Rhapsody-G simulations: galaxy clusters as baryonic closed boxes and the
  covariance between hot gas and galaxies
  Within a sufficiently large cosmic volume, conservation of baryons implies a
simple `closed box' view in which the sum of the baryonic components must equal
a constant fraction of the total enclosed mass. We present evidence from
Rhapsody-G hydrodynamic simulations of massive galaxy clusters that the
closed-box expectation may hold to a surprising degree within the interior,
non-linear regions of haloes. At a fixed halo mass, we find a significant
anti-correlation between hot gas mass fraction and galaxy mass fraction (cold
gas + stars), with a rank correlation coefficient of -0.69 within $R_{500c}$.
Because of this anti-correlation, the total baryon mass serves as a low-scatter
proxy for total cluster mass. The fractional scatter of total baryon fraction
scales approximately as $0.02 (\Delta_c/100)^{0.6}$, while the scatter of
either gas mass or stellar mass is larger in magnitude and declines more slowly
with increasing radius. We discuss potential observational tests using cluster
samples selected by optical and hot gas properties; the simulations suggest
that joint selection on stellar and hot gas has potential to achieve 5% scatter
in total halo mass.
