Beyond the diffraction limit of optical/IR interferometers I. Angular diameter and rotation parameters of Achernar from differential phases

Context. Spectrally resolved long-baseline optical/IR interferometry of rotating stars opens perspectives to investigate their fundamental parameters and the physical mechanisms that govern their interior, photosphere, and circumstellar envelope structures. Aims. Based on the signatures of stellar rotation on observed interferometric wavelength-differential phases, we aim to measure angular diameters, rotation velocities, and orientation of stellar rotation axes. Methods. We used the AMBER focal instrument at ESO-VLTI in its high-spectral resolution mode to record interferometric data on the fast rotator Achernar. Differential phases centered on the hydrogen Br gamma line (K band) were obtained during four almost consecutive nights with a continuous Earth-rotation synthesis during similar to 5h/night, corresponding to similar to 60 degrees position angle coverage per baseline. These observations were interpreted with our numerical code dedicated to long-baseline interferometry of rotating stars. Results. By fitting our model to Achernar's differential phases from AMBER, we could measure its equatorial radius R-eq = 11.6 +/- 0.3 R-circle dot, equatorial rotation velocity V-eq = 298 +/- 9 km s(-1), rotation axis inclination angle i = 101.5 +/- 5.2 degrees, and rotation axis position angle (from North to East) PA(rot) = 34.9 +/- 1.6 degrees. From these parameters and the stellar distance, the equatorial angular diameter circle divide(eq) of Achernar is found to be 2.45 +/- 0.09 mas, which is compatible with previous values derived from the commonly used visibility amplitude. In particular, circle divide(eq) and PA(rot) measured in this work with VLTI/AMBER are compatible with the values previously obtained with VLTI/VINCI. Conclusions. The present paper, based on real data, demonstrates the super-resolution potential of differential interferometry for measuring sizes, rotation velocities, and orientation of rotating stars in cases where visibility amplitudes are unavailable and/or when the star is partially or poorly resolved. In particular, we showed that differential phases allow the measurement of sizes up to similar to 4 times smaller than the diffraction-limited angular resolution of the interferometer.