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Imaging the Surface of Altair

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Science  20 Jul 2007:
Vol. 317, Issue 5836, pp. 342-345
DOI: 10.1126/science.1143205

Abstract

Spatially resolving the surfaces of nearby stars promises to advance our knowledge of stellar physics. Using optical long-baseline interferometry, we constructed a near-infrared image of the rapidly rotating hot star Altair with a resolution of <1 milliarcsecond. The image clearly reveals the strong effect of gravity darkening on the highly distorted stellar photosphere. Standard models for a uniformly rotating star cannot explain our findings, which appear to result from differential rotation, alternative gravity-darkening laws, or both.

Whereas solar astronomers can take advantage of high-resolution, multiwavelength, real-time imaging of the Sun's surface, stellar astronomers know most stars—whether located parsecs or kiloparsecs away—as simple points of light. To discover and understand the processes around stars unlike the Sun, we must rely on stellar spectra averaged over the entire photosphere. Despite their enormous value, spectra alone have been inadequate to resolve central questions in stellar astronomy, such as the role of angular momentum in stellar evolution (1), the production and maintenance of magnetic fields (2), the launching of massive stellar winds (3), and the interactions between very close binary companions (4).

Fortunately, solar astronomers no longer hold a monopoly on stellar imaging. Long-baseline visible and infrared interferometers have enabled the cataloging of photospheric diameters of hundreds of stars and high-precision dynamical masses for dozens of binaries, offering exacting constraints for theories of stellar evolution and stellar atmospheres (5). This work requires an angular resolution of ∼1 milliarcsecond (mas) (1 part in 2 × 108, or 5 nanoradians) for resolving even nearby stars, which is more than an order of magnitude better than that achievable with the Hubble Space Telescope or ground-based 8-m telescopes equipped with adaptive optics.

Stellar imaging can be used to investigate the rapid rotation of hot, massive stars. A large fraction of hot stars are rapid rotators with surface rotational velocities of more than 100 km/s (6, 7). These rapid rotators are expected to traverse evolutionary paths very different from those of their slowly rotating kin (1), and rotation-induced mixing alters stellar abundances (8). Although hot stars are relatively rare by number in the Milky Way Galaxy, they have a disproportionate effect on galactic evolution due to their high luminosities, their strong winds, and their final end as supernovae (for the most massive stars). Recently, rapid rotation in single stars has been invoked to explain at least one major type of gamma-ray bursts (9) and binary coalescence of massive stars or remnants (10).

The distinctive observational signatures of rapid rotation were first described by von Zeipel (11), beginning with the expectation that centrifugal forces would distort the photospheric shape and that the resulting oblateness would induce lower effective temperatures at the equator. This latter effect, known as gravity darkening, will cause distortions in the observed line profiles as well as the overall spectral energy distribution. Precise predictions can be made, but these rely on uncertain assumptions, in particular the distribution of angular momentum in the star; uniform rotation is often assumed for simplicity.

The most basic predictions of von Zeipel theory—centrifugal distortion and gravity darkening—have been confirmed to some extent. The Palomar Testbed Interferometer (PTI), the first instrument to measure photospheric elongation in a rapid rotator, found the diameter of the nearby A-type star Altair to be ∼14% larger in one dimension than the other (12). The Navy Prototype Optical Interferometer (NPOI) and the Center for High Angular Resolution Astronomy (CHARA) interferometric array both measured strong limb-darkening profiles for the photometric standard Vega (13, 14), consistent with a rapid rotator viewed nearly pole-on. A brightness asymmetry for Altair was also reported by NPOI (15, 16), suggestive of the expected pole-to-equator temperature difference from gravity darkening. In recent years, a total of five rapid rotators have been measured to be elongated by interferometers (1719).

