Left: effective temperature map of Achernar corresponding to the best-fit of the CHARRON RVZ model to the VLTI/PIONIER H band observations (model parameters in Table 6). The spatial coordinates are normalized to the measured equatorial radius R_eq = 9.16 R_⊙. The polar and equatorial effective temperatures of Achernar are T_p = 17 124 K (white) and T_eq = 12 673 K (black). Right: log T_eff as a function of log g_eff of Achernar for the ELR model (solid line from Espinosa Lara & Rieutord 2011). The calculations were performed considering a Roche model with the same stellar parameters as in Table 6, except for the gravity darkening, which is directly obtained from the ELR model. The dashed straight line shows the log T_eff versus log g_eff corresponding to the best-fit RVZ model with the measured gravity-darkening coefficient β ( =. The vertical bar indicates the uncertainty in T_eff associated with the measured uncertainty in this best-fit β value alone. We also note that by fitting a straight line to the ELR model (solid curve) results in an identical β (=0.166) as measured with the CHARRON RVZ model, which exactly matches the dashed straight line. Thus, although the ELR model predicts a slightly more complex gravity-darkening relation than the RVZ model (Eq. (3)), these two gravity-darkening models agree within the uncertainties derived from the RVZ model fit to the PIONIER observations.