# The Volume-Complete Sample of M Dwarfs with Masses $0.1\leq
M/\hbox{M${}_{\odot}$}\leq 0.3$ within 15 Parsecs

Jennifer G. Winters Center for Astrophysics $|$ Harvard & Smithsonian, 60
Garden Street, Cambridge, MA 02138, USA  David Charbonneau Center for
Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138,
USA  Todd J. Henry RECONS Institute, Chambersburg, Pennsylvania, 17201, USA
Jonathan Irwin  Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden
Street, Cambridge, MA 02138, USA  Wei-Chun Jao Department of Physics and
Astronomy, Georgia State University, Atlanta, GA 30302-4106, USA  Adric R.
Riedel Space Telescope Science Institute, Baltimore, MD 21218, USA  Kenneth
Slatten  RECONS Institute, Chambersburg, Pennsylvania, 17201, USA

###### Abstract

M dwarfs with masses $0.1\leq M/\hbox{M${}_{\odot}$}\leq 0.3$ are under
increasing scrutiny because these fully convective stars pose interesting
astrophysical questions regarding their magnetic activity and angular momentum
history. They also afford the most accessible near-future opportunity to study
the atmospheres of terrestrial planets. Because they are intrinsically low in
luminosity, the identification of the nearest examples of these M dwarfs is
essential for progress. We present the volume-complete, all-sky list of $512$
M dwarfs with masses $0.1\leq M/\hbox{M${}_{\odot}$}\leq 0.3$ and with
trigonometric distances placing them within 15 pc ($\pi_{trig}$ $\geq$ 66.67
mas) from which we have created a sample of $413$ M dwarfs for spectroscopic
study. We present the mass function for these $512$ M dwarfs, which increases
with decreasing stellar mass in linear mass space, but is flat in logarithmic
mass space. As part of this sample, we present new $V_{J}R_{KC}I_{KC}$
photometry for 17 targets, measured as a result of the RECONS group’s long-
term work at the CTIO/SMARTS 0.9m telescope. We also note the details of
targets that are known to be members of multiple systems and find a
preliminary multiplicity rate of $21\pm 2$% for the primary M dwarfs in our
sample, when considering known stellar and brown dwarf companions at all
separations from their primaries. We further find that $43\pm 2$% of all M
dwarfs with masses $0.1\leq M/\hbox{M${}_{\odot}$}\leq 0.3$ are found in
multiple systems with primary stars of all masses within 15 pc.

††facilities: CTIO:0.9m††software: IRAF (Tody, 1986, 1993), IDL, python

##  1 Introduction

Nearby stars provide the best samples of stars for study. First, nearby stars
afford the brightest examples of any type, which is particularly valuable for
those classes of stars with intrinsically low luminosities, such as M dwarfs
with masses $0.1\leq M/\hbox{M${}_{\odot}$}\leq 0.3$ (corresponding roughly to
spectral types M4 V $-$ M7 V). Much remains unknown about these fully
convective stars, such as their magnetic activity, angular momentum history,
multiplicity, ages, and sizes. Thus, the nearest examples offer perhaps the
best opportunity for progress in understanding the physics of this population
as a whole. Second, their proximities allow angular resolution to translate
into finer physical resolution than for more distant objects, permitting
deeper probes for companions and direct measurements of stellar radii. In
addition to the value of these targets for understanding stellar astrophysics,
results have shown that it is only the terrestrial planets transiting the
nearest M dwarfs with radii $<$0.3 R/R⊙ that will be accessible for
atmospheric studies with large telescopes in the near future (Charbonneau &
Deming, 2007; Snellen et al., 2013; Rodler & López-Morales, 2014; Morley et
al., 2017; López-Morales et al., 2019). Our knowledge of these precious
planets depends critically upon understanding their faint host stars.

Even for the nearest stars, the creation of a census has historically been
challenging, resulting in many samples that are biased because they are
magnitude-limited. Volume-limited samples ameliorate many of the biases
inherent to magnitude-limited samples, but all targets require accurate
distances, which are only available via trigonometric parallaxes.

Trigonometric parallaxes have been measured from the ground for the very
nearest M dwarfs for decades (van Altena et al., 1995; Gatewood et al., 2003;
Costa et al., 2005; Henry et al., 2006; Smart et al., 2010; Khovritchev et
al., 2013; Dahn et al., 2017; Henry et al., 2018). However, robust results
require significant time investment, so not all nearby stars have parallax
measurements. The typical sequence of adding a target to an astrometry program
for a parallax measurement is a long one. Searches are conducted for stars
with large proper motions that indicate objects that are potentially nearby.
The next step is to estimate the distances of the nearby candidates via
spectroscopy and/or photometry. Only after an object has shown some evidence
that it is nearby is it added to a program. It is then usually a number of
years before a measurement is considered robust. Due to the low proper motion
and/or faintness of a particular target (which requires significant telescope
investment), some nearby stars have been missed or purposely omitted from
target lists; thus, they lack a parallax measurement.

Astrometry measured from space is generally superior to that measured from the
ground. The astrometric satellite mission $Hipparcos$ measured parallaxes for
more than 100,000 stars, but was magnitude-limited, and thus provided very few
new parallax measurements for the nearest M dwarfs with masses within our mass
range of interest (Perryman et al. 1997, updated in van Leeuwen 2007). The
Gaia satellite (Gaia Collaboration et al., 2016) provided an unprecedented
number of trigonometric parallaxes for astronomical objects in its second data
release (DR2; Gaia Collaboration et al., 2018; Lindegren et al., 2018). But
because it is an ongoing survey, it is still incomplete, even for the nearest
stars. This is a known phenomenon (Arenou et al., 2018; Winters et al., 2019a)
and is due to nearby stars’ typically large proper motions and/or due to
unresolved binary star systems that make fitting a parallax-only model to the
data difficult, at least for the first 22 months of data included in the DR2.

By augmenting the precise parallaxes from the Gaia DR2 with those from long-
term, ground-based astrometry programs and $Hipparcos$, it is now possible to
create volume-complete or nearly volume-complete samples for some types of
stars within carefully defined distance horizons.

While the nearest 5 or 10 pc volumes are conventional distance horizon limits
(van de Kamp, 1971; Henry et al., 2006, 2018)111updates found at recons.org
for nearby star studies, samples encompassing larger volumes provide a basis
for more robust statistics for various astrophysical studies. If we are to
study the atmospheres of terrestrial planets, they need to orbit small stars
that are nearby. Studies have shown that spaced-based missions such as the
James Webb Space Telescope and upcoming giant, ground-based, telescopes such
as the European Extremely Large Telescope, the Thirty Meter Telescope, or the
Giant Magellan Telescope require stars smaller than 0.3 R/R⊙ and closer than
15 pc. However, M dwarfs less massive than 0.1 M/M⊙ that are beyond even 10 pc
are too faint ($R>15$ mag) to achieve the signal-to-noise ratios needed for
high-resolution spectroscopic work on 1.5-m telescopes without exposure times
that are prohibitively long (longer than one-hour). Thus, we choose 15 pc as
our distance horizon and choose M dwarfs within the mass range $0.1\leq
M/\hbox{M${}_{\odot}$}\leq 0.3$ as our sample. We expect that roughly 368 M
dwarf primaries222 We use primary to denote either a single star that is not
currently known to have a companion or the most massive (or brightest in $V$)
component in a multiple system; we use companion to refer to a physical member
of a multiple system that is less massive (or fainter, again in $V$) than the
primary star.  with masses $0.1\leq M/\hbox{M${}_{\odot}$}\leq 0.3$ lie within
15 pc, extrapolating from the 109 found within 10 pc (from Winters et al.,
2019a) and assuming a constant stellar density. Here we present our volume-
complete list of M dwarfs with masses $0.1\leq M/\hbox{M${}_{\odot}$}\leq 0.3$
within 15 pc.

