R. W. Schmidt

Constraints on dark energy from Chandra observations 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, � m, dark energy density, � DE, and the dark energy equation of state parameter, w, using Chandra measurements of the X-ray gas mass fraction (fgas )i n 42 hot (kT > 5 keV), X-ray luminous, dynamically relaxed galaxy clusters spanning the redshift range 0.05 < z < 1.1. Using only the fgas data for the six lowest redshift clusters at z < 0.15, for which dark energy has a negligible effect on the measurements, we measurem = 0.28 ± 0.06 (68 per cent confidence limits, using standard priors on the Hubble constant, H0, and mean baryon density, � b h 2 ). Analysing the data for all 42 clusters, employ- ing only weak priors on H0 andb h 2 , we obtain a similar result onm and a detection of the effects of dark energy on the distances to the clusters at ∼99.99 per cent confidence, with � DE = 0.86 ± 0.21 for a non-flatCDM model. The detection of dark energy is comparable in significance to recent type Ia supernovae (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 per cent. For a flat cosmology with a constant dark energy equation of state, we measurem = 0.28 ± 0.06 and w =− 1.14 ± 0.31. Combining the fgas data with independent constraints from cosmic mi- crowave background and SNIa studies removes the need for priors onb h 2 and H0 and leads to tighter constraints: � m = 0.253 ± 0.021 and w =− 0.98 ± 0.07 for the same constant-w model. Our most general analysis allows the equation of state to evolve with redshift. Marginalizing over possible transition redshifts 0.05 < zt < 1, the combined fgas + CMB + SNIa data set constrains the dark energy equation of state at late and early times to be w0 =− 1.05 ± 0.29 and wet =− 0.83 ± 0.46, respectively, in agreement with the cosmological constant paradigm. Relaxing the assumption of flatness weakens the constraints on the equation of state by only a factor of ∼2. Our analysis includes conservative allowances for systematic uncertainties as- sociated with instrument calibration, cluster physics and data modelling. The measured small systematic scatter, tight constraint onm and powerful constraints on dark energy from the fgas data bode well for future dark energy studies using the next generation of powerful X-ray observatories, such as Constellation-X.

A deep Chandra observation of the Perseus cluster: shocks and ripples

We present preliminary results from a deep observation lasting almost 200 ks of the centre of the Perseus cluster of galaxies around NGC 1275. The X-ray surface brightness of the intracluster gas beyond the inner 20 kpc, which contains the inner radio bubbles, is very smooth apart from some low-amplitude quasi-periodic ripples. A clear density jump at a radius of 24 kpc to the north-east, about 10 kpc out from the bubble rim, appears to be due to a weak shock driven by the northern radio bubble. A similar front may exist around both inner bubbles but is masked elsewhere by rim emission from bright cooler gas. The continuous blowing of bubbles by the central radio source, leading to the propagation of weak shocks and viscously dissipating sound waves seen as the observed fronts and ripples, gives a rate of working which balances the radiative cooling within the inner 50 kpc of the cluster core.

The X-ray virial relations for relaxed lensing clusters observed with Chandra

We examine the relations linking mass, X-ray temperature and bolometric luminosity for a sample of luminous, relatively relaxed clusters of galaxies observed with the Chandra Observatory, for which independent confirmation of the mass results is available from gravitational lensing studies. Within radii corresponding to a fixed overdensity with respect to the critical density at the redshifts of the clusters, the observed temperature profiles, scaled in units of T2500 and r2500, exhibit an approximately universal form which rises within and then remains approximately constant out to r2500. We obtain best-fitting slopes for the mass–temperature and temperature–luminosity relations consistent with the predictions from simple scaling arguments i.e. and , respectively. We confirm the presence of a systematic offset of ∼40 per cent between the normalizations of the observed and predicted mass–temperature relations for both SCDM and ΛCDM cosmologies.

Cosmological constraints from the X-ray gas mass fraction in relaxed lensing clusters observed with Chandra

We present precise measurements of the X-ray gas mass fraction for a sample of luminous, relatively relaxed clusters of galaxies observed with the Chandra Observatory, for which independent confirmation of the mass results is available from gravitational lensing studies. Parameterizing the total (luminous plus dark matter) mass profiles using the model of Navarro, Frenk & White (1997), we show that the X-ray gas mass fractions in the clusters asymptote towards an approximately constant value at a radius r_2500, where the mean interior density is 2500 times the critical density of the Universe at the redshifts of the clusters. Combining the Chandra results on the X-ray gas mass fraction and its apparent redshift dependence with recent measurements of the mean baryonic matter density in the Universe and the Hubble Constant determined from the Hubble Key Project, we obtain a tight constraint on the mean total matter density of the Universe, Omega_m = 0.30^{+0.04}_{-0.03}, and measure a positive cosmological constant, Omega_Lambda = 0.95^{+0.48}_{-0.72}. Our results are in good agreement with recent, independent findings based on analyses of anisotropies in the cosmic microwave background radiation, the properties of distant supernovae, and the large-scale distribution of galaxies.

