Resolving the Effects of Rotation in Altair with Long-Baseline
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Submitted to the Astrophysical Journal June 9, 2005 Revised draft of June 21, 2018 A Preprint typeset using LTEX style emulateapj v. 6/22/04 RESOLVING THE EFFECTS OF ROTATION IN ALTAIR WITH LONG-BASELINE INTERFEROMETRY D. M. Peterson1, C. A. Hummel2,4, T. A. Pauls3, J. T. Armstrong3, J. A. Benson5, C. G. Gilbreath3, R. B. Hindsley3, D. J. Hutter5, K. J. Johnston4, D. Mozurkewich6, & H. Schmitt3,7 (Received 2005 June 9) Submitted to the Astrophysical Journal June 9, 2005 Revised draft of June 21, 2018 ABSTRACT 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 asym- metric 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 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. Subject headings: stars: rotation—stars: imaging—stars: individual (α Aql)— techniques: interfero- metric 1. INTRODUCTION nificant convection disappears at this point on the up- per main sequence. We note that α Cep also has a high Altair (variously α Aql, 53 Aql, HR 7557, HD 187642, −1 of spectral type A7VI-V) is one of the brightest stars projected rotation velocity with estimates of 246 km s −1 in the Northern sky, sharing membership in the “Sum- (Uesugi & Fukuda 1982), 196 km s (Royer et al. 2002), mer Triangle” with two other notable A stars. Unlike and 180kms−1 (Abt & Morrel 1995) listed. Vega and Deneb, Altair shows a rather diffuse spectrum Altair’s known high rotation rate has prompted at- which was early recognized to be due to a large projected tempts to measure the geometrical effects of its rota- rotational velocity variously estimated at 242 km s−1 tion over the years, starting with the Intensity Inter- (Uesugi & Fukuda 1982), 217 km s−1 (Royer et al. 2002), ferometer (Hanbury Brown et al. 1974). However, it and 200kms−1 (Abt & Morrel 1995). These estimates of was not until the near-IR observations with the Palo- its projected velocity, a lower limit for the true rotational mar Testbed Interferometer (PTI; Colavita et al. 1999) velocity, are already a significant fraction of the breakup by van Belle et al. (2001) that a significant flattening −1 was detected. Comparison to classical (von Zeipel 1924) velocity, estimated near 400 km s . Roche models showed the flattening was completely con- arXiv:astro-ph/0509236v1 9 Sep 2005 Altair has become a significant object in understanding sistent with the observed projected rotation. the atmospheres of main sequence stars at masses near Although this agreement between theory and observa- but above that of the Sun. Specifically, Altair and α Cep tion is nothing short of epochal, it is incomplete. Except are the two hottest stars showing Lyα and C II emis- near breakup, apparent oblateness, interpreted through sion, taken as indicators of a chromosphere (Simon et al. Roche theory, displays the same degeneracy between 1994; Walter et al. 1995). The absence of these indica- equatorial velocity and tilt (inclination) as the apparent tors at earlier spectral types is taken to mean that sig- rotation velocity: one determines the quantity veq sin i 1 Department of Physics and Astronomy, Stony Brook well, but not the two separately. Nor can one determine University, Stony Brook, NY 11794-3800 email: dpeter- the sense of rotation, pro- or retrograde. Besides provid- [email protected] 2 ing a test of the flattening predicted by theory, oblateness European Southern Observatory (ESO), Casilla 19001, Santi- measurements do yield the position angle of the angular ago 19, Chile email: [email protected] 3 Naval Research Laboratory, Code 7215, 4555 Overlook momentum vector, the projection of that vector on the Ave. SW, Washington, DC 20375 email: [email protected], plane of the sky. [email protected], [email protected], hen- In addition to flattening, von Zeipel (1924) predicted [email protected] 4 U.S. Naval Observatory, 3450 Massachusetts Ave. NW, that for moderate rotation stellar disks would display Washington, DC, 20392-5420 email: [email protected] variable surface temperatures, hotter on the rotational 5 U.S. Naval Observatory, Flagstaff Station, 10391 W. Naval axes and cooler at the equator. Specifically, if one de- Observatory Rd., Flagstaff, AZ 86001-8521 email: jben- fines a local effective gravity accounting for centrifugal [email protected], [email protected] 6 acceleration, then the local effective temperature is re- Seabrook Engineering, 9310 Dubarry Rd., Seabrook, MD 4 20706 email: [email protected] lated to the effective gravity as Teff ∝ geff , which is 7 Interferometrics, Inc., 13454 Sunrise Valley Drive, Suite 240, referred to as “gravity darkening”. With sufficient rota- Herndon, VA20171 2 Peterson et al. tion and at intermediate inclinations, gravity darkening 2. OBSERVATIONS predicts that stellar disks will display asymmetric inten- Altair was observed on four nights, 25–27 May and sity distributions. 