SIMBAD references

We test asteroseismic radii of Kepler main-sequence and subgiant stars by deriving their parallaxes which are compared with those of the first Gaia data release. We compute radii based on the asteroseismic scaling relations as well as by fitting observed oscillation frequencies to stellar models for a subset of the sample, and test the impact of using effective temperatures from either spectroscopy or the infrared flux method. An offset of 3 per cent, showing no dependency on any stellar parameters, is found between seismic parallaxes derived from frequency modelling and those from Gaia. For parallaxes based on radii from the scaling relations, a smaller offset is found on average; however, the offset becomes temperature dependent which we interpret as problems with the scaling relations at high stellar temperatures. Using the hotter infrared flux method temperature scale, there is no indication that radii from the scaling relations are inaccurate by more than about 5 per cent. Taking the radii and masses from the modelling of individual frequencies as reference values, we seek to correct the scaling relations for the observed temperature trend. This analysis indicates that the scaling relations systematically overestimate radii and masses at high temperatures, and that they are accurate to within 5 per cent in radius and 13 per cent in mass for main-sequence stars with temperatures below 6400 K. However, further analysis is required to test the validity of the corrections on a star-by-star basis and for more evolved stars.