Although von Zeipel theory appears to work at a basic level, serious discrepancies between theory and observations have emerged. Most notably, the diameter of the B3V-type star Achernar (17) was measured to be ∼56% longer in one dimension than the other, a discrepancy too large to be explained by von Zeipel theory. Explanations for this include strong differential rotation of the star (20) or the presence of a polar wind (3), either of which have far-reaching consequences for our understanding of stellar evolution. To address these issues, we must move beyond the simplest models for rapidly rotating stars, and this will require a corresponding jump in the quality and quantity of interferometry data. Indeed, all previous results were based on limited interferometer baselines that lacked the capability to form model-independent images, and relied entirely on model fitting for interpretation. Thus, previous confirmations of von Zeipel theory, although suggestive, were incomplete.

Here we report a development in imaging capabilities that enables a test of von Zeipel theory, both through basic imaging and precise model-fitting. By combining near-infrared light from four telescopes of the CHARA interferometric array, we have synthesized an elliptical aperture with dimensions 265 m by 195 m (Fig. 1), allowing us to reconstruct images of the prototypical rapid rotator Altair (spectral type A7V) with an angular resolution of ∼0.64 mas, the diffraction limit defined by λ/2D, the observing wavelength divided by twice the longest interferometer baseline. The recently commissioned Michigan Infrared Combiner (MIRC) (21) was essential for this work, allowing the light from the CHARA telescopes to be combined simultaneously into eight spectral channels spanning the astronomical H band (λ = 1.50 to 1.74 μm). The Altair data presented here were collected on 31 August and 1 September 2006 (UT); complete observational information is available (22). In addition, we used some K-band (λ = 2.2 μm) observations by the PTI to constrain the short-baseline visibilities in subsequent analysis.

Fig. 1.

Fourier (u, v) coverage for the Altair observations, where each point represents the projected separation between one pair of the four CHARA telescopes S2, E2, W1, and W2 (31). The dashed ellipse shows the equivalent coverage for an elliptical aperture of 265 m by 195 m oriented along a position angle of 135° east of north.

With the use of four CHARA telescopes, interferometric imaging of Altair is now possible, although this requires specialized image reconstruction techniques. We used the publicly available application MACIM (Markov-Chain Imager for Optical Interferometry) (23) in this work, applying the maximum entropy method (MEM) (24). We restricted the stellar image to fall within an elliptical boundary, similar in principle to limiting the field of view in standard aperture synthesis procedures. This restriction biases our imaging against faint emission features arising outside the photosphere; however, we do not expect any circumstellar emission in Altair, which is relatively cool, lacking signs of gas emission or strong winds. Further details of our imaging procedures, along with results from validation tests, can be found in (22). Our image shows the stellar photosphere of Altair to be well resolved (Fig. 2A), appearing elongated in the northeast-southwest direction with a bright dominant feature covering the northwest quadrant of the star. To reduce the influence of possible low-level artifacts that are beyond the diffraction limit of our interferometer, we have followed the standard procedure (25) of convolving the reconstructed image with a Gaussian beam matching the resolution of the interferometer (Fig. 2B).

Fig. 2.

(A) Intensity image of the surface of Altair (λ = 1.65 μm) created with the MACIM/MEM imaging method using a uniform brightness elliptical prior (Embedded Image = 0.98). Typical photometric errors in the image correspond to ±4% in intensity. (B) Reconstructed image convolved with a Gaussian beam of 0.64 mas, corresponding to the diffraction limit of CHARA for these observations. For both panels, the specific intensities at 1.65 μm were converted into the corresponding blackbody temperatures; contours for 7000, 7500, and 8000 K are shown. North is up and east is left.