1 June of 2001, with the NPOI. These are the same ob- As we describe below, this prediction is of great inter- servations used by Ohishi et al. (2003) and Ohishi et al. est in the field of optical interferometry. Asymmetric in- (2004); we refer the reader to those papers for a journal tensity distributions produce significant imaginary com- of observations and a description of the observing details, ponents in the visibilities, usually represented as a non- but we briefly reprise them here. We have focused here trivial visibility phase. Recently developed techniques on the data set obtained May 25, 2001. This is by far the for recovering a closely related quantity, “closure phase” largest set of data, while the other data do not increase (Baldwin et al. 1996; Benson et al. 1997), are now be- the range of hour angles observed in the first night. ing applied to the first round of stellar objects, (e.g., The observations used the Astrometric West (AW), As- Wittkowski et al. 2001). trometric East (AE), and West 7 (W7) stations, form- Although originally proposed as a follow-up on the ing a triangle of interferometric baselines with lengths oblateness observations, Altair was observed at the of 37.5 m (AW–AE), 29.5 m (W7–AW), and 64.4 m (AE– Navy Prototype Optical Interferometer (hereafter NPOI, W7). The backend combined these three input beams to Armstrong et al. 1998) while the three beam combiner produce three output beams, with one baseline on each. was in operation, allowing measurement of closure phase The output beams were dispersed into 32 spectral chan- around one complete triangle. Examination of the data nels covering λλ443 − 852 nm, although the bluest four immediately revealed the intermediate phase angles, un- channels (λλ443 − 460 nm) of the W7–AW output were ambigiously signaling the presence of an asymmetric in- not functioning. tensity profile (Ohishi et al. 2003). The Altair observations were interleaved with obser- Using a model consisting of a limb-darkened disk and a vations of a calibrator, ζ Aql (A0 V), about 12◦ away bright spot, Ohishi et al. (2004) demonstrated both the on the sky. We initially estimated its diameter to be previously discovered oblateness and the necessity of in- around 0.85 mas, with which it would have acted as cluding asymmetries in the intensity distribution. They a quite acceptable calibrator. However, as noted by argued that the probable interpretation was that of ro- Ohishi et al. (2004), ζ Aql is a rapid rotator with values tational flattening and gravity darkening. − − of 345kms 1 (Uesugi & Fukuda 1982) and 317kms 1 In the meantime we have become aware of some lim- −1 itations in those data due to inadequate corrections for (Royer et al. 2002) reported. We adopted 325kms , “deadtimes” in the avalanche photodiode detectors which raising the question of aspect dependent corrections to affect the high signal levels from objects as bright as Al- the squared visibilities and phases. This possibility was tair. We therefore reconsider a subset of these data that discussed by Ohishi et al. (2004) who concluded that the is relatively immune to the detector problems, using a effects were not important at the level of the analysis they full implementation of von Zeipel’s theory (von Zeipel conducted, but who cautioned that the problem needed 1924) for the model fitting, and redoing the reductions to be reconsidered if a detailed analysis of Altair was in a way that dramatically reduces noise in the bluest attempted with these observations. channels. We find that a Roche model rotating at 90% We have found a number of occasions in 2004 when ◦ ζ Aql was observed with a second calibrator, γ Lyr of the breakup angular velocity and inclined ∼ 64 from −1 pole-on fits the observations with high fidelity. (B9 III). γ Lyr is a relatively slow rotator (∼ 70kms , We show that the parameter that sets the overall tem- Royer et al.