A Comparative Study of Local Galaxy Clusters: II: X-ray and SZ Scaling
  Relations
  We compare cluster scaling relations published for three different samples
selected via X-ray and Sunyaev-Zel'dovich (SZ) signatures. We find tensions
driven mainly by two factors: i) systematic differences in the X-ray cluster
observables used to derive the scaling relations, and ii) uncertainty in the
modeling of how the gas mass of galaxy clusters scales with total mass. All
scaling relations are in agreement after accounting for these two effects. We
describe a multivariate scaling model that enables a fully self-consistent
treatment of multiple observational catalogs in the presence of property
covariance, and apply this formalism when interpreting published results. The
corrections due to scatter and observable covariance can be significant. For
instance, our predicted Ysz-Lx scaling relation differs from that derived using
the naive "plug in" method by \approx 25%. Finally, we test the mass
normalization for each of the X-ray data sets we consider by applying a space
density consistency test: we compare the observed REFLEX luminosity function to
expectations from published Lx-M relations convolved with the mass function for
a WMAP7 flat \Lambda CDM model.