Since September 2016, several of us (JW, DC, and JI) have been conducting an
all-sky, multi-epoch, high-resolution spectroscopic survey of all known M
dwarfs with masses $0.1\leq M/\hbox{M${}_{\odot}$}\leq 0.3$ within 15 pc. For
targets north of $\delta$ $=-$15°, we are using the Tillinghast Reflector
Echelle Spectrograph (TRES; $R\approx 44,000$) on the 1.5m telescope at the
Fred Lawrence Whipple Observatory (FLWO) on Mt. Hopkins, AZ. For targets south
of $\delta=-$15°, we are using the CTIO HIgh ResolutiON (CHIRON; $R\approx
80,000$ via slicer mode) spectrograph at the Cerro Tololo Inter-American
Observatory / Small and Moderate Aperture Research Telescope System (CTIO /
SMARTS) 1.5m telescope.

The goals of our survey are numerous: measure multi-epoch radial (RV) and
rotational velocities ($v\sin i$); identify binaries and, for the ones with
periods less than 3 years, characterize their orbits; and measure the
equivalent widths of chromospheric activity indicators, including H${\alpha}$.
Previous papers presented spectroscopic orbits for some of the binaries in our
sample (Winters et al., 2018, 2020). Future papers from this project will
present the radial and rotational velocities and $UVW$ space motions of these
stars, as well as an analysis of their multiplicity characteristics. Others in
our group are combining the spectroscopic results with $TESS$ data on these
stars, with which we are determining their flare rates and photometric
rotation periods (Medina et al., 2020), and are determining the occurrence
rates of massive planetary companions around these stars. Finally, we are
gathering high-resolution speckle imaging data for the sample, which will
complete the coverage for companions at all separation regimes for this
important population of stars.

We began acquiring data in September 2016, but revised our target list in 2018
with the availability of the second data release from Gaia. Thus, we describe
the history of the sample in §2 and the characteristics of our sample in §3.
We then discuss in §4 the completeness and biases of the sample presented.

##  2 Creation of the Sample

Our goal was to compile a complete sample of M dwarfs with masses $0.1\leq
M/\hbox{M${}_{\odot}$}\leq 0.3$ within 15 pc for our spectroscopic survey.
Creating this list requires knowledge of the stars’ distances and masses. For
nearby stars with small parallax uncertainties, the trigonometric parallax
provides their distances.333For a description of calculating distances from
parallaxes for non-nearby stars, see Luri et al. (2018). But because we can
only directly measure masses for stars in binary systems, we rely on the Mass-
Luminosity Relation (MLR) to estimate the masses of single stars. As we
describe below, we accomplish this through the use of 2MASS $K_{s}-$band
photometry. A third, more subtle constraint on sample membership is the
consideration of close binaries in the sample.

###  2.1 Initial Sample Selection

Our initial sample was created in 2016. We first identified all types of M
dwarfs (main sequence stars with estimated masses 0.075 – 0.64 M/M⊙) that had
trigonometric distances placing them within 15 pc ($\pi_{trig}$ $\geq$ 66.67
mas), with no constraint on the parallax uncertainties. We began with the
volume-limited, all-sky sample of 1120 M dwarfs presented in Winters et al.
(2019a)444We used the target list while the paper was in preparation. that
contains many M dwarfs with mass estimates that lie within 25 pc via a
trigonometric parallax; however, that sample was finalized as of 01 January
2014, and thus did not include M dwarfs with parallaxes that were subsequently
published. We then identified M dwarfs that had new parallaxes placing them
within 15 pc from more recent parallax papers (Dittmann et al., 2014;
Weinberger et al., 2016; Finch & Zacharias, 2016), which we added to our list.
As new parallaxes for nearby M dwarfs were published (e.g., by Dahn et al.,
2017; Finch et al., 2018), we added these to our list.

We then determined which targets fell into our mass region of interest. We
extracted $JHK_{s}$ magnitudes from the 2MASS Point Source Catalog (Cutri et
al., 2003; Skrutskie et al., 2006), which we confirmed by eye to correspond to
the star in question. We calculated the masses of all the M dwarfs using the
mass-luminosity relation by Benedict et al. (2016) with the assumption that
they were single, main-sequence stars. We used the absolute $K_{s}-$band
magnitude for the mass estimation because it is known to be less sensitive to
metallicity effects (Henry & McCarthy, 1993; Delfosse et al., 2000; Benedict
et al., 2016). In the cases where trigonometric parallaxes were not
available555This was the case only for the initial sample creation. As we note
below in §2.2, the DR2 provided parallaxes for all stars that previously had
only photometric distance estimates., photometric distance estimates from
Winters et al. (2015) were used for the mass estimate.

Known binaries with blended $K_{s}-$band photometry required special treatment
to determine the primary stars’ masses. These fell into four categories: 1)
binaries with published orbital solutions that reported masses for the
individual components; 2) binaries with published orbital solutions that
reported mass ratios, but not individual masses (i.e., spectroscopic
binaries); 3) binaries with high-resolution imaging results that reported a
magnitude difference ($\Delta m$) between the components; 4) astrometric
binaries with no reported $\Delta m$.

For the multiple systems with orbital solutions that reported masses (category
1), we simply adopted these masses. For binaries with published orbital
solutions for double-lined spectroscopic binaries that offered mass ratios but
no reported masses (category 2), we estimated the masses of the component
stars in the same way as presented in Winters et al. (2019a). We describe it
here. We first estimated a $\Delta K_{s}$ magnitude based on an assumed flux
ratio between the components. We then deblended the $K_{s}-$band photometry
and calculated the components’ M${}_{K_{s}}$. We then estimated the
components’ masses using the MLR and then calculated the mass ratio for the
system. We repeated these steps after adjusting the $\Delta K_{s}$ until our
estimated mass ratio agreed with the mass ratio in the published orbital
solution. As a check that this method results in accurately estimated masses,
we calculated the masses of the binary star components in category 1 the same
way. Overall, we find a standard deviation of 0.013 M/M⊙when comparing the
published masses to our estimated masses for the binary systems in category 1,
in agreement with the scatter of 0.014 M/M⊙ in the MLR, as reported in
Benedict et al. (2016). We did not include GJ 866ABC as part of this check
because the photometry includes three unresolved stars, making the test more
complicated. When checking the results for GJ 791.2AB, we found discrepancies
of 0.083 M/M⊙ and 0.014 M/M⊙ for the primary and secondary components,
respectively, which we attribute to the DR2 parallax. There is a difference of
20 mas between the DR2 and weighted mean literature parallax values (see
Figure 6). It also has large values for the DR2 astrometric flags ‘astrometric
excess noise’ (6.71 mas, the highest point in Figure 7) and its significance
(20300). Therefore, we used the ground-based parallax for GJ 791.2AB for our
check and find differences of 0.050 M/M⊙ and 0.004 M/M⊙ for the primary and
secondary star masses. The discrepancy between our calculated and the
published mass for GJ 791.2A is by far the largest of the 28 components’
masses we checked. We therefore conclude that our method is robust.

