The Prospects for Constraining Dark Energy withFuture X-ray Cluster Gas Mass Fraction Measurements

We examine the ability of a future X-ray observatory, with capabilities similar to those planned for the Constellation-X mission, to constrain dark energy via measurements of the cluster X-ray gas mass fraction, fgas. We find that fgas measurements for a sample of {approx}500 hot (kT{approx}> 5keV), X-ray bright, dynamically relaxed clusters, to a precision of {approx}5 percent, can be used to constrain dark energy with a Dark Energy Task Force (DETF; Albrecht et al. 2006) figure of merit of 20-50. Such constraints are comparable to those predicted by the DETF for other leading, planned 'Stage IV' dark energy experiments. A future fgas experiment will be preceded by a large X-ray or SZ survey that will find hot, X-ray luminous clusters out to high redshifts. Short 'snapshot' observations with the new X-ray observatory should then be able to identify a sample of {approx}500 suitably relaxed systems. The redshift, temperature and X-ray luminosity range of interest has already been partially probed by existing X-ray cluster surveys which allow reasonable estimates of the fraction of clusters that will be suitably relaxed for fgas work to be made; these surveys also show that X-ray flux contamination from point sources is likely to be small for the majority of the targets of interest. Our analysis uses a Markov Chain Monte Carlo method which fully captures the relevant degeneracies between parameters and facilities the incorporation of priors and systematic uncertainties in the analysis. We explore the effects of such uncertainties, for scenarios ranging from optimistic to pessimistic. We conclude that the fgas experiment offers a competitive and complementary approach to the best other large, planned dark energy experiments. In particular, the fgas experiment will provide tight constraints on the mean matter and dark energy densities, with a peak sensitivity for dark energy work at redshifts midway between those of supernovae and baryon acoustic oscillation/weak lensing/cluster number counts experiments. In combination, these experiments should enable a precise measurement of the evolution of dark energy