On the past star formation rate in the solar neighbourhood

The history of star formation in the Galactic region within 20 pc of the sun is investigated analytically. The present-day mass function (PDMF) is derived from published observational data, with consideration of the luminosity function, the mass-Mv relation, corrections for post-main-sequence evolution and main-sequence (MS) brightening, the scale heights of the MS stars, MS lifetimes, and the age of the Galactic disk (here taken as 12 Gyr). The mean past star-formation rate (SFR) is estimated by comparing the PDMFs for stars lighter and heavier than the sun and assuming a time-independent initial mass function (IMF). A range of values from 0.08 to 2.0 times the present SFR is calculated. The arguments favoring an IMF governed by a power law (with an exponent decreasing monotonically with time) are reviewed, and PDMFs are calculated for a range of SFRs on this basis. Since no agreement with actual PDMF is found, it is concluded that any such IMF decrease must vary with mass.