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Within a sufficiently large cosmic volume, conservation of baryons implies asimple `closed box' view in which the sum of the baryonic components must equala constant fraction of the total enclosed mass. We present evidence fromRhapsody-G hydrodynamic simulations of massive galaxy clusters that theclosed-box expectation may hold to a surprising degree within the interior,non-linear regions of haloes. At a fixed halo mass, we find a significantanti-correlation between hot gas mass fraction and galaxy mass fraction (coldgas + 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-scatterproxy for total cluster mass. The fractional scatter of total baryon fractionscales approximately as $0.02 (\Delta_c/100)^{0.6}$, while the scatter ofeither gas mass or stellar mass is larger in magnitude and declines more slowlywith increasing radius. We discuss potential observational tests using clustersamples selected by optical and hot gas properties; the simulations suggestthat joint selection on stellar and hot gas has potential to achieve 5% scatterin total halo mass.

Rhapsody-G simulations: galaxy clusters as baryonic closed boxes and the covariance between hot gas and galaxies