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The absolute magnitudes $M_J$, the binary fraction, and the binary mass ratios of M7 to M9.5 dwarfs
 Title: The absolute magnitudes $M_J$, the binary fraction, and the binary mass ratios of M7 to M9.5 dwarfs Authors: Laithwaite, RCWarren, SJ Item Type: Journal Article 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. Issue Date: 6-Oct-2020 Date of Acceptance: 22-Sep-2020 URI: http://hdl.handle.net/10044/1/83138 DOI: 10.1093/mnras/staa2979 ISSN: 0035-8711 Publisher: Royal Astronomical Society Start Page: 2587 End Page: 2597 Journal / Book Title: Monthly Notices of the Royal Astronomical Society Volume: 499 Issue: 2 Copyright Statement: © 2020 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model). This is a pre-copy-editing, author-produced version of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review. The definitive publisher-authenticated version [insert complete citation information here] is available online at: https://doi.org/10.1093/mnras/staa2979 Keywords: astro-ph.SRastro-ph.SRastro-ph.EPastro-ph.SRastro-ph.SRastro-ph.EP0201 Astronomical and Space SciencesAstronomy & Astrophysics Notes: 11 pages, 12 figures Publication Status: Published Online Publication Date: 2020-10-06 Appears in Collections: PhysicsAstrophysicsFaculty of Natural Sciences