Cluster Mass Scale Research Articles

Characterising large-scale structure with the REFLEX II cluster survey

AbstractWe study the large-scale structure with superclusters from the REFLEX X-ray cluster survey together with cosmological N-body simulations. It is important to construct superclusters with criteria such that they are homogeneous in their properties. We lay out our theoretical concept considering future evolution of superclusters in their definition, and show that the X-ray luminosity and halo mass functions of clusters in superclusters are found to be top-heavy, different from those of clusters in the field. We also show a promising aspect of using superclusters to study the local cluster bias and mass scaling relation with simulations.

The generalized scaling relations for X-ray galaxy clusters: the most powerful mass proxy

The application to observational data of the generalized scaling relations (gSR) presented in Ettori et al. (2012) is here discussed. We extend further the formalism of the gSR in the self-similar model for X-ray galaxy clusters, showing that for a generic relation M_tot ~ L^a M_g^b T^c, where L, M_g and T are the gas luminosity, mass and temperature, respectively, the values of the slopes lay in the plane 4*a+3*b+2*c=3. Using published dataset, we show that some projections of the gSR are the most efficient relations, holding among observed physical X-ray quantities, to recover the cluster mass. This conclusion is based on the evidence that they provide the lowest chi^2, the lowest total scatter and the lowest intrinsic scatter among the studied scaling laws on both galaxy group and cluster mass scales. By the application of the gSR, the intrinsic scatter is reduced in all the cases down to a relative error on M_tot below 16 per cent. The best-fit relations are: M_tot ~ M_g^a T^{1.5-1.5a}, with a~0.4, and M_tot ~ L^a T^{1.5-2a}, with a~0.15. As a by product of this study, we provide the estimates of the gravitating mass at Delta=500 for 120 objects (50 from the Mahdavi et al. 2013 sample, 16 from Maughan 2012; 31 from Pratt et al. 2009; 23 from Sun et al. 2009), 114 of which are unique entries. The typical relative error in the mass provided from the gSR only (i.e. not propagating any uncertainty associated with the observed quantities) ranges between 3-5 per cent on cluster scale and is about 10 per cent for galaxy groups. With respect to the hydrostatic values used to calibrate the gSR, the masses are recovered with deviations in the order of 10 per cent due to the different mix of relaxed/disturbed objects present in the considered samples. In the extreme case of a gSR calibrated with relaxed systems, the hydrostatic mass in disturbed objects is over-estimated by about 20 per cent.

THE DARK MATTER HALO CONCENTRATION AND STELLAR INITIAL MASS FUNCTION OF A CASSOWARY GROUP

We exploit the group environment of the CAmbridge Sloan Survey Of Wide ARcs in the skY (CASSOWARY) z=0.3 lens J2158+0257 to measure the group dynamical mass as a complement to the central dynamical and lensing mass constraints. Follow-up spectroscopy of candidate group members is performed using VLT/FORS2. From the resulting N=21 confirmed members we measure the group dynamical mass by calibrating an analytic tracer mass estimator with cosmological simulations. The luminosity weighted line-of-sight velocity dispersion and the Einstein radius of the lens are used as mass probes in the inner regions of the galaxy. Combining these three observational probes allows us to independently constrain the mass and concentration of the dark matter halo, in addition to the total stellar mass of the central galaxy. We find a dark matter halo in remarkably good agreement with simulations (log_10 M_200/M_sun = 14.2 +/- 0.2, c_200 = 4.4 (+1.6, -1.4)) and a stellar mass-to-light ratio which favors a Salpeter initial mass function ((M/L)* = 5.7 +/- 1.2). Our measurement of a normal halo concentration suggests that there is no discrepancy between simulations and observations at the group mass scale. This is in contrast to the cluster mass scale for which a number of studies have claimed over-concentrated halos. While the halo mass is robustly determined, and the halo concentration is not significantly affected by systematics, the resulting stellar mass-to-light ratio is sensitive to the choice of stellar parameters, such as density profile and velocity anisotropy.

HALO-TO-HALO SIMILARITY AND SCATTER IN THE VELOCITY DISTRIBUTION OF DARK MATTER

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 scale radius.

