Cosmology and astrophysics from relaxed galaxy clusters - II. Cosmological constraints

This is the second in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. The data set employed here consists of Chandra observations of 40 such clusters, identified in a comprehensive search of the Chandra archive for hot (kT greater than or similar to 5 keV), massive, morphologically relaxed systems, as well as high-quality weak gravitational lensing data for a subset of these clusters. Here we present cosmological constraints from measurements of the gas mass fraction, f(gas), for this cluster sample. By incorporating a robust gravitational lensing calibration of the X-ray mass estimates, and restricting our measurements to the most self-similar and accurately measured regions of clusters, we significantly reduce systematic uncertainties compared to previous work. Our data for the first time constrain the intrinsic scatter in f(gas), 7.4 +/- 2.3 per cent in a spherical shell at radii 0.8-1.2 r(2500) (similar to 1/4 of the virial radius), consistent with the expected level of variation in gas depletion and non-thermal pressure for relaxed clusters. From the lowest redshift data in our sample, five clusters at z < 0.16, we obtain a constraint on a combination of the Hubble parameter and cosmic baryon fraction, h(3/2) Omega(b)/Omega(m) = 0.089 +/- 0.012, that is insensitive to the nature of dark energy. Combining this with standard priors on h and (b)h(2) provides a tight constraint on the cosmic matter density, Omega(m) = 0.27 +/- 0.04, which is similarly insensitive to dark energy. Using the entire cluster sample, extending to z > 1, we obtain consistent results for Omega(m) and interesting constraints on dark energy: Omega(Lambda) =0.65(-0.22)(+0.17) for non-flat Lambda CDM (cosmological constant) models, and w = -0.98 +/- 0.26 for flat models with a constant dark energy equation of state. Our results are both competitive and consistent with those from recent cosmic microwave background, Type Ia supernova and baryon acoustic oscillation data. We present constraints on more complex models of evolving dark energy from the combination of f(gas) data with these external data sets, and comment on the possibilities for improved f(gas) constraints using current and next-generation X-ray observatories and lensing data.