Christian A. Hummel

Constraints on the Geometry of Circumstellar Envelopes: Optical Interferometric and Spectropolarimetric Observations of Seven Be Stars

We have obtained contemporaneous optical interferometry and spectropolarimetry of seven Be stars. The interferometry was done using both continuum and narrow Ha line -lters to observe the circumstel- lar envelope emission. The envelopes of all seven stars were resolved interferometrically in Ha. Of these seven stars, the envelopes of four were not circularly symmetric and showed clear evidence of elongation. The position angles of the major axis of the elongation were in good agreement with the disk orientation inferred from the intrinsic polarization data, which samples material within a few stellar radii, and also agreed with previous results from the radio, which samples material out as far as 100 stellar radii but at lower resolution. This -nding indicates that the envelope alignment persists over 2 orders of magnitude in radius. Minimum inclination angle estimates from the interferometry are presented for six of the seven stars. Under the assumption that the envelopes are fairly thin circularly symmetric disks, there is a straightfor- ward explanation of the interferometric results. The stars with the greatest elongations, f Tau, / Per, and t Per, are seen nearly equator-on; c Cas is seen at a more intermediate latitude, consistent with previous results; and 48 Per and g Tau, which are only slightly asymmetric, are nearly pole-on. b CMi had insuf- -cient coverage to determine whether its envelope is asymmetric. These results are consistent with inde- pendent indications of the inclinations based on the polarimetry. Spectral diagnostics have been used in the past to classify Be stars as pole-on or as shell stars (usually interpreted to indicate an equator-on orientation). Our inclination angle for 48 Per is consistent with its pole-on classi-cation by Slettebak, and the three equator-on stars have all been previously classi-ed as shell stars. However, both c Cas and g Tau have also been previously classi-ed as shell stars, but we -nd that they have intermediate and pole-on orientations, respectively. We interpret this -nding as evidence that, while equator-on stars may preferentially be shell stars, not all shell stars are actually equator-on. Our results show that the Ha emission region extends up to about 12 stellar radii, possibly depending on spectral type. The size of this region correlates with the equivalent width of the Ha emission. Our results also provide strong constraints for allowed models of Be star envelopes. In particular, for f Tau, we derive an upper limit to the disk opening angle of 20i, which limits the vertical extent of the envelope. We also -nd that the polarization position angle is perpendicular to the interferometric major axis in all cases. This rules out envelope models that are both optically and geometrically thick, since these models produce polarization parallel to the plane of the disk. We conclude that results from the combined interferometry and polarimetry strongly favor the disk paradigm for Be stars over mildly ellip- soidal models. Subject headings: circumstellar matter E stars: emission-line, Be E techniques: interferometric E techniques: polarimetric

ANGULAR DIAMETERS OF STARS FROM THE MARK III OPTICAL INTERFEROMETER

Observations of 85 stars were obtained at wavelengths between 451 and 800 nm with the Mark III Stellar Interferometer on Mount Wilson, near Pasadena, California. Angular diameters were determined by fitting a uniform-disk model to the visibility amplitude versus projected baseline length. Half the angular diameters determined at 800 nm have formal errors smaller than 1%. Limb-darkened angular diameters, effective temperatures, and surface brightnesses were determined for these stars, and relationships between these parameters are presented. Scatter in these relationships is larger than would be expected from the measurement uncertainties. We argue that this scatter is not due to an underestimate of the angular diameter errors; whether it is due to photometric errors or is intrinsic to the relationship is unresolved. The agreement with other observations of the same stars at the same wavelengths is good; the width of the difference distribution is comparable to that estimated from the error bars, but the wings of the distribution are larger than Gaussian. Comparison with infrared measurements is more problematic; in disagreement with models, cooler stars appear systematically smaller in the near-infrared than expected, warmer stars larger.

Vega is a Rapidly Rotating Star

Vega, the second brightest star in the northern hemisphere, serves as a primary spectral type standard. Although its spectrum is dominated by broad hydrogen lines, the narrower lines of the heavy elements suggested slow to moderate rotation, giving confidence that the ground-based calibration of its visible spectrum could be safely extrapolated into the ultraviolet and near-infrared (through atmosphere models), where it also serves as the primary photometric calibrator. But there have been problems: the star is too bright compared to its peers and it has unusually shaped absorption line profiles, leading some to suggest that it is a distorted, rapidly rotating star seen pole-on. Here we report optical interferometric observations that show that Vega has the asymmetric brightness distribution of the bright, slightly offset polar axis of a star rotating at 93 per cent of its breakup speed. In addition to explaining the unusual brightness and line shape peculiarities, this result leads to the prediction of an excess of near-infrared emission compared to the visible, in agreement with observations. The large temperature differences predicted across its surface call into question composition determinations, adding uncertainty to Vegas age and opening the possibility that its debris disk could be substantially older than previously thought.