SIMULATIONS OF THE SUNYAEV-ZEL'DOVICH POWER SPECTRUM WITH ACTIVE GALACTIC NUCLEUS FEEDBACK

We explore how radiative cooling, supernova feedback, cosmic rays and a new model of the energetic feedback from active galactic nuclei (AGN) affect the thermal and kinetic Sunyaev-Zel'dovich (SZ) power spectra. To do this, we use a suite of hydrodynamical TreePM-SPH simulations of the cosmic web in large periodic boxes and tailored higher resolution simulations of individual galaxy clusters. Our AGN feedback simulations match the recent universal pressure profile and cluster mass scaling relations of the REXCESS X-ray cluster sample better than previous analytical or numerical approaches. For multipoles $\ell\lesssim 2000$, our power spectra with and without enhanced feedback are similar, suggesting theoretical uncertainties over that range are relatively small, although current analytic and semi-analytic approaches overestimate this SZ power. We find the power at high 2000-10000 multipoles which ACT and SPT probe is sensitive to the feedback prescription, hence can constrain the theory of intracluster gas, in particular for the highly uncertain redshifts $>0.8$. The apparent tension between $\sigma_8$ from primary cosmic microwave background power and from analytic SZ spectra inferred using ACT and SPT data is lessened with our AGN feedback spectra.

The tidal streams of disrupting subhaloes in cosmological dark matter haloes

We present a detailed analysis of the properties of tidally stripped material from disrupting substructure haloes or subhaloes in a sample of high-resolution cosmological N-body host haloes ranging from galaxy- to cluster-mass scales. We focus on devising methods to recover the infall mass and infall eccentricity of subhaloes from the properties of their tidally stripped material (i.e. tidal streams). Our analysis reveals that there is a relation between the scatter of stream particles about the best-fitting debris plane and the infall mass of the progenitor subhalo. This allows us to reconstruct the infall mass from the spread of its tidal debris in space. We also find that the spread in radial velocities of the debris material (as measured by an observer located at the centre of the host) correlates with the infall eccentricity of the subhalo, which allows us to reconstruct its orbital parameters. We devise an automated method to identify the leading and trailing arms that can, in principle at least, be applied to observations of stellar streams from satellite galaxies. This method is based on the energy distribution of material in the tidal stream. Using this method, we show that the masses associated with the leading and trailing arms differ. While our analysis indicates that tidal streams can be used to recover certain properties of their progenitor subhaloes (and consequently satellites), we do not find strong correlations between host halo properties and stream properties. This likely reflects the complicated relationship between the stream and the host, which in a cosmological context is characterized by a complex mass accretion history, an asymmetric mass distribution and the abundance of substructure. Finally, we confirm that the so-called ‘backsplash’ subhalo population is present not only in galaxy cluster haloes but also in galaxy haloes. The orbits of backsplash subhaloes brought them inside the virial radius of their host at some earlier time, but they now reside in its outskirts at the present-day, beyond the virial radius. Both backsplash and bound subhaloes experience similar mass loss, but the contribution of the backsplash subhaloes to the overall tidal debris field is negligible.

Arc Statistics in Triaxial Dark Matter Halos: Testing the Collisionless Cold Dark Matter Paradigm

Statistics of lensed arcs in clusters of galaxies serve as a powerful probe of both the non-sphericity and the inner slope of dark matter halos. We develop a semi-analytic method to compute the number of arcs in triaxial dark matter halos. This combines the lensing cross section from the Monte Carlo ray-tracing simulations, and the probability distribution function (PDF) of the axis ratios evaluated from cosmological N-body simulations. This approach enables one to incorporate both asymmetries in the projected mass density and elongations along the line-of-sight analytically, for the first time in cosmological lensed arc statistics. As expected, triaxial dark matter halos significantly increase the number of arcs relative to spherical models; the difference amounts to more than one order of magnitude while the value of enhancement depends on the specific properties of density profiles. Then we compare our theoretical predictions with the observed number of arcs from 38 X-ray selected clusters. In contrast to the previous claims, our triaxial dark matter halos with inner density profile \rho \propto r^{-1.5} in a Lambda-dominated cold dark matter (CDM) universe reproduces well the observation. Since both the central mass concentration and triaxial axis ratios (minor to major axis ratio ~0.5) required to account for the observed data are consistent with cosmological N-body simulations, our result may be interpreted to lend strong support for the collisionless CDM paradigm at the mass scale of clusters.

