RASS-SDSS Galaxy Cluster Survey. VII. On the Cluster Mass to Light ratio and the Halo Occupation Distribution

We explore the mass-to-light ratio in galaxy clusters and its relation to the cluster mass. We study the relations among the optical luminosity ($L_{op}$), the cluster mass ($M_{200}$) and the number of cluster galaxies within $r_{200}$ ($N_{gal}$) in a sample of 217 galaxy clusters with confirmed 3D overdensity. We correct for projection effects, by determining the galaxy surface number density profile in our cluster sample. This is best fitted by a cored King profile in low and intermediate mass systems. The core radius decreases with cluster mass, and, for the highest mass clusters, the profile is better represented by a generalized King profile or a cuspy Navarro, Frenk & White profile. We find a very tight proportionality between $L_{op}$ and $N_{gal}$, which, in turn, links the cluster mass-to-light ratio to the Halo Occupation Distribution $N_{gal}$ vs. $M_{200}$. After correcting for projection effects, the slope of the $L_{op}-M_{200}$ and $N_{gal}-M_{200}$ relations is found to be $0.92\pm0.03$, close, but still significantly less than unity. We show that the non-linearity of these relations cannot be explained by variations of the galaxy luminosity distributions and of the galaxy M/L with the cluster mass. We suggest that the nonlinear relation between number of galaxies and cluster mass reflects an underlying nonlinear relation between number of subhaloes and halo mass.Comment: 15 pages, 15 figures, accepted for publication in A&

Optical properties of periodic systems within the current-current response framework: pitfalls and remedies

We compare the optical absorption of extended systems using the density-density and current-current linear response functions calculated within many-body perturbation theory. The two approaches are formally equivalent for a finite momentum $\mathbf{q}$ of the external perturbation. At $\mathbf{q}=\mathbf{0}$, however, the equivalence is maintained only if a small $q$ expansion of the density-density response function is used. Moreover, in practical calculations this equivalence can be lost if one naively extends the strategies usually employed in the density-based approach to the current-based approach. Specifically we discuss the use of a smearing parameter or of the quasiparticle lifetimes to describe the finite width of the spectral peaks and the inclusion of electron-hole interaction. In those instances we show that the incorrect definition of the velocity operator and the violation of the conductivity sum rule introduce unphysical features in the optical absorption spectra of three paradigmatic systems: silicon (semiconductor), copper (metal) and lithium fluoride (insulator). We then demonstrate how to correctly introduce lifetime effects and electron-hole interactions within the current-based approach.Comment: 17 pages, 6 figure

Reduced Density-Matrix Functional Theory: correlation and spectroscopy

In this work we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard molecule at 1/4 and 1/2 filling as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison we also report the results of the $GW$ approximation, where the self-energy functional is approximated, but no further hypothesis are made concerning the approximations of the observables. In particular we focus on the atomic limit, where the two sites of the molecule are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard molecule at 1/2 filling with or without a spin-symmetry-broken ground state, allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in $GW$ the signature of strong correlation are present in the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover we show how the spectroscopic properties change from one spin structure to the other. Our findings can be generalized to other situations, which allows us to make connections to real materials and experiment

Photoemission Spectra from Reduced Density Matrices: the Band Gap in Strongly Correlated Systems

We present a method for the calculation of photoemission spectra in terms of reduced density matrices. We start from the spectral representation of the one-body Green's function G, whose imaginary part is related to photoemission spectra, and we introduce a frequency-dependent effective energy that accounts for all the poles of G. Simple approximations to this effective energy give accurate spectra in model systems in the weak as well as strong correlation regime. In real systems reduced density matrices can be obtained from reduced density-matrix functional theory. Here we use this approach to calculate the photoemission spectrum of bulk NiO: our method yields a qualitatively correct picture both in the antiferromagnetic and paramagnetic phases, contrary to mean-field methods, in which the paramagnet is a metal

The metallicity dependence of the Cepheid PL-relation

A sample of 37 Galactic, 10 LMC and 6 SMC cepheids is compiled for which individual metallicity estimates exist and BVIK photometry in almost all cases. The Galactic cepheids all have an individual distance estimate available. For the MC objects different sources of photometry are combined to obtain improved periods and mean magnitudes. A multi-parameter Period-Luminosity relation is fitted to the data which also solves for the distance to the LMC and SMC. When all three galaxies are considered, without metallicity effect, a significant quadratic term in log P is found, as previously observed and also predicted in some theoretical calculations. For the present sample it is empirically determined that for log P < 1.65 linear PL-relations may be adopted, but this restricts the sample to only 4 LMC and 1 SMC cepheid. Considering the Galactic sample a metallicity effect is found in the zero point in the VIWK PL-relation (-0.6 \pm 0.4 or -0.8 \pm 0.3 mag/dex depending on the in- or exclusion of one object), in the sense that metal-rich cepheids are brighter. The small significance is mostly due to the fact that the Galactic sample spans a narrow metallicity range. The error is to a significant part due to the error in the metallicity determinations and not to the error in the fit. Including the 5 MC cepheids broadens the observed metallicity range and a metallity effect of about -0.27 \pm 0.08 mag/dex in the zero point is found in VIWK, in agreement with some previous empirical estimates, but now derived using direct metallicity determinations for the cepheids themselves.Comment: Accepted Astronomy and Astrophysics, February 20, 200

