The Solar Neighborhood XXVIII: The Multiplicity Fraction of Nearby Stars from 5 to 70 AU and the Brown Dwarf Desert Around M Dwarfs

We report on our analysis of HST/NICMOS snapshot high resolution images of 255 stars in 201 systems within ~10 parsecs of the Sun. Photometry was obtained through filters F110W, F180M, F207M, and F222M using NICMOS Camera 2. These filters were selected to permit clear identification of cool brown dwarfs through methane contrast imaging. With a plate scale of 76 mas/pixel, NICMOS can easily resolve binaries with sub-arcsecond separations in the 19".5x19".5 field of view. We previously reported five companions to nearby M and L dwarfs from this search. No new companions were discovered during the second phase of data analysis presented here, confirming that stellar/substellar binaries are rare. We establish magnitude and separation limits for which companions can be ruled out for each star in the sample, and then perform a comprehensive sensitivity and completeness analysis for the subsample of 138 M dwarfs in 126 systems. We calculate a multiplicity fraction of 0.0{-0.0}^{+3.5}% for L companions to M dwarfs in the separation range of 5 to 70 AU, and 2.3_{-0.7}^{+5.0}% for L and T companions to M dwarfs in the separation range of 10 to 70 AU. We also discuss trends in the color-magnitude diagrams using various color combinations and present astrometry for 19 multiple systems in our sample. Considering these results and results from several other studies, we argue that the so-called "brown dwarf desert" extends to binary systems with low mass primaries and is largely independent of primary mass, mass ratio, and separations. While focusing on companion properties, we discuss how the qualitative agreement between observed companion mass functions and initial mass functions suggests that the paucity of brown dwarfs in either population may be due to a common cause and not due to binary formation mechanisms.