Cosmology and astrophysics from relaxed galaxy clusters - IV: Robustly calibrating hydrostatic masses with weak lensing

This is the fourth in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Here, we use measurements of weak gravitational lensing from the Weighing the Giants project to calibrate Chandra X-ray measurements of total mass that rely on the assumption of hydrostatic equilibrium. This comparison of X-ray and lensing masses provides a measurement of the combined bias of X-ray hydrostatic masses due to both astrophysical and instrumental sources. Assuming a fixed cosmology, and within a characteristic radius (r_2500) determined from the X-ray data, we measure a lensing to X-ray mass ratio of 0.96 +/- 9% (stat) +/- 9% (sys). We find no significant trends of this ratio with mass, redshift or the morphological indicators used to select the sample. In accordance with predictions from hydro simulations for the most massive, relaxed clusters, our results disfavor strong, tens-of-percent departures from hydrostatic equilibrium at these radii. In addition, we find a mean concentration of the sample measured from lensing data of c_200 = $3.0_{-1.8}^{+4.4}$. Anticipated short-term improvements in lensing systematics, and a modest expansion of the relaxed lensing sample, can easily increase the measurement precision by 30--50%, leading to similar improvements in cosmological constraints that employ X-ray hydrostatic mass estimates, such as on Omega_m from the cluster gas mass fraction.Comment: 13 pages. Submitted to MNRAS. Comments welcom

New Constraints on Dark Energy from Chandra X-rayObservations of the Largest Relaxed Galaxy Clusters

We present constraints on the mean matter density, {Omega}{sub m}, dark energy density, {Omega}{sub DE}, and the dark energy equation of state parameter, w, using Chandra measurements of the X-ray gas mass fraction (fgas) in 42 hot (kT > 5keV), X-ray luminous, dynamically relaxed galaxy clusters spanning the redshift range 0.05 < z < 1.1. Using only the fgas data for the 6 lowest redshift clusters at z < 0.15, for which dark energy has a negligible effect on the measurements, we measure {Omega}{sub m}=0.28{+-}0.06 (68% confidence, using standard priors on the Hubble Constant, H{sub 0}, and mean baryon density, {Omega}{sub b}h{sup 2}). Analyzing the data for all 42 clusters, employing only weak priors on H{sub 0} and {Omega}{sub b}h{sup 2}, we obtain a similar result on {Omega}{sub m} and detect the effects of dark energy on the distances to the clusters at {approx}99.99% confidence, with {Omega}{sub DE}=0.86{+-}0.21 for a non-flat LCDM model. The detection of dark energy is comparable in significance to recent SNIa studies and represents strong, independent evidence for cosmic acceleration. Systematic scatter remains undetected in the f{sub gas} data, despite a weighted mean statistical scatter in the distance measurements of only {approx}5%. For a flat cosmology with constant w, we measure {Omega}{sub m}=0.28{+-}0.06 and w=-1.14{+-}0.31. Combining the fgas data with independent constraints from CMB and SNIa studies removes the need for priors on {Omega}{sub b}h{sup 2} and H{sub 0} and leads to tighter constraints: {Omega}{sub m}=0.253{+-}0.021 and w=-0.98{+-}0.07 for the same constant-w model. More general analyses in which we relax the assumption of flatness and/or allow evolution in w remain consistent with the cosmological constant paradigm. Our analysis includes conservative allowances for systematic uncertainties. The small systematic scatter and tight constraints bode well for future dark energy studies using the f{sub gas} method

Improved constraints on dark energy from Chandra X-ray observations of the largest relaxed galaxy clusters

