The Astrophysical Journal, 807:23 (10pp), 2015 July 1 doi:10.1088/0004-637X/807/1/23 © 2015. The American Astronomical Society. All rights reserved. DETECTING THE COMPANIONS AND ELLIPSOIDAL VARIATIONS OF RS CVn PRIMARIES. I. σGEMINORUM Rachael M. Roettenbacher1, John D. Monnier1, Gregory W. Henry2, Francis C. Fekel2, Michael H. Williamson2, Dimitri Pourbaix3, David W. Latham4, Christian A. Latham4, Guillermo Torres4, Fabien Baron1, Xiao Che1, Stefan Kraus5, Gail H. Schaefer6, Alicia N. Aarnio1, Heidi Korhonen7, Robert O. Harmon8, Theo A. ten Brummelaar6, Judit Sturmann6, Laszlo Sturmann6, and Nils H. Turner6 1 Department of Astronomy, University of Michigan, Ann Arbor, MI 48109, USA; [email protected] 2 Center of Excellence in Information Systems, Tennessee State University, Nashville, TN 37209, USA 3 FNRS, Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles (ULB), Belgium 4 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA 5 School of Physics, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK 6 Center for High Angular Resolution Astronomy, Georgia State University, Mount Wilson, CA 91023, USA 7 Finnish Centre for Astronomy with ESO (FINCA), University of Turku, Väisäläntie 20, FI-21500 Piikkiö, Finland 8 Department of Physics and Astronomy, Ohio Wesleyan University, Delaware, OH 43015, USA Received 2015 February 27; accepted 2015 April 17; published 2015 June 25 ABSTRACT To measure the properties of both components of the RS Canum Venaticorum binary σGeminorum (σ Gem),we directly detect the faint companion, measure the orbit, obtain model-independent masses and evolutionary histories, detect ellipsoidal variations of the primary caused by the gravity of the companion, and measure gravity darkening. We detect the companion with interferometric observations obtained with the Michigan InfraRed Combiner at Georgia State University’s Center for High Angular Resolution Astronomy Array with a primary-to- secondary H-band flux ratio of 270 ± 70. A radial velocity curve of the companion was obtained with spectra from the Tillinghast Reflector Echelle Spectrograph on the 1.5 m Tillinghast Reflector at Fred Lawrence Whipple Observatory. We additionally use new observations from the Tennessee State University Automated Spectroscopic and Photometric Telescopes (AST and APT, respectively). From our orbit, we determine model-independent masses of the components (M1 =1.28 0.07 M, M2 =0.73 0.03 M), and estimate a system age of 5 1 Gyr. An average of the 27 year APT light curve of σGem folded over the orbital period (P =19.6027 0.0005 days) reveals a quasi-sinusoidal signature, which has previously been attributed to active longitudes 180° apart on the surface of σ Gem. With the component masses, diameters, and orbit, we find that the predicted light curve for ellipsoidal variations due to the primary star partially filling its Roche lobe potential matches well with the observed average light curve, offering a compelling alternative explanation to the active longitudes hypothesis. Measuring gravity darkening from the light curve gives b < 0.1, a value slightly lower than that expected from recent theory. Key words: binaries: close – stars: activity – stars: imaging – stars: individual (sigma Geminorum) – stars: variables: general Supporting material: machine-readable tables 1. INTRODUCTION σ Geminorum (σ Gem, HD 62044, HIP 37629, HR 2973) is an RS CVn system known to exhibit starspots, often ascribed to RS Canum Venaticorum (RS CVn) stars are spotted, active “active longitudes” (e.g., Hall et al. 1977; Henry et al. 1995). binary systems exhibiting photometric and Ca H and ( ) The system has been characterized as a single-lined spectro- K variability Hall & Stars 1976 . Often tidally locked, these scopic binary (Herbig & Spalding 1955) with a K1III primary systems are composed of an evolved primary star (giant or ( ) σ ) ( Roman 1952 . The orbital period of Gem is slightly longer subgiant and a subgiant or dwarf companion Berdyu- than the primary star’s rotation period derived from the fastest gina 2005; Strassmeier 2009). With active binaries, not only rotating spots (Porb = 19.60 days, Prot,min = 19.47 days; Kajat- is there potential to determine the component masses and kari et al. 2014). system evolutionary history, but there is also the opportunity to Because of its large starspots, σ Gem is a frequent target for fi understand the magnetic eld interactions through active understanding starspot evolution. Eberhard & Schwarzschild ° longitudes, particular longitudes that are 180 apart with (1913) first reported σ Gem as active and potentially spotted persistent, long-lived starspots (Berdyugina & Tuominen 1998; due to fluctuations in the Ca H and K lines as the star rotated. Berdyugina 2005). Decades later, Hall et al. (1977) identified