SZE Observables, Pressure Profiles and Center Offsets in Magneticum
  Simulation Galaxy Clusters
  We present a detailed study of the galaxy cluster thermal \ac{sze} signal $Y$
and pressure profiles using {\it Magneticum} Pathfinder hydrodynamical
simulations. With a sample of 50,000 galaxy clusters ($M_{\rm
500c}>1.4\times10^{14} \rm M_{\odot}$) out to $z=2$, we find significant
variations in the shape of the pressure profile with mass and redshift and
present a new generalized NFW model that follows these trends. We show that the
thermal pressure at $R_{\rm 500c}$ accounts for only 80~percent of the pressure
required to maintain hydrostatic equilibrium, and therefore even idealized
hydrostatic mass estimates would be biased at the 20~percent level. We compare
the cluster \ac{sze} signal extracted from a sphere with different virial-like
radii, a virial cylinder within a narrow redshift slice and the full light
cone, confirming small scatter ($\sigma_{\ln Y}\simeq 0.087$) in the sphere and
showing that structure immediately surrounding clusters increases the scatter
and strengthens non self-similar redshift evolution in the cylinder.
Uncorrelated large scale structure along the line of sight leads to an increase
in the \ac{sze} signal and scatter that is more pronounced for low mass
clusters, resulting in non self-similar trends in both mass and redshift and a
mass dependent scatter that is $\sim0.16$ at low masses. The scatter
distribution is consistent with log-normal in all cases. We present a model of
the offsets between the center of the gravitational potential and the \ac{sze}
center that follows the variations with cluster mass and redshift.
