Polarization Due to Rotational Distortion in the Bright Star Regulus
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LETTERS DOI: 10.1038/s41550-017-0238-6 Polarization due to rotational distortion in the bright star Regulus Daniel V. Cotton 1*, Jeremy Bailey1, Ian D. Howarth2, Kimberly Bott3,4, Lucyna Kedziora-Chudczer1, P. W. Lucas5 and J. H. Hough5 Polarization in stars was first predicted by Chandrasekhar1, was considered a possibility. Models had previously been calcu- who calculated a substantial linear polarization at the stellar lated10 for rapidly rotating stars of types B0, B1, B2 and B5, and limb for a pure electron-scattering atmosphere. This polariza- extrapolation of these to Regulus’ B7V spectral type suggested tion will average to zero when integrated over a spherical star that the polarization was about what was expected for a star but could be detected if the symmetry was broken, for exam- rotating at 95% of the critical angular velocity for break-up, very ple, by the eclipse of a binary companion. Nearly 50 years ago, similar to the rotation rate determined from interferometric Harrington and Collins2 modelled another way of breaking the observations at the time5. However, as only one wavelength was symmetry and producing net polarization—the distortion of a observed, further observations and modelling were needed to rapidly rotating hot star. Here we report the first detection of confirm the interpretation. this effect. Observations of the linear polarization of Regulus, Here we combine the PlanetPol observations with new obser- with two different high-precision polarimeters, range from vations of Regulus obtained with the High Precision Polarimetric + 42 ppm at a wavelength of 741 nm to –22 ppm at 395 nm. Instrument, HIPPI14, on the 3.9-m Anglo-Australian Telescope at The reversal from red to blue is a distinctive feature of rota- Siding Spring Observatory. These observations were made in four tion-induced polarization. Using a new set of models for the broad wavelength bands with effective wavelengths of 393, 461, 597 polarization of rapidly rotating stars, we find that Regulus is and 618 nm. The PlanetPol observations are in a redder band with +0.6 rotating at 96.5%−0.8 of its critical angular velocity for break- an effective wavelength of 741 nm. In Fig. 1 we show the measured up, and has an inclination greater than 76.5°. The rotation polarizations, averaging all observations in each band and correct- axis of the star is at a position angle of 79.5 ± 0.7°. The con- ing for a small amount of interstellar polarization (see Methods). clusions are independent of, but in good agreement with, the The data are plotted in the form of a Q–U diagram, where the nor- results of previously published interferometric observations malized Stokes parameters Q/I and U/I are related to the degree of Regulus3. The accurate measurement of rotation in early- of polarization p and position angle θ (measured eastwards from type stars is important for understanding their stellar envi- north) through Q/I = p cos 2θ and U/I = p sin 2θ. ronments4 and the course of their evolution5. It can be seen from Fig. 1 that the polarization varies strongly Initial efforts to detect Chandrasekhar’s polarization effect with wavelength, and the points lie nearly on a line passing through proved unsuccessful, leading instead to the discovery of interstel- the diagram’s origin. This is exactly what is expected for polariza- lar polarization6,7. The predicted polarization in an eclipsing binary tion due to rotational distortion, where gravity darkening toward has been observed only once, in Algol8. The early models of these the equator induces a wavelength-dependent asymmetry in the stel- effects used pure electron scattering atmospheres1,6. When more lar disk. The Sonneborn models10 show just this reversal of direc- realistic non-grey stellar-atmosphere models were applied to rotat- tion with the polarization being parallel to the star’s rotation axis at ing stars9,10, the expected polarization at visible wavelengths was red wavelengths, and perpendicular to the star’s rotation axis in the found to be much smaller. Indeed, the low predicted polarizations ultraviolet (when the coordinate system is rotated to align Stokes Q were used to infer that this mechanism could not explain the large with the star’s rotation axis, this corresponds to positive and polarizations observed11 in Be stars, which are now attributed to cir- negative polarization respectively, and we present data by this cumstellar decretion disks12,13. convention later). In the Sonneborn B5 model10, the reversal of The development, over the past decade or so, of a new gen- polarization occurs at ~380 nm. In our Regulus observations, it eration of polarimeters14–16 that can measure stellar polarization occurs at ~480 nm. However, this is entirely consistent with the at the ppm level brings the small atmospheric