Unfolding kinematics from galaxy spectra: A Bayesian method

Deconvolving line-of-sight velocity distributions (broadening functions) from absorption line spectra of galaxies is a problem with low signal to noise; we argue that for this reason more robust parameter estimates and confidence intervals would be obtained by treating the statistics in a more general way than in available deconvolution methods. We review the theory of Bayesian parameter fitting, which turns out to be formally equivalent to solving a statistical mechanics problem; least squares appears as the high S/N or low temperature limit. We then implement these ideas in a new deconvolution method, which allows one to reconstruct the broadening function either as some parametrized model, or nonparametrically, on a set of velocity bins. As an illustration, we analyze long-slit spectra of the major axes of NGC 4406 and NGC 1700. Both galaxies have been previously observed to have kinematically distinct cores, which we confirm. In addition we find the velocity distribution in the core of NGC 4406 to be significantly skewed in the direction of rotation.