SPOTS: The Search for Planets Orbiting Two Stars. III. Complete Sample and Statistical Analysis

Binary stars constitute a large percentage of the stellar population, yet relatively little is known about the planetary systems orbiting them. Most constraints on circumbinary planets (CBPs) so far come from transit observations with the Kepler telescope, which is sensitive to close-in exoplanets but does not constrain planets on wider orbits. However, with continuous developments in high-contrast imaging techniques, this population can now be addressed through direct imaging. We present the full survey results of the Search for Planets Orbiting Two Stars (SPOTS) survey, which is the first direct imaging survey targeting CBPs. The SPOTS observational program comprises 62 tight binaries that are young and nearby, and thus suitable for direct imaging studies, with VLT/NaCo and VLT/SPHERE. Results from SPOTS include the resolved circumbinary disk around AK Sco, the discovery of a low-mass stellar companion in a triple packed system, the relative astrometry of up to 9 resolved binaries, and possible indications of non-background planetary-mass candidates around HIP 77911. We did not find any CBP within 300 AU, which implies a frequency upper limit on CBPs (1--15 $M_{\rm Jup}$) of 6--10 % between 30-300 AU. Coupling these observations with an archival dataset for a total of 163 stellar pairs, we find a best-fit CBP frequency of 1.9 % (2--15 $M_{\rm Jup}$) between 1--300 AU with a 10.5 % upper limit at a 95 % confidence level. This result is consistent with the distribution of companions around single stars.