictions, in contrast to a large body of observational work. I demonstrate that the method used to derive this conclusion is incapable of distinguishing the characteristic steep CDM mass-density distribution from the core-dominated mass-density distributions found observationally: even core-dominated pseudo-isothermal haloes would be inferred to be consistent with CDM. This method can therefore make no definitive statements on the (dis)agreement between the data and CDM simulations. After introducing an additional criterion that does take the slope of the mass-distribution into account I find that only about a quarter of the LSB galaxies investigated are possibly consistent with CDM. However, for most of these the fit parameters are so weakly constrained that this is not a strong conclusion. Only 3 out of 52 galaxies have tightly constrained solutions consistent with $\Lambda$CDM. Two of these galaxies are likely dominated by stars, leaving only one possible dark matter dominated, CDM-consistent candidate, forming a mere 2 per cent of the total sample. These conclusions are based on comparison of data and simulations at identical radii and fits to the entire rotation curves. LSB galaxies that are consistent with CDM simulations, if they exist, seem to be rare indeed.Comment: Accepted for publication in Astrophysical Journa

A model for the postcollapse equilibrium of cosmological structure: truncated isothermal spheres from top-hat density perturbations

The postcollapse structure of objects which form by gravitational condensation out of the expanding cosmological background universe is a key element in the theory of galaxy formation. Towards this end, we have reconsidered the outcome of the nonlinear growth of a uniform, spherical density perturbation in an unperturbed background universe - the cosmological ``top-hat'' problem. We adopt the usual assumption that the collapse to infinite density at a finite time predicted by the top-hat solution is interrupted by a rapid virialization caused by the growth of small-scale inhomogeneities in the initial perturbation. We replace the standard description of the postcollapse object as a uniform sphere in virial equilibrium by a more self-consistent one as a truncated, nonsingular, isothermal sphere in virial and hydrostatic equilibrium, including for the first time a proper treatment of the finite-pressure boundary condition on the sphere. The results differ significantly from both the uniform sphere and the singular isothermal sphere approximations for the postcollapse objects. These results will have a significant effect on a wide range of applications of the Press-Schechter and other semi-analytical models to cosmology. The truncated isothermal sphere solution presented here predicts the virial temperature and integrated mass distribution of the X-ray clusters formed in the CDM model as found by detailed, 3D, numerical gas and N-body dynamical simulations remarkably well. This solution allows us to derive analytically the numerically-calibrated mass-temperature and radius-temperature scaling laws for X-ray clusters which were derived empirically by Evrard, Metzler and Navarro from simulation results for the CDM model. (Shortened)Comment: 29 pages, 7 ps figures, MNRAS-style, LaTeX. Accepted for publication in MNRAS. Minor revisions only (including additional panel in Fig.3 and additional comparison with X-ray cluster simulations

Reconstructing the Initial Density Field of the Local Universe: Method and Test with Mock Catalogs

Our research objective in this paper is to reconstruct an initial linear density field, which follows the multivariate Gaussian distribution with variances given by the linear power spectrum of the current CDM model and evolves through gravitational instability to the present-day density field in the local Universe. For this purpose, we develop a Hamiltonian Markov Chain Monte Carlo method to obtain the linear density field from a posterior probability function that consists of two components: a prior of a Gaussian density field with a given linear spectrum, and a likelihood term that is given by the current density field. The present-day density field can be reconstructed from galaxy groups using the method developed in Wang et al. (2009a). Using a realistic mock SDSS DR7, obtained by populating dark matter haloes in the Millennium simulation with galaxies, we show that our method can effectively and accurately recover both the amplitudes and phases of the initial, linear density field. To examine the accuracy of our method, we use $N$-body simulations to evolve these reconstructed initial conditions to the present day. The resimulated density field thus obtained accurately matches the original density field of the Millennium simulation in the density range 0.3 <= rho/rho_mean <= 20 without any significant bias. Especially, the Fourier phases of the resimulated density fields are tightly correlated with those of the original simulation down to a scale corresponding to a wavenumber of ~ 1 h/Mpc, much smaller than the translinear scale, which corresponds to a wavenumber of ~ 0.15 h\Mpc.Comment: 43 pages, 15 figures, accepted for publication in Ap

