Gravitational-darkening of Altair from interferometry

Interferometric observations have revealed that the rapid rotator Altair is a flattened star with a non-centrally symmetric intensity distribution. In this work we perform for the first time a physically consistent analysis of all interferometric data available so far, corresponding to three different interferometers operating in several spectral bands. These observations include new data ( squared visibilities in the H and K bands from VLTI-VINCI) as well as previously published data ( squared visibilities in the K band from PTI and squared visibilities, triple amplitudes, and closure phases in the visible between 520 nm and 850 nm from NPOI). To analyze these data we perform chi(2) minimization using an interferometry-oriented model for fast rotators, which includes Roche approximation, limb-darkening, and von Zeipel-like gravity-darkening. Thanks to the rich interferometric data set available and to this physical model, the main uniqueness problems were avoided. As a result, we show that the observations can only be explained if Altair has a gravity-darkening compatible with the expected value for hot stars, i.e., the von Zeipel effect (T-eff proportional to g(0.25)).