of Be stars made with the CHARA Array on Mount Wilson, California. We present observations of the Be stars Phi Per, Zeta Tau, Gamma Cas, and Kappa.
Active OB Stars: Laboratories for Stellar and Circumstellar Physics ASP Conference Series, Vol. 361, 2007 ˇ S. Stefl, S. P. Owocki and A. T. Okazaki
CHARA Array Observations of Be Stars and Regulus D. R. Gies, E. K. Baines, D. H. Berger, C. Farrington, E. D. Grundstrom, W. Huang, H. A. McAlister, and T. A. ten Brummelaar Department of Physics and Astronomy, Georgia State University, P.O. Box 4106, Atlanta, GA 30302-4106 and M. V. McSwain1 Department of Astronomy, Yale University, P.O. Box 208101, New Haven, CT 06520-8101 Abstract. The disks of Be stars produce an infrared flux excess that is predicted to have an angular size much larger than the stellar diameter in the sky. Here we report on the first K-band long baseline interferometric observations of Be stars made with the CHARA Array on Mount Wilson, California. We present observations of the Be stars Phi Per, Zeta Tau, Gamma Cas, and Kappa Dra that clearly reveal the disk flux, and we use simple disk models to fit the interferometric visibilities. We also report on CHARA K-band observations of the bright, rapidly rotating star Regulus (type B7 V). Through a combination of interferometric and spectroscopic measurements, we have determined for Regulus the equatorial and polar diameters and temperatures, the rotational velocity and period, the inclination and position angle of the spin axis, and the gravity darkening coefficient. These results provide the first interferometric measurement of gravity darkening in a rapidly rotating star and represent the first detection of gravity darkening in a star that is not a member of an eclipsing binary system.
1.
Introduction
The CHARA Array is an optical long baseline (34-331 m) interferometer located at Mount Wilson Observatory. It consists of six 1-m aperture telescopes on altaz mounts in a Y-shaped configuration. Currently, the Array operates in the near IR using H and K and produces fringes using a pairwise combination of beams over a wide range of baselines and sky orientations. A more complete discussion of the CHARA Array can be found in ten Brummelaar et al. (2005). Be stars have long been a popular target for interferometry because their disks contribute significant flux excess in Hα (Chesneau 2007). Their disks also radiate at longer wavelengths, causing an IR excess that in φ Per contributes as much as 50% of the K-band flux (Gehrz 1974). Stee & Bittar (2001) present an outflow model for γ Cas that also predicts a large flux contribution from the disk in K and the Brγ line. They predict that the disk of γ Cas is three times larger at these wavelengths than at Hα, suggesting that Be star disks can be resolved 1
NSF Astronomy and Astrophysics Postdoctoral Fellow
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with K-band interferometry. Because of CHARA’s capabilities and versatility, it is an ideal instrument to resolve the near-IR disks of bright Be stars. We have used the instrument to obtain the first interferometric observations of Be star disks in the K-band, and we present here preliminary disk models for φ Per, γ Cas, ζ Tau, and κ Dra based on our observations. The star Regulus (spectral type B7 V; Johnson & Morgan 1953) is a wellknown rapid rotator, and its large projected rotational velocity V sin i, near the expected critical breakup velocity, suggests that the inclination of its rotational axis is nearly 90 deg (see McAlister et al. 2005 and references therein). Therefore, Regulus is expected to have a significant rotationally induced oblateness and a surface flux modified by gravitational darkening. Previous measurements of its angular diameter using the Narrabri Intensity Interferometer and lunar occultations failed to detect this oblateness (see McAlister et al. 2005 and references therein). We present here new results from K-band interferometric measurements with the CHARA Array combined with optical spectroscopy that provide accurate measurements of the equatorial and polar diameters and temperatures, the rotational velocity and period, the inclination and position angle of the spin axis, and the gravity darkening coefficient.
2.
