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 FWHM of approx. 1 arcmin), the method indirectly measures its structure related parameters (amplitude, size, etc.) by fitting a model function to the higher order wavelet momenents of the cluster's SZ morphology. The applicability and accuracy of the wavelet method is assessed by applying it 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 approx. 4-5% out to z = 1.2, which is comparable to photometric redshifts. For single-frequency SZ interferometers, where the ambient fluctuating CMB is the main noise source, the accuracy of the method drops slightly to <Delta z/(1+z)> = 6-7%.