15 000 ellipsoidal binary candidates in TESS: Orbital periods, binary fraction, and tertiary companions

We present a homogeneously selected sample of 15 779 candidate binary systems with main sequence primary stars and orbital periods shorter than 5 d. The targets were selected from TESS full-frame image light curves on the basis of their tidally induced ellipsoidal modulation. Spectroscopic follow-up suggests a sample purity of 83 +/- 13 per cent. Injection-recovery tests allow us to estimate our overall completeness as 28 +/- 3 per cent with P-orb < 3 d and to quantify our selection effects. 39 +/- 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 lognormal distribution previously found for solar-type stars at longer periods, but with a significant steepening at P-orb less than or similar to 3 d, and a pile-up of contact binaries at P-orb approximate to 0.4 d. Companions in the period range of 1-5 d are an order of magnitude more frequent around stars hotter than $\approx 6250\, \rm K$ (the Kraft break) when compared to cooler stars, suggesting that magnetic braking shortens the lifetime of cooler binary systems. However, the period distribution in the range 1-10 d is independent of temperature. We detect resolved tertiary companions to 9.0 +/- 0.2 per cent of our binaries with a median separation of 3200 au. The frequency of tertiary companions rises to 29 +/- 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-orb<5 d.