Deane M. Peterson

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.

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.

Space Interferometry Mission: taking the measure of the universe

In 1991 the Astrophysics Division of NASAs Office of Space Science convened the Space Interferometry Science Working Group to consider in more detail the science goals of a space interferometer mission to do wide-angle astrometry at optical wavelengths. In addition, the working group considered the merits of alternative mission concepts for achieving those goals. We describe the current state of the adopted mission concept, and review the candidate astrometric science program. In addition to the main goal of precision astrometry, the concept interferometer has a limited capability for high- resolution imaging using rotational aperture synthesis. A phase A start on this mission has been made in 1996, an launch is planned for 2003.

Resolving the effects of rotation in early type stars

We review the theory of rotating stars, first developed 80 years ago. Predictions include a specific relation between shape and angular velocity and between surface location and effective temperature and effective gravity. Seen at arbitrary orientation rapidly rotating stars will display ellipsoidal shapes and possibly quite asymmetric intensity distributions. The flattening due to rotation has recently been detected at PTI and VLTI. With the increasing baselines available in the visible and the implementation of closure phase measurements at the NPOI it is now possible to search for the surface brightness effects of rotation. Roche theory predicts only large scale deviations from the usual centro-symmetric limb-darkened models, ideal when the stellar disks are only coarsely imaged as now. We report here observations of Altair and Vega with the NPOI using baselines that detect fringes beyond the first Airy zero in both objects. Asymmetric, non-classical intensity distributions are detected. Both objects appear to be rotating at a large fraction of their breakup velocity. Vega is nearly pole on, accounting for its low apparent rotational velocity. Altairs inclination is intermediate, allowing high S/N detection of all the predicted features of a Roche spheroid. We describe how these objects will test this fundamental theory and how Vegas role as a standard will need reinterpretation.

Coherent integrations, fringe modeling, and bootstrapping with the NPOI

Atmospheric turbulence is a major impediment to ground-based optical interferometry. It causes fringes to move on ms time-scales, forcing very short exposures. Because of the semi-random phase shifts, the traditional approach averages exposure power spectra to build signal-to-noise ratio (SNR). This incoherent average has two problems: (1) A bias of correlated noise is introduced which must be subtracted. The smaller the visibility/the fainter the target star, the more diffcult bias subtraction becomes. SNR builds only slowly in this case. Unfortunately, these most difficult small visibility baselines contain most of the image information. (2) Baseline phase information is discarded. These are serious challenges to imaging with ground based optical interferometers. But if we were able to determine fringe phase, we could shift and integrate all the short exposures. We would then eliminate the bias problem, improve the SNR, and we would have preserved most of the phase information. This coherent averaging becomes possible with multi-spectral measurements. The group delay presents one option for determining phase. A more accurate approach is to use a time-dependent model of the fringe. For the most interesting low-visibility baselines, the atmospheric phase information can be bootstrapped from phase determinations on high-visibility baselines using the closure relation. The NPOI, with 32 spectral channels and a bootstrapping configuration, is well-suited for these approaches. We will illustrate how the fringe modeling approach works, compare it to the group-delay approach, and show how these approaches can be used to derive bias-free visibility amplitude and phase information. Coherent integration provides the highest signal-to-noise (SNR) improvement precisely in the situations where SNR builds most slowly using incoherent averaging. Coherent integration also produces high-SNR phase measurements which are calibration-free and thus have high real uncertainties as well. In this paper we will show how to coherently integration on NPOI data, and how to use baseline visibilities and calibrate coherently integrated visibility amplitudes.

Coherent integration of NPOI phase closure data on Altair

We applied an algorithm for the coherent integration of visibility data of the Navy Prototype Optical Interferometer in the reduction of observations of Altair. This algorithm was first presented at the SPIE meeting in Kona in 2002 and is based on the principle of phase bootstrapping a long baseline using the fringe delays and phases measured on the two shorter baselines with which it forms a triangle in a three-station array. We show that the SNR of the visibility amplitudes and closure phases is significantly increased compared to the standard incoherent integration, also enabling us to use all 28 wavelength channels (instead of 20) afforded by the NPOI spectrometers. The recovery of the data at the blue end is important for constraining any models of this star.

