Improving the surface brightness-color relation for early-type stars using optical interferometry

The aim of this work is to improve the SBC relation for early-type stars in the $-1 leq V-K leq 0$ color domain, using optical interferometry. Observations of eight B- and A-type stars were secured with the VEGA/CHARA instrument in the visible. The derived uniform disk angular diameters were converted into limb darkened angular diameters and included in a larger sample of 24 stars, already observed by interferometry, in order to derive a revised empirical relation for O, B, A spectral type stars with a V-K color index ranging from -1 to 0. We also took the opportunity to check the consistency of the SBC relation up to $V-K simeq 4$ using 100 additional measurements. We determined the uniform disk angular diameter for the eight following stars: $gamma$ Ori, $zeta$ Per, $8$ Cyg, $iota$ Her, $lambda$ Aql, $zeta$ Peg, $gamma$ Lyr, and $delta$ Cyg with V-K color ranging from -0.70 to 0.02 and typical precision of about $1.5%$. Using our total sample of 132 stars with $V-K$ colors index ranging from about $-1$ to $4$, we provide a revised SBC relation. For late-type stars ($0 leq V-K leq 4$), the results are consistent with previous studies. For early-type stars ($-1 leq V-K leq 0$), our new VEGA/CHARA measurements combined with a careful selection of the stars (rejecting stars with environment or stars with a strong variability), allows us to reach an unprecedented precision of about 0.16 magnitude or $simeq 7%$ in terms of angular diameter.