For reported binaries with blended $K_{s}-$band photometry but without
published orbits (category 3), we deblended the photometry based on delta-
magnitude ($\Delta m$) information available in the literature from high-
resolution imaging studies (e.g., adaptive optics, speckle, lucky imaging
work) before calculating the mass of the primary star. In the cases where the
$\Delta m$ was measured in a filter that was not $K_{s}$, we converted the
$\Delta m$ to $\Delta K_{s}$ using the transformations in Riedel et al.
(2014).

Six systems are astrometric binaries reported in publications by the REsearch
Consortium On Nearby Stars (RECONS)666www.recons.org group, which had no
reported $\Delta m$ information (category 4). For these systems, we assumed
all companions were stellar in nature, unless otherwise stated, and we follow
the same procedure for astrometric binaries as in Winters et al. (2019a),
which we describe here. We calculated the photometric distance estimates for
these six systems using the relations from Henry et al. (2004). All of the
photometric distances were in agreement with or smaller than the trigonometric
distances. We then calculated the ratio of the trigonometric distance to the
photometric distance, which we used to estimate the $\Delta m$ between the
components. We note that an equal luminosity binary, with $\Delta m$ near
zero, will not be detected astrometrically because the photocenter will not be
perturbed. For systems where the ratio was $\leq 1.3$, we adopted a $\Delta m$
of 3 mag between the components, as the agreement between the two distances
indicates that the companion contributes a negligible amount of light to the
system’s photometry. For systems where the ratio was $>1.3$, indicating a
luminous companion which contributes light to the system’s photometry, we
adopted a $\Delta m$ of 2 mag between the components. Because of the 15%
uncertainties on the photometric distances, it is difficult to place tighter
constraints on the distance ratio. Thus, we are unable to fine-tune the
magnitude differences until we acquire high-resolution imaging of these
astrometric binaries. The adopted magnitude difference was in the filter in
which the parallax was measured, which we then converted to $\Delta K_{s}$,
again using the transformations in Riedel et al. (2014). Finally, we selected
all stars with masses $0.1<M/\hbox{M${}_{\odot}$}<0.3$, regardless of the mass
uncertainty.

###  2.2 Sample Revision with DR2

With the availability in 2018 of parallaxes in the Gaia second data release
(DR2) (Gaia Collaboration et al., 2018; Lindegren et al., 2018), we revised
our sample. We first searched the DR2 via Vizier for all objects with
parallaxes larger than 66.667 mas (distances nearer than 15 pc) with no
astrometric quality cuts and no constraint on parallax uncertainty. Using
their proper motions, we adjusted the coordinates of the stars in our initial
sample from J2000.0 to J2015.5, the epoch of the DR2 positions, which we then
cross-matched against the DR2 15 pc list. The Gaia archive cross-match to the
2MASS Point Source Catalog (Cutri et al., 2003; Skrutskie et al., 2006)
provides only a 2MASS identifier, so 2MASS $K_{s}$ magnitudes were not readily
available for mass calculations. To determine which were M dwarfs with masses
within our mass range of interest, we used the presumed single stars in our
initial list to determine the typical ($B_{p}-R_{p}$) colors and $G$
magnitudes for these M dwarfs. We then imposed color limits of
$2.3<(B_{p}-R_{p})<4.5$ mag to identify nearby M dwarfs with masses within our
range of interest that previously did not have published parallaxes that
placed them within 15 pc. We also only chose stars with $G<$ 16 mag, as the
least massive star LHS 1604, with mass 0.10 M/M⊙ at roughly 15 pc has $G=$
15.34 mag. This apparent magnitude cut also served to eliminate any false
stars or artefacts, as suggested by Lindegren et al. (2018) and Arenou et al.
(2018). Finally, we extracted 2MASS $JHK_{s}$ magnitudes for the newly
identified nearby stars and recalculated masses using the DR2 parallaxes,
where available, for the entire list because a revision in the parallax will
affect the mass estimate and thus the sample membership. Again, we selected
all stars with masses $0.1<M/\hbox{M${}_{\odot}$}<0.3$, regardless of the mass
uncertainty.

###  2.3 Sample Members That Are Secondaries

We did not restrict our search to primary stars alone. We identified a total
of 143 secondaries with masses within our mass range of interest, as outlined
in Table 1. Sixty-seven of these M dwarfs are companions to M dwarf primaries
with masses $0.1<M/\hbox{M${}_{\odot}$}<0.3$ within 15 pc. Ten companions are
widely separated ($>$ 4″) from their primaries and are included explicitly in
our spectroscopic sample. The remaining 55 are at separations $<$ 4″ from
their primaries and are thus implicitly included in our sample, along with 28
companions that are less massive than 0.1 M/M⊙ (all separated by $<$4″ from
their primaries). Included in the 143 are three M dwarf pairs (GJ 376C, LP
993-116B and GJ 630.1B) that are members of hierarchical triples with massive
primaries with separations $<$4″ between the pair.

The remaining 73 M dwarf companions with masses $0.1\leq
M/\hbox{M${}_{\odot}$}\leq 0.3$ we identified during our search of more
massive stars within 15 pc. From the sample in Winters et al. (2019a), we
searched the early M dwarf primaries (masses $0.30<M/\hbox{M${}_{\odot}$}\leq
0.64$) to identify those with M dwarf companions. We then used the RECONS 25
pc database to identify M dwarf companions to primaries that were not M dwarfs
(i.e., A,F,G,K, and white dwarfs)777We consider the M dwarf to be the
secondary in the cases of M dwarf - white dwarf systems, as the white dwarf
was previously the more massive, and thus primary, component in the system.
within 15 pc. We searched the literature and flagged as M dwarf companions
those that had reported masses or estimated spectral types within our range of
interest. In a few cases, magnitude differences were reported, from which we
estimated the component’s mass using the MLR. There are 33 M dwarfs with
masses $0.1\leq M/\hbox{M${}_{\odot}$}\leq 0.3$ that are companions to AFGK,
early M, and white dwarf primaries, which are separated by more than 4″ from
their primaries. These are all included in our spectroscopic sample because
they are not contaminated by light from the more massive components. We
additionally include the one M dwarf (G 203-47) that is a close companion to a
white dwarf in a 15.7-day orbital period (Delfosse et al., 1999a); the white
dwarf adds a negligible amount of light to the system at 7100Å, the part of
the spectrum that we use for our RV measurements. The remaining 39 of the
identified M dwarf companions have angular separations $<$4″ from their more
massive primaries. One additional unseen component of a single-lined
spectroscopic binary (GJ 92B) has only a mass range reported, meaning that the
secondary could very well be an M dwarf with a mass in our range of interest,
but more data are needed to constrain its mass.

