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We introduce an observational tool based on visibility nulls in optical spectro-interferometry fringe data to probe the structure of stellar atmospheres. In a preliminary demonstration, we use both Navy Precision Optical Interferometer (NPOI) data and stellar atmosphere models to show that this tool can be used, for example, to investigate limb darkening. Using bootstrapping with either multiple linked baselines or multiple wavelengths in optical and infrared spectro-interferometric observations of stars makes it possible to measure the spatial frequency $u_0$ at which the real part of the fringe visibility ${\rm Re}(V)$ vanishes. That spatial frequency is determined by $u_0 = B_\perp/\lambda_0$, where $B_\perp$ is the projected baseline length, and $\lambda_0$ is the wavelength at which the null is observed. Since $B_\perp$ changes with the Earth's rotation, $\lambda_0$ also changes. If $u_0$ is constant with wavelength, $\lambda_0$ varies in direct proportion to $B_\perp$. Any departure from that proportionality indicates that the brightness distribution across the stellar disk varies with wavelength via variations in limb darkening, in the angular size of the disk, or both. In this paper, we introduce the use of variations of $u_0$ with $\lambda$ as a means of probing the structure of stellar atmospheres. Using the equivalent uniform disk diameter $\theta_{\rm UD, 0}(\lambda_0)$, given by $\theta_{\rm UD, 0} = 1.22/u_0(\lambda_0)$, as a convenient and intuitive parameterization of $u_0(\lambda_0)$, we demonstrate this concept by using model atmospheres to calculate the brightness distribution for $\nu$ Ophiuchi and predict $\theta_{\rm UD, 0}(\lambda_0)$, and then comparing the predictions to coherently averaged data from observations taken with the NPOI.

Recovering images from optical interferometric observations is one of the major challenges in the field. Unlike the case of observations at radio wavelengths, in the optical the atmospheric turbulence changes the phases on a very short time scale, which results in corrupted phase measurements. In order to overcome these limitations, several groups developed image reconstruction techniques based only on squared visibility and closure phase information, which are unaffected by atmospheric turbulence. We present the results of two techniques used by our group, which employed coherently integrated data from the Navy Prototype Optical Interferometer. Based on these techniques we were able to recover complex visibilities for several sources and image them using standard radio imaging software. We describe these techniques, the corrections applied to the data, present the images of a few sources, and discuss the implications of these results., Comment: 8 pages, 2008 SPIE Astronomical Telescopes and Instrumentation, Eds. M. Schoeller, W. C. Danchi, F. Delplancke

In this paper we use coherently integrated visibilities (see separate paper in these proceedings, Jorgensen et al. 2008) to measure the properties of binary stars. We use only the phase of the complex visibility and not the amplitude. The reason for this is that amplitudes suffer from the calibration effect (the same for coherent and incoherent averages) and thus effectively provide lower accuracy measurements. We demonstrate that the baseline phase alone can be used to measure the separation, orientation and brightness ratio of a binary star, as a function of wavelength., Comment: 2008 SPIE Astronomical Telescopes and Instrumentation

We present the results of an experiment to image the interacting binary star beta Lyrae with data from the Navy Prototype Optical Interferometer (NPOI), using a differential phase technique to correct for the effects of the instrument and atmosphere on the interferometer phases. We take advantage of the fact that the visual primary of beta Lyrae and the visibility calibrator we used are both nearly unresolved and nearly centrally symmetric, and consequently have interferometric phases near zero. We used this property to detect and correct for the effects of the instrument and atmosphere on the phases of beta Lyrae and to obtain differential phases in the channel containing the Halpha emission line. Combining the Halpha-channel phases with information about the line strength, we recovered complex visibilities and imaged the Halpha emission using standard radio interferometry methods. We find that the results from our differential phase technique are consistent with those obtained from a more-standard analysis using squared visibilities (V^2's). Our images show the position of the Halpha emitting regions relative to the continuum photocenter as a function of orbital phase and indicate that the major axis of the orbit is oriented along p.a.=248.8+/-1.7 deg. The orbit is smaller than previously predicted, a discrepancy that can be alleviated if we assume that the system is at a larger distance from us, or that the contribution of the stellar continuum to the Halpha channel is larger than estimated. Finally, we also detected a differential phase signal in the channels containing HeI emission lines at 587.6 and 706.5nm, with orbital behavior different from that of the Halpha, indicating that it originates from a different part of this interacting system., Comment: Submitted to ApJ

Vega, the second brightest star in the northern hemisphere, serves as a primary spectral type standard. While 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 visibile 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 of Vega which detect the asymmetric brightness distribution of the bright, slightly offset polar axis of a star rotating at 93% of breakup speed. In addition to explaining the unusual brightness and line shape pecularities, 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 Vega's age and opening the possibility that its debris disk could be substantially older than previously thought., Comment: 10 pages, 2 figures, a Letter to Nature, tentatively scheduled for April 13