photometric Observing the magnetic phenomena of rapidly rotating variations that suggested starspots (DV ~ 0.07). Initial models evolved stars also sheds light on the magnetic activity of of the surface of σ Gem often showed the surface with two rapidly rotating young stars, such as T Tauri stars. Both T Tauri starspots oriented on opposite sides of the primary star (Fried and RS CVn systems have starspots that areanalogous to et al. 1983). Berdyugina & Tuominen (1998) emphasize that, sunspots—cool starspots resulting from stifled convection in due to tidal locking, the starspots are located such that one spot the outer layers of the stars due to strong magnetic fields constantly faces the companion and the other spot is 180° (Petrov 2003; Berdyugina 2005). offset. The majority of spot models applied to the light curves 1 The Astrophysical Journal, 807:23 (10pp), 2015 July 1 Roettenbacher et al. Table 1 Calibrators for σ Geminorum Calibrator Name Calibrator Size (mas) Source UT Date of Observation HD 37329 0.71 ± 0.05 Bonneau et al. (2006) 2012 Nov 8 HD 50019 (θ Gem) 0.81 ± 0.06 Bonneau et al. (2006) 2012 Nov 7, 8, 25 HD 63138 0.65 ± 0.04 MIRC calibration 2011 Dec 8; 2012 Nov 8 HD 69897 (χ Cnc) 0.73 ± 0.05 Bonneau et al. (2006) 2012 Nov 7, 24, 25 of σ Gem consistof two spots on a spherical star (Eker 1986; Table 2 Strassmeier et al. 1988; Olah et al. 1989; Henry et al. 1995; Radial Velocity Data of σ Gem (CfA) ) Jetsu 1996; Padmakar & Pandey 1999; Kajatkari et al. 2014 . HJD−2400000 Primary (kms-1) Secondary (kms-1) Doppler images have suggested the surface is covered with a ( ő 56202.0199 10.66 103.44 larger number of smaller spots Hatzes 1993;Kvári − et al. 2001, 2014). 56230.0436 77.98 9.80 57002.9567 14.17 94.68 To understand the binary system, we present our analysis of fi 57003.9301 9.71 101.50 the rst detections of the companion in our interferometric and 57014.8600 79.02 −12.11 radial velocity data sets, as well as photometric data. In 57015.8427 75.96 −10.77 Section 2, we describe the observations for our data sets. In 57018.8519 51.08 28.91 Section 3, we discuss our analysis of the data sets, including the 57019.9181 38.76 60.57 first astrometric and spectroscopic detections of the companion 57020.9452 27.84 78.02 star and orbital parameters. In Section 4, we present 57021.8962 19.05 84.20 evolutionary constraints and a Hertzsprung–Russell (H–R) 57024.9812 9.10 104.10 diagram. In Section 5, we discuss our analysis of the 57025.9317 12.59 99.41 photometric data set, including detected ellipsoidal variations 57026.8891 18.88 85.69 57028.9057 38.58 K and measured gravity darkening. In Section 6, we present the σ 57029.8670 49.81 27.28 conclusions of our study of Gem. 57031.8806 69.76 −2.88 2. OBSERVATIONS Note. Errors on the primary radial velocities are 0.84 kms-1. Errors on the -1 2.1. Interferometry secondary radial velocities are 3.8 kms . These were then scaled for our orbit fit to have a total c2 = 1.00. Note that these radial velocities are on the native We obtained interferometric data with Georgia State CfA system. We added 0.14 kms-1 for use in our analysis (Stefanik et al. University’s Center for High Angular Resolution Astronomy 1999). (CHARA) Array. The CHARA Array is a Y-shaped array of (This table is available in machine-readable form.) six 1 m class telescopes with non-redundant baselines varying from 34 to 331 m located at Mount Wilson Observatory, California (ten Brummelaar et al. 2005). Using all six ) fl ( telescopes and the Michigan InfraRed Combiner (MIRC; Ridge Observatory and 1.5 m Tillinghast Re ector Fred ) ( Monnier et al. 2004, 2006), we obtained H-band Lawrence Whipple Observatory, FLWO telescopes 2003 – ) (1.5- 1.8 mm) data (eight channels across the photometric December 30 2007 June 5 . band with l D~l 40) on UT 2011 November 9 and From 2012 October 1 to 2015 January 9, using the fl December 7, 8, 9; 2012 November 7, 8, 21, 22, 24, 25,and Tillinghast telescope with the Tillinghast Re ector Echelle ( ű ) December 4, 5. Spectrograph TRES; F rész 2008 , we were able to make 15 fi We made detections of the companion in the data from UT detections of the secondary spectra for the rst time. Along 2011 December 8; 2012 November 7, 8, 24, and 25. The with 16 new primary star measurments, these new radial -1 remaining nights of observation had insufficient uv coverage velocities are presented in Table 2. We add 0.14 km s to these due to poor seeing or short observation lengths, leaving the sets of radial velocities to account for these data being reported ( companion undetected. We reduced and calibrated these data on the CfA native system Stefanik et al. 1999; note that the with the standard MIRC pipeline (see Monnier 2007; Zhao correction is inaccurately stated as a subtraction in this ) et al.