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 Rsun. We find no
significant offset for main-sequence (<~ 1.5 Rsun) and low-luminosity RGB stars
(~ 3-8 Rsun), but seismic radii appear to be systematically underestimated by
~5% for subgiants (~ 1.5-3 Rsun). 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 (Dnu)
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.