The Three-Dimensional Shapes of Galaxy Clusters

While clusters of galaxies are considered one of the most important cosmological probes, the standard spherical modelling of the dark matter and the intracluster medium is only a rough approximation. Indeed, it is well established both theoretically and observationally that galaxy clusters are much better approximated as triaxial objects. However, investigating the asphericity of galaxy clusters is still in its infancy. We review here this topic which is currently gathering a growing interest from the cluster community. We begin by introducing the triaxial geometry. Then we discuss the topic of deprojection and demonstrate the need for combining different probes of the cluster's potential. We discuss the different works that have been addressing these issues. We present a general parametric framework intended to simultaneously fit complementary data sets (X-ray, Sunyaev Zel'dovich and lensing data). We discuss in details the case of Abell 1689 to show how different models/data sets lead to different haloe parameters. We present the results obtained from fitting a 3D NFW model to X-ray, SZ, and lensing data for 4 strong lensing clusters. We argue that a triaxial model generally allows to lower the inferred value of the concentration parameter compared to a spherical analysis. This may alleviate tensions regarding, e.g. the over-concentration problem. However, we stress that predictions from numerical simulations rely on a spherical analysis of triaxial halos. Given that triaxial analysis will have a growing importance in the observational side, we advocate the need for simulations to be analysed in the very same way, allowing reliable and meaningful comparisons. Besides, methods intended to derive the three dimensional shape of galaxy clusters should be extensively tested on simulated multi-wavelength observations.Comment: (Biased) Review paper. Comments welcome. Accepted for publication in Space Science Reviews. This is a product of the work done by an international team at the International Space Science Institute (ISSI) in Bern on "Astrophysics and Cosmology with Galaxy Clusters: the X-ray and lensing view

Dark Matter In Disk Galaxies II: Density Profiles as Constraints on Feedback Scenarios

The disparity between the density profiles of galactic dark matter haloes predicted by dark matter only cosmological simulations and those inferred from rotation curve decomposition, the so-called cusp-core problem, suggests that baryonic physics has an impact on dark matter density in the central regions of galaxies. Feedback from black holes, supernovae and massive stars may each play a role by removing matter from the centre of the galaxy on shorter timescales than the dynamical time of the dark matter halo. Our goal in this paper is to determine constraints on such feedback scenarios based on the observed properties of a set of nearby galaxies. Using a Markov Chain Monte Carlo (MCMC) analysis of galactic rotation curves, via a method developed in a previous paper, we constrain density profiles and an estimated minimum radius for baryon influence, $r_1$, which we couple with a feedback model to give an estimate of the fraction of matter within that radius that must be expelled to produce the presently observed halo profile. We show that in the case of the gas rich dwarf irregular galaxy DDO 154, an outflow from a central source (e.g. a black hole or star forming region) could produce sufficient feedback on the halo without removing the disk gas. We examine the rotation curves of 8 galaxies taken from the THINGS data set and determine constraints on the radial density profiles of their dark matter haloes. For some of the galaxies, both cored haloes and cosmological $\rho \propto r^{-1}$ cusps are excluded. These intermediate central slopes require baryonic feedback to be finely tuned. We also find for galaxies which exhibit extended cores in their haloes (e.g. NGC 925), the use of a split power-law halo profile yields models without the unphysical, sharp features seen in models based on the Einasto profile.Comment: 17 pages, 19 figures Submitted to MNRA

The Birmingham-CfA cluster scaling project - I: gas fraction and the M-T relation

We have assembled a large sample of virialized systems, comprising 66 galaxy clusters, groups and elliptical galaxies with high quality X-ray data. To each system we have fitted analytical profiles describing the gas density and temperature variation with radius, corrected for the effects of central gas cooling. We present an analysis of the scaling properties of these systems and focus in this paper on the gas distribution and M-T relation. In addition to clusters and groups, our sample includes two early-type galaxies, carefully selected to avoid contamination from group or cluster X-ray emission. We compare the properties of these objects with those of more massive systems and find evidence for a systematic difference between galaxy-sized haloes and groups of a similar temperature. We derive a mean logarithmic slope of the M-T relation within R_200 of 1.84+/-0.06, although there is some evidence of a gradual steepening in the M-T relation, with decreasing mass. We recover a similar slope using two additional methods of calculating the mean temperature. Repeating the analysis with the assumption of isothermality, we find the slope changes only slightly, to 1.89+/-0.04, but the normalization is increased by 30%. Correspondingly, the mean gas fraction within R_200 changes from (0.13+/-0.01)h70^-1.5 to (0.11+/-0.01)h70^-1.5, for the isothermal case, with the smaller fractional change reflecting different behaviour between hot and cool systems. There is a strong correlation between the gas fraction within 0.3*R_200 and temperature. This reflects the strong (5.8 sigma) trend between the gas density slope parameter, beta, and temperature, which has been found in previous work. (abridged)Comment: 27 pages, accepted for publication in MNRAS; uses longtable.sty & lscape.st