We list in Table 1 the distributions of the known M dwarfs with masses
$0.1\leq M/\hbox{M${}_{\odot}$}\leq 0.3$ within 15 pc. We show the running
unbinned stellar density of these M dwarfs within 15 pc in Figure 1, broken
into four subsets: 1) 369 presumed single and primary stars; 2) subset one,
plus the addition of 43 companions at separations $>$4″ from their primaries,
plus G 203-47; 3) subset two, plus the addition of unresolved companions to
subset two stars; and 4) subset three, plus the addition of unresolved
companions to massive stars. Each bump in each curve indicates the addition of
a new M dwarf within our selected mass range. Also highlighted is that the
nearest primary (Barnard’s Star) is more distant than than the nearest of
these M dwarfs (Proxima Centauri), a companion to a more massive primary.
Illustrated is a fairly uniform stellar density from 8-15 pc, once small
number statistics are overcome at the closest horizons. This implies the
sample is volume-complete.

Table 1: Known M Dwarfs With Masses $0.1\leq M/\hbox{M${}_{\odot}$}\leq 0.3$
Within 15 pc

Type of Star | Sep $<$4″ | Sep $>$4″ | Total
---|---|---|---
Single Mid-M Dwarf |  |  | 290
Mid-M Dwarf Primary |  |  | 79
Comp. to Mid-M Dwarf Primary | 57 | 10 | 67
Comp. to Mid-M Dwarf Comp. | 3 | 0 | 3
Comp. to Early M Dwarf Primary | 26 | 16 | 42
Comp. to K Dwarf Primary | 5 | 7 | 12
Comp. to G Dwarf Primary | 8 | 3 | 11
Comp. to F Dwarf Primary | 0 | 1 | 1
Comp. to A Dwarf Primary | 0 | 1 | 1
Comp. to White Dwarf Primary | 1 | 5 | 6
| 100 | 43 | 512

Note. — In bold are noted the numbers of stars from each type that are
included in our spectroscopic sample of $413$ M dwarfs. In italics are noted
the 60 mid-M dwarfs that are implicitly included as unresolved companions in
the spectroscopic sample $413$ M dwarfs.

Table 2: Parameters of the M Dwarfs Presented in this Paper  Parameter | Value
---|---
Mass (M/M⊙) | $0.1\leq M/\hbox{M${}_{\odot}$}\leq 0.3$
$M_{G}$ (mag) | $10.4\leq M_{G}\leq 14.5$
($B_{p}-R_{p}$) (mag) | $2.3\leq(B_{p}-R_{p})\leq 4.5$
$M_{K}$ (mag) | $7.0\leq M_{K}\leq 9.5$
($R_{KC}-K_{S}$) (mag) | $3.1\leq(R_{KC}-K_{S})\leq 6.0$
Figure 1: The number of M dwarfs with masses $0.1\leq
M/\hbox{M${}_{\odot}$}\leq 0.3$ per cubic parsec as a function of distance. In
blue are noted the 369 primaries; the red line indicates the $413$ in our
spectroscopic sample (369 primaries plus 44 companions); the purple line
includes the 60 close M dwarf companions (separations $<$ 4″) to the $413$
stars in our core sample; in green are all known M dwarfs with masses $0.1\leq
M/\hbox{M${}_{\odot}$}\leq 0.3$ within 15 pc, which includes the 39 close
companions to more massive stars. Illustrated is the fairly constant density
from 8-15 pc, once small number statistics are overcome at the closest
horizons. This implies the sample is volume-complete. Uncertainty bands
indicate the Poisson errors on the number of stars in each bin.

###  2.4 Possibly Hidden Sample Members

Because one of the goals of our survey is a search for companions, we wanted
to gather data for presumably single M dwarfs that had estimated masses larger
than our upper mass limit of $0.3$ M/M⊙, but which would result in stellar
components with masses within our mass range, should they be discovered to
host equal or nearly-equal mass companions. An unresolved, equal-luminosity M
dwarf binary where both components have masses of $0.3$ M/M⊙ will have an
estimated total mass of $0.44$ M/M⊙ from its blended M${}_{K_{s}}$ photometry.
These types of systems would be distinguishable by their overluminosity. We
identified from the master M dwarf list described in §2.1 18 stars with
estimated masses $0.30-0.44$ M/M⊙, which were overluminous and for which we
are gathering reconnaissance spectroscopy. We excluded targets in this mass
range that had both high-resolution imaging and spectroscopy results in the
literature, under the assumption that those programs would have detected a
companion. We further include in this list of candidates four stars that have
estimated masses $0.300-0.304$ M/M⊙ and two M dwarfs just beyond the 15 pc
horizon with large parallax uncertainties.

It is possible that there are M dwarf companions to AFGKs that have not yet
been identified. In fact, three candidate members have been noted recently as
unresolved companions to nearby K dwarfs (D.Nusdeo, in review), but which need
follow-up observations for confirmation. Should any new M dwarfs within our
mass range of interest be detected, we will take note, but they will likely
not become part of our spectroscopic survey due to their proximity to their
bright primary stars.

##  3 The Sample

Of all the M dwarfs described above, the final sample for our spectroscopic
survey comprises $413$ M dwarfs with masses $0.1\leq
M/\hbox{M${}_{\odot}$}\leq 0.3$ within 15 pc. All have trigonometric
parallaxes. These $413$ include 292 presumably single M dwarfs, 77 M dwarf
primaries of multiple systems, 43 companions that are separated by more than
4″ from their primary (of any mass), and one close companion to a faint white
dwarf. In Table 1, these numbers are in bold print. We refer to this as our
‘spectroscopic’ sample for the remainder of the paper. We list the range of
masses for these kinds of stars, as well as some of their observational
parameters in Table 2. In Table 3.1, we present the relevant astrometry,
photometry, and multiplicity information for all $512$ M dwarfs with masses
$0.1\leq M/\hbox{M${}_{\odot}$}\leq 0.3$ within 15 pc. The $413$ stars in our
spectroscopic survey are indicated with the sample code ‘s’, their 60 close
companions are noted with code ‘sc’, and the 39 close companions to more
massive stars are noted with code ‘mc’. Although the 39 companions to more
massive stars are M dwarfs within 15 pc within our mass range of interest (or
a candidate, as in the case of GJ 92B), we do not include them in our
spectroscopic survey sample because their separations are too small to avoid
contamination from their bright primaries. The DR2 reports parallaxes for 388
of the $413$ stars in our spectroscopic sample, while accurate parallaxes
existed for 394 of these $413$ before the availability of the DR2.

In Table 3.1, we list 120 stars in the same format as Table 3.1. These include
the 95 that we excluded from our spectroscopic sample due to mass or distance
revisions with the availability of the DR2 parallaxes, and the 25 candidate
stars. Some of these 25 could move into our spectroscopic sample, should they
be revealed to be equal-luminosity binaries.

###  3.1 Astrometry

For our spectroscopic sample membership determination and for all analyses, we
adopt only the DR2 parallaxes, where available; otherwise, we use the weighted
mean literature values. Parallaxes that were measured for these nearby M
dwarfs before the availability of the Gaia DR2 come from myriad sources. The
largest source is the General Catalogue of Trigonometric Parallaxes, Fourth
Edition by Yale University Observatory, usually called the Yale Parallax
Catalog (YPC; van Altena et al., 1995), which is a compendium of ground-based
parallaxes that were published before 1995. The YPC provides trigonometric
parallaxes for 182 of the M dwarfs in our spectroscopic sample, 23 of which
have measurement uncertainties larger than 10 mas. RECONS has added 101 new
parallaxes for these nearby M dwarfs and improved the large uncertainties on
an additional 20, primarily in the southern hemisphere (Costa et al. 2005; Jao
et al. 2005, 2011, 2017; Henry et al. 2006, 2018; Riedel et al. 2010, 2011,
2014, 2018; Dieterich et al. 2014; Lurie et al. 2014; Bartlett et al. 2017;
Subasavage et al. 2017; Winters et al. 2017; Halley Vrijmoet et al. 2020. The
remaining 111 published parallaxes for the M dwarfs in our spectroscopic
sample is mainly due to work by Dittmann et al. (2014); Finch & Zacharias
(2016); Weinberger et al. (2016); Dahn et al. (2017); Finch et al. (2018). The
$Hipparcos$ satellite provided only 6 new measurements for these stars
(Perryman et al. 1997, with results updated in van Leeuwen 2007), largely due
to its magnitude limit of $V\lesssim$ 12 mag.

