Spatio-spectral encoding of fringes in optical long ... - GSU Astronomy

A&A 531, A110 (2011)significant improvement in the stellar atmosphere models (1Dand 3D) of all stars.Fig. 10. Number of sky regions of 1h in right ascension and 5 ◦ in declinationas a function of existing calibrators.4.2. Fundamental parametersThanks to direct angular diameter measurements by optical interferometrycombined with the bolometric flux, it is possibleto derive the fundamental stellar parameters, such as the effectivetemperature, the luminosity, and the stellar radius. The determinationof the angular diameter is based on visibility measurementsthat are directly linked to the Fourier transform of theobject intensity distribution. For a single circular star, the visibilitycurve as a function of spatial frequency B/λ (where B isthe interferometric baseline and λ is the operating wavelength)is related to the first Bessel function, and contains a central lobe,that is almost only sensitive to the size of the object, and an everdecreasing series of side lobes, separated by nulls, which one observeswith an increasing angular resolution. As a rule of thumb,the side lobes are sensitive to limb darkening and atmosphericstructure but consist of very low visibilities. With VEGA, beingable to measure very low visibilities will allow us to determinethe angular diameters of stars of sub-mas sizes to an accuracybetter than 2% (Mourard et al. 2010). We limit ourselves to starspresenting an angular diameter smaller than 3.0 mas in order tobe able to cover both the central lobe and the side lobes of thevisibility function.Moreover, using triplets of the longest baselines in the visibleis a powerful means of determining accurate limb darkeninglaws throughout the HR diagram. Limb darkening is a functionof the wavelength, and in particular limb darkening in a givenspectral line depends upon the physical location in the atmosphereof the line-forming region of the element. Thus, an accuratemeasurement of the limb-darkening within spectral lineswill allow us to study the temperature and density structure of theatmosphere, hence the strong interest in using multi-telescopecombiners operating with dispersed fringes.For VEGA, by adopting the same approach used for searchingto calibrators and considering the standard VEGA squaredvisibility measurement accuracy of 2% and the CHARA longestbaseline (330 m), we have determined the minimum measurablediameter for a given accuracy. This corresponds to 0.16 mas(resp. 0.12, 0.075) for a 1% (resp. 2%, 5%) accuracy in the angulardiameter determination. We have then determined that suchlimb-darkening studies will be possible for stars spread overnearly the whole Hertzsprung-Russell diagram (excluding compactobjects) as illustrated in Fig. 11, and will result in a very4.3. Towards chromatic imaging of stellar surfacesand complex environmentsVisibility measurements close to zero and closure phases aresensitive to departures from circular symmetry (due to stellarspots, for instance). Both the 3T and 4T operations are thereforewell adapted to stellar activity studies and/or spot detectionon stellar surfaces. In various contexts, high angular resolutionmeasurements provided by optical interferometry appearsto be very relevant to the study of geometrical constraints onstellar spotty surfaces and to be very complementary to existingspectro-photometric techniques. As an example, this techniquecan be well suited to the detection of spots on exoplanet hoststars and to accurately quantify the stellar noise that can mimicplanetary signals in radial-velocity and/or transit methods whensearching for exoplanets (Lagrange et al. 2010). Provided thathigh spectral resolution is coupled to long-baseline interferometry,another challenge is to be able to detect and image the abundanceinhomogeneities of chemically peculiar stars, which willbe an important step in more clearly understanding this peculiarclass of objects and the physical processes that occur in a stronglarge-scale organized magnetic field.4.4. Other scientific goalsCoupling high angular resolution to high spectral resolution isalso of interest for kinematic studies that use emission lines.Being able to reconstruct velocity-resolved images is a powerfulmeans of studying the complex environments of hot stars,permitting us to probe the geometry and kinematics of the dustand the gas that surrounds these objects or to provide constraintson the size, the inclination, or the position angle of the circumstellardisks. It could also provide information about the stellarrotation and the differential rotation for fast rotators (Zorec et al.2011).Binary star study will also greatly benefit from a combinationof high spectral and high spatial resolutions. This is indeedthe ideal way to achieve accurate measurements of mass and luminosity,which are the primary parameters of stellar evolutionmodels.Finally, it has been demonstrated that using spectral differentialobservables to reconstruct images greatly improves the qualityof the reconstructed images, which are then astrometricallylinked from wavelength-to-wavelength (Millour et al. 2011).5. ConclusionWe have described the principles and the formalism of thespatio-spectral encoding of fringes. This mode is well adaptedto multi-axial dispersed fringe instruments for optical longbaselineinterferometry and allows us to simultaneously reducethe size of the optics to accommodate the beams, decrease thenumber of pixels that have to be read to correctly analyze allthe fringe systems, and increase the SNR and thus the limitingmagnitude of these instruments.Thanks to the dual instrument capabilities of the CHARA arrayoperating system, we have been able to use the visible spectrographVEGA in parallel with the infrared instruments CLIMBand MIRC. A low-frequency group-delay tracking of fringes inthe infrared has been shown to permit an excellent stabilizationA110, page 8 of 9