We introduce STECKMAP (STEllar Content and Kinematics via Maximum A Posteriori), a method to recover the kinematical properties of a galaxy simultaneously with its stellar content from integrated light spectra. It is an extension of STECMAP (astro-ph/0505209) to the general case where the velocity distribution of the underlying stars is also unknown. %and can be used as is for the analysis of large sets of data. The reconstructions of the stellar age distribution, the age-metallicity relation, and the Line-Of-Sight Velocity Distribution (LOSVD) are all non-parametric, i.e. no specific shape is assumed. The only a propri we use are positivity and the requirement that the solution is smooth enough. The smoothness parameter can be set by GCV according to the level of noise in the data in order to avoid overinterpretation. We use single stellar populations (SSP) from PEGASE-HR (R=10000, lambda lambda = 4000-6800 Angstrom, Le Borgne et al. 2004) to test the method through realistic simulations. Non-Gaussianities in LOSVDs are reliably recovered with SNR as low as 20 per 0.2 Angstrom pixel. It turns out that the recovery of the stellar content is not degraded by the simultaneous recovery of the kinematic distribution, so that the resolution in age and error estimates given in Ocvirk et al. 2005 remain appropriate when used with STECKMAP. We also explore the case of age-dependent kinematics (i.e. when each stellar component has its own LOSVD). We separate the bulge and disk components of an idealized simplified spiral galaxy in integrated light from high quality pseudo data (SNR=100 per pixel, R=10000), and constrain the kinematics (mean projected velocity, projected velocity dispersion) and age of both components.
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