We report 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, Nordgren, & Hutter 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 degrees to the line of sight. Of particular interest, we conclude that instead of being substantially evolved as indicated by its classification, A7 VI-V, Altair is only barely off the ZAMS and represents a good example of the difficulties rotation can introduce in the interpretation of this part of the HR diagram., Comment: Accepted by the Astrophysical Journal

We present direct measurements of the limb-darkened intensity profiles of the late-type giant stars HR5299, HR7635, and HR8621 obtained with the Navy Prototype Optical Interferometer (NPOI) at the Lowell Observatory. A triangle of baselines with lengths of 18.9 m, 22.2 m, and 37.5 m was used. We utilized squared visibility amplitudes beyond the first minimum, as well as triple amplitudes and phases in up to 10 spectral channels covering a wavelength range of ~650 nm to ~850 nm. We find that our data can best be described by featureless symmetric limb-darkened disk models while uniform disk and fully darkened disk models can be rejected. We derive high-precision angular limb-darkened diameters for the three stars of 7.44 mas +/- 0.11 mas, 6.18 mas +/- 0.07 mas, and 6.94 mas +/- 0.12 mas, respectively. Using the HIPPARCOS parallaxes, we determine linear limb-darkened radii of 114 R$_\odot \pm $13 R$_\odot$, 56 R$_\odot \pm $4 R$_\odot$, and 98 R$_\odot \pm $9 R$_\odot$, respectively. We compare our data to a grid of Kurucz stellar model atmospheres, with them derive the effective temperatures and surface gravities without additional information, and find agreement with independent estimates derived from empirical calibrations and bolometric fluxes. This confirms the consistency of model predictions and direct observations of the limb-darkening effect., Comment: 13 pages, accepted for publication in A&A

We have measured the diameters of the Cepheid variables delta Cephei (18 nights) and eta Aquilae (11 nights) with the Navy Prototype Optical Interferometer. The primary results of these observations are the mean angular diameters of these Cepheids: 1.520 +/- 0.014 milliseconds of arc (mas) for delta Cep and 1.69 +/- 0.04 mas for eta Aql. We also report limb-darkened diameters for the check stars in this program: for beta Lac, theta(LD) = 1.909 +/- 0.011 mas, and for 12 Aql, theta(LD) = 2.418 +/- 0.010 mas. When combined with radius estimates from period-radius relations in the literature, the Cepheid angular diameters suggest distances slightly smaller than, but still consistent with, the Hipparcos distances. Pulsations are weakly detected at a level of about 1.5 sigma to 2 sigma for both Cepheids., Comment: 15 pages, including one figure; LaTeX 2e; uses aastex, aas_symbols, natbib; accepted for publication in the Astronomical Journal

For over two decades, astronomers have considered the possibilities for interferometry in space. The first of these missions was the Space Interferometry Mission (SIM), but that was followed by missions for studying exoplanets (e.g Terrestrial Planet Finder, Darwin), and then far-infrared interferometers (e.g. the Space Infrared Interferometric Telescope, the Far-Infrared Interferometer). Unfortunately, following the cancellation of SIM, the future for space-based interferometry has been in doubt, and the interferometric community needs to reevaluate the path forward. While interferometers have strong potential for scientific discovery, there are technological developments still needed, and continued maturation of techniques is important for advocacy to the broader astronomical community. We review the status of several concepts for space-based interferometry, and look for possible synergies between missions oriented towards different science goals.

Stellar Imager (SI) will be a Space-Based telescope consisting of 20 to 30 separated apertures. It is designed for UV/Optical imaging of stellar surfaces and asteroseismology. This report describes details of an alternative optical design for the beam combiner, dubbed the Spatial Frequency Remapper (SFR). It sacrifices the large field of view of the Fizeau combiner. In return, spectral resolution is obtained with a diffraction grating rather than an array of energy-resolving detectors. The SFR design works in principle and has been implemented with MIRC at CHARA for a small number of apertures. Here, we show the number of optical surfaces can be reduced and the concept scales gracefully to the large number of apertures needed for Stellar Imager. We also describe a potential application of this spatial frequency remapping to improved imaging with filled aperture systems. For filled-aperture imaging, the SFR becomes the core of an improved aperture masking system. To date, aperture-masking has produced the best images with ground-based telescopes but at the expense of low sensitivity due to short exposures and discarding most of the light collected by the telescope. This design eliminates the light-loss problem previously claimed to be inherent in all aperture-masking designs. We also argue that at least in principle, the short-integration time limit can also be overcome. With these improvements, it becomes an ideal camera for TPF-C; since it can form speckle-free images in the presence of wavefront errors, it should significantly relax the stability requirements of the current designs.

