Comparison of fringe-tracking algorithms for single-mode near-infrared long-baseline interferometers

To enable optical long baseline interferometry toward faint objects, long integrations are necessary despite atmospheric turbulence. Fringe trackers are needed to stabilize the fringes and thus increase the fringe visibility and phase signal-to-noise ratio (SNR), with efficient controllers robust to instrumental vibrations, and to subsequent path fluctuations and flux drop-outs. We report on simulations, analysis and comparison of the performances of a classical integrator controller and of a Kalman controller, both optimized to track fringes under realistic observing conditions for different source magnitudes, disturbance conditions, and sampling frequencies. The key parameters of our simulations (instrument photometric performance, detection noise, turbulence and vibrations statistics) are based on typical observing conditions at the Very Large Telescope observatory and on the design of the GRAVITY instrument, a 4-telescope single-mode long baseline interferometer in the near-infrared, next in line to be installed at VLT Interferometer. We find that both controller performances follow a two-regime law with the star magnitude, a constant disturbance limited regime, and a diverging detector and photon noise limited regime. Moreover, we find that the Kalman controller is optimal in the high and medium SNR regime due to its predictive commands based on an accurate disturbance model. In the low SNR regime, the model is not accurate enough to be more robust than an integrator controller. Identifying the disturbances from high SNR measurements improves the Kalman performances in case of strong optical path difference disturbances.

The molecular and dusty composition of Betelgeuses inner circumstellar environment

The study of the atmosphere of red supergiant stars in general and of Betelgeuse (alpha Orionis) in particular is of prime importance to understand dust formation and how mass is lost to the interstellar medium in evolved massive stars. A molecular shell, the MOLsphere (Tsuji, 2000a), in the atmosphere of Betelgeuse has been proposed to account for the near- and mid-infrared spectroscopic observations of Betelgeuse. The goal is to further test this hypothesis and to identify some of the molecules in this MOLsphere. We report on measurements taken with the mid-infrared two-telescope beam combiner of the VLTI, MIDI, operated between 7.5 and 13.5 $mu$m. The data are compared to a simple geometric model of a photosphere surrounded by a warm absorbing and emitting shell. Physical characteristics of the shell are derived: size, temperature and optical depth. The chemical constituents are determined with an analysis consistent with available infrared spectra and interferometric data. We are able to account for the measured optical depth of the shell in the N band, the ISO-SWS spectrum and K and L band interferometric data with a shell whose inner and outer radii are given by the above range and with the following species: H2O, SiO and Al2O3. These results confirm the MOLsphere model. We bring evidence for more constituents and for the presence of species participating in the formation of dust grains in the atmosphere of the star, i.e. well below the distance at which the dust shell is detected. We believe these results bring key elements to the understanding of mass loss in Betelgeuse and red supergiants in general and bring support to the dust-driven scenario.