The formation rate and mass and luminosity functions of DA white dwarfs from the Palomar Green Survey

Spectrophotometric observations at high signal-to-noise ratio were obtained of a complete sample of 348 DA white dwarfs from the Palomar Green (PG) Survey. Fits of observed Balmer lines to synthetic spectra calculated from pure-hydrogen model atmospheres were used to obtain robust values of T(eff), log g, masses, radii, and cooling ages. The luminosity function of the sample, weighted by 1/V(max), was obtained and compared with other determinations. Incompleteness of the sample due to selection by photographic m(u)-m(b) color and magnitude limits was found to be a serious problem, and an attempt is made to correct for this. The mass distribution of the white dwarfs is derived, after important corrections for the radii of the white dwarfs in this magnitude-limited survey and for the cooling time scales. This distribution has (1) a peak'' component centered near 0.6 M(circle dot), (2) a low-mass component centered near 0.4 M(circle dot), and (3) a high-mass component above about 0.8 M(circle dot). The formation rate of DA white dwarfs from the PG is estimated to be 0.6x10(-12) pc(-3) yr(-1). Of these, 75% are from the peak component, 10% from the low-mass component, and 15% from the high-mass component. The low-mass component requires binary evolution for 100% of the objects, with a degenerate companion likely in the majority of cases. Comparison with predictions from a theoretical study of the white dwarf formation rate for single stars indicates that greater than or equal to80% of the high-mass component requires a different origin, presumably mergers of lower mass double degenerate stars. The need for a binary channel may not be as great for the massive, very hot white dwarfs found in the EUV all-sky surveys. In an Appendix, we even suggest that an enhanced density of the massive white dwarfs at lower Galactic latitudes might be due to some of them being the progeny of B stars in Gould's Belt. In order to estimate the recent formation rate of all white dwarfs in the local Galactic disk, corrections for incompleteness of the PG, addition of the DB-DO white dwarfs, and allowance for stars hidden by luminous binary companions had to be applied to enhance the rate. An overall formation rate of white dwarfs recently in the local Galactic disk of (1+/-0.25)x10(-12) pc(-3) yr(-1) is obtained. Admittedly, the systematic errors in this estimate are difficult to quantify. Two recent studies of samples of nearby Galactic planetary nebulae lead to estimates around twice as high. Difficulties in reconciling these determinations are discussed.