Solar neighborhood. XXVIII. Substellar companions

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^+3.5^_-0.0_% for L companions to M dwarfs in the separation range of 5-70 AU, and 2.3^+5.0^_-0.7_% for L and T companions to M dwarfs in the separation range of 10-70AU.

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.