Asteroseismology and Gaia: Testing ccaling relations using 2200 Kepler stars with TGAS parallaxes

We present a comparison of parallaxes and radii from asteroseismology and Gaia DR1 (TGAS) for 2200 $Kepler$ stars spanning from the main sequence to the red giant branch. We show that previously identified offsets between TGAS parallaxes and distances derived from asteroseismology and eclipsing binaries have likely been overestimated for parallaxes $\leq$ 5 − 10 mas (≈ 90–98 % of the TGAS sample). The observed differences in our sample can furthermore be partially compensated by adopting a hotter T$_{eff}$ scale (such as the infrared flux method) instead of spectroscopic temperatures for dwarfs and subgiants. Residual systematic differences are at the ≈ 2 % level in parallax across three orders of magnitude. We use TGAS parallaxes to empirically demonstrate that asteroseismic radii are accurate to ≈ 5 % or better for stars between ≈ 0.8 − 8 R$_\odot$. We find no significant offset for main-sequence ($\leq$1.5R $_\odot$) and low-luminosity RGB stars (≈3– 8R$_\odot$), but seismic radii appear to be systematically underestimated by ≈ 5% for subgiants (≈1.5–3R$_\odot$). We find no systematic errors as a function of metallicity between [Fe/H] ≈ −0.8 to +0.4 dex, and show tentative evidence that corrections to the scaling relation for the large frequency separation (∆ν) improve the agreement with TGAS for RGB stars. Finally, we demonstrate that beyond ≈ 3 kpc asteroseismology will provide more precise distances than end-of-mission Gaia data, highlighting the synergy and complementary nature of Gaia and asteroseismology for studying galactic stellar populations