Sunyaev-Zel'dovich scaling relations from a simple phenomenological
  model for galaxy clusters
  We build a simple, {\it top-down} model for the gas density and temperature
profiles for galaxy clusters. The gas is assumed to be in hydrostatic
equilibrium along with a component of non-thermal pressure taken from
simulations and the gas fraction approaches the cosmic mean value only at the
virial radius or beyond. The free parameters of the model are the slope and
normalisation of the concentration-mass relation, the gas polytropic index, and
slope and normalisation of the mass-temperature relation. These parameters can
be fixed from X-Ray and lensing observations. We compare our gas pressure
profiles to the recently proposed `Universal' pressure profile by
\cite{Arnaud09} and find very good agreement. We find that the
Sunyaev-Zel'dovich Effect (SZE) scaling relations between the integrated SZE
flux, $Y$, the cluster gas temperature, $T_{\rm sl}$, the cluster mass, $M_{\rm
tot}$, and the gas mass, $M_{\rm gas}$ are in excellent agreement with the
recently observed $r_{2500}$ SZE scaling relations by \cite{Bonamente08} and
$r_{500}$ relation by \cite{Arnaud09}. The gas mass fraction increases with
cluster mass and is given by $f_{\rm gas}(r_{500}) = 0.1324 + 0.0284
\,\rm{log}\, (\frac{M_{500}}{10^{15}h^{-1}M_\odot})$. This is within $10%$ of
observed $f_{\rm gas}(r_{500})$. The consistency between the global properties
of clusters detected in X-Rays and in SZE shows that we are looking at a common
population of clusters as a whole, and there is no deficit of SZE flux relative
to expectations from \xr scaling properties. Thus, it makes it easier to
compare and cross-calibrate clusters from upcoming \xr and SZE surveys.
