Theoretical impact of fast rotation on calibrating the surface brightness-color relation for early-type stars

Context. The eclipsing binary method for determining distance in the local group is based on the surface brightness-color relation (SBCR), and early-type stars are preferred targets because of their intrinsic brightness. However, this type of star exhibits wind, mass-loss, pulsation, and rotation, which may generate bias on the angular diameter determination. An accurate calibration of the SBCR relation thus requires careful analysis. Aims. In this paper we aim to quantify the impact of stellar rotation on the SBCR when the calibration of the relation is based on interferometric measurements of angular diameters. Methods. Six stars with V - K color indices ranging between -1 and 0.5 were modeled using the code for high angular resolution of rotating objects in nature (CHARRON) with various rotational velocities (0, 25, 50, 75, and 95% of the critical rotational velocity) and inclination (0, 25, 50, 75, and 90 degrees). All these models have their equatorial axis aligned in an east-west orientation in the sky. We then simulated interferometric observations of these theoretical stars using three representative sets of the CHARA baseline configurations. The simulated data were then interpreted as if the stars were non-rotating to determine an angular diameter and estimate the surface-brightness relation. The V - K color of the rotating star was calculated directly from the CHARRON code. This provides an estimate of the intrinsic dispersion of the SBCR relation when the rotation effects of flattening and gravity darkening are not considered in the analysis of interferometric data. Results. We find a clear relation between the rotational velocity and (1) the shift in zero point (Delta a(0)) of the SBCR (compared to the static relation) and (2) its dispersion (sigma). When considering stars rotating at less than 50% of their critical velocity, Delta a(0) and sigma have about 0.01 mag, while these quantities can reach 0.08 and 0.04 mag, respectively, when the rotation is larger than 75% of the critical velocity. Besides this, the inclination angle mostly has an impact on the V - K color: i < 50 degrees (resp. i > 50 degrees) makes the star redder (resp. bluer). When considering the 150 models, Delta a(0) and sigma have 0.03 and 0.04 mag, respectively. These values are slightly but not significantly modified (about 0.03 and 0.01 mag in Delta a(0) and sigma, respectively) when considering different CHARA configurations. Interestingly, these 150 models, regardless of the interferometric configuration, are consistent with the empirical SBCR, which is within its dispersion of 0.16 mag. In addition, if one only considers projected rotational velocity V-rot sin i lower than 100 km s(-1), then Delta a(0) and sigma have 0.02 and 0.03 mag, respectively. Conclusions. To calibrate the SBCR interferometrically at the 0.02 mag precision (or lower), one should consider (1) a baseline configuration covering all directions of the (u, v) plan; (2) a sample of stars with rotational velocity lower than 50% of their critical velocity or, alternatively, stars with V-rot sin i lower than 100 km s(-1); (3) homogeneous visible and infrared photometry precisely at the 0.02 mag level or lower.