The Effect of Rotation on Calibrators for Ground-based Interferometry

We consider the problem introduced by rotation in the use of early-type stars as calibrators for optical interferometry. These objects have high surface brightnesses and hence are relatively bright, even with small angular diameters. However, rotation can introduce changes in the predicted visibilities well in excess of the uncertainties in the various diameter-magnitude-color calibrations. Measurements of the projected rotational velocity constrain these effects, but the constraints are complicated and not easily evaluated when selecting potential calibrators. Furthermore, the magnitude of the variations depends on the details of the interferometer, such as latitude, baseline length, and operating wavelength. Nevertheless, using measured magnitudes, colors, parallaxes, and projected rotational velocities, and estimating masses from standard evolutionary grids, we are able to calculate histograms that approximate the probability distribution of the visibilities and allow us to characterize the width of the distribution of squared visibilities and the total range induced by rotation. We have found that proximity to the ZAMS adds a valuable constraint, allowing stars with moderate rotation to be reliable calibrators in a number of cases. Catalogs characterizing the sensitivity of the visibilities of potential calibrators to rotation are presented for a number of standard interferometer configurations.

Imaging the Effects of Rotation in Altair and Vega

After a brief review of rotation among upper main sequence stars and von Zeipel’s vZ24 theory for the interiors, we describe our interferometric measurements of two bright A stars, Altair and Vega. The Navy Prototype Optical Interferometer (jointly operated by the US Naval Observatory, the Naval Research Laboratory and Lowell Observatory) which works at visible wavelengths has implemented baselines of sufficient length to initiate true imaging of the disks of the brightest A stars. We report here measurements of Altair, the third brightest A star in the sky. “Closure phase” techniques show that Altair deviates dramatically from a normal limb-darkened isk, indicating a strongly asymmetric intensity distribution. A oche model provides a good fit to the data, indicating that Altair is rotating at about 90% of its breakup (angular) velocity. We find that a gravity darkening law exponent appropriate for a radiative star is required by the observations and we describe the potential of this object for testing the assumption of solid body rotation throughout its envelope. We will also describe recent measurements of Vega which confirm the proposed interpretation of spectral line measurements indicating that this star is also rapidly rotating, but seen nearly pole on.

Early type stars as calibrators for ground-based interferometry

Visibility measurements with Michelson interferometers, particularly the measurement of fringe contrast, are affected by various atmospheric and instrumental effects, all of which reduce the measured contrast. To compensate for this, stars with known or predictable diameters (calibrators) are observed so that the overall reduction in the visibility can be measured. Objects with the smallest possible diameters are preferred as calibrators, since the predicted visibilities become less sensitive to any uncertainties. Therefore, unreddened, early type stars are usually chosen if they are available because they are relatively bright for a given angular diameter. However, early type stars bring additional complications. Rapid rotation, common with these stars can cause variations in the visibility amplitudes due to oblateness and surface brightness asymmetries that are larger than implied by the usual error estimates. In addition, rotation can introduce significant phase offsets. Using Roche models, von Zeipel theory, and the observed constraints of V, B-V, and v sin i, it is possible to put limits on the size of these effects and even estimate the distribution of possible visibilities. To make this easily available to the community, we are in the process of creating a catalog of possible calibrators, including histograms of the visibilities, calculated for configurations used at a number of observatories. We show the examples of several early type stars which are potential calibrators using parameters appropriate for the Navy Prototype Optical Interferometer.

Scientific support for space interferometry

In the two years since the last SPIE meeting on this topic there has been much activity in both ground and space based interferometry. I review those developments, I also summarize the Strawman Science Proposal prepared by the Space Interferometry Science Working Group as a gauge for evaluating the AIM instrument proposals. I then review the recent discovery of the disk structure in M106 using radio interferometry. As an example of where we want to go with optical interferometry, the M106 case argues for infrared capabilities, significant fields of view, and the availability of auxiliary instruments, e.g. spectrographs, in the imaging focal plane.