Single-mode interferometric field of view in partial turbulence correction. Application to the observation of the environment of Sgr A* with GRAVITY

Context. The GRAVITY instrument on the ESO VLTI is setting a new mark in the landscape of optical interferometers. Long exposures are possible for the first time in this wavelength domain, delivering a dramatic improvement for astrophysics. In particular, faint objects can be observed at the angular resolution of the VLTI, with exposures exceeding by many orders of magnitude the coherence time of atmospheric turbulence. Aims. Modern interferometers, especially those that combine light collected by large telescopes such as the Unit Telescopes of the VLT, benefit from partial correction of atmospheric turbulence. We investigate in this paper the influence of atmospheric turbulence on the maximum field of view of interferometers such as GRAVITY, where wavefronts are filtered with single-mode fibres. The basic question is whether the maximum field of view is restricted to the diffraction limit of single apertures or if it is wider in practice. We discuss in particular the case of the field around Sgr A* , with an emphasis on the detectability of the massive main-sequence star S2. Methods. We theoretically investigated the interferometric and photometric lobes of the interferometer and took atmospheric turbulence into account. We computed the lobe functions with and without partial correction for atmospheric turbulence. Results. The main result of the paper is that the field of view of the interferometer is widened by tip-tilt residues if higher orders of atmospheric turbulence are corrected for. As a particular case, the S2 star can be detected in interferometric frames centred on Sgr A* even when the distance between the two objects is up to about twice the diffraction limit of a single aperture. We also show that the visibilities are not biased in this case if the pointing accuracies of the fibres are of the order of 10 mas.