Biasing and Genus Statistics of Dark Matter Halos in the Hubble Volume Simulation

Abstract We present a numerical analysis of genus statistics for dark matter halo catalogs from the Hubble volume simulation. The huge box-size of the Hubble volume simulation enables us to carry out a reliable statistical analysis of the biasing properties of halos at a Gaussian smoothing scale of $R_\mathrm{G} \ge 30 \,h^{-1} \,\mathrm{Mpc}$ with a cluster-mass scale of between $7\times 10^{13} \,h^{-1} \,{{{M}_{\odot}}}$ and $6\times 10^{15} \,h^{-1} \,{{{M}_{\odot}}}$. A detailed comparison of the genus for dark matter halos with that for the mass distribution shows that the non-Gaussianity induced by the halo biasing is comparable to that by nonlinear gravitational evolution, and both the shape and the amplitude of the genus are almost insensitive to the halo mass at $R_\mathrm{G} \ge 30 \,h^{-1} \,\mathrm{Mpc}$. In order to characterize the biasing effect on the genus, we apply a perturbative formula developed by Matsubara (1994, AAA 062.161.289). We find that the perturbative formula well describes the simulated halo genus at $R_\mathrm{G} \ge 50\,h^{-1} \,\mathrm{Mpc}$. The result indicates that the biasing effect on the halo genus is well approximated by nonlinear deterministic biasing up to the second-order term in the mass density fluctuation. The two parameters describing the linear and quadratic terms in the nonlinear biasing accurately specify the genus for galaxy clusters.

The Dark Matter Density Profile of the Lensing Cluster MS 2137−23: A Test of the Cold Dark Matter Paradigm

We present new spectroscopic observations of the gravitational arcs and the brightest cluster galaxy (BCG) in the cluster MS 2137-23 (z = 0.313) obtained with the Echelle Spectrograph and Imager on the Keck II telescope. We find that the tangential and radial arcs arise from sources at almost identical redshifts (z = 1.501, 1.502). We combine the measured stellar velocity dispersion profile of the BCG with a lensing analysis to constrain the distribution of dark and stellar matter in the central 100 kpc of the cluster. Our data indicate a remarkably flat inner slope for the dark matter profile, ?d r-?, with ? < 0.9 at a 99% CL. Steep inner slopes obtained in cold dark matter cosmological simulations?such as Navarro, Frenk, & White (? = 1) or Moore (1.5) universal dark matter profiles?are ruled out at better than 99% CL. As baryon collapse is likely to have steepened the dark matter profile from its original form, our data provide a powerful test of the cold dark matter paradigm at the cluster mass scale.

The Formation of the First Globular Clusters in Dwarf Galaxies before the Epoch of Reionization

We explore a mechanism for the formation of the first globular clusters, operating during the assembly of dwarf galaxies at high redshifts, z ≳ 10. The substructure in the dark matter and the corresponding potential wells are responsible for setting the cluster scale of ~105 M☉. The second mass scale in the formation problem, the stellar scale of ~1 M☉, is determined in turn by the processes that cool the gas. We address the origin of the first, cluster mass scale by means of three-dimensional numerical simulations of the collapsing dark matter and gaseous components. We find that the gas falls into the deepest dark subhalos, resulting in a system of approximately five protoglobular clouds. The incipient globular clusters lose their individual dark halos in the process of violent relaxation, leading to the buildup of the general dark halo around the dwarf galaxy.

Clustering of Dark Matter Halos on the Light Cone: Scale, Time, and Mass Dependence of the Halo Biasing in the Hubble Volume Simulations

We develop a phenomenological model to predict the clustering of dark matter halos on the light-cone by combining several existing theoretical models. Assuming that the velocity field of halos on large scales is approximated by linear theory, we propose an empirical prescription of a scale-, mass-, and time-dependence of halo biasing. We test our model against the Hubble Volume $N$-body simulation and examine its validity and limitations. We find a good agreement in two-point correlation functions of dark matter halos between the phenomenological model predictions and measurements from the simulation for $R>5h^{-1}$Mpc both in the real and redshift spaces. Although calibrated on the mass scale of groups and clusters and for redshifts up to $z\sim2$, the model is quite general and can be applied to a wider range of astrophysical objects, such as galaxies and quasars, if the relation between dark halos and visible objects is specified.

