HISTORY OF THE MILKY-WAY STAR FORMATION RATE FROM THE WHITE-DWARF LUMINOSITY FUNCTION

The sensitivity of the white dwarf luminosity function (WDLF) to the history of the star formation rate (SFR) is examined. It is shown that the WDLF is much more sensitive to the SFR than to variations in the initial mass function (IMF). If the SFR is assumed to be a smooth and monotonic function of time, existing observations of the WDLF require that the ratio of the SFR within the past 109 yr to the SFR (4-10) × 109 yr ago be not much different from unity, the main uncertainty being the white dwarf cooling times at the faintest luminosities. The WDLF is also capable of revealing nonmonotonic SFR behavior, such as bursts and lulls. We show that a marginal feature in the WDLF at log (L/L⊙) ≈ -2 can be identified with a burst of star formation which occurred 3 × 108 yr ago, consistent with two other lines of evidence. If the feature is real, the burst is constrained to have a duration ≲ 108 yr and must have produced roughly a tenth of the stars in the solar neighborhood. WDLFs computed using the SFR histories derived from the isochrone and chromospheric age distributions of Twarog and Barry, both of which show a definite maximum around (5-8) × 109 yr ago, are compared with the observations. The major discrepancy is that both studies find significant numbers of old (≳9 Gyr) stars, which yield far too many very faint white dwarfs, at least for the cooling rates adopted here. Either the ages of the oldest stars from both methods are overestimated, the low-luminosity cooling rates are too large, or the observed WDLF at lowest luminosities should be larger by a factor of 10-100. We emphasize the ability of larger WDLF samples to test definitely for irregularities in the SFR history for all times less than about (4-5) × 109 yr in the past. A derivation of the relation between the WDLF, the SFR, and the IMF is given in the Appendix.