INVESTIGATION OF THE ERRORS IN SLOAN DIGITAL SKY SURVEY PROPER-MOTION MEASUREMENTS USING SAMPLES OF QUASARS

Abstract

We investigate in detail the probability distribution function (pdf) of the proper-motion measurement errors in the SDSS+USNO-B proper-motion catalog of Munn et al. using clean quasar samples. The pdf of the errors is well represented by a Gaussian core with extended wings, plus a very small fraction (<0.1%) of “outliers.” We find that while formally the pdf could be well fit by a five-parameter fitting function, for many purposes it is also adequate to represent the pdf with a one-parameter approximation to this function. We apply this pdf to the calculation of the confidence intervals on the true proper motion for an SDSS+USNO-B proper-motion measurement, and discuss several scientific applications of the SDSS proper-motion catalog. Our results have various applications in studies of the galactic structure and stellar kinematics. Specifically, they are crucial for searching hyper-velocity stars in the Galaxy.