Issue A&A Volume 420, Number 2, June III 2004 Page(s) 459 - 466 Section Extragalactic astronomy DOI http://dx.doi.org/10.1051/0004-6361:20034366

A&A 420, 459-466 (2004)
DOI: 10.1051/0004-6361:20034366

Constraining the solutions of an inverse method of stellar population synthesis

J. Moultaka^{1, 2}, C. Boisson², M. Joly² and D. Pelat<sup>2

1</sup>  Physikalisches Institut, Zülpicher Str. 77, 50937 Köln, Germany
²  LUTH, Observatoire de Meudon, 5 place Jules Janssen, 92190 Meudon Cedex, France

(Received 19 September 2003 / Accepted 10 February 2004 )

Abstract
In three previous papers (Pelat 1997, MNRAS, 284, 365; Pelat 1998, MNRAS, 299, 877; Moultaka & Pelat 2000, MNRAS, 314, 409), we set out an inverse stellar population synthesis method that uses a database of stellar spectra. Unlike other methods, this one provides full knowledge of all possible solutions as well as a good estimation of their stability; moreover, it provides the unique approximate solution, when the problem is overdetermined, using a rigorous minimization procedure. In Boisson et al. (2000, A&A, 357, 850), this method was applied to 10 active and 2 normal galaxies. In this paper we analyse the results of the method after constraining the solutions. Adding a priori physical conditions to the solutions constitutes a good way to regularize the synthesis problem. As an illustration we introduce physical constraints on the relative number of stars taking into account our present knowledge of the initial mass function in galaxies. To avoid biases on the solutions due to such constraints, we use constraints involving only inequalities between the number of stars, after dividing the H-R diagram into various groups of stellar masses. We discuss the results for a well-known globular cluster of the galaxy M 31 and discuss some of the galaxies studied in Boisson et al. (2000, A&A, 357, 850). We find that, given the spectral resolution and the spectral domain, the method is very stable according to such constraints (i.e. the constrained solutions are almost the same as the unconstrained one). However, additional information can be derived about the evolutionary stage of the last burst of star formation, but the precise age of this particular burst seems to be questionable.

Key words: galaxies: stellar content -- galaxies: active -- methods: analytical

Offprint request: J. Moultaka, moultaka@ph1.uni-koeln.de

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