With the release of the DR2 parallaxes, 34 M dwarfs fit our membership
criteria and were thus added to our final sample. Of these, 19 (5%) targets in
our spectroscopic sample had no previously published parallax; all but two of
these stars (2MA J0049+6518 and 2MA J0943-3833) had previously been identified
as nearby candidates, but lacked a parallax. The DR2 provided improved
parallaxes for fifteen additional targets that had literature parallaxes with
uncertainties larger than 10 mas or parallaxes smaller than 66.67 mas. With
the sample revision, 100 stars in our initial sample no longer fit the sample
membership criteria and were removed from our spectroscopic sample due to
distance or mass revisions.

In our spectroscopic sample, 25 ($6$%) of the stars do not have Gaia DR2
parallaxes, but have published ground-based parallaxes. This is in agreement
with the 6% of the volume-limited sample of 1120 M dwarfs within 25 pc that
lack parallaxes in the DR2, as noted in Winters et al. (2019a). In some cases,
the typically large proper motions of nearby stars make centroiding
challenging (Arenou et al., 2018). In other cases, they are binaries with
companions at sub-arcsecond separations that also make it hard to determine
the photocenter of light that is needed for the accurate measurement of a
parallax (Arenou et al., 2018; Ziegler et al., 2018). The DR2 only uses 22
months of data, and as yet only uses a single-star model for the astrometric
solution. It is expected that data releases starting with the full DR3 will
include multiplicity information. Seventeen of the 25 lacking DR2 parallaxes
have only two-parameter astrometric solutions (i.e., coordinates, but no
proper motion or parallax measurements). All but five of these 20 targets are
known to be binaries or triples with separations $<$1″ and $\lesssim$
1$\farcs$5, respectively, between components. It is possible that these five
(LEP 0617+8353, LP 549-6, LHS 296, GJ 1227, and LHS 3746) are therefore
multiples; however, LHS 296 and GJ 1227 have proper motions exceeding 1″yr-1,
which could have made it difficult to fit a parallax solution for these two
stars. Two of the 17 (LP 993-116(BC) and LTT 1445BC) are wide companions to
more massive stars and for which we have adopted the parallax of the primary
component. The remaining 8 stars do not have an entry in the DR2 (including GJ
406 $=$ Wolf 359). Six are binaries or triples with subarcsecond separations
between components, while GJ 406 has a proper motion of 4$\farcs$7 yr-1. GJ
618B is a wide companion whose primary has a DR2 parallax, which we have
adopted.

Figure 2: Distribution on the sky in equatorial coordinates of the
spectroscopic sample of $413$ nearby M dwarfs.

Figure 3: The mass distributions of the $512$ nearby M dwarfs with masses
$0.1\leq M/\hbox{M${}_{\odot}$}\leq 0.3$ within 15 pc, illustrated as stacked
histograms in linear (top panel) and log forms (bottom panel). In blue are
noted the 369 primaries; red indicates the 43 wide companions, plus G 203-47;
purple indicates the 60 close M dwarf companions (separations $<$ 4″) to the
$413$ stars in our spectroscopic sample (noted in blue and red); in green are
the 39 close companions to more massive stars. The uncertainties in both
panels are Poisson. We note that the bin sizes differ between the two panels.
Close binaries with blended photometry were deblended before the mass estimate
calculation. Masses are noted along the top of the lower panel, with points
corresponding to each of the indicated masses to guide the eye. An increase in
the number of objects per mass bin with decreasing mass is evident in the
linear histogram, while the distribution is flat in the log version.

We show the all-sky distribution of our spectroscopic sample of $413$ M dwarfs
in Figure 2 in equatorial coordinates. Figure 3 shows the mass distribution of
the different subsets of M dwarfs shown in Figure 1 as a stacked histogram. In
addition to the distribution in linear form (top panel), we include a version
in log form (bottom panel). In the top panel, we note the increase in number
of stars per mass bin with decreasing stellar mass, in agreement with other
mass functions for nearby M dwarfs, such as Figure 24 from Winters et al.
(2019a). The log version (bottom panel) is flat when including all the known
primaries and companions. While other mass functions typically represent the
y-axis as the logarithm of the number density per logarithmic mass bin, we do
not adopt that form. However, we note that the log version of our mass
function is in agreement with the single-star mass function in this mass range
from Bochanski et al. (2010) (their Figure 23). In contrast, our mass function
does not resemble Figure 2 from Chabrier (2003) because that work presents a
system mass function, where photometry of the known components of multiple
systems are blended into one system magnitude from which a mass estimate is
made.

We showcase the volume-completeness and uniform distribution of the sample in
Figures 1 (discussed in §2.3) and 4. In Figure 4, the mass uncertainties for
most objects are dominated by the scatter (0.014 M/M⊙) in the MLR. The
distance uncertainties are calculated to be symmetric as follows:

$\sigma_{pc}=\Bigg{\langle}\Bigg{|}\left(\frac{1}{\pi}-\frac{1}{\pi\pm\sigma_{\pi}}\right)\Bigg{|}\Bigg{\rangle}$
(1)

A few objects without DR2 parallaxes are noticeable by their large distance
uncertainties, but most objects have distance errors that are smaller than the
points.

Figure 4: Stellar density of the sample. Plotted is mass versus distance in
eight equal volume shells for the $413$ stars in our spectroscopic, all-sky
sample. Close binaries with blended photometry were deblended before the mass
estimate calculation. Illustrated is the fairly uniform distribution of stars
to 15 pc.

