On the discrepancy between asteroseismic and Gaia DR1 TGAS parallaxes

Recently, a deviation of the Gaia Tycho–Gaia Astrometric Solution (TGAS) parallaxes from the asteroseismic ones for giants was found. We show that for parallaxes ϖ < 1.5 mas it can be explained by a selection effect in favour of bright and luminous giants in the Tycho-2 and TGAS catalogues. Another explanation of this deviation seems to be valid for ϖ > 1.5 mas based on the best extinction estimates: The deviation may be caused not by a bias of parallax, but by an underestimation of the extinction (and, consequently, an overestimation of the calculated absolute magnitude) in the asteroseismic results. We demonstrate that the reliable estimates of the reddening and extinction (about 0.22 mag of the visual extinction for the Kepler field) better fit both the giants and main-sequence stars to the PARSEC, MIST and YaPSI isochrones.