Lensing Constraints on the Cores of Massive Dark Matter Halos

The statistics of wide-separation (6'' < θ < 15'') gravitational lenses constrain the amount of mass in the cores of dark matter halos on group and cluster mass scales. For a family of halo models with a central cusp ρ ∝ r-α (1.0 ≤ α ≤ 1.9), the lack of wide-separation lenses in the large Cosmic Lens All-Sky Survey yields an upper limit on the fraction of the halo mass that is contained within ~4% of the virial radius, fcore < 0.023 (95% confidence level, Λ cold dark matter). This limit offers an important test of the cold dark matter paradigm. While the halo profiles derived from numerical simulations appear to be consistent with this upper limit, larger surveys currently underway such as the Two-degree Field and Sloan Digital Sky Survey should detect wide-separation lenses and thus provide a measurement of the core mass fraction in massive dark matter halos.

Detection of the Entropy of the Intergalactic Medium: Accretion Shocks in Clusters, Adiabatic Cores in Groups

The thermodynamics of the diffuse, X-ray-emitting gas in clusters of galaxies is linked to the entropy level of the intracluster medium. In particular, models that successfully reproduce the properties of local X-ray clusters and groups require the presence of a minimum value for the entropy in the center of X-ray halos. Such a minimum entropy is most likely generated by nongravitational processes in order to produce the observed break in self-similarity of the scaling relations of X-ray halos. Likely candidates are supernova heating, stellar winds, radiative processes, and nuclear activity. At present, there is no consensus on the level, the source, or the time evolution of this excess entropy. In this framework a key question is whether the central entropy is the residual of the entropy originally present in the precollapse or intergalactic medium or whether it is generated within the halos after collapse. Answering this question will allow a more precise determination of the energetic budget required to build an entropy floor and lead toward an understanding of the nature of the sources of heating. In this paper we describe a strategy to investigate the physics of the heating processes acting in groups and clusters. We show that the best way to extract information from the local data is by observation of the entropy profile at large radii in nearby X-ray halos (z 0.1), at both the upper and lower extremes of the cluster mass scale. The spatially and spectrally resolved observation of such X-ray halos provides information on the mechanism of the heating. We demonstrate how measurements of the size of constant entropy (adiabatic) cores in clusters and groups can directly constrain heating models and the minimum entropy value. We also consider two specific experiments: the detection of the shock fronts expected at the virial boundary of rich clusters and the detection of the isentropic, low surface brightness emission extending to radii larger than the virial ones in low-mass clusters and groups. Both experiments are designed to measure the entropy in the low-density gas far from the core, taking advantage of the large collecting power of the present X-ray telescopes (in this case, XMM). Such observations will be a crucial probe of both the physics of clusters and the relationship of nongravitational processes to the thermodynamics of the intergalactic medium.

Structure of Hydrous Ferric Oxide Aggregates

The small angle light scattering behavior of hydrous ferric oxide flocs is examined here and found to provide useful insights into the nature of the aggregates formed despite the large size of these aggregates at later times. The flocs appear to exhibit fractal properties over a significant size range though the aggregates appear to be easily disrupted through mixing effects resulting in breakup and/or restructuring to denser assemblages. Background electrolyte concentrations also have some impact on floc structure but mixing effects and apparent destabilization by ferric ions limit the effect of added electrolytes on the stability and structure of ferric oxyhydroxides. Similar estimates of fractal dimensions of these hydrous ferric oxide flocs are obtained both by static light scattering analysis and by a cluster mass scaling approach. The choice of density distribution cutoff function has some impact on derived size and structure parameters and further refinement in this area is needed.

Determining [formula omitted] from the cluster correlation function

It is shown how data on the cluster correlation function can be used to reconstruct the density of the pregalactic density field on the cluster mass scale. The method is applied to data on the cluster correlation amplitude-richness dependence. The spectrum of the recovered density field has the same shape as that derived from data on the galaxy correlation function is measured as a function of a linear scale. Matching the two amplitudes relates the mass to the comoving scale it contains and thereby leads to a direct determination of Ω. The resultant density parameter turns out to be Ω=0.25.

