Solar-like oscillations and ellipsoidal variations in TESS observations of the binary 12 Bo\"otis

Binary stars in which oscillations can be studied in either or both components can provide powerful constraints on our understanding of stellar physics. The bright binary 12 Bo\"otis (12 Boo) is a particularly promising system because the primary is roughly 60 per cent brighter than the secondary despite being only a few per cent more massive. Both stars have substantial surface convection zones and are therefore, presumably, solar-like oscillators. We report here the first detection of solar-like oscillations and ellipsoidal variations in the TESS light curve of 12 Boo. Though the solar-like oscillations are not clear enough to unambiguously measure individual mode frequencies, we combine global asteroseismic parameters and a precise fit to the spectral energy distribution (SED) to provide new constraints on the properties of the system that are several times more precise than values in the literature. The SED fit alone provides new effective temperatures, luminosities and radii of $6115\pm45\,\mathrm{K}$, $7.531\pm0.110\,\mathrm{L}_\odot$ and $2.450\pm0.045\,\mathrm{R}_\odot$ for 12 Boo A and $6200\pm60\,\mathrm{K}$, $4.692\pm0.095\,\mathrm{L}_\odot$ and $1.901\pm0.045\,\mathrm{R}_\odot$ for 12 Boo B. When combined with our asteroseismic constraints on 12 Boo A, we obtain an age of $2.67^{+0.12}_{-0.16}\,\mathrm{Gyr}$, which is consistent with that of 12 Boo B.