The star formation history of the Local Group dwarf galaxy Leo I

We present a quantitative analysis of the star formation history (SFH) of t he Local Group dSph galaxy Leo I, from the information in its Hubble Space Telescope [(V-I),I] color-magnitude diagram (CMD). It reaches the level of the oldest main-sequence turnoffs, and this allows us to retrieve the SFH i n considerable detail. The method we use is based on comparing, via synthet ic CMDs, the expected distribution of stars in the CMD for different evolut ionary scenarios with the observed distribution. We consider the SFH to be composed by the SFR(t), the chemical enrichment law Z(t), the initial mass function (IMF), and a function beta(f, q) controlling the fraction f and ma ss ratio distribution a of binary stars. We analyze a set of similar or equ al to 50 combinations of four Z(t), three IMFs, and more than four beta(f; a). For each of them, the best SFR(t) is searched for among similar or equa l to 6 x 10(7) models. The comparison between the observed CMD and the mode l CMDs is done through chi(v)(2) minimization of the differences in the num ber of stars in a set of regions of the CMD, chosen to sample stars of diff erent ages or in specific stellar evolutionary phases. We empirically deter mine the range of chi(v)(2) values that indicate acceptable models for our set of data using tests with models with known SFHs. Our solution for the S FH of Leo I defines a minimum of chi(v)(2) in a well-defined position of th e parameter space, and the derived SFR(t) is robust, in the sense that its main characteristics are unchanged for different combinations of the remain ing parameters. However, only a narrow range of assumptions for Z(t), IMF, and beta(f,q) result in a good agreement between the data and the models, n amely, Z = 0.0004, a IMF Kroupa et al. or slightly steeper, and a relativel y large fraction of binary stars, with f = 0.3-0.6, q > 0.6, and an approxi mately flat IMF for the secondaries, or particular combinations of these pa rameters that would produce a like fraction of similar mass binaries. Most star formation activity (70% to 80%) occurred between 7 and 1 Gyr ago. At I Gyr ago, it abruptly dropped to a negligible value, but seems to have been active until at least similar or equal to 300 million years ago. Our resul ts do not unambiguously answer the question of whether Leo I began forming stars around 15 Gyr ago, but it appears that the amount of this star format ion, if it existed at all, would be small.