Baryon Content in a Sample of 91 Galaxy Clusters Selected by the South
  Pole Telescope at 0.2 < z < 1.25
  We estimate total mass ($M_{500}$), intracluster medium (ICM) mass
($M_{\mathrm{ICM}}$) and stellar mass ($M_{\star}$) in a Sunyaev-Zel'dovich
effect (SZE) selected sample of 91 galaxy clusters with masses
$M_{500}\gtrsim2.5\times10^{14}M_{\odot}$ and redshift $0.2 < z < 1.25$ from
the 2500 deg$^2$ South Pole Telescope SPT-SZ survey. The total masses $M_{500}$
are estimated from the SZE observable, the ICM masses $M_{\mathrm{ICM}}$ are
obtained from the analysis of $Chandra$ X-ray observations, and the stellar
masses $M_{\star}$ are derived by fitting spectral energy distribution
templates to Dark Energy Survey (DES) $griz$ optical photometry and $WISE$ or
$Spitzer$ near-infrared photometry. We study trends in the stellar mass, the
ICM mass, the total baryonic mass and the cold baryonic fraction with cluster
mass and redshift. We find significant departures from self-similarity in the
mass scaling for all quantities, while the redshift trends are all
statistically consistent with zero, indicating that the baryon content of
clusters at fixed mass has changed remarkably little over the past $\approx9$
Gyr. We compare our results to the mean baryon fraction (and the stellar mass
fraction) in the field, finding that these values lie above (below) those in
cluster virial regions in all but the most massive clusters at low redshift.
Using a simple model of the matter assembly of clusters from infalling groups
with lower masses and from infalling material from the low density environment
or field surrounding the parent halos, we show that the measured mass trends
without strong redshift trends in the stellar mass scaling relation could be
explained by a mass and redshift dependent fractional contribution from field
material. Similar analyses of the ICM and baryon mass scaling relations provide
evidence for the so-called "missing baryons" outside cluster virial regions.
