Optimal estimates of line-of-sight velocity distributions from absorption line spectra of galaxies: nuclear discs in elliptical galaxies

Abstract

We have developed methods for extracting line-of-sight velocity distributions (LOSVDs) from the broadening of absorption lines in early-type galaxies. These methods operate exclusively in pixel space, they use the full information content of the data, they permit a rigorous treatment of the errors, and they relax the standard a priori assumption that the LOSVD is a Gaussian. We have considered two problems: optimal noise filtering for model-independent extraction of the LOSVD, subject only to the constraint that it be bandwidth-limited; and optimal parameter estimation when the LOSVD can be assumed to belong to a parametrized family of models, for example, single or double Gaussians. The latter broadening model is of particular interest when a disc-like, rotating component is suspected to coexist with a dynamically hot spheroid. We find that for typical instrumental set-ups a signal-to-noise ratio (S/N) of 30 per pixel is required to discriminate between such a two-component LOSVD and a single Gaussian. Monte-Carlo simulations demonstrate that mismatch of spectral features between galaxy and template can produce significant systematic errors in the reconstructed LOSVD. These errors are substantially reduced if an optimally matched composite template is used. Applying our methods to two elliptical galaxies with kinematically distinct cores (NGC 5322 and NGC 3610), we find LOSVDs which deviate significantly from a Gaussian. Interpreting these LOSVDs in terms of a disc spheroid model, we find order-of-magnitude variations in the degree of rotational support in the discs; |$v/\sigma \approx 1.4$| in NGC 5322, whereas |$v/\sigma \approx 4.5$| in NGC 3610. By modelling NGC 5322 in some detail, we show explicitly that a small disc embedded in the spheroid is a viable explanation for all the available photometric and kinematic information on this galaxy.