Measure the distance and extinction for stars in LAMOST survey with Bayesian method

Using a Bayesian technique, which combines both photometric and spectral information, as well as prior knowledge on the Milky Way, we measured the distance and extinction for about one million stars in the first data release of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) survey. Simulations have been performed based on the observed distributions for both the sky position and the magnitude, which show that the parallaxes have been underestimated by 10 per cent for dwarfs, while for giants the parallaxes have been overestimated by 15 per cent. The true fractional errors for dwarfs (giants) increase systematically with the fractional uncertainties in the output when the fractional uncertainties greater than ∼0.4(0.5). A comparison with Hipparcos parallaxes and related clusters distance shows good agreement with our measurements. We also compared the distances with those of the empirical photometric parallax for main-sequence thin-disc stars, which reveal that the distances have been systematically underestimated due to uncertainties in the stellar parameters for cold dwarfs with T_eff < 4500 K. The kinematic corrections introduced by Schönrich et al. from two proper motion catalogues, Position and Proper Motion Extended-L (PPMXL) and Fourth US Naval Observatory CCD Astrograph Catalog (UCAC4), are calculated to detect and correct any systematic errors, which confirm the systematically underestimated distance for cold dwarfs, and the corrections from PPMXL are consistent with those from UCAC4 when the errors of proper motion are well accounted for. We also compared our extinction results with those of Berry et al., and the Rayleigh-Jeans Color Excess method. The extinction is well recovered over 4 mag.