Table 3: Astrometry, Photometry, and Multiplicity Information for $512$ M
Dwarfs

Column | Format | Units | Description
---|---|---|---
1 | A11 | hh:mm:ss | Right Ascension (J2000.0)
2 | A11 | dd:mm:ss | Declination (J2000.0)
3 | A15 |  | Name
4 | A1 |  | Component
5 | A16 |  | 2MASS Identifier
6 | A5 |  | Configuration of Multiple Components
7 | A10 | arcsec | Separation ($\rho$) Between Multiple Components
8 | A3 | deg | Position Angle ($\theta$) Between Multiple Components
9 | I4 |  | Year of Multiplicity Measurement
10 | A6 |  | Technique for Multiplicity Detection (1)
11 | A21 |  | Reference for Multiplicity Detection
12 | F4.2 | mag | Magnitude Difference ($\Delta m$) between Multiple Components
13 | A3 |  | Filter of Magnitude Difference Multiple Components
14 | A21 |  | Reference for Multiple Component’s Magnitude Difference
15 | F8.2 | mas yr-1 | Proper Motion in RA ($\mu_{\alpha}$)
16 | F8.2 | mas yr-1 | Proper Motion in Dec ($\mu_{\delta}$)
17 | A21 |  | Reference for Proper Motion
18 | F8.4 | mas |  Gaia DR2 Parallax ($\pi_{DR2}$)
19 | F6.4 | mas | Uncertainty on Gaia DR2 Parallax
20 | A1 |  | Note on DR2 parallax (2)
21 | F5.3 | mas | DR2 Astrometric Excess Noise
22 | F8.2 |  | Significance of DR2 Astrometric Excess Noise
23 | F6.2 | mas | Weighted Mean Literature Parallax ($\pi_{wt}$)
24 | F4.2 | mas | Uncertainty on Lit. Parallax
25 | A131 |  | Reference(s) for Parallaxes included in Weighted Mean Parallax
26 | F5.2 | mag |  $G$ Magnitude
27 | F4.2 | mag |  $(G_{B_{P}}-G_{R_{P}})$ Color
28 | F5.2 | mag |  $V_{\rm J}$ Magnitude
29 | F5.2 | mag |  $R_{\rm KC}$ Magnitude
30 | F5.2 | mag |  $I_{\rm KC}$ Magnitude
31 | A21 |  | Reference for $V_{\rm J}R_{\rm KC}I_{\rm KC}$ Magnitudes
32 | F4.1 | mag | Transformed $R_{KC}$ Magnitude from $G$ and $K_{s}$
33 | F6.3 | mag | 2MASS $J$ Magnitude
34 | F5.3 | mag | Uncertainty on 2MASS J Magnitude
35 | F6.3 | mag | 2MASS $H$ Magnitude
36 | F5.3 | mag | Uncertainty on 2MASS H Magnitude
37 | F6.3 | mag | 2MASS $K_{s}$ Magnitude
38 | F5.3 | mag | Uncertainty on 2MASS $K_{s}$ Magnitude
39 | A1 |  | Note on 2MASS $K_{s}$ Magnitude (3)
40 | F5.3 | M/M⊙ | Stellar Mass
41 | F5.3 | M/M⊙ | Uncertainty on Mass
42 | A1 |  | Note on Mass (4)
43 | A1 |  | Note on Sample Membership (5)

References. — This work; Allen et al. (2012); Balega et al. (2013); Baroch et
al. (2018); Bartlett et al. (2017); Benedict et al. (1999); Benedict et al.
(2000); Benedict et al. (2001); Benedict et al. (2016); Bergfors et al.
(2010); Bessel (1990); Bessell (1991); Beuzit et al. (2004); Bowler et al.
(2015); Cortés-Contreras et al. (2017); Costa et al. (2005); Dahn et al.
(1988); Dahn et al. (2017); Davison et al. (2015); Delfosse et al. (1999a);
Delfosse et al. (1999b); Dieterich et al. (2012); Dieterich et al. (2014);
Dittmann et al. (2014); Docobo et al. (2006); Dupuy & Liu (2017); Duquennoy &
Mayor (1988); Eggenberger et al. (2007); Fabricius & Makarov (2000); Faherty
et al. (2012); Farihi et al. (2005); Finch & Zacharias (2016); Finch et al.
(2018); Gatewood et al. (2003); Gatewood (2008); Gatewood & Coban (2009);
Golimowski et al. (2004); Halbwachs et al. (2000); Han & Gatewood (2002);
Harrington et al. (1981); Heintz (1974); Heintz (1988); Heintz (1990); Heintz
(1991); Heintz (1993); Heintz (1994); Henry & McCarthy (1993); Henry et al.
(1997); Henry et al. (1999); Henry et al. (2004); Henry et al. (2006); Henry
et al. (2018); Hershey & Taff (1998); Høg et al. (2000); Horch et al. (2010);
Horch et al. (2011); Horch et al. (2012); Horch et al. (2015); Hosey et al.
(2015); Ianna et al. (1996); Janson et al. (2014); Jao et al. (2003); Jao et
al. (2005); Jao et al. (2011); Jao et al. (2017); Jódar et al. (2013);
Khovritchev et al. (2013); Koen et al. (2002); Koen et al. (2010); Köhler et
al. (2012); Lacy (1977); Law et al. (2008); Leinert et al. (1994); Lèpine &
Shara (2005); Lèpine et al. (2009); Lindegren et al. (1997); Lindegren et al.
(2018); Lowrance et al. (2002); Lurie et al. (2014); Luyten (1979); Mamajek et
al. (2013); Martin & Mignard (1998); Martinache et al. (2007); Martinache et
al. (2009); Mason et al. (2018); Mason et al. (2019); McArthur et al. (2010);
McCarthy (1984); Montagnier et al. (2006); Morales et al. (2009); Pravdo et
al. (2004); Reid et al. (2002); Reid et al. (2003); Reid et al. (2004); Riedel
et al. (2010); Riedel et al. (2011); Riedel et al. (2014); Riedel et al.
(2018); Salim & Gould (2003); Ségransan et al. (2000); Shakht (1997); Shkolnik
et al. (2012); Silverstein, in prep; Skrutskie et al. (2006); Smart et al.
(2007); Smart et al. (2010); Söderhjelm (1999); Subasavage et al. (2017);
Tanner et al. (2010); Tokovinin et al. (2006); Tokovinin & Lépine (2012);
Tokovinin & Horch (2016); van Altena et al. (1995); Vanderspek et al. (2019);
van Leeuwen (2007); Halley Vrijmoet et al. (2020); Wahhaj et al. (2011); Ward-
Duong et al. (2015); Weinberger et al. (2016); Weis & Upgren (1982); Weis
(1984); Weis (1986); Weis (1987); Weis (1988); Weis (1991a); Weis (1991b);
Weis (1996); Weis (1999); Winters et al. (2011); Winters et al. (2015);
Winters et al. (2017); Winters et al. (2018); Winters et al. (2019a); Winters
et al. (2019b); Winters et al. (2020). Winters, in prep.

Note. — (1) The codes for the techniques and instruments used to detect and
resolve systems are: AO det — adaptive optics; astdet — detection via
astrometric perturbation, companion often not detected directly; astorb —
orbit from astrometric measurements; astrad — orbit from combination of
astrometric and radial velocity measurements; eclorb — eclipsing binary orbit;
lkydet — detection via lucky imaging; radorb — orbit from radial velocity
measurements; spkdet — detection via speckle interferometry; visdet —
detection via visual astrometry; visorb — visual orbit.

Note. — (2) The codes for notes on the DR2 parallax are: w — weighted mean of
two components; A — adopted parallax and proper motion of primary component;
2p — 2 parameter astrometric solution; n — no DR2 data point.

Note. — (3) ’J’ indicates blended photometry.

Note. — (4) Mass adopted from aBaroch et al. (2018); bBenedict et al. (2001);
cBenedict et al. (2016); dDuquennoy & Mayor (1988); eEggenberger et al.
(2007); fHalbwachs et al. (2000); gHan & Gatewood (2002); hHeintz (1988);
iHeintz (1993); jHeintz (1994); kHenry & McCarthy (1993); lHenry et al.
(1999); mMartinache et al. (2007); nMartinache et al. (2009); oMcCarthy
(1984); pMorales et al. (2009); qSégransan et al. (2000); rTokovinin et al.
(2006); sTokovinin & Horch (2016); tWinters et al. (2019b); uMass calculated
from orbital mass ratio; vMass from deblended photometry; wMass assumed from
astrometric orbit.

