Beyond the diffraction limit of optical/IR interferometers II. Stellar parameters of rotating stars from differential phases

Context. As previously demonstrated on Achernar, one can derive the angular radius, rotational velocity, axis tilt, and orientation of a fast-rotating star from the di ff erential phases obtained by spectrally resolved long baseline interferometry using earth-rotation synthesis. Aims. We applied this method on a small sample of stars for di ff erent spectral types and classes, in order to generalize the technique to other rotating stars across the H-R diagram and determine their fundamental parameters. Methods. We used di ff erential phase data from the AMBER /VLTI instrument obtained prior to refurbishing its spectrometer in 2010. With the exception of Fomalhaut, which has been observed in the medium-resolution mode of AMBER (lambda/delta lambda approximate to 1500), our three other targets, Achernar, Altair, and delta Aquilae o ff ered high-resolution (lambda/delta lambda approximate to 12 000) spectro-interferometric data around the Br gamma absorption line in K band. These data were used to constrain the input parameters of an analytical, still realistic model to interpret the observations with a systematic approach for the error budget analysis in order to robustly conclude on the physics of our 4 targets. We applied the super resolution provided by differential phases phi(diff) to measure the size (equatorial radius R-eq and angular diameter circle divide(eq)), the equatorial rotation velocity (V-eq), the inclination angle (i), and the rotation axis position angle (PA(rot)) of 4 fast-rotating stars: Achernar, Altair, delta Aquilae, and Fomalhaut. The stellar parameters of the targets were constrained using a semi-analytical algorithm dedicated to fast rotators SCIROCCO. Results. The derived parameters for each star were R-eq = 11 : 2 +/- 0 : 5 R fi, Veq sin i = 290 +/- 17 km s 1, PArot = 35 : 4 degrees +/- 1 : 4 degrees, for Achernar; R-eq = 2 : 0 +/- 0 : 2 R-circle dot, V-eq sin i = 226 +/- 34 km s(-1), PA(rot) = -65 : 5 degrees +/- 5 : 5 degrees, for Altair; Req = 2 : 2 +/- 0 : 3 R fi, Veq sin i = 74 +/- 35 km s 1, PArot = 101 : 2 degrees +/- 14 degrees, for delta Aquilae; and R-eq = 1 : 8 +/- 0 : 2 R-circle dot, V-eq sin i = 93 +/- 16 km s(-1), PArot = 65 : 6 degrees +/- 5 degrees, for Fomalhaut. They were found to be compatible with previously published values from di ff erential phase and visibility measurements, while we were able to determine, for the first time, the inclination angle i of Fomalhaut (i = 90 degrees +/- 9 degrees) and Aquilae (i = 81 degrees +/- 13 degrees), and the rotation-axis position angle PA(rot) of Aquilae. Conclusions. Beyond the theoretical di ff raction limit of an interferometer (ratio of the wavelength to the baseline), spatial super resolution is well suited to systematically estimating the angular diameters of rotating stars and their fundamental parameters with a few sets of baselines and the Earth-rotation synthesis provided a high enough spectral resolution.