Constraints on the orbital separation distribution and binary fraction of M dwarfs

Department of Astronomy, University of Michigan, Ann Arbor, MI, USA
e-mail: nsusemiehl@gmail.com

Received: 4 June 2020
Accepted: 9 September 2021

Abstract

Aims. We present a new estimate for the binary fraction (the fraction of stars with a single companion) for M dwarfs using a log-normal fit to the orbital separation distribution.

Methods. We used point estimates of the binary fraction (binary fractions over specific separation and companion mass ratio ranges) from four M dwarf surveys sampling distinct orbital radii to fit a log-normal function to the orbital separation distribution. This model, alongside the companion mass ratio distribution given by Reggiani & Meyer (2013, A&A, 553, A124), is used to calculate the frequency of companions over the ranges of mass ratio (q) and orbital separation (a) over which the referenced surveys were collectively sensitive – [0.60 ≤ q ≤ 1.00] and [0.00 ≤ a ≤ 10 000 AU]. This method was then extrapolated to calculate a binary fraction which encompasses the broader ranges of [0.10 ≤ q ≤ 1.00] and [0.00 ≤ a <  ∞ AU]. Finally, the results of these calculations were compared to the binary fractions of other spectral types.

Results. The binary fraction over the constrained regions of [0.60 ≤ q ≤ 1.00] and [0.00 ≤ a ≤ 10 000 AU] was calculated to be 0.229 ± 0.028. This quantity was then extrapolated over the broader ranges of q (0.10−1.00) and a (0.00 − ∞ AU) and found to be 0.462_−0.052^+0.057. We used a conversion factor to estimate the multiplicity fraction from the binary fraction and found the multiplicity fraction over the narrow region of [0.60 ≤ q ≤ 1.00] and [0.00 ≤ a ≤ 10 000 AU] to be 0.270 ± 0.111. Lastly, we estimated the multiplicity fractions of FGK, and A stars using the same method (taken over [0.60 ≤ q ≤ 1.00] and [0.00 ≤ a ≤ 10 000 AU]). We find that the multiplicity fractions of M, FGK, and A stars, when considered over common ranges of q and a, are more similar than generally assumed.