Visibility Models of Be Star Disks
Tycner et al. (2004) show that the visibility curve of a Be star and its disks can be modeled with five parameters: the angular diameter of the uniform photospheric disk, θU D , the fraction of the monochromatic flux contributed by the photosphere, cp , the FWHM of an assumed Gaussian disk, θmajor , the apparent ratio of the minor to major axes of the inclined disk, r, and the major axis position angle, φ. The flux contribution of the disk is then 1 − cp , and the inclination of the disk can be determined from r assuming a circularly symmetric disk. Because the stellar photosphere can only be partially resolved in K with the CHARA Array, the interferometric visibility curve based on a uniform disk model is consistent with models using limb darkening and distortions due to rapid rotation (i.e., the visibility curves diverge only at much larger baselines), so these effects were neglected. We calculated visibility models for the Be stars φ Per, γ Cas, ζ Tau, and κ Dra using constraints on θU D , φ, and r from the literature (Quirrenbach et al. 1997; Tycner et al. 2004). The models were fit to our observed K-band visibilities over a range in baselines to determine cp and θmajor for each star. The model visibility curves are compared to our observations in Figures 1 − 4, and the resulting disk parameters are summarized in Table 1. Most of the scatter in our figures arises because we only plot the modeled visibility for the disk major and minor axes, although our observations include many position angles that are not aligned with these axes. At the 250 m baseline used in our observations of φ Per, the disk is over-resolved and only a lower limit for the size of the disk could be determined. For ζ Tau, we were able to measure r directly since our observations include the position angles corresponding to the major and minor axes of the flattened disk. The low r of ζ Tau indicates that the disk is viewed nearly edge-on.
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Figure 1. Visibility model of φ Per. Solid circles represent observations at position angles that are within 45 deg of the disk’s major axis, while open circles represent points within 45 deg of the minor axis.
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Figure 2.
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Visibility model of γ Cas, shown in the same format as Figure 1.
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Visibility model of ζ Tau, shown in the same format as Figure 1.
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Visibility model of κ Dra, shown in the same format as Figure 1.
CHARA Array Observations of Be Stars and Regulus Table 1.
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Disk parameters from K-band visibility models
Star φ Per γ Cas ζ Tau κ Dra
θU D 0.39∗ 0.56∗ 0.39∗ 0.39∗
cp 0.53 0.46 0.43 0.70
θmajor (mas) > 1.5 1.3 − 1.8 2.1 − 3.0 1.1 − 3.7 ∗ Fixed.
r 0.46∗ 0.70∗ 0.13 0.91∗
φ (deg) −66∗ +21∗ −58∗ −67∗
Our observations of these Be stars indicate that the disks are bright in K as predicted, although they are comparable in size or smaller than in Hα (Quirrenbach et al. 1997; Tycner et al. 2004). This is surprising considering the expected disk sizes from the model of Stee & Bittar (2001), and further observations are necessary to confirm this result. We plan to obtain new observations in fall 2005 at a 100 m baseline to fit the most sensitive parts of the visibility curves for each of these stars.
3.
The Rapidly Rotating Star Regulus
We determined a physical model for the star Regulus using a combination of interferometric and spectroscopic observations (McAlister et al. 2005). We observed the rapid rotator Regulus in K-band with the CHARA Array at a wide range of baselines and position angles to measure the angular diameter of its major and minor axes, θmajor = 1.65 ± 0.02 mas and θminor = 1.25 ± 0.02 mas, gravitational darkening coefficient, β = 0.25 ± 0.11, and rotation axis inclination, i = 90+0 −15 deg. The K-band image of the star and its associated Fourier transform visibility pattern in the (u,v)-plane are shown in Figure 5. Fits of the Hγ and Mg II λ 4481 line profiles in our optical spectra provide further confirmation of i and β as well as measurements of its projected rotational velocity, V sin i = 317 ± 3 km s−1 , polar and equatorial effective temperatures, Tp = 15400 ± 1400 K and Te = 10314 ± 1000 K, and effective gravity. Using the Hipparcos parallax for Regulus, we determined directly its mass, M = 3.4 ± 0.2M⊙ , and polar and equatorial radii, Rp = 3.14 ± 0.06R⊙ and Re = 4.16 ± 0.08R⊙ . Our results for Regulus indicate that its luminosity, L = 347 ± 36L⊙ , is overluminous for its mass when compared to evolutionary models of non-rotating stars (Schaller et al. 1992). However, this is consistent with models of rapid rotators, which experience rotational mixing that replenishes the H core to increase the star’s luminosity and extend its lifetime along the main-sequence (Meynet & Maeder 2000). The high values of i and V sin i we measure for Regulus indicate that the star is rotating at 86% of its critical breakup velocity. The star shows no sign of Hα emission in our spectra, nor has it been noted as a Be star in the literature. Since Be stars are believed to be a population of rapid rotators near their critical breakup velocity, our result for Regulus prompts the question of whether Be stars require V > 0.86 Vcrit . The CHARA Array and other interferometers will play
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Figure 5. K-band image of the star in the sky (left) and its associated Fourier transform visibility pattern in the (u,v )-plane (right). The dotted black line indicates the direction of the rotational axis for the best fit model. The upper part of the visibility figure shows a gray-scale representation of the visibility and the positions of the CHARA measurements (black squares), and the lower part shows the normalized residuals from the fit as a gray-scale intensity ranging from −5 (black ) to +5 (white).
