Bias from gas inhomogeneities in the pressure profiles as measured from X-ray and SZ observations. (arXiv:1211.3358v1 [astro-ph.CO])

Bias from gas inhomogeneities in the pressure profiles as measured from X-ray and SZ observations. (arXiv:1211.3358v1 [astro-ph.CO]):
X-ray observations of galaxy clusters provide emission measure weighted
spectra, arising from a range of density and temperature fluctuations in the
intra-cluster medium (ICM). This is fitted to a single temperature plasma
emission model to provide an estimate of the gas density and temperature, which
are sensitive to the gas inhomogeneities. Therefore, X-ray observations yield a
potentially biased estimate of the thermal gas pressure, P_X. At the same time
Sunyaev-Zeldovich (SZ) observations directly measure the integrated gas
pressure, P_SZ. If the X-ray pressure profiles are strongly biased with respect
to to the SZ, then one has the possibility to probe the gas inhomogeneities,
even at scales unresolved by the current generation of telescopes. At the same
time, a weak bias has implications for the use of mass proxies like Y_SZ and
Y_X as cosmological probes. In this paper we investigate the dependence of the
bias, P_X(r)/P_SZ(r)-1, on the characteristics of fluctuations in the ICM
taking into account the correlation between temperature and density
fluctuations. We made a simple prediction of the irreducible bias in idealised
X-ray vs SZ observations using multi-temperature plasma emission model. We also
provide a simple fitting form to estimate the bias given the distribution of
fluctuations. Analysing a sample of 16 simulated clusters extracted from
hydrodynamical simulations, we find that the median value of bias is within
+/-3% within R_500, it decreases to -5% at R_500 < r < 1.5R_500 and then rises
back to ~0% at > 2R_500. The scatter of b_P(r) between individual relaxed
clusters is small -- at the level of <0.03 within R_500, but turns
significantly larger (0.25) and highly skewed at r > 1.5 R_500. Unrelaxed
clusters display larger scatter (both from radius to radius and from cluster to
cluster). Nevertheless, the bias remains within +/-20% within 0.8R_500 for all
clusters.