polarization effects trend shown in the Sonneborn models10 of the reversal shifting to into the range of observations. Using one of these instruments, longer wavelengths for later-type stars. PlanetPol15 on the 4.2-m William Herschel Telescope, the polar- Several factors give us confidence in the reliability of the ization of Regulus was measured17 as 36.7 ± 0.8 ppm, which stood observations. All wavelength bands have been observed multiple out from the much smaller polarizations measured for other times. The repeat observations agree very well even with obser- stars at similar distance in the same part of the sky. It was con- vations separated by months to years (see Methods). There is no cluded that the polarization was likely to be intrinsic. As Regulus indication of any variability. We can exclude the possibility of is a rapidly rotating star, polarization due to rotational distortion Regulus’ companion significantly affecting our measurements 1 School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia. 2 Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK. 3 Virtual Planetary Laboratory, Seattle, WA 98195, USA. 4 Astronomy Department, University of Washington, Box 351580, Seattle, WA 98195, USA. 5 Centre for Astrophysics Research, School of Physics, Astronomy and Mathematics, University of Hertfordshire, Hatfield AL10 9AB, UK. *e-mail: [email protected] NATURE ASTRONOMY | www.nature.com/natureastronomy © 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. LETTERS NATURE ASTRONOMY We then create a set of 46 ATLAS921 stellar-atmosphere mod- l 40 els each calculated for the pair of Teff and log g values that apply at colatitudes from 0 to 90° with 2° intervals. We calculate the emer- gent specific intensity (radiance) and polarization as a function of 20 740.9618.3 μ (cosine of the viewing zenith angle) and wavelength for each of these models with a version of the SYNSPEC spectral-synthesis 461.0 code22 that we have modified to do radiative transfer with full polar- 596.7 0 ization using the Vector Linearized Discrete Ordinate (VLIDORT) (ppm) I 23 / code from RT Solutions . U 392.5 We then select an inclination at which to view the star, and set –20 up a grid of ‘pixels’ covering the observed view, spaced at intervals of 0.01 of the polar radius. For each pixel that overlaps the star, we calculate the colatitude Θ and viewing angle μ. We can then interpo- –40 late in our grid of 46 models and 21 μ-values to obtain the specific intensity and polarization for that pixel. These can then be plotted to create images such as those in Fig. 2 for a specific wavelength –40 –20 0 20 40 range, or integrated across the star to provide the flux and polariza- Q/I (ppm) tion spectrum at high resolution. The polarization wavelength dependence is a complex com- Fig. 1 | Polarization observations of Regulus on a Q–U diagram. bination of effects arising from the change in polarization as a Polarization observations of Regulus averaged for each band (grey points) function of μ (see, for example, Supplementary Fig. 4) and the and the same observations corrected for interstellar polarization change in relative contributions of equatorial and polar regions (red points). Error bars (1σ) for the observations are derived from the at different wavelengths (for example Fig. 2) and temperatures internal measurement statistics and those of the telescope polarization; according primarily to the Planck function9. Figure 3 shows the interstellar corrected points also include a contribution derived how the modelled parameters affect the polarization wavelength from the scatter in interstellar polarization measured in nearby stars. dependence. All four main parameters are significant. Increasing Labels show effective wavelength in nanometres. The blue line is Tp shifts the whole curve upwards, and therefore shifts the cross- the fitted orientation for the rotation axis of the star (see Methods). over from negative to positive polarization to shorter wavelengths. The green dashed lines show the bounds on the rotation axis of the star Decreasing the inclination reduces the positive polarization at red 3 as determined by interferometry . wavelengths while having little effect on the negative polariza- tion in the blue. Increasing ω/ωc or decreasing log gp increases all polarization, making the red polarization more positive, and the (see Supplementary Information). The observations obtained with blue more negative. As a result, the effects of ω/ωc and gravity can- the two different instruments are very consistent, with polariza- not be readily distinguished. tion (after correction for interstellar polarization) in HIPPI’s It is not, therefore, possible to uniquely determine all four param- reddest band being p = 35.4 ± 1.6 ppm at θ = 77.1 ± 1.3°, and that eters from polarization data alone. To progress further, we need measured by PlanetPol being p = 42.1 ± 1.2 ppm at θ = 79.9 ± 0.7°.