2022A&A...657A..48S

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 (2013A&A...553A.124R), 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 ≥ 10000 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 < infinity 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 ≥ 10000 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 - infinity 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 ≥ 10000 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 ≥ 10000 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.