Cosmology in 2D: the concentration-mass relation for galaxy clusters

The aim of this work is to perform a systematic study of the measures of the mass and concentration estimated by fitting the convergence profile of a large sample of mock galaxy cluster size lenses, created with the publicly available code MOKA. We found that the main contribution to the bias in mass and in concentration is due to the halo triaxiality and second to the presence of substructures within the host halo virial radius. We show that knowing the cluster elongation along the line of sight helps in correcting the mass bias, but still keeps a small negative bias for the concentration. If these mass and concentration biases will characterize the galaxy cluster sample of a wide field survey it will be difficult to well recover within one sigma the cosmological parameters that mainly influence the c - M relation, using as reference a 3D c - M relation measured in cosmological N-body simulation. In this work we propose how to correct the c - M relation for projection effects and for adiabatic contraction and suggest to use these as reference for real observed data. Correcting mass and concentration estimates, as we propose, gives a measurement of the cosmological parameter within 1 - {\sigma} confidence contours.Comment: 18 pages, 14 figures - replaced to match the accepted version for publication by MNRA

The strongest gravitational lenses: I. The statistical impact of cluster mergers

For more than a decade now, it has been controversial whether or not the high rate of giant gravitational arcs and the largest observed Einstein radii are consistent with the standard cosmological model. Recent studies indicate that mergers provide an efficient mechanism to substantially increase the strong-lensing efficiency of individual clusters. Based on purely semi-analytic methods, we investigated the statistical impact of cluster mergers on the distribution of the largest Einstein radii and the optical depth for giant gravitational arcs of selected cluster samples. Analysing representative all-sky realizations of clusters at redshifts z < 1 and assuming a constant source redshift of z_s = 2.0, we find that mergers increase the number of Einstein radii above 10 arcsec (20 arcsec) by ~ 35 % (~ 55 %). Exploiting the tight correlation between Einstein radii and lensing cross sections, we infer that the optical depth for giant gravitational arcs with a length-to-width ratio > 7.5 of those clusters with Einstein radii above 10 arcsec (20 arcsec) increases by ~ 45 % (85 %). Our findings suggest that cluster mergers significantly influence in particular the statistical lensing properties of the strongest gravitational lenses. We conclude that semi-analytic studies must inevitably take these events into account before questioning the standard cosmological model on the basis of the largest observed Einstein radii and the statistics of giant gravitational arcs.Comment: 23 pages, 18 figures; accepted for publication in Astronomy and Astrophysics; v2: minor corrections (added clarifying comments; added Fig. 19) to match the accepted versio

Dark matter haloes: an additional criterion for the choice of fitting density profiles

Simulated dark matter haloes are fitted by self-similar, universal density profiles, where the scaled parameters depend only on a scaled (truncation) radius which, in turn, is supposed to be independent on the mass and the formation redshift. A criterion for the choice of the best fitting density profile is proposed, with regard to a set of high-resolution simulations, where some averaging procedure on scaled density profiles has been performed, in connection with a number of fitting density profiles. An application is made to a pair of sets each made of a dozen of high-resolution simulations, which are available in literature, in connection with two currently used fitting density profiles, where the dependence of the scaled radius on the mass and the formation redshift, may be neglected to a first extent. Some features of the early evolution of dark matter haloes represented by fitting density profiles, are discussed in the limit of the spherical top-hat model.Comment: 62 pages, 9 figures, accepted for publication on SAJ (Serbian Astronomical Journal), paragraph and reference added for section