The angular sizes of dwarf stars and subgiants Surface brightness relations calibrated by interferometry

The availability of a number of new interferometric measurements of Main Sequence and subgiant stars makes it possible to calibrate the surface brightness relations of these stars using exclusively direct angular diameter measurements. These empirical laws make it possible to predict the limb darkened angular diameters $\theta_{\rm LD}$ of dwarfs and subgiants using their dereddened Johnson magnitudes, or their effective temperature. The smallest intrinsic dispersions of $\sigma \le 1\%$ in $\theta_{\rm LD}$ are obtained for the relations based on the K and L magnitudes, for instance $\log \theta_{\rm LD} = 0.0502\,(B-L) + 0.5133 - 0.2\,L$ or $\log \theta_{\rm LD} = 0.0755\,(V-K) + 0.5170 - 0.2\rm \,K$. Our calibrations are valid between the spectral types A0 and M2 for dwarf stars (with a possible extension to later types when using the effective temperature), and between A0 and K0 for subgiants. Such relations are particularly useful for estimating the angular sizes of calibrators for long-baseline interferometry from readily available broadband photometry.