The orbit of the double-lined spectroscopic binary Phi Cygni, the distance to the system, and the masses and absolute magnitudes of its components are presented via measurements with the Mar III Optical Interferometer. On the basis of a reexamination of the spectroscopic data of Rach & Herbig (1961), the values and uncertainties are adopted for the period and the projected semimajor axes from the present fit to the spectroscopic data and the values of the remaining elements from the present fit to the Mark III data. The elements of the true orbit are derived, and the masses and absolute magnitudes of the components, and the distance to the system are calculated.

Before contemplating an optical interferometer on the Moon one must first review the accomplishments achieved by this technology in scientific applications for astronomy. This will be done by presenting the technical status of optical interferometry as achieved by the Mount Wilson Optical Interferometer. The further developments needed for a future lunar-based interferometer are discussed.

The apparent orbit of the double-lined spectroscopic binary Alpha Equulei was measured using observations, from June 13, 1989 to September 15, 1990, with the Mark III Optical Interferometer. The results, combined with the spectroscopic results of Rosvick and Scarfe (1991), were used to obtain estimates of the masses of the components, their absolute magnitudes, and the distance to the system. In addition, the magnitude differences between the components were determined at four wavelengths; these were combined with the colors reported by Stickland (1976) to derive colors for the two Alpha Equulei components and to estimate their spectral types.

The long-period variable Mira Omicron Ceti has been observed at 800 nm wavelength with the Mk III Optical Interferometer at photometric phases 0 = 0.96, 0.05, and 0.14 in 1990; some additional data were taken in 1989. The star is not spherically symmetric, and temporal variations of the size and the position angle of the asymmetry are detected. The visibility data can be represented by two uniform elliptical disks, which could correspond to different layers in Mira's atmosphere. If the size variations are interpreted in terms of physical motion of the emitting material, an infall velocity of about 15 km/s around phi = 0 is derived.

Angular diameters determined with the Mark III Optical Interferometer are presented for 12 stars at wavelengths of 450 and 800 nm. The uniform disk diameters resulting from fits to the visibility observations have rms residuals of order 1 percent for the 800 nm measurements and less than 3 percent for the 450 nm measurements. The improvement over previous observations with this instrument is due to improved data analysis and the use of a wider range of baseline lengths. An analysis of the calibration systematics for the Mark III Optical Interferometer is included. There is good agreement between these measurements and previously published data. The changes in uniform disk diameter between wavelengths of 450 and 800 nm agree with models of stellar atmospheres.

The spectroscopic binary Beta Ari has been directly resolved with the Mark III Stellar Interferometer. Observations in 1988 were analyzed to determine the visual orbit of the system with the following results: eccentricity = 0.903 +/- 0.012, semimajor axis = 0.0361 +/- 0.0003 arcsec, inclination = 44.7 +/- 1.3 deg, longitude of periastron = 209.1 deg +/- 1.2 deg, position angle of ascending node = 79.1 deg +/- 0.8 deg. The measured magnitude difference between two components, Delta m = 2.63 +/- 0.22 at 800 nm, yields individual visual magnitudes of m(v1) = 2.70 +/- 0.02 and m(v2) = 5.80 +/- 0.20. Combined with data from spectroscopic observations, masses M1 = (2.34 +/- 0.10) solar masses, M2 = (1.34 +/- 0.07) solar masses, and geometrical parallax pi = 0.053 arcsec +/- 0.002 arcsec are derived. These results demonstrate that both components of Beta Ari agree well with the empirical mass-luminosity relation.

For the first time, four spectroscopic binaries have been directly resolved with the Mark III Stellar Interferometer. Observations in 1988 and 1989 were analyzed, and visual orbits for four binaries have been determined. The semimajor axes for Beta Tri, Alpha Equ, Alpha And and Beta Ari are approximately 0.008 arcsec, 0.012 arcsec, 0.024 arcsec and 0.037 arcsec, respectively. The magnitude differences between two components are 0.5, 0.7, 1.8 and 2.6 mag, respectively. All of the orbital elements for Alpha And and Beta Ari were determined from interferometric data only, and agree well with spectroscopic observations. Predictions of relative position between the two components for these binaries are consistent with the measurements to less than 0.001 arcsec. Combined with data from spectroscopy, masses and distance for the double-lined spectroscopic binary Beta Ari are derived, and the results indicate that both components of Beta Ari agree well with the empirical mass-luminosity relation.

Reliable stellar angular diameters can now be determined using the Mark III Optical Interferometer located on Mt. Wilson, California. The Mark III is a Michelson Interferometer capable of measuring the interferometric fringe visibility for stars using interferometer baselines varying from 3 to 31.5 meters in length. Angular diameters measured with the Mark III Optical Interferometer are presented for 12 stars at wavelengths of 450 and 800 nm.