We introduce STECKMAP (STEllar Content and Kinematics via Maximum A Posteriori likelihood), a method for recovering the kinematic properties of a galaxy simultaneously with its stellar content from integrated light spectra. It is an extension of STECMAP (presented recently by Ocvirk et al.) to the general case where the velocity distribution of the underlying stars is also unknown. 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 priori conditions that we use are positivity and the requirement that the solution is smooth enough. The smoothness parameter can be set by generalized cross-validation according to the level of noise in the data in order to avoid overinterpretation.

We use single stellar populations (SSPs) from PÉGASE-HR (R= 10000, λ= 4000-6800 Å, from Le Borgne et al.) to test the method through realistic simulations. Non-Gaussianities in LOSVDs are reliably recovered with signal-to-noise ratio (SNR) as low as 20 per 0.2 Åpixel. 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. 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 disc 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.