a key role in determining the true rotational velocities of Be stars to determine whether they are in fact rotating near critical breakup velocity. 4.
The Future of CHARA
Our observations of 4 Be stars with the CHARA Array demonstrates that high angular resolution observations of Be stars in the K-band are important probes of the disk geometry and dimensions, and observations of these Be stars at shorter baselines will better constrain our models of their disks. CHARA observations of the nearby star Regulus also suggest that the Be star photospheres may be resolved at shorter wavelengths and long baselines, leading to direct estimates of their rotational deformation and equatorial rotational velocities. High signal-to-noise observations at shorter wavelengths may also be used to detect binary companions to Be stars. References Abt, H. A., Levato, H., & Grosso, M. 2002, ApJ, 573, 359 Chesneau, O. 2007, these proceedings, p. 288. Gehrz, R. D., Hackwell, J. A., & Jones, T. W. 1974, ApJ, 191, 675 Johnson, H. L., & Morgan, W. W. 1953, ApJ, 117, 313 McAlister, H. A., ten Brummelaar, T. A., Gies, D. R., et al. 2005, ApJ, 628, 439 Meynet, G., & Maeder, A. 2000, A&A, 361, 101 Quirrenbach, A., Bjorkman, K. S., Bjorkman, J. E., et al. 1997, ApJ, 479, 477
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Schaller, G., Schaerer, D., Meynet, G., & Maeder, A. 1992, A&AS, 96, 269 Stee, P., & Bittar, J. 2001, A&A, 367, 532 ten Brummelaar, T. A., McAlister, H. A., Ridgway, S. T., et al. 2005, ApJ, 628, 453 Tycner, C., Hajian, A. R., Armstrong, J. T., et al. 2004, AJ, 127, 1194
Discussion P. Stee: It’s very interesting that you find a smaller size in the K band compared to Hα. As you said, we predict larger extensions using our SIMECA model and thus it will put very strong constraints on the modeling. By the way, how do you estimate the size of the emitting envelope? Since you use gaussians where do you “cut” the gaussian to obtain the size? (50% of the total emission? 80%?) V. McSwain: We can determine the flux contribution from the disk from the spectral energy distribution and implied infrared excess or from the interferometric visibilities at the longest baselines (dominated by the stellar). Our preliminary results indicate that both methods give consistent answers. O. Chesneau: In my opinion, the error of V sin i for Regulus is slightly underestimated but the inclination seems well-constrained. This could provide even more near-critical parameters. The estimation of V sin i is really the main difficulty of the interpretation of such observations. V. McSwain: The constraints on V sin i come from Wenjin Huang’s detailed spectroscopic model of this rotationally distorted star. He did not use the traditional approach of convolving a rotational broadening function to a model line profile; rather, he used a grid of model atmospheres over the representative range of T and log g across the stellar surface to model accurately the gravitationallydarkened flux. Therefore, the constraints on V sin i are much more accurate than in most spectroscopic studies. S. Owocki : Your results for Regulus provide a direct test of how well one can infer Vrot and Vcrit for unresolved stars since you can measure both directly. How does your value of Vcrit in particular agree with standard values for the spectral properties of this star if it were unresolved? V. McSwain: In the literature, measurements of the V sin i range from 249−350 km s−1 . Assuming an inclination close to 90 deg for such a rapid rotator, these estimates place the star’s rotation anywhere from 67−95% of V crit . We measured V sin i = 317 km s−1 for Regulus, which is much faster than the average for B7 V stars (152 km s−1 ; Abt, Levato, & Grosso 2002).