Cosmological constraints from the local X-ray luminosity function of the most X-ray-luminous galaxy clusters

We present precise constraints on the normalization of the power spectrum of mass fluctuations in the nearby Universe, σ 8, as a function of the mean local matter density, � m. Using the observed local X-ray luminosity function of galaxy clusters from the extended BCS and REFLEX studies, a mass‐luminosity relation determined from Chandra and ROSAT X-ray data and weak gravitational lensing observations, and the mass function predicted by the Hubble Volume simulations of Evrard et al., we obtain σ 8 = (0.508 ± 0.019) � −(0.253±0.024) ,

The dark matter haloes of massive, relaxed galaxy clusters observed with Chandra

We use the Chandra X-ray Observatory to study the dark matter halos of 34 massive, dynamically relaxed galaxy clusters, spanning the redshift range 0.06 < z < 0.7. The observed dark matter and total mass (dark-plus-luminous matter) profiles can be approximated by the Navarro Frenk & White (hereafter NFW) model for cold dark matter (CDM) halos; for {approx} 80 percent of the clusters, the NFW model provides a statistically acceptable fit. In contrast, the singular isothermal sphere model can, in almost every case, be completely ruled out. We observe a well-defined mass-concentration relation for the clusters with a normalization and intrinsic scatter in good agreement with the predictions from simulations. The slope of the mass-concentration relation, c {infinity} M{sub vir}{sup a}/(1 + z){sup b} with a = -0.41 {+-} 0.11 at 95 percent confidence, is steeper than the value a {approx} -0.1 predicted by CDM simulations for lower mass halos. With the slope a included as a free fit parameter, the redshift evolution of the concentration parameter, b = 0.54 {+-} 0.47 at 95 percent confidence, is also slower than, but marginally consistent with, the same simulations (b {approx} 1). Fixing a {approx} -0.1 leads to an apparent evolution that is significantly slower, b = 0.20 {+-} 0.45, although the goodness of fit in this case is significantly worse. Using a generalized NFW model, we find the inner dark matter density slope, a, to be consistent with unity at 95 percent confidence for the majority of clusters. Combining the results for all clusters for which the generalized NFW model provides a good description of the data, we measure ? = 0.88 {+-} 0.29 at 95 percent confidence, in agreement with CDM model predictions.

Mapping small-scale temperature and abundance structures in the core of the Perseus cluster

We report further results from a 191-ks Chandra observation of the core of the Perseus cluster, Abell 426. The emission-weighted temperature and abundance structures are mapped in detail. There are temperature variations down to ∼ 1 kpc in the brightest regions. Globally, the strongest X-ray surface brightness features appear to be caused by temperature changes. Density and temperature changes conspire to give approximate azimuthal balance in pressure showing that the gas is in hydrostatic equilibrium. Si, S, Ar, Ca, Fe and Ni abundance profiles rise inwards from about 100 kpc, peaking at about 30-40 kpc. Most of these abundances drop inwards of the peak, but Ne shows a central peak, all of which may be explained by resonance scattering. There is no evidence for a widespread additional cooler temperature component in the cluster with a temperature greater than a factor of 2 from the local temperature. There is, however, evidence for a widespread hard component which may be non-thermal. The temperature and abundance of gas in the cluster are observed to be correlated in a manner similar to that found between clusters.

Chandra temperature and metallicity maps of the Perseus cluster core

We present temperature and metallicity maps of the Perseus cluster core obtained with the Chandra X-ray Observatory. We find an overall temperature rise from ∼3.0 keV in the core to ∼5.5 keV at 120 kpc and a metallicity profile that rises slowly from ∼0.5 solar to ∼0.6 solar inside 60 kpc, but drops to ∼0.4 solar at 120 kpc. Spatially resolved spectroscopy in small cells shows that the temperature distribution in the Perseus cluster is not symmetrical. There is a wealth of structure in the temperature map on scales of ∼10 arcsec (5.2 kpc) showing swirliness and a temperature rise that coincides with a sudden surface brightness drop in the X-ray image. We obtain a metallicity map of the Perseus cluster core and find that the spectra extracted from the two central X-ray holes as well as the western X-ray hole are best-fit by gas with higher temperature and higher metallicity than is found in the surroundings of the holes. A spectral deprojection analysis suggests, however, that this is due to a projection effect; for the northern X-ray hole we find tight limits on the presence of an isothermal component in the X-ray hole, ruling out volume-filling X-ray gas with temperatures below 11 keV at 3σ.

Chandra observations of RX J1347.5−1145: the distribution of mass in the most X‐ray‐luminous galaxy cluster known

We present Chandra observations of RX J1347.5−1145, the most X-ray-luminous cluster of galaxies known. We report the discovery of a region of relatively hot, bright X-ray emission, located approximately 20 arcsec to the south-east of the main X-ray peak at a position consistent with the region of enhanced Sunyaev‐Zel’dovich effect reported recently by Komatsu et al. We suggest that this region contains shocked gas resulting from a recent subcluster merger event. Excluding the data for the south-east quadrant, the cluster appears relatively relaxed. The X-ray gas temperature rises from kT ∼ 6 keV within the central 25 h −1 kpc radius to a mean value of ∼16 keV between 0.1 and 0.5 h −1 Mpc. The mass profile for the relaxed regions of the cluster, determined under the assumption of hydrostatic equilibrium, can be parametrized by a Navarro, Frenk and White model with a scale radius rs ∼ 0.4 h −1 Mpc and a concentration parameter c ∼ 6. The best-fitting Chandra mass model is in good agreement with independent measurements from weak gravitational lensing studies. Strong lensing data for the central regions of the cluster can also be explained by the introduction of an additional mass clump centred on the second brightest galaxy. We argue that this galaxy is likely to have been the dominant galaxy of the recently merged subcluster.