Abstract
The GRAVITY instrument on the ESO VLTI pioneers the field of high-precision near-infrared interferometry by providing astrometry at the 10−100 μas level. Measurements at this high precision crucially depend on the control of systematic effects. We investigate how aberrations introduced by small optical imperfections along the path from the telescope to the detector affect the astrometry. We develop an analytical model that describes the effect of these aberrations on the measurement of complex visibilities. Our formalism accounts for pupil-plane and focal-plane aberrations, as well as for the interplay between static and turbulent aberrations, and it successfully reproduces calibration measurements of a binary star. The Galactic Center observations with GRAVITY in 2017 and 2018, when both Sgr A* and the star S2 were targeted in a single fiber pointing, are affected by these aberrations at a level lower than 0.5 mas. Removal of these effects brings the measurement in harmony with the dual-beam observations of 2019 and 2020, which are not affected by these aberrations. This also resolves the small systematic discrepancies between the derived distance R0 to the Galactic Center that were reported previously.
Highlights
The distance to the Galactic Center (GC), R0, can be measured directly from stellar orbits around Sgr A*, the radio source associated with the GC massive black hole (MBH)
To infer the source separations, we fit a binary model based on Eq (25), which we extended to account for the effect of finite spectral resolution and for a homogeneous background with flux ratio f bkg relative to the first binary component
In the following we evaluate the effect of the aberration correction on the S2 orbit
Summary
The distance to the Galactic Center (GC), R0, can be measured directly from stellar orbits around Sgr A*, the radio source associated with the GC massive black hole (MBH) (see, e.g., Genzel et al 2010 and Bland-Hawthorn & Gerhard 2016 for a recent overview of alternative methods). Static aberrations along the optical path of the instrument affect the measured visibilities by introducing a complex fielddependent factor for each telescope We express this gain in its polar representation and decompose it into a phase map φi (α) and an amplitude map Ai (α). For binaries with a separation comparable to the fiber width, a configuration in which the phase- and amplitude-maps are irrelevant cannot be obtained in principle In this case, the effect of static aberrations needs to be modeled and corrected for in the data analysis. In the case of GRAVITY observations, atmospheric phase variations across the telescope apertures are corrected for by the adaptive optics system, and the turbulent aberrations are dominated by tip-tilt jitter. The tip-tilt jitter acts like a Gaussian convolution kernel on the static maps, which is applied to the amplitude map squared in case of the photometric lobe, but to the full complex map in the case of the interferometric lobe
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