The absolute magnitudes MJ, the binary fraction, and the binary mass ratios of M7–M9.5 dwarfs

Abstract

We use the large homogeneous sample of late M dwarfs, M7 to M9.5, of Ahmed & Warren (2019) matched to 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 MJ 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 $16.5\pm 0.8\%$, 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)∝qγ, where q = Ms/Mp. We infer a very steep distribution over this spectral range, with γ > 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 MJ for ultracool M dwarfs at fixed G − J colour is measured to be 0.21 mag.

The local vertical density distribution of ultracool dwarfs M7 to L2.5 and their luminosity function

“…The sample of Ahmed and Warren ( 2019) is homogeneous and the classifications are accurately cal-ibrated to the classifications of the BOSS spectroscopic sample of Schmidt et al (2015), which itself is homogeneous and was subject to careful checks for systematics. Laithwaite and Warren (2020) found 10 stars in common between Schmidt et al (2015) and Dupuy and Liu (2012), and the classifications of Schmidt et al (2015) are on average 0.7 spectral types later. Some additional evidence that the Schmidt et al (2015) M7 to M9 classifications are later than older classifications comes from the recent CARMENES paper by Cifuentes et al (2020).…”

“…Therefore we make no corrections for extinction. Laithwaite and Warren (2020) have made a detailed study of the unresolved binaries in the Ahmed and Warren (2019) sample of M7 to M9.5 dwarfs. They find that unresolved binaries comprise 16.2% of all the systems, and that the binaries are almost exclusively equal mass systems.…”

“…The large difference in M J for spectral types M7 to M9.5 compared to Dupuy and Liu (2012) requires further comment. The matter was considered in detail by Laithwaite and Warren (2020), in their Section 6.1. The reason for the discrepancy is not due to incorrect parallaxes in Dupuy and Liu (2012) but is apparently due to differences in spectral classifications between the two samples.…”

“…To summarise, there is now good evidence that the differences in absolute magnitude between the relation of Laithwaite and Warren (2020) and the other two samples are due to differences in spectral classifications between the BOSS sample of Schmidt et al (2015) and older samples. The advantage of using the M7 to M9.5 sample of Ahmed and Warren ( 2019) is that it is large and homogeneous, and the relation between M J and spectral type has been accurately calibrated with Gaia with a large sample of 2706 systems.…”

“…We then fit a linear relation between absolute magnitude and spectral type, allowing for binaries by fitting a double Gaussian profile to the distribution of absolute magnitudes at fixed spectral type. The method is very similar to that employed by Laithwaite and Warren (2020) for the M7 to M9.5 stars, except they used G − J colour rather than spectral type. The result for single stars is the linear relation M J = 0.359 SpT+7.882 where SpT denotes spectral type and L0, L3 are 10, 13 2 .…”