Optimizing observational strategy for future f(gas) constraints

The Planck cluster catalog is expected to contain of order one thousand galaxy clusters, both newly discovered and previously known, detected through the Sunyaev-Zeldovich effect over the redshift range 0 less than or similar to z less than or similar to 1. Follow-up x-ray observations of a dynamically relaxed subsample of newly discovered Planck clusters will improve constraints on the dark energy equation of state found through measurement of the cluster gas mass fraction (f(gas)). In view of follow-up campaigns with XMM-Newton and Chandra satellites, we determine the optimal redshift distribution of a cluster sample to most tightly constrain the dark energy equation of state. The distribution is nontrivial even for the standard w(0)-w(a) parametrization. We then determine how much the combination of expected data from the Planck satellite and f(gas) data will be able to constrain the dark energy equation of state. Our analysis employs a Markov Chain Monte Carlo method as well as a Fisher Matrix analysis. With a suitably large program of observational time to observe only hot relaxed clusters, we find that these upcoming data would be able to improve the figure of merit by at least a factor two.