Beyond the diffraction limit of optical/IR interferometers

Abstract

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 differential phases obtained by spectrally resolved long baseline interferometry using earth-rotation synthesis.Aims. We applied this method on a small sample of stars for different 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 differential 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 (λ/δλ ≈ 1500), our three other targets, Achernar, Altair, and δ Aquilae offered high-resolution (λ/δλ ≈ 12 000) spectro-interferometric data around the Brγ 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 φ diff to measure the size (equatorial radius R eq and angular diameter / 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, δ 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 , V eq sin i = 290 ± 17 km s −1 , PA rot = 35.4• ± 1.4• , for Achernar; R eq = 2.0 ± 0.2 R , V eq sin i = 226 ± 34 km s −1 , PA rot = −65.5 • ± 5.5• , for Altair; R eq = 2.2 ± 0.3 R , V eq sin i = 74 ± 35 km s −1 , PA rot = −101.2• ± 14 • , for δ Aquilae; and R eq = 1.8 ± 0.2 R , V eq sin i = 93 ± 16 km s −1 , PA rot = 65.6 • ± 5 • , for Fomalhaut. They were found to be compatible with previously published values from differential phase and visibility measurements, while we were able to determine, for the first time, the inclination angle i of Fomalhaut (i = 90• ± 9 • ) and δ Aquilae (i = 81 • ± 13 • ), and the rotation-axis position angle PA rot of δ Aquilae. Conclusions. Beyond the theoretical diffraction 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.

A CO-multilayer outer atmosphere for eight evolved stars revealed with VLTI/AMBER

“…By applying our new continuous and multilayer MOLsphere approach, we present first in this section the results of three published stars, BK Vir, α Boo, and SW Vir (where we compare, for these latter, the results of our multilayer approach with the results from the bi-layers approach, using the values given in Table. B1 and computations with PAMPERO), then we present the new results of four evolved stars (including one Mira observed for two epochs), γ Cru, λ Vel, α Sco and W Hya (Fig.D1 to D8). We determine the uncertainties of the six free parameters (T0, N0, ζT, ζN, R mol,0 , & R mol,end ) that we presented in Section 4.2, using the same method that was used for the other model, which is dedicated to Hot Active Stars (SCIROCCO; Hadjara et al 2014;Hadjara 2015;Hadjara et al 2018), when the χ 2 -minimization was used, after localizing the global minimums by using a large grid of six free parameters. The results are given in Tab.…”

“…D1 to D8). We determine the uncertainties of the six free parameters (T0, N0, ζT, ζN, R mol,0 , & R mol,end ) that we presented in Section 4.2, using the same method that was used for the other model, which is dedicated to Hot Active Stars (SCIROCCO; Hadjara et al 2014;Hadjara 2015;Hadjara et al 2018), when the χ 2 -minimization was used, after localizing the global minimums by using a large grid of six free parameters. The results are given in Tab.…”

Differential interferometry of the rapid rotator Regulus

“…The combination of high spatial and high spectral resolution allows us to measure physical properties of fast rotators beyond the diffraction limit, as shown by Domiciano de Souza et al (2012) and Hadjara et al (2014) who used the differential phases from AMBER/VLTI (Astronomical Multi-BEam combineR). Indeed, AMBER (Petrov et al 2007) is a spectro-interferometric instrument specifically designed to go well beyond the resolution limit (e.g., Meilland et al 2007;Le Bouquin et al 2009).…”

High contrast imaging with Fizeau interferometry: The case of Altair

“…In the meantime, other aspects of Altair have been characterized and have set the stage for detailed study of whatever exoplanet system it may host. Near-infared and optical long-baseline interferometry (OLBI) have revealed the star's angular width, high inclination, asymmetric surface brightness, an oblate spheroid shape due to the star's spin, and variable K-band-emissive exozodiacal dust in tight orbits of ∼0.1 AU, though no emission has been detected from a cold debris disk or Nband-emissive habitable-zone dust (Kuchner et al 1998;Ohishi et al 2004;Reiners & Royer 2004;de Souza et al 2005;Suarez et al 2005;Peterson et al 2006;Monnier et al 2007;Richichi et al 2009;Lara & Rieutord 2011;Millan-Gabet et al 2011;van Belle 2012;Absil et al 2013;Gáspár et al 2013;Hadjara et al 2014;Mennesson et al 2014;Thureau et al 2014;van Lieshout et al 2014;Baines et al 2017;Kirchschlager et al 2017;Nunez et al 2017;Ertel et al 2018;Bouchaud et al 2020;Ertel et al 2020). van Belle et al (2001) also note that visibility data from the Palomar Testbed Interferometer (PTI) consistent with an elliptical shape for Altair is probably not an artifact of a tight binary companion, as Altair's proper motion and the sensitivity of the PTI do not bring apparent binary companions within range that could masquerade as an elliptical star.…”