On The Orbital Separation Distribution and Binary Fraction of M Dwarfs

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. We use 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), 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 $\leq$ q $\leq$ 1.00] and [0.00 $\leq$ a $\leq$ 10,000 AU]. This method was then extrapolated to calculate a binary fraction which encompasses the broader ranges of [0.10 $\leq$ q $\leq$ 1.00] and [0.00 $\leq$ a < $\infty$ AU]. Finally, the results of these calculations were compared to the binary fractions of other spectral types. The binary fraction over the constrained regions of [0.60 $\leq$ q $\leq$ 1.00] and [0.00 $\leq$ a $\leq$ 10,000 AU] was calculated to be $0.229 \pm 0.028$. This quantity was then extrapolated over the broader ranges of q (0.10 - 1.00) and a (0.00 - $\infty$ AU) and found to be $0.462^{+0.057}_{-0.052}$. 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 $\leq$ q $\leq$ 1.00] and [0.00 $\leq$ a $\leq$ 10,000 AU] to be $0.270 \pm 0.111$. Lastly, we estimate the multiplicity fractions of FGK, and A stars using the same method (taken over [0.60 $\leq$ q $\leq$ 1.00] and [0.00 $\leq$ a $\leq$ 10,000 AU]) and 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.