To measure the properties of both components of the RS CVn binary \sigma Geminorum ( \sigma 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 ( MIRC ) at Georgia State University ’ s Center for High Angular Resolution Astronomy ( CHARA ) Array with a primary-to-secondary H -band flux ratio of 270 \pm 70 .
A radial velocity curve of the companion was obtained with spectra from the Tillinghast Reflector Echelle Spectrograph ( TRES ) on the 1.5-m Tillinghast Reflector at Fred Lawrence Whipple Observatory ( FLWO ) .
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 \sigma 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 ^ { \circ } apart on the surface of \sigma 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 < 0.1 , a value slightly lower than that expected from recent theory .