A NEW METHOD FOR OBTAINING STELLAR VELOCITY DISTRIBUTIONS FROM ABSORPTION-LINE SPECTRA - UNRESOLVED GAUSSIAN DECOMPOSITION

We have developed a new algorithm for extracting the line-of-sight vel ocity distributions (LOSVDs) of galaxies from the broadening of absorp tion lines in their spectra relative to those of a stellar 'template'. This method models the LOSVD as the sum of a set of Gaussian distribu tions uniformly spaced in velocity. By choosing the dispersion, DELTAu psilon, of these Gaussians so that the separate components are unresol ved according to the Rayleigh criterion, such a sum can model any LOSV D that is smooth on scales smaller than DELTAupsilon. The velocity sca le on which the LOSVD is forced to be smooth is thus set explicitly by the user. The algorithm then involves solving for the amplitudes of t he individual components to produce the LOSVD that, when convolved wit h the stellar template, best reproduces the observed galaxy spectrum i n a least-squares sense. This procedure is an example of quadratic pro gramming for which efficient algorithms exist, and, since all of the c onvolutions in the analysis involve similar Gaussians, the computation al expense in calculating the model is also small. The physical constr aint that the LOSVD must be non-negative can be readily included in th e quadratic programming, and the method allows an explicit treatment o f the errors in the derived LOSVD. Monte Carlo tests show that this al gorithm can, indeed, efficiently extract a wide range of LOSVDs from a bsorption-line spectra with attainable signal-to-noise ratios. Applica tion to the early-type disc galaxy UGC 12591 illustrates the potential of this approach for constraining dynamical models of galaxies.