A Bayesian Inference Analysis of the X-ray Cluster Luminosity-Temperature Relation

We present a Bayesian inference analysis of the Markevitch (1998) and Allen & Fabian (1998) cooling flow corrected X-ray cluster temperature catalogs that constrains the slope and the evolution of the empirical X-ray cluster luminosity-temperature (L-T) relation. We find that for the luminosity range 10^44.5 erg s^-1 < L_bol < 10^46.5 erg s^-1 and the redshift range z < 0.5, L_bol is proportional to T^2.80(+0.15/-0.15)(1+z)^(0.91-1.12q_0)(+0.54/-1.22). We also determine the L-T relation that one should use when fitting the Press- Schechter mass function to X-ray cluster luminosity catalogs such as the Einstein Medium Sensitivity Survey (EMSS) and the Southern Serendipitous High- Redshift Archival ROSAT Catalog (Southern SHARC), for which cooling flow corrected luminosities are not determined and a universal X-ray cluster temperature of T = 6 keV is assumed. In this case, L_bol is proportional to T^2.65(+0.23/-0.20)(1+z)^(0.42-1.26q_0)(+0.75/-0.83) for the same luminosity and redshift ranges.Comment: Accepted to The Astrophysical Journal, 20 pages, LaTe

The effects of velocities and lensing on moments of the Hubble diagram

We consider the dispersion on the supernova distance-redshift relation due to peculiar velocities and gravitational lensing, and the sensitivity of these effects to the amplitude of the matter power spectrum. We use the MeMo lensing likelihood developed by Quartin, Marra & Amendola (2014), which accounts for the characteristic non-Gaussian distribution caused by lensing magnification with measurements of the first four central moments of the distribution of magnitudes. We build on the MeMo likelihood by including the effects of peculiar velocities directly into the model for the moments. In order to measure the moments from sparse numbers of supernovae, we take a new approach using Kernel Density Estimation to estimate the underlying probability density function of the magnitude residuals. We also describe a bootstrap re-sampling approach to estimate the data covariance matrix. We then apply the method to the Joint Light-curve Analysis (JLA) supernova catalogue. When we impose only that the intrinsic dispersion in magnitudes is independent of redshift, we find $\sigma_8=0.44^{+0.63}_{-0.44}$ at the one standard deviation level, although we note that in tests on simulations, this model tends to overestimate the magnitude of the intrinsic dispersion, and underestimate $\sigma_8$. We note that the degeneracy between intrinsic dispersion and the effects of $\sigma_8$ is more pronounced when lensing and velocity effects are considered simultaneously, due to a cancellation of redshift dependence when both effects are included. Keeping the model of the intrinsic dispersion fixed as a Gaussian distribution of width 0.14 mag, we find $\sigma_8 = 1.07^{+0.50}_{-0.76}$.Comment: 16 pages, updated to match version accepted in MNRA

An Isocurvature CDM Cosmogony. II. Observational Tests

A companion paper presents a worked model for evolution through inflation to initial conditions for an isocurvature model for structure formation. It is shown here that the model is consistent with the available observational constraints that can be applied without the help of numerical simulations. The model gives an acceptable fit to the second moments of the angular fluctuations in the thermal background radiation and the second through fourth moments of the measured large-scale fluctuations in galaxy counts, within the possibly significant uncertainties in these measurements. The cluster mass function requires a rather low but observationally acceptable mass density, 0.1\lsim\Omega\lsim 0.2 in a cosmologically flat universe. Galaxies would be assembled earlier in this model than in the adiabatic version, an arguably good thing. Aspects of the predicted non-Gaussian character of the anisotropy of the thermal background radiation in this model are discussed.Comment: 14 pages, 3 postscript figures, uses aas2pp4.st

The Mean and Scatter of the Velocity Dispersion-Optical Richness Relation for maxBCG Galaxy Clusters

The distribution of galaxies in position and velocity around the centers of galaxy clusters encodes important information about cluster mass and structure. Using the maxBCG galaxy cluster catalog identified from imaging data obtained in the Sloan Digital Sky Survey, we study the BCG-galaxy velocity correlation function. By modeling its non-Gaussianity, we measure the mean and scatter in velocity dispersion at fixed richness. The mean velocity dispersion increases from 202+/-10 km/s for small groups to more than 854+/-102 km/s for large clusters. We show the scatter to be at most 40.5+/-3.5%, declining to 14.9+/-9.4% in the richest bins. We test our methods in the C4 cluster catalog, a spectroscopic cluster catalog produced from the Sloan Digital Sky Survey DR2 spectroscopic sample, and in mock galaxy catalogs constructed from N-body simulations. Our methods are robust, measuring the scatter to well within one-sigma of the true value, and the mean to within 10%, in the mock catalogs. By convolving the scatter in velocity dispersion at fixed richness with the observed richness space density function, we measure the velocity dispersion function of the maxBCG galaxy clusters. Although velocity dispersion and richness do not form a true mass-observable relation, the relationship between velocity dispersion and mass is theoretically well characterized and has low scatter. Thus our results provide a key link between theory and observations up to the velocity bias between dark matter and galaxies.Comment: 25 pages, 15 figures, 2 tables, published in Ap