Statistics on the population of distant substellar companions to nearby stars

Context . Wide substellar companions to stars provide valuable benchmarks for investigating the formation and evolutionary pathways of brown dwarfs and giant planets far beyond the extent of protoplanetary discs. An association to their primary also provides age and metallicity constraints that are otherwise challenging to obtain for isolated objects. Aims . We present a statistical approach to determine the properties of the population of substellar companions to nearby main-sequence stars. This work uses proper motion measurements derived from multi-epoch WISE imaging. Our sample includes 2103 stars within 20 parsecs (pc) and has a sensitivity sufficient to detect substellar companions down to ∼300 K and out to orbital separations of 20 000 AU. Methods . We used a Bayesian approach, based on Markov chain Monte Carlo (MCMC) methods, to constrain the parameters of the companion mass and semi-major axis distributions. We accounted for observational biases, notably the decreasing detectability of fainter objects with increasing absolute magnitude M W 2 , and we robustly explored the underlying population properties. We assumed that the companion mass (M) and semi-major axis (a) follow power laws, described by d 2 n ∝ M α a β dM da . Results . Fitting this model to the data yields the following constraints at the 1 σ confidence level α = −0.21 +0.31 −0.27 and β = −1.38 ± 0.32 and an occurrence rate of 1.07 +0.31 −0.24 % for companions between 5 and 80 M J and at separations of 1000–20 000 AU. The occurrence rate of companions increases for tighter orbits and for more massive host stars. Conclusions . The inferred mass properties of the substellar companion population are broadly consistent with previous results from direct imaging surveys, despite differences in target selection. Notably, the power-law distributions in both mass and separation are consistent with those of stellar binaries. As the input sample is about an order of magnitude larger than that of any previous imaging survey of substellar companions, we significantly improved the statistical characterisation of these objects. Our results suggest that the wide-separation companions represent the low-mass tail of the stellar companion population, rather than a direct extension of the population of close-in giant planets.