RASS-SDSS Galaxy Cluster Survey. VI. The dependence of the cluster SFR on the cluster global properties

Using a subsample of 79 nearby clusters from the RASS-SDSS galaxy cluster catalogue of Popesso et al. (2005a), we perform a regression analysis between the cluster integrated star formation rate (Sigma_SFR) the cluster total stellar mass (M_star), the fractions of star forming (f_SF) and blue (f_b) galaxies and other cluster global properties, namely its richness (N_gal, i.e. the total number of cluster members within the cluster virial radius), velocity dispersion (sigma_v), virial mass (M_200), and X-ray luminosity (L_X). All cluster global quantities are corrected for projection effects before the analysis. Galaxy SFRs and stellar masses are taken from the catalog of Brinchmann et al. (2004), which is based on SDSS spectra. We only consider galaxies with M_r <= -20.25 in our analysis, and exclude AGNs. We find that both Sigma_SFR and M_star are correlated with all the cluster global quantities. A partial correlation analysis show that all the correlations are induced by the fundamental one between Sigma_SFR and N_gal, hence there is no evidence that the cluster properties affect the mean SFR or M_star per galaxy. The relations between Sigma_SFR and M_star, on one side, and both N_gal and M_200, on the other side, are linear, i.e. we see no evidence that different clusters have different SFR or different M_star per galaxy and per unit mass. The fraction f_SF does not depend on any cluster property considered, while f_b does depend on L_X. We note that a significant fraction of star-forming cluster galaxies are red (~25% of the whole cluster galaxy population). We conclude that the global cluster properties are unable to affect the SF properties of cluster galaxies, but the presence of the X-ray luminous intra-cluster medium can affect their colors, perhaps through the ram-pressure stripping mechanism.Comment: 14 pages, 12 figures, accepted for publication on A&A; corrected coefficient in Tab.

The peculiar horizontal branch morphology of the Galactic globular clusters NGC 6388 and NGC 6441: new insights from UV observations

Context. In this paper we present multiband optical and UV Hubble Space Telescope photometry of the two Galactic globular clusters NGC 6388 and NGC 6441. Aims. We investigate the properties of their anomalous horizontal branches in different photometric planes in order to shed light on the nature of the physical mechanism(s) responsible for the existence of an extended blue tail and of a slope in the horizontal branch, visible in all the color-magnitude diagrams. Methods. New photometric data have been collected and carefully reduced. Empirical data have been compared with updated stellar models of low-mass, metal-rich, He-burning structures, transformed to the observational plane with appropriate model atmospheres. Results. We have obtained the first UV color-magnitude diagrams for NGC 6388 and NGC 6441. These diagrams confirm previous results, obtained in optical bands, about the presence of a sizeable stellar population of extremely hot horizontal branch stars. At least in NGC 6388, we find a clear indication that at the hot end of the horizontal branch the distribution of stars forms a hook-like feature, closely resembling those observed in NGC 2808 and Omega Cen. We briefly review the theoretical scenarios that have been suggested for interpreting this observational feature. We also investigate the tilted horizontal branch morphology and provide further evidence that supports early suggestions that this feature cannot be interpreted as an effect of differential reddening. We show that a possible solution of the puzzle is to assume that a small fraction - ranging between 10-20% - of the stellar population in the two clusters is strongly helium-enriched (Y ~ 0.40 in NGC 6388 and Y ~ 0.35 in NGC 6441). The occurrence of a spread in the He abundance between the canonical value (Y ~ 0.26) and the quoted upper limits can significantly help in explaining the "whole" morphology of the horizontal branch and the pulsational properties of the variable stars in the target clusters

Galactic abundance gradients from Cepheids : On the iron abundance gradient around 10-12 kpc

Context: Classical Cepheids can be adopted to trace the chemical evolution of the Galactic disk since their distances can be estimated with very high accuracy. Aims: Homogeneous iron abundance measurements for 33 Galactic Cepheids located in the outer disk together with accurate distance determinations based on near-infrared photometry are adopted to constrain the Galactic iron gradient beyond 10 kpc. Methods: Iron abundances were determined using high resolution Cepheid spectra collected with three different observational instruments: ESPaDOnS@CFHT, Narval@TBL and [email protected] ESO/MPG telescope. Cepheid distances were estimated using near-infrared (J,H,K-band) period-luminosity relations and data from SAAO and the 2MASS catalog. Results: The least squares solution over the entire data set indicates that the iron gradient in the Galactic disk presents a slope of -0.052+/-0.003 dex/kpc in the 5-17 kpc range. However, the change of the iron abundance across the disk seems to be better described by a linear regime inside the solar circle and a flattening of the gradient toward the outer disk (beyond 10 kpc). In the latter region the iron gradient presents a shallower slope, i.e. -0.012+/-0.014 dex/kpc. In the outer disk (10-12 kpc) we also found that Cepheids present an increase in the spread in iron abundance. Current evidence indicates that the spread in metallicity depends on the Galactocentric longitude. Finally, current data do not support the hypothesis of a discontinuity in the iron gradient at Galactocentric distances of 10-12 kpc. Conclusions: The occurrence of a spread in iron abundance as a function of the Galactocentric longitude indicates that linear radial gradients should be cautiously treated to constrain the chemical evolution across the disk.Comment: 5 tables, 8 figures, Accepted in A&