Distance and extinction determination for APOGEE stars with Bayesian method

Using a Bayesian technology, we derived distances and extinctions for over 100 000 red giant stars observed by the Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey by taking into account spectroscopic constraints from the APOGEE stellar parameters and photometric constraints from Two Micron All-Sky Survey, as well as a prior knowledge on the Milky Way. Derived distances are compared with those from four other independent methods, the Hipparcos parallaxes, star clusters, APOGEE red clump stars, and asteroseismic distances from APOKASC and Strömgren survey for Asteroseismology and Galactic Archaeology catalogues. These comparisons covers four orders of magnitude in the distance scale from 0.02 to 20 kpc. The results show that our distances agree very well with those from other methods: the mean relative difference between our Bayesian distances and those derived from other methods ranges from -4.2 per cent to +3.6 per cent, and the dispersion ranges from 15 per cent to 25 per cent. The extinctions towards all stars are also derived and compared with those from several other independent methods: the Rayleigh-Jeans Colour Excess (RJCE) method, Gonzalez's 2D extinction map, as well as 3D extinction maps and models. The comparisons reveal that, overall, estimated extinctions agree very well, but RJCE tends to overestimate extinctions for cool stars and objects with low log g.