Asteroseismology and Gaia: Testing scaling 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 ≲5-10 mas (≈90%-98% of the TGAS sample). The observed differences in our sample can furthermore be partially compensated by adopting a hotter Teff 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_⊙. We find no significant offset for main-sequence (≲1.5 R_⊙) and low-luminosity RGB stars (≈3-8 R_⊙), but seismic radii appear to be systematically underestimated by ≈5% for subgiants (≲1.5-3 R_⊙). 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 (Δν) 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.