These images confirm the basic picture of gravity darkening induced by rapid rotation. We see Altair's photosphere to be oblate with a bright region identifiable as the stellar polar region. The intensity of the dark equatorial band is about 60 to 70% of the brightness at the pole, broadly consistent with expectations for the near-infrared from previous models. Although we see some evidence for deviations from axi-symmetry (small excess emission on the northern limb), this feature is at the limit of our image fidelity and will require additional Fourier coverage to investigate further. We have also fitted our data set with a rapid rotator model, following the prescription set out in Aufdenberg et al. (14) and references therein, assuming a Roche potential (central point mass) and solid-body rotation. The main parameters of the model are the stellar radius and temperature at the pole, the angular rotation rate as a fraction of breakup (ω), the gravity darkening coefficient (β), and the viewing angles (inclination and position angle). We used the stellar atmosphere models of Kurucz (26) to determine the specific intensity of each point on the surface as a function of local gravity, effective temperature, and limb darkening. In addition to matching the new MIRC/CHARA data, we forced the model to match the measured V- and H-band photometric magnitudes (0.765 ± 0.015 and 0.235 ± 0.043, respectively) derived from a broad literature survey. When fixing the gravity-darkening coefficient to β = 0.25 appropriate for radiative envelopes, our derived parameters (Table 1) agree well with the best-fit parameters of Peterson et al. (15) on the basis of visible data. However, our best-fit model reached only a reduced Math of 1.79, which suggests a need for additional degrees of freedom in our model. To improve our fits, we explored an extension to the von Zeipel model, allowing the gravity-darkening coefficient β to be a free parameter. We found that a model with β = 0.190 significantly improved the goodness of fit (Table 1), and this improvement is visually apparent when comparing synthetic model images to the Altair image from CHARA (Fig. 3). In addition to a lower β, the new model prefers a slightly less inclined orientation, a cooler polar temperature, and a faster rotation rate.

Fig. 3.

Synthetic images of Altair (λ = 1.65 μm) adopting conventional rapid-rotation models. (A) The best-fit model assuming standard gravity-darkening coefficient for radiative envelopes (β = 0.25, Embedded Image = 1.79). (B) The result when β is a free parameter (β = 0.190, Embedded Image = 1.37). For both panels, the specific intensities at 1.65 μm were converted into the corresponding blackbody temperatures; contours for 7000, 7500, and 8000 K are shown. We have overplotted the contours from the CHARA image (Fig. 2A) as dotted lines to facilitate intercomparison.

Table 1.

Best-fit parameters for Roche–von Zeipel models of Altair. Parameter descriptions: Inclination (0° is pole-on, 90° is edge-on) and position angle (degrees east of north) describe our viewing angle, Tpole and Rpole describe the temperature and radii of the pole (alternatively, one can describe the temperature and radii at the equator as Teq and Req), ω is the angular rotation rate as a fraction of critical breakup rate, and β is the gravity-darkening coefficient. Models assumed stellar mass = 1.791 M (15), metallicity [Fe/H] = –0.2 (32), and distance = 5.14 pc (33).

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Both our imaging and modeling results point to important deficiencies in the currently popular models for rapid rotators. Previous workers have also encountered problems explaining high-resolution interferometry data with standard prescriptions for rotating stars. In addition to the Achernar case previously cited, Peterson et al. (15) were unable to find a satisfactory fit for Altair assuming a standard Roche–von Zeipel model (Math), consistent with the need for additional stellar physics. Recent results for Alderamin (19) also specifically favor models with smaller βs, in line with our findings. Although model fitting has revealed deviations from standard theory, our model-independent imaging allows new features to be discovered outside current model paradigms. The most striking difference between our CHARA image and the synthetic model images (Fig. 3) is that our image shows stronger darkening along the equator, inconsistent with any von Zeipel–like gravity-darkening prescription assuming uniform rotation. Lower equatorial surface temperatures could naturally arise if the equatorial rotation rate were higher than the rest of the star (differential rotation), reducing the effective gravity at the surface (27). Another possibility is that the cooler equatorial layers could be unstable to convection (28, 29), invalidating a single gravity-darkening “law” applicable to all stellar latitudes. Other studies (30) have found further faults with simple application of the von Zeipel law due to opacity effects in the surface layers. Even though it is difficult to isolate or untangle these various effects from one another, the new interferometric results and our modeling convincingly establish the case for stellar physics beyond the standard models used today to describe rotating stars. A path forward is clear: Differential rotation will leave both geometric and kinematic signatures different from opacity or convection-related phenomena. Observers must be armed with a new generation of models incorporating these physical processes in order to exploit the powerful combination of detailed line profile analysis and multiwavelength interferometric imaging now available.

Supporting Online Material

www.sciencemag.org/cgi/content/full/sci;317/5836/342/DC1

Materials and Methods

Figs. S1 to S5

References

References and Notes

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