AN IMPROVED CALIBRATION OF CEPHEID VISUAL AND INFRARED SURFACE BRIGHTNESS RELATIONS FROM ACCURATE ANGULAR DIAMETER MEASUREMENTS OF COOL GIANTS AND SUPERGIANTS

We have calibrated optical and near-infrared surface brightness - colo ur relations for cool giant and supergiant stars using high-precision angular diameters of these stars determined from Michelson interferome try. We find that the giant and supergiant relations are undistinguish able over a wide range of intrinsic colours. We independently determin e the slopes of these relations obeyed by Cepheid variables and find t hat in all the diagrams considered, these agree very well with the slo pes derived from the stable giants and supergiants. Forcing the slopes to the values derived from the Cepheids, we determine a very precise value of the zero point of the surface brightness - colour relations v alid for Cepheid variables, which is 3.947 +/- 0.003. This value is in agreement with the one derived from the Cepheid effective temperature scale of Pel (1978), and from the lunar occultation angular diameter of the Cepheid zeta Gem (Ridgway et al. 1982). We apply our newly cali brated surface brightness - colour relations to the cluster Cepheid U Sgr to find its radius and distance from the optical V, V - R-J and th e infrared V, V - K and K, J - K Barnes-Evans technique. While the num erical values derived from the three different versions of the techniq ue do agree within 1 sigma, the near-infrared distance and radius Valu es are 5 - 10 times more accurate than the optical one; in particular, the distance and radius of the star derived from the V, V - K solutio n are 592 +/- 3 pc and 48.7 +/- 0.3 solar radii, respectively, with er rors less than 1 percent. We briefly discuss the potential of the near -infrared versions of the Barnes-Evans technique to set a very accurat e (0.02 mag) zero point to Cepheid period-luminosity relations and thu s make a very important contribution to the absolute calibration of th e extragalactic distance scale.