We present constraints on the mean matter density, Omega_m, dark energy density, Omega_de, and the dark energy equation of state parameter, w, using Chandra measurements of the X-ray gas mass fraction (fgas) in 42 hot (kT>5keV), X-ray luminous, dynamically relaxed galaxy clusters spanning the redshift range 0.05<z<1.1. Using only the fgas data for the 6 lowest redshift clusters at z<0.15, for which dark energy has a negligible effect on the measurements, we measure Omega_m=0.28+-0.06 (68% confidence, using standard priors on the Hubble Constant, H_0, and mean baryon density, Omega_bh^2). Analyzing the data for all 42 clusters, employing only weak priors on H_0 and Omega_bh^2, we obtain a similar result on Omega_m and detect the effects of dark energy on the distances to the clusters at ~99.99% confidence, with Omega_de=0.86+-0.21 for a non-flat LCDM model. The detection of dark energy is comparable in significance to recent SNIa studies and represents strong, independent evidence for cosmic acceleration. Systematic scatter remains undetected in the fgas data, despite a weighted mean statistical scatter in the distance measurements of only ~5%. For a flat cosmology with constant w, we measure Omega_m=0.28+-0.06 and w=-1.14+-0.31. Combining the fgas data with independent constraints from CMB and SNIa studies removes the need for priors on Omega_bh^2 and H_0 and leads to tighter constraints: Omega_m=0.253+-0.021 and w=-0.98+-0.07 for the same constant-w model. More general analyses in which we relax the assumption of flatness and/or allow evolution in w remain consistent with the cosmological constant paradigm. Our analysis includes conservative allowances for systematic uncertainties. The small systematic scatter and tight constraints bode well for future dark energy studies using the fgas method. (Abridged)Comment: Published in MNRAS. 20 pages, 11 figures. The data and analysis code (in the form of a patch to CosmoMC) are now available at http://www.stanford.edu/~drapetti/fgas_module

The Observed Growth of Massive Galaxy Clusters I: Statistical Methods and Cosmological Constraints

(Abridged) This is the first of a series of papers in which we derive simultaneous constraints on cosmological parameters and X-ray scaling relations using observations of the growth of massive, X-ray flux-selected galaxy clusters. Our data set consists of 238 clusters drawn from the ROSAT All-Sky Survey, and incorporates extensive follow-up observations using the Chandra X-ray Observatory. Here we describe and implement a new statistical framework required to self-consistently produce simultaneous constraints on cosmology and scaling relations from such data, and present results on models of dark energy. In spatially flat models with a constant dark energy equation of state, w, the cluster data yield Omega_m=0.23 +- 0.04, sigma_8=0.82 +- 0.05, and w=-1.01 +- 0.20, marginalizing over conservative allowances for systematic uncertainties. These constraints agree well and are competitive with independent data in the form of cosmic microwave background (CMB) anisotropies, type Ia supernovae (SNIa), cluster gas mass fractions (fgas), baryon acoustic oscillations (BAO), galaxy redshift surveys, and cosmic shear. The combination of our data with current CMB, SNIa, fgas, and BAO data yields Omega_m=0.27 +- 0.02, sigma_8=0.79 +- 0.03, and w=-0.96 +- 0.06 for flat, constant w models. For evolving w models, marginalizing over transition redshifts in the range 0.05-1, we constrain the equation of state at late and early times to be respectively w_0=-0.88 +- 0.21 and w_et=-1.05 +0.20 -0.36. The combined data provide constraints equivalent to a DETF FoM of 15.5. Our results highlight the power of X-ray studies to constrain cosmology. However, the new statistical framework we apply to this task is equally applicable to cluster studies at other wavelengths.Comment: 16 pages, 7 figures. v4: final version (typographic corrections). Results can be downloaded at https://www.stanford.edu/group/xoc/papers/xlf2009.htm

New constraints on dark energy from the observed growth of the most X-ray luminous galaxy clusters

We present constraints on the mean matter density, Omega_m, the normalization of the density fluctuation power spectrum, sigma_8, and the dark-energy equation-of-state parameter, w, obtained from measurements of the X-ray luminosity function of the largest known galaxy clusters at redshifts z<0.7, as compiled in the Massive Cluster Survey (MACS) and the local BCS and REFLEX galaxy cluster samples. Our analysis employs an observed mass-luminosity relation, calibrated by hydrodynamical simulations, including corrections for non-thermal pressure support and accounting for the presence of intrinsic scatter. Conservative allowances for all known systematic uncertainties are included, as are standard priors on the Hubble constant and mean baryon density. We find Omega_m=0.28 +0.11 -0.07 and sigma_8=0.78 +0.11 -0.13 for a spatially flat, cosmological-constant model, and Omega_m=0.24 +0.15 -0.07, sigma_8=0.85 +0.13 -0.20 and w=-1.4 +0.4 -0.7 for a flat, constant-w model. Future work improving our understanding of redshift evolution and observational biases affecting the mass--X-ray luminosity relation have the potential to significantly tighten these constraints. Our results are consistent with those from recent analyses of type Ia supernovae, cosmic microwave background anisotropies, the X-ray gas mass fraction of relaxed galaxy clusters, baryon acoustic oscillations and cosmic shear. Combining the new X-ray luminosity function data with current supernova, cosmic microwave background and cluster gas fraction data yields the improved constraints Omega_m=0.269 +- 0.016, sigma_8=0.82 +- 0.03 and w=-1.02 +- 0.06. (Abridged)Comment: Submitted to MNRAS. 15 pages, 15 figures. v2: Improved modeling of the mass-luminosity relation, including additional systematic allowances for evolution in the scatter and non-thermal pressure support. Constraints are somewhat weaker, but overall conclusions are unchanged

