  Sunyaev-Zeldovich (SZ) surveys find massive clusters of galaxies by measuring
the inverse Compton scattering of cosmic microwave background off of
intra-cluster gas. The cluster selection function from such surveys is expected
to be nearly independent of redshift and cluster astrophysics. In this work, we
estimate the effect on the observed SZ signal of centrally-peaked gas density
profiles (cool cores) and radio emission from the brightest cluster galaxy
(BCG) by creating mock observations of a sample of clusters that span the
observed range of classical cooling rates and radio luminosities. For each
cluster, we make simulated SZ observations by the South Pole Telescope and
characterize the cluster selection function, but note that our results are
broadly applicable to other SZ surveys. We find that the inclusion of a cool
core can cause a change in the measured SPT significance of a cluster between
0.01% - 10% at z > 0.3, increasing with cuspiness of the cool core and angular
size on the sky of the cluster (i.e., decreasing redshift, increasing mass). We
provide quantitative estimates of the bias in the SZ signal as a function of a
gas density cuspiness parameter, redshift, mass, and the 1.4 GHz radio
luminosity of the central AGN. Based on this work, we estimate that, for the
Phoenix cluster (one of the strongest cool cores known), the presence of a cool
core is biasing the SZ significance high by ~ 6%. The ubiquity of radio
galaxies at the centers of cool core clusters will offset the cool core bias to
varying degrees.
