Annealing a Follow-up Program: Improvement of the Dark Energy Figure of
  Merit for Optical Galaxy Cluster Surveys
  The precision of cosmological parameters derived from galaxy cluster surveys
is limited by uncertainty in relating observable signals to cluster mass. We
demonstrate that a small mass-calibration follow-up program can significantly
reduce this uncertainty and improve parameter constraints, particularly when
the follow-up targets are judiciously chosen. To this end, we apply a simulated
annealing algorithm to maximize the dark energy information at fixed
observational cost, and find that optimal follow-up strategies can reduce the
observational cost required to achieve a specified precision by up to an order
of magnitude. Considering clusters selected from optical imaging in the Dark
Energy Survey, we find that approximately 200 low-redshift X-ray clusters or
massive Sunyaev-Zel'dovich clusters can improve the dark energy figure of merit
by 50%, provided that the follow-up mass measurements involve no systematic
error. In practice, the actual improvement depends on (1) the uncertainty in
the systematic error in follow-up mass measurements, which needs to be
controlled at the 5% level to avoid severe degradation of the results; and (2)
the scatter in the optical richness-mass distribution, which needs to be made
as tight as possible to improve the efficacy of follow-up observations.