Cosmology with X-ray Cluster Baryons

X-ray cluster measurements interpreted with a universal baryon/gas mass fraction can theoretically serve as a cosmological distance probe. We examine issues of cosmological sensitivity for current (e.g. Chandra X-ray Observatory, XMM-Newton) and next generation (e.g. Con-X, XEUS) observations, along with systematic uncertainties and biases. To give competitive next generation constraints on dark energy, we find that systematics will need to be controlled to better than 1% and any evolution in f_gas (and other cluster gas properties) must be calibrated so the residual uncertainty is weaker than (1+z)^{0.03}.Comment: 6 pages, 5 figures; v2: 13 pages, substantial elaboration and reordering, matches JCAP versio

The Observed Growth of Massive Galaxy Clusters II: X-ray Scaling Relations

(Abridged) This is the second in a series of papers in which we derive simultaneous constraints on cosmology and X-ray scaling relations using observations of massive, X-ray flux-selected galaxy clusters. The data set consists of 238 clusters drawn from the ROSAT All-Sky Survey with 0.1-2.4 keV luminosities >2.5e44 erg/second, and incorporates extensive follow-up observations using the Chandra X-ray Observatory. Our analysis accounts self-consistently for all selection effects, covariances and systematic uncertainties. Here we describe the reduction of the follow-up X-ray observations, present results on the cluster scaling relations, and discuss their implications. Our constraints on the luminosity-mass and temperature-mass relations, measured within r_500, lead to three important results. First, the data support the conclusion that excess heating of the intracluster medium has altered its thermodynamic state from that expected in a simple, gravitationally dominated system; however, this excess heating is primarily limited to the central regions of clusters (r<0.15r_500). Second, the intrinsic scatter in the center-excised luminosity-mass relation is remarkably small, being undetected at the <10% level in current data; for the hot, massive clusters under investigation, this scatter is smaller than in either the temperature-mass or Y_X-mass relations (10-15%). Third, the evolution with redshift of the scaling relations is consistent with the predictions of simple, self-similar models of gravitational collapse, indicating that the mechanism responsible for heating the central regions of clusters was in operation before redshift 0.5 (the limit of our data) and that its effects on global cluster properties have not evolved strongly since then.Comment: 25 pages, 7 figures, 14 tables. v3: final version (typographic corrections). Results can be downloaded at https://www.stanford.edu/group/xoc/papers/xlf2009.htm

The Hubble constant and dark energy from cosmological distance measures

We study how the determination of the Hubble constant from cosmological distance measures is affected by models of dark energy and vice versa. For this purpose, constraints on the Hubble constant and dark energy are investigated using the cosmological observations of cosmic microwave background, baryon acoustic oscillations and type Ia suprenovae. When one investigates dark energy, the Hubble constant is often a nuisance parameter, thus it is usually marginalized over. On the other hand, when one focuses on the Hubble constant, simple dark energy models such as a cosmological constant and a constant equation of state are usually assumed. Since we do not know the nature of dark energy yet, it is interesting to investigate the Hubble constant assuming some types of dark energy and see to what extent the constraint on the Hubble constant is affected by the assumption concerning dark energy. We show that the constraint on the Hubble constant is not affected much by the assumption for dark energy. We furthermore show that this holds true even if we remove the assumption that the universe is flat. We also discuss how the prior on the Hubble constant affects the constraints on dark energy and/or the curvature of the universe.Comment: 45 pages, 15 figure