SDSS DR4: Progress on the hot white dwarf luminosity function

A large collection of white dwarf (WD) spectra from Sloan Digital Sky Survey (SDSS) data release 4 (DR4) WD catalog data allowed us to obtain a luminosity function (LF) for the hottest WDs. The LF was calculated basing on spectra of the WDs from a special class of SDSS objects called hot standards (HS), for which the WD sample completeness can be estimated. WD distances were determined from the observed and absolute SDSS g filter magnitudes derived from WD stellar atmosphere model fits to the SDSS spectra. The result LF covers -0.5 up to 7 absolute bolometric magnitude range. It shows a slight disagreement at the cold end comparing to the literature LFs but it can be due to some problems with HS WD sample completeness estimations. It is clearly visible that the LF has unexpected plateau between 1.5 and 4 absolute bolometric magnitudes. There is nothing similar visible in a LF built only for non-DA WDs. The plateau might be real but we are concern that its existence can be connected to the problems with spectra calibration of the blue objects in SDSS DR4 data and lack of good stellar atmosphere models for the hottest DA white dwarfs.