On the Cluster Physics of Sunyaev-Zel'dovich Surveys II: Deconstructing
  the Thermal SZ Power Spectrum
  Secondary anisotropies in the cosmic microwave background are a
treasure-trove of cosmological information. Interpreting current experiments
probing them are limited by theoretical uncertainties rather than by
measurement errors. Here we focus on the secondary anisotropies resulting from
the thermal Sunyaev-Zel'dovich (tSZ) effect; the amplitude of which depends
critically on the average thermal pressure profile of galaxy groups and
clusters. To this end, we use a suite of SPH simulations that include radiative
cooling, star formation, supernova feedback, and energetic feedback from active
galactic nuclei (AGN). We examine in detail how the pressure profile depends on
cluster radius, mass, and redshift and provide an empirical fitting function.
We employ three different approaches for calculating the tSZ power spectrum: an
analytical approach that uses our pressure profile fit, a semi-analytical
method of pasting our pressure fit onto simulated clusters, and a direct
numerical integration of our simulated volumes. We demonstrate that the
detailed structure of the intracluster medium and cosmic web affect the tSZ
power spectrum. In particular, the substructure and asphericity of clusters
increase the tSZ power spectrum by 10-20% at ell ~2000-8000, with most of the
additional power being contributed by substructures. The contributions to the
power spectrum from radii larger than R_500 is ~ 20% at ell = 3000, thus
clusters interiors (r < R_500) dominate the power spectrum amplitude at these
angular scales.
