On The Orbital Separation Distribution and Binary Fraction of M Dwarfs

Abstract

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 $\le$ q $\le$ 1.00] and [0.00 $\le$ a $\le$ 10,000 AU]. This method was then extrapolated to calculate a binary fraction which encompasses the broader ranges of [0.10 $\le$ q $\le$ 1.00] and [0.00 $\le$ 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 $\le$ q $\le$ 1.00] and [0.00 $\le$ a $\le$ 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 $0.462_{-0.052}^{+0.057}$. 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 $\le$ q $\le$ 1.00] and [0.00 $\le$ a $\le$ 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 $\le$ q $\le$ 1.00] and [0.00 $\le$ a $\le$ 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.

6 pages, 2 figures. Accepted for publication in A&A

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