Note. — (5) Note on Sample Membership: ‘s’: member of spectroscopic sample;
‘sc’: close companion to member of spectroscopic sample; ‘mc’: close companion
to massive primary.

Note. — This table is available in its entirety in machine-readable form.

Table 4: Astrometry, Photometry, and Multiplicity Information for 120 Rejected
and Candidate M Dwarfs

Column | Format | Units | Description
---|---|---|---
1 | A10 | hh:mm:ss | Right Ascension (J2000.0)
2 | A9 | dd:mm:ss | Declination (J2000.0)
3 | A15 |  | Name
4 | A1 |  | Component
5 | A16 |  | 2MASS Identifier
6 | A5 |  | Configuration of Multiple Components
7 | F10.4 | arcsec | Separation ($\rho$) Between Multiple Components
8 | A20 |  | Reference for Multiplicity Detection
9 | F4.2 | mag | Magnitude Difference ($\Delta m$) between Multiple Components
10 | A3 |  | Filter of Magnitude Difference Multiple Components
11 | A20 |  | Reference for Multiple Component’s Magnitude Difference
12 | F8.4 | mas |  Gaia DR2 Parallax ($\pi_{DR2}$)
13 | F6.4 | mas | Uncertainty on Gaia DR2 Parallax
14 | A1 |  | Note on DR2 parallax (1)
15 | F6.2 | mas | Weighted Mean Literature Parallax ($\pi_{wt}$)
16 | F4.2 | mas | Uncertainty on Literature Parallax
17 | A20 |  | Reference(s) for Parallaxes included in Weighted Mean Parallax
18 | F5.2 | mag |  $G$ Magnitude
19 | F4.2 | mag |  $(G_{B_{P}}-G_{R_{P}})$ Color
20 | F5.2 | mag |  $V_{\rm J}$ Magnitude
21 | F5.2 | mag |  $R_{\rm KC}$ Magnitude
22 | F5.2 | mag |  $I_{\rm KC}$ Magnitude
23 | A20 |  | Reference for $V_{\rm J}R_{\rm KC}I_{\rm KC}$ Magnitudes
24 | F4.1 | mag | Transformed $R_{KC}$ Magnitude from $G$ and $K_{s}$
25 | F6.3 | mag | 2MASS $J$ Magnitude
26 | F5.3 | mag | Uncertainty on 2MASS J Magnitude
27 | F6.3 | mag | 2MASS $H$ Magnitude
28 | F5.3 | mag | Uncertainty on 2MASS H Magnitude
29 | F6.3 | mag | 2MASS $K_{s}$ Magnitude
30 | F5.3 | mag | Uncertainty on 2MASS $K_{s}$ Magnitude
31 | A1 |  | Note on 2MASS $K_{s}$ Magnitude (2)
32 | F5.3 | M/M⊙ | Mass
33 | F5.3 | M/M⊙ | Uncertainty on Mass
34 | A1 |  | Note on Mass (3)
35 | A1 |  | Note on Sample Membership (4)

References. — This work; Baroch et al. (2018); Bartlett et al. (2017);
Benedict et al. (2002); Bergfors et al. (2010); Bessel (1990); Bessell (1991);
Beuzit et al. (2004); Bowler et al. (2015); Burningham et al. (2009); Costa et
al. (2005); Dahn et al. (2017); Delfosse et al. (1999a); Dieterich et al.
(2012); Dittmann et al. (2014); Doyle & Butler (1990); Finch & Zacharias
(2016); Finch et al. (2018); Gatewood (2008); Harrington et al. (1985); Heintz
(1993); Heintz (1994); Henry et al. (2018); Horch et al. (2015); Hosey et al.
(2015); Hummel et al. (1995); Ireland et al. (2008); Janson et al. (2012);
Janson et al. (2014); Jao et al. (2005); Jódar et al. (2013); Khovritchev et
al. (2013); Koen et al. (2010); Lindegren et al. (1997); Lindegren et al.
(2018); Lurie et al. (2014); Luyten (1997); Reid et al. (2002); Riedel et al.
(2010); Riedel et al. (2011); Riedel et al. (2018); Silverstein, in prep;
Skrutskie et al. (2006); Söderhjelm (1999); van Altena et al. (1995); van
Leeuwen (2007); Halley Vrijmoet et al. (2020); Weinberger et al. (2016); Weis
& Upgren (1982); Weis (1984); Weis (1986); Weis (1987); Weis (1988); Weis
(1991a); Weis (1991b); Weis (1993); Weis (1996); Weis (1999); Winters et al.
(2011); Winters et al. (2015); Winters et al. (2017); Winters et al. (2019a);
Winters et al. (2020); Woitas et al. (2003).

Note. — (1) The codes for notes on the DR2 parallax are: ‘w’ — weighted mean
of two components; ‘2p’ — 2 parameter astrometric solution.

Note. — (2) ’J’ indicates blended photometry.

Note. — (3) Mass adopted from aBaroch et al. (2018); bPiccotti et al. (2020);
cMass from deblended photometry.

Note. — (4) Note on Sample Membership: ‘c’: candidate spectroscopic member,
‘r’: rejected.

Note. — This table is available in its entirety in machine-readable form.

###  3.2 Optical & Infrared Photometry

In order to estimate exposure times for the objects in our spectroscopic
survey, which uses the TiO-bands near 7100 Å, we required $R_{KC}$ magnitudes.
Absolute $V_{\rm J}R_{\rm KC}I_{\rm KC}$888The central wavelengths for the
$V_{J}$, RKC, and IKC filters at the 0.9m are 5438Å, 6425Å, and 8075Å,
respectively. We henceforth omit the subscripts on these filters’
designations. photometry for many of the M dwarfs presented here was taken
from the literature. The extensive compilations of absolute $VRI$ photometry
from Weis (Weis & Upgren, 1982; Weis, 1984, 1986, 1987, 1988, 1991a, 1991b,
1993, 1996, 1999), Bessel (Bessel, 1990; Bessell, 1991), and SAAO (Koen et
al., 2002, 2010; Reid et al., 2002, 2003, 2004) are valuable resources of M
dwarf photometry and provide $VRI$ for 165 of the $413$ nearby M dwarfs in our
spectroscopic sample presented here. All photometry from Weis has been
converted to the Johnson-Kron-Cousins (JKC) system using the relation in
Bessell & Weis (1987). $VRI$ for an additional 148 objects has been presented
previously by RECONS (e.g., in Costa et al., 2005; Davison et al., 2015;
Dieterich et al., 2014; Henry et al., 2004, 2006, 2018; Hosey et al., 2015;
Jao et al., 2005, 2011, 2017; Lurie et al., 2014; Mamajek et al., 2013; Riedel
et al., 2010, 2011, 2014; Vanderspek et al., 2019; Winters et al., 2011, 2015,
2017, 2019a).

