Redshift estimation of clusters by wavelet decomposition of their Sunyaev–Zel'dovich morphology

A method for estimating redshifts of galaxy clusters based solely on resolved Sunyaev–Zel'dovich (SZ) images is proposed. Given a high‐resolution SZ cluster image (with a FWHM of ∼1 arcmin), the method indirectly measures its structure‐related parameters (amplitude, size, etc.) by fitting a model function to the higher‐order wavelet moments of the cluster's SZ morphology. The applicability and accuracy of the wavelet method are assessed by applying the method to maps of a set of clusters extracted from hydrodynamical simulations of cosmic structure formation. The parameters, derived by a fit to the spectrum of wavelet moments as a function of scale, are found to show a dependence on redshift z that is of the type x ( z ) = x 1 exp(− z / x 2 ) + x 3 , where the monotony of this functional behaviour and the non‐degeneracy of those parameters allow inversion and estimation of the redshift z . The average attainable accuracy in the z estimation relative to 1 + z is ∼4–5 per cent out to z ≃ 1.2 , which is comparable with photometric redshifts. For single‐frequency SZ interferometers, in which the ambient fluctuating CMB is the main noise source, the accuracy of the method drops slightly to 〈Δ  z /(1 + z )〉∼ 6–7 per cent. Other complications addressed include instrumental noise, cold cores and systematic trends in baryon fraction with cluster mass.