Stellar populations and their kinematics from high and medium resolution spectra: mixed inversions P. Ocvirk, A. Lançon, C. Pichon, Observatoire de Strasbourg P.Prugniel, E.Thiébaut (Lyon), D. Le Borgne, B. Rocca-Volmerange, M.Fioc (Paris), E. Soubiran (Bordeaux) We present inversion techniques which aim at recovering the stellar content (age, metallicity, extinction) and kinematics of a stellar population from its observed high resolution absorption line spectrum. The originality of the mixed inversion technique is its potential to recover both stellar content and kinematics at the same time. These techniques use new synthetic high resolution spectra produced by PEGASE and minimization algorithms. The mixed inversions are safe enough to be applied to large ensembles of data, which could not be interpreted without such automated methods. We apply them to SDSS data and to mock data representing the bulge and disc population of the inner region of spiral galaxies. Introduction The high resolution spectrographs now installed on 10m-class telescopes open new perspectives in the exploration of the formation of galaxies. Absorption line spectra with a good spatial sampling will provide new information on the nature of the stellar components of a galaxy, as well as on their kinematics. This poster presents the first attempt to fit simultaneously the local line-of-sight velocity distribution (LOSVD) and the nature of the stellar population. It is based on efficient non- parametric inversion procedures. Synthetic spectra are constructed with the most recent version of the population synthesis code PEGASE. The input library consists of 1791 stellar spectra obtained with the ELODIE spectrograph at the Observatoire de Haute Provence (a significant extension of the archive of 908 spectra of Prugniel & Soubiran, 2001). The spectra range from 4000 to 6800, with R= Figure 1: Evolutionary tracks in the log(Te)- log(g) plane: 1, 2, 5, 20 M (Padova group). Coverage is satisfactory for < Z < At low Z, old populations can be synthesized. Extensions are planned. An interpolator has been constructed to produce spectra on a regular grid in log(g), Teff and Z (Prugniel et al., in prep.). Bolometric corrections are based on the library of Lejeune et al. (1998). Observatoire Astronomique de Strasbourg PEGASE2 produces high resolution synthetic spectra of evolved Single Stellar Populations (SSPs) assuming a given IMF and stellar evolution model for a set of given ages and metallicities. These are the building blocks of the models of galactic spectra. A galaxy Spectral Energy Distribution is made of an intrinsic stellar light model obscured by a dust extinction model and convolved by a velocity distribution, as shown in figure 2. Each step of the construction of the model has a number of parameters. 3 - Inversion of galaxy spectra 1 - Synthetic spectra at R=10000 Inverting an observed spectrum involves recovering the 4 functions , E, Z and g when , fext, and B are known. 4 - Application to SDSS data The reliability of the proposed method allows us to apply it to large sets of data such as SDSS spectra. We recover the luminous weight function , age-metallicity relation, extinction and losvd by fitting the observed spectra. Example : SDSS Application to a large subset of SDSS data is on course. Velocity(km/s) Figure 4: Monte Carlo experiments (50 realizations) for simulated SDSS-like spectroscopic data (R=4000, = Å, SNR=30). The first column displays the luminous weight function, which is related to the SFH, the second column shows the age- metallicity relation, the third column is the time-dependent color excess and the last one is the losvd. The rows correspond to different input models. The symbols and the bars represent the median of and dispersion of 50 realizations. In every case, the reconstruction is satisfactory for the 4 fields. Log10(age(yr))  log10(Z/Zsun)Color excess ELOSVD g 5 - Application to Disc-bulge separation Bulges in spiral galaxies are puzzling systems, and are difficult to study. In particular, observations of bulges are systematically contaminated by the disc component. We studied the possibility of separating the disc light from the bulge light in an idealized case where the disc and bulge stellar populations are different in formation history AND in kinematics, as shows figure 6. A slightly different formulation of the inversion algorithms allows to determine one LOSVD for each SSP in the basis. Figure 6: Model and median reconstruction (50 realizations, SNR=100) of the age-velocity distribution of an idealized disc-bulge overlap region. The bulge is old, non rotating with high velocity dispersion, while the disc is young, rotating, with little dispersion. The separation of the two components is clear. STELLAR LIGHT MODEL : The intrinsic stellar light model is a weighted sum of synthetic spectra of SSPs computed by PEGASE2. Relevant parameters: luminous weight function  (t) (directly related to SFR), age-metallicity relation Z(t). EXTINCTION MODEL : The ISM in outer galaxies is rarely homogeneous, and therefore all the stars of a galaxy are seen through different amounts of dust. In order to account for this complexity, we allow each model SSP to possess its own color excess. Relevant parameter: color excess function E(t) which represents the color excess E(B-V) seen by the SSP of age t. MODEL KINEMATICS : The motion of the stars is in most cases accounted for by assuming that all stars of all ages have the same LOSVD. The relevant parameter for this step is the LOSVD. Age-dependent stellar LOSVD are described in section 5. Figure 2: Schematic representation of the building procedure of a galactic spectrum model ELODIE Stellar spectra library PEGASE2 Conclusion The galaxy spectra inversion methods proposed are computationnally efficient and reliable, as shows the Monte Carlo simulations and the application to SDSS data. They are a useful tool to interpret galaxy spectra in terms of star formation history and kinematics, and can be applied to large sets of data. Future work involves building statistics from SDSS data in order to draw a general picture of SDSS galaxies evolution, and comparison with works of other groups. Observations of disc galaxies with bulges were proposed with GIRAFFE and FORS in order to study the disc-bulge relationship with the above separation technique. Model and data Velocity(km/s)Log10(age(yr)) Wavelength ( Å)  log10(Z/Zsun)Color excess ELOSVD g Model A Model B 2 - Models of galaxy spectra