The Mass and Luminosity Functions and the Formation Rate of DA White Dwarfs in the Sloan Digital Sky Survey

A large sample of white dwarfs is essential to the study of the formation and evolution of white dwarfs. The SDSS Data Release 1 includes 1833 DA white dwarfs (WDs), which is by now the largest homogeneous sample of WDs and provides us the best opportunity to study the statistical properties of WDs. In this paper we firstly choose a recently established theoretical model to calculate the mass and distance of each WD from the observational data. Then we adopt a delicate bin-correction method to correct the selection effects and use the 1/V weight-factor method to calculate the luminosity function, the continuous mass function and the formation rate of these WDs. We find that the SDSS DA WD sample is incomplete and suffers seriously from the selection effects. After corrections for the selection effects, only 531 WDs remain in a much completed sample. Based on it we derive the most up-to-date luminosity function and mass function, in which we find a broad peak of WD masses centered around 0.58M\. The DA WD's space density is calculated as 8.81\×10⁻⁵pc⁻³ and the formation rate is 2.579\× 10⁻¹³pc⁻³yr⁻¹. We conclude that the statistical properties of the SDSS DA WD sample are generally in good agreement with both the previous observational and theoretical studies, and provide us abundant information on the formation and evolution of WDs. However, a larger and more complete all-sky WD sample is still needed in the future to explain some subtle disagreements and unresolved puzzles.