The absolute magnitudes $M_J$, the binary fraction, and the binary mass ratios of M7 to M9.5 dwarfs

Abstract

We use the large homogeneous sample of late M dwarfs, M7 to M9.5, of Ahmed & Warren (2019) matched to $\textit{Gaia}$ DR2, to measure the relation between absolute magnitude and spectral type, and to infer the multiplicity fraction of the population, and the distribution of mass ratios in the binary systems. Binaries are identified photometrically as overluminous sources. In order to define a sample that is unbiased with respect to multiplicity we use distance limits that are a function of $G-J$ colour to define a volume-complete sample of 2706 systems. The $G-J$ colours are very precise, with random errors all less than 0.02. We measure absolute magnitudes $M_J$ that are on average 0.5 mag. brighter than previous determinations. We find evidence that the discrepancies arise from differences in spectral types in different samples. The measured binary fraction is $16.5\pm0.8\%$, of which $98\%$ are unresolved: both values are consistent with results of previous studies. The distribution of excess flux in the binaries, compared to the singles, is used to infer the mass ratio distribution $f(q)\propto q^\gamma$, where $q=M_s/M_p$. We infer a very steep distribution over this spectral range, with $\gamma>10$ ($99\%$ probability). This says that unresolved ultracool M dwarf binaries reside almost exclusively in equal mass systems, and implies that the spectral types of the unresolved binaries match to with 0.5 spectral subtypes. The intrinsic scatter in absolute magnitude $M_J$ for ultracool M dwarfs at fixed $G-J$ colour is measured to be 0.21 mag.