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Aims. We present a hot white dwarf (WD) luminosity function (LF) using data taken from the Sloan Digital Sky Survey (SDSS) Data Release 4. We present and discuss a combined LF, along with separate DA and non-DA as LFs. We explore the completeness of our LFs and interpret a sudden drop in the non-DA LF near 2 M bol as a transition of the non-DA WD atmosphere into the DA one during WD evolution. Our LF extends roughly between -0.5 T eff > ∼25 000 K. Our LF should now be useful for estimates of recent star formation and for studies of neutrino and other potential particle emission losses in hot WDs. Methods. To create a sample whose completeness can be characterized fully, we used stars whose spectra were obtained via the SDSS's "hot standard" target selection criteria. The hot standard stars were purposefully targeted to a high level of completeness by the SDSS for calibration purposes. We are fortunate that many of them are hot white dwarfs stars. We further limited the sample to stars with fitted temperatures exceeding 23 500 K and log g > 7.0. We determined stellar distances for our sample based on their absolute SDSS g filter magnitudes, derived from WD stellar atmosphere model fits to the SDSS stellar spectra. Results. We compared our LF with those of other researchers where overlap occurs; however, our LFs are unique in their extension to the most luminous/hottest WDs. The cool end of our LF connects with the hot end of previously determined SDSS WD LFs and agreement here is quite good. It is also good with previous non-SDSS WD LFs. We note distinct differences between the DA and non-DA LFs and discuss the reliability of the DA LF at its hot end. We have extended the range of luminosities covered in the most recent WD LFs. The SDSS sample is understood quite well and its exploration should contribute to a number of new insights into early white dwarf evolution.

A hot white dwarf luminosity function from the Sloan Digital Sky Survey