Cold dark matter variant cosmological models — I. Simulations and preliminary comparisons

We present two matched sets of five dissipationless simulations each, including four presently favoured minimal modifications to the standard cold dark matter (CDM) scenario. One simulation suite, with a linear box size of 75 h−1 Mpc, is designed for high resolution and good statistics on the group/poor cluster scale, and the other, with a box size of 300 h−1 Mpc, is designed for good rich cluster statistics. All runs had 57 million cold particles, and models with massive neutrinos (CHDM-2ν) had an additional 113 million hot particles. We consider separately models with massive neutrinos, tilt, curvature, and a non-zero cosmological constant (Λ ≡ 3H20ΩΛ) in addition to the standard CDM model. We find that the dark matter in each of our tilted Ω0+ΩΛ = 1 (TΛCDM) model with Ω0 = 0.4, our tilted Ω01 model (TCDM), and our open Λ = 0 (OCDM) model with Ω = 0.5 has too much small-scale power by a factor of ∼2, while CHDM-2ν and SCDM are acceptable fits. In addition, we take advantage of the large dynamic range in detectable halo masses afforded by the combination of the two sets of simulations to test the Press–Schechter approximation. We find good fits at cluster masses for δc,g = 1.27–1.35 for a Gaussian filter and δc,t = 1.57 − 1.73 for a top hat filter. However, when we adjust δc to obtain a good fit at cluster mass scales, we find that the Press–Schechter model overpredicts the number density of haloes compared to the simulations by a weakly cosmology-dependent factor of 1.5–2 at galaxy and group masses. It is impossible to obtain a good fit over the entire range of masses simulated by adjusting δc within reasonable bounds.

The properties of the hot gas in galaxy groups and clusters from ID hydrodynamical simulations - I. Cosmological infall models

We report the results of 1D hydrodynamical modelling of the evolution of gas in galaxy clusters. We have incorporated many of the effects missing from earlier 1D treatments: improved modelling of the dark matter and galaxy distributions, cosmologically realistic evolution of the cluster potential, and the effects of a multiphase cooling flow. The model utilizes a fairly standard 1D Lagrangian hydrodynamical code to calculate the evolution of the intracluster gas. This is coupled to a theoretical model for the growth of dark matter density perturbations. The main advantages of this treatment over 3D codes are (1) improved spatial resolution within the cooling flow region, (2) much faster execution time, allowing a fuller exploration of parameter space, and (3) the inclusion of additional physics. In the present paper, we explore the development of infall models — in which gas relaxes into a deepening potential well — covering a wide range of cluster mass scales. We find that such simple models reproduce many of the global properties of observed clusters. Very strong cooling flows develop in these 1D cluster models. In practice, disruption by major mergers probably reduces the cooling rate in most clusters. The models overpredict the gas fraction in low-mass systems, indicating the need for additional physical processes, such as pre-heating or galaxy winds, which become important on small mass scales.

The cluster distribution as a test of dark matter models - I. Clustering properties

We present simulations of the cluster distribution in several dark matter models, using an optimized version of the truncated Zel'dovich approximation (TZA). We compare them with N-body cluster simulations and find that the TZA provides a very accurate description of the cluster distribution as long as fluctuations on the cluster mass scale are in the mildly non-linear regime. The simulated dark matter models are: Standard CDM (SCDM), Tilted CDM (TCDM) with n=0.7, Cold+Hot DM (CHDM) with 30% of hot component, low Hubble constant (h=0.3) CDM (LOWH) and a spatially flat low-density CDM model with \Omega_0=0.2. We compare the simulations with a redshift sample of Abell/ACO clusters, using the integral of the 2-point correlation function and the probability density function. We find that the best models at reproducing the data are CHDM and LCDM. All the other models are ruled out. The reduced skewness S_3 is fairly constant with S_3=1.9, independent of the DM model and consistent with observational data. The abundances of clusters predicted using the Press--Schechter theory provide strong constraints: only the CHDM, LOWH and LCDM models appear to produce the correct number-density of clusters.

On the spatial correlations of Abell clusters

If rich clusters formed where the primordial density enhancement, when averaged over an appropriate volume, was unusually large, then they give a biased measure of the large-scale density correlation function determiend by the probability distribution of the density fluctuations on a rich cluster mass scale. If this distribution was Gaussian, the correlation function is amplified. The amplification for rich clusters is estimated to be eaual about ten and predicted trend of amplification with richness agrees qualitatively with that observed. Some implications of these results for the large-scale density correlations are discussed.