Galactic archaeology:: initial mass function and depletion in the 'thin disc'

We determine the initial mass function (IMF) of the 'thin disc' in the range of, approximately, 1.1 to 4 M-circle dot by means of a direct comparison between synthetic stellar samples [for different matching choices of IMF, star formation rate (SFR) and depletion] and a complete (volume-limited) sample of single stars near the Galactic plane (\z \ < 25 pc), selected from the Hipparcos catalogue (d < 100 pc, M-V < +4.0). Our synthetic samples are computed from first principles: stars are created with a random distribution of mass M (*) and age t (*) , which follow a given (genuine) IMF and SFR(t (*) ). They are then placed on the Hertzsprung-Russell (HR) diagram by means of a grid of empirically well-tested evolution tracks. The quality of the match (synthetic versus observed sample) is assessed by means of star counts in specific regions in the HR diagram. Seven regions are located along the main sequence (MS, mass sensitive), while four regions represent different evolved (age-sensitive) stages of the stars. We find a bent slope of the IMF (using the Scalo notation, i.e. a power law on a logarithmic mass scale), with Gamma(1) =-1.70 +/- 0.15 (for approximate to1.1 < M (*) < 1.6 M-circle dot ) and Gamma(2) =-2.1 +/- 0.15 (for 1.6 < M (*) less than or similar to 4 M-circle dot ). In addition, comparison of the observed MS star counts with those of synthetic samples with a different prescription of the MS core overshooting reveals sensitively that the right overshoot onset is at M (*) = 1.50 Mcircle dot. The counts of evolved stars, in particular, give valuable evidence of the history of the 'thin-disc' (apparent) star formation and lift the ambiguities in models restricted to MS star counts. The actual counts of evolved stars yield a stellar depletion, when compared with counts created by a constant SFR0 in the sample volume. This depletion becomes more pronounced with age. A very good match of all observed star counts is achieved with a simplistic diffusion approximation, with an age-independent diffusion time-scale of tau(dif) = 6.3 x 10(9) yr and a (local) SFR0 = 2.0 +/- 0.15 stars (with M (*) > 0.9 M-circle dot ) formed per 1000 yr and (kpc)(3) . We also discuss this 'thin-disc' depletion in terms of a geometrical dilution of the expanding stellar 'gas', with H-z (t (*) ) proportional tosigma(W) (t (*) ). This model applies to all stars old enough to have reached thermalization, i.e. for t (*) > 7 x 10(8) yr and H-z > 230 pc. It yields a column-integrated (non-local) 'thin-disc' SFRcol , which has not changed much over time (<30 per cent), SFRcol approximate to 0.82 stars pc(-2) Gyr(-1) (for stars with M (*) > 0.9 M-circle dot).