Probing cosmology and galaxy cluster structure with the Sunyaev-Zel'dovich decrement versus X-ray temperature scaling relation

Scaling relations among galaxy cluster observables, which will become available in large future samples of galaxy clusters, could be used to constrain not only cluster structure, but also cosmology. We study the utility of this approach, employing a physically motivated parametric model to describe cluster structure and applying it to the expected relation between the Sunyaev-Zel'dovich decrement (S_ν) and the emission-weighted X-ray temperature (T_ew). The slope and normalization of the entropy profile, the concentration of the dark matter potential, the pressure at the virial radius and the level of non-thermal pressure support as well as the mass and redshift dependence of these quantities are described by free parameters. With a suitable choice of fiducial parameter values, the cluster model satisfies several existing observational constraints. We employ a Fisher matrix approach to estimate the joint errors on cosmological and cluster structure parameters from a measurement of S_ν versus T_ew in a future survey. We find that different cosmological parameters affect the scaling relation differently: predominantly through the baryon fraction (Ω_m and Ω_b), the virial overdensity (w₀ and w_a for low-z clusters) and the angular diameter distance (w₀ and w_a for high-z clusters; Ω_DE and h). We find that the cosmology constraints from the scaling relation are comparable to those expected from the number counts (dN/dz) of the same clusters. The scaling-relation approach is relatively insensitive to selection effects and it offers a valuable consistency check; combining the information from the scaling relation and dN/dz is also useful to break parameter degeneracies and help disentangle cluster physics from cosmology. Our work suggests that scaling relations should be a useful component in extracting cosmological information from large future cluster surveys.