Detecting the Companions and Ellipsoidal Variations of RS CVn Primaries. I. σ Geminorum

To measure the properties of both components of the RS Canum Venaticorum binary σ Geminorum (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\u27s 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 (${M}_{1}=1.28\pm 0.07$ ${M}_{\odot }$, ${M}_{2}=0.73\pm 0.03$ ${M}_{\odot }$), and estimate a system age of $5\mp 1$ Gyr. An average of the 27 year APT light curve of σ Gem folded over the orbital period ($P=19.6027\pm 0.0005$ 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 $\beta \lt 0.1$, a value slightly lower than that expected from recent theory