15000 Ellipsoidal Binary Candidates in TESS: Orbital Periods, Binary Fraction, and Tertiary Companions

We present a homogeneously-selected sample of 15779 candidate binary systems with main sequence primary stars and orbital periods shorter than 5 days. The targets were selected from TESS full-frame image lightcurves on the basis of their tidally-induced ellipsoidal modulation. Spectroscopic follow-up suggests a sample purity of $83 \pm 13$ per cent. Injection-recovery tests allow us to estimate our overall completeness as $28 \pm 3$ per cent with $P_\mathrm{orb} < 3$ days and to quantify our selection effects. We estimate that $39 \pm 4$ per cent of our sample are contact binary systems, and we disentangle the period distributions of the contact and detached binaries. We derive the orbital period distribution of the main sequence binary population at short orbital periods, finding a distribution continuous with the log-normal distribution previously found for solar-type stars at longer periods, but with a significant steepening at $P_\mathrm{orb} \lesssim 3$ days, and a pile-up of contact binaries at $P_\mathrm{orb} \approx 0.4$ days. Companions in the period range 1--5 days are found to be an order of magnitude more frequent around stars hotter than $\approx 6250 K$ (the Kraft break) when compared to cooler stars, suggesting that magnetic braking plays an important role in shaping the temperature and period distributions. We detect resolved tertiary companions to $9.0 \pm 0.2$ per cent of our binaries with a median separation of 3200 AU. The frequency of tertiary companions rises to $29 \pm 5$ per cent among the systems with the shortest ellipsoidal periods. This large binary sample with quantified selection effects will be a powerful resource for future studies of detached and contact binary systems with $P_\mathrm{orb} < 5$ days.