Navy Prototype Optical Interferometer Observations of the Double Stars Mizar A and Matar

We present a detailed analysis of two spectroscopic binaries based on new observations obtained with the Navy Prototype Optical Interferometer (NPOI). While the data calibration needs refinement, first results show the impressive potential of NPOI, both in terms of speed and precision, for imaging and modeling the orbits of spectroscopic binaries. We determine the orbital parameters of Mizar A (ζ1 Ursae Majoris) and Matar (η Pegasi), and derive masses and luminosities using published radial velocities and Hipparcos trigonometric parallaxes. The results on Mizar A are compared to earlier work done with the Mark III interferometer, while data from this instrument were combined with NPOI data in the Matar analysis.

First Observations with a Co-phased Six-Station Optical Long-Baseline Array: Application to the Triple Star ? Virginis

We report on the first successful simultaneous combination of six independent optical telescopes in an interferometric array. This is double the number of independent telescopes, and 5 times the number of independent baselines, heretofore combined simultaneously. This was accomplished with the Navy Prototype Optical Interferometer at Lowell Observatory, near Flagstaff, Arizona. We describe the main technologies demonstrated, including hybrid six-way beam combination, nonredundant multiple optical path modulation for fringe separation, and the fringe detection electronics. To test the array’s suitability for high

Direct Confirmation of Stellar Limb Darkening with the Navy Prototype Optical Interferometer

Using three elements of the Navy Prototype Optical Interferometer and observing in 20 spectral channels covering 520-850 nm, we have implemented a phase bootstrapping technique in which short baselines with high visibilities are used to keep the longer baselines with low visibilities in phase. Using this method, we have been able to extend the spatial frequency coverage beyond the first zero of the stellar visibility function for two K giants α Arietis, and α Cassiopeiae. The data are inconsistent with a uniform-disk model and confirm the presence of limb-darkened radial profiles. Adopting a particular limb-darkening law enables us to determine the diameter with small formal errors (one part in 1000). In addition, we have measured closure phases for both stars. The closure phases show a jump of 180° at the first zero in the visibility amplitude, which was expected.

Resolving the effects of rotation in altair with long-baseline interferometry

We report the successful fitting of a Roche model, with a surface temperature gradient following the von Zeipel gravity darkening law, to observations of Altair made with the Navy Prototype Optical Interferometer. We confirm the claim by Ohishi et al. that Altair displays an asymmetric intensity distribution due to rotation, the first such detection in an isolated star. Instrumental effects due to the high visible flux of this first magnitude star appear to be the limiting factor in the accuracy of this fit, which nevertheless indicates that Altair is rotating at 0.90 ? 0.02 of its breakup (angular) velocity. Our results are consistent with the apparent oblateness found by van Belle et al. and show that the true oblateness is significantly larger owing to an inclination of the rotational axis of ~64? to the line of sight. Of particular interest, we conclude that instead of being substantially evolved as indicated by its classification, A7 IV-V, Altair is only barely off the zero-age main sequence and represents a good example of the difficulties rotation can introduce in the interpretation of this part of the HR diagram.

Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales

We have measured power spectra of atmospheric phase fluctuations with the Mark III stellar interferometer on Mt. Wilson under a wide variety of seeing conditions. On almost all nights, the high-frequency portions of the temporal power spectra closely follow the form predicted by the standard Kolmogorov-Tatarski model. At lower frequencies, a variety of behavior is observed. On a few nights, the spectra clearly exhibit the low-frequency flattening characteristic of turbulence with an outer-scale length of the order of 30 m. On other nights, examination of individual spectra yields no strong evidence of an outer scale less than a few kilometers in size, but comparison of the spectra on different interferometer baselines shows a saturation of the spatial structure function on long baselines. This saturation is consistent with the assumption of an outer-scale length similar to that derived for the nights when low-frequency flattening of the spectra is clearly seen. We discuss possible explanations of this behavior and conclude that power spectra from a single interferometer baseline are a poor diagnostic for the effective outer scale compared with multiple-baseline spectra.

A purely geometric distance to the binary star Atlas, a member of the Pleiades

We present radial velocity and new interferometric measurements of the double star Atlas, which permit, with the addition of published interferometric data, to precisely derive the orbital parameters of the binary system and the masses of the components. The derived semi-major axis, compared with its measured angular size, allows to determine a distance to Atlas of 132 ± 4 pc in a purely geometrical way. Under the assumption that the location of Atlas is representative of the average distance of the cluster, we confirm the distance value generally obtained through main sequence fitting, in contradiction with the early Hipparcos result (118.3 ± 3. 5p c).

An interferometry imaging beauty contest

We present a formal comparison of the performance of algorithms used for synthesis imaging with optical/infrared long-baseline interferometers. Five different algorithms are evaluated based on their performance with simulated test data. Each set of test data is formatted in the OI-FITS format. The data are calibrated power spectra and bispectra measured with an array intended to be typical of existing imaging interferometers. The strengths and limitations of each algorithm are discussed.