As part of the long-term effort by the RECONS group at the CTIO/SMARTS 0.9m
telescope, we have measured new absolute $VRI$ photometry for 17 objects (plus
3 objects at distances $>$ 15 pc), which is presented here for the first time.
Following the methodology outlined in previous RECONS work, various standard
star fields from Graham (1982); Bessel (1990); Landolt (1992, 2007, 2013) were
observed multiple times each night to derive transformation equations and
extinction curves. Apertures 14″ in diameter, matching those used by Landolt,
were used to determine the stellar fluxes, except in cases where close
contaminating sources required deblending. In these cases, smaller apertures
were used and aperture corrections were applied. More details about the data
reduction procedures, transformation equations, etc., can be found in Jao et
al. (2005) and Winters et al. (2011, 2015).

For the remaining 82 stars in our spectroscopic sample with both a $G$ and
$R_{KC}$ magnitude999LHS 1901AB is the only object in the sample that lacks
both., we created a transformation to estimate an $R_{KC}$ magnitude using a
($G-K_{s}$) color. To create the transformation, we first excluded from the
$413$ stars in our spectroscopic sample any multiple systems with less than 4″
separations, as well as GJ 1194A, which has a blended $R$, but not $K$
magnitude. We also then excluded objects that lack a Gaia DR2 parallax. While
there exists a $G$ magnitude for many of them, these objects are generally
binaries with separations less than 1″. We thus exclude them all under the
suspicion that they are all multiple systems. There were three outliers (GJ
1230B, GJ 896B, and GJ 754.1B) that we also excluded from the fit. The final
number of M dwarfs used in our fit is 253. We present our second-order fit
below:

$R_{\rm KC}=K_{\rm s}-0.3098+0.8436*(G-K_{\rm s})+0.0725*(G-K_{\rm s})^{2}$
(2)

We explored higher order fits, but the calculated root-mean-square (RMS)
deviation was similar to that of the second order fit presented here;
therefore, we adopt the relation with the smallest order. We find a RMS
deviation of 0.05 mag. This transformation is valid for M dwarfs with
$3.2<(G-K_{s})<5.1$ mag and $2.3<(B_{P}-R_{P})<4.5$ mag. We list all
photometry, which includes that gathered from the literature, the newly
measured magnitudes presented here, and the transformed $R_{KC}$ magnitudes,
in Tables 3.1 and 3.1.

Figure 5 shows our spectroscopic sample plotted on an observational
Hertzsprung-Russell Diagram. We have assumed $R-$band uncertainties of 0.05
mag for the transformed magnitudes and 0.03 mag for all others. GJ 1194A is
excluded from this plot because, as noted above, its $R$ magnitude is blended,
while its $K$ magnitude is resolved. We also excluded LHS 1901AB because it
has no published $R_{KC}$ magnitude and no Gaia G magnitude from which to
estimate it. The red points indicate the elevated sequence of known binaries
with separations less than 4″ from their companions. Three obvious black
points among the elevated binaries are AP COL, GJ 896B, and GJ 1230B. AP COL
is a known nearby young star (Riedel et al., 2011) 101010The few young M
dwarfs in this sample, including AP COL, will have slightly revised masses
from the values we present once they are on the main sequence, but they are
almost certainly within the mass range of the stars in this paper., whereas GJ
896B and GJ 1230B could be as yet unknown unresolved binaries.

Figure 5: An observational Hertzsprung-Russell Diagram for the $413$ stars in
our spectroscopic sample, except for GJ 1194A and LHS 1901AB. Stars presumed
to be single are shown in black, binaries with blended photometry (generally
with separations less than 4″) are noted in red, and objects for which only a
transformed $R_{KC}$ is available are shown in blue. Three black points among
the elevated red points, two of which are unresolved binary candidates, are
labeled.

###  3.3 Multiples

For the stars in Tables 3.1 and 3.1, we provide the multiplicity information
for those that are known to host stellar or brown dwarf companions. For the
systems that are common to both the objects presented here and those in
Winters et al. (2019a), we duplicate the results presented there. The
remaining noted multiples are the result of a literature search, which
includes previous results from our spectroscopic survey (i.e., from Winters et
al., 2018, 2020).

We note that where orbit determinations from the literature are reported, the
semi-major axis, $a$ or $a\sin i$, is listed instead of angular separation
$\rho$. If $a$ was not reported in the reference given, it was calculated from
the period and the estimated masses of the components in question via Kepler’s
third law. Magnitude differences from photographic plates are denoted by “V*.”
In a few cases, the position angles and/or $\Delta m$ measurements are not
available. In many cases, there are multiple separation and $\Delta m$
measurements available in the literature from different groups using different
techniques. An exhaustive list of these results is beyond the scope of this
work; instead, a single recent result for each system is listed.

We are systematically searching many of the stars listed in Table 3.1 for
stellar companions. In our spectroscopic sample, we are surveying all $413$ M
dwarfs via both high-resolution, multi-epoch spectroscopy and high-resolution
speckle imaging. Some of the stars outside our spectroscopic sample have been
observed with either or both techniques, as well. It is not our intention to
report here the results of these companion searches, but we do note those that
we have detected to host a companion. These objects are indicated with a
separation of 1″ to indicate that a companion has been detected, but not yet
resolved, with a reference of Winters et al., in prep. These systems will be
described more thoroughly in a future paper.

To date, 74 M dwarf primary stars within 15 pc with masses $0.1\leq
M/\hbox{M${}_{\odot}$}\leq 0.3$ are known to host stellar companions at all
separations. We can calculate a preliminary and uncorrected stellar
multiplicity rate (MR) for the primary stars in our spectroscopic sample,
where the MR is the percentage of all systems that are multiple, regardless of
whether the system is a binary, triple, or higher-order multiple. We find that
$20\pm 2$% ($74/369$) of systems within 15 pc with these types of M dwarf
primaries consist of more than one star. Because the MR is known to be a
decreasing function of primary mass (Duchêne & Kraus, 2013), we expect the MR
for our mass range of interest to be smaller than that for the entire M dwarf
sequence. Comparison to M dwarf MRs reported by others indicates agreement:
$26\pm 3$%, $23.5\pm 3.2$%, $26.8\pm 1.4$% (Duchêne & Kraus, 2013; Ward-Duong
et al., 2015; Winters et al., 2019a). Further, the stellar MR of $21.4\pm
2.0$% for the mass range $0.15-0.30$ M/M⊙ reported in Winters et al. (2019a),
which is not corrected for incompleteness, is in excellent agreement with the
preliminary MR we find here for our target stars of similar mass range
($0.1\leq M/\hbox{M${}_{\odot}$}\leq 0.3$). When including the five systems
within 15 pc known to be composed of an M dwarf primary within our mass range
of interest and exclusively brown dwarf (or candidate brown dwarf) companions
(GJ 1001, LHS 1610, G 123-45, GJ 595, GJ 1215), we find a preliminary MR of
$21\pm 2$% ($79/369$).

We also find that $43\pm 2$% (222/512) of all M dwarfs with masses $0.1\leq
M/\hbox{M${}_{\odot}$}\leq 0.3$ within 15 pc reside in multiple systems with
stars of all masses. That is, while 20% are hosts to less massive stars, a
nearly equal percentage are companions to more massive stars. We emphasize
that these MRs are preliminary. We have not completed our high-resolution
surveys of these stars, so more companions may be detected in the future.

###  3.4 Gaia DR2 Astrometry Comparison

It is interesting to compare the weighted mean parallaxes available pre-DR2 to
the DR2 parallaxes. Of the $413$ M dwarfs in our spectroscopic sample, 372
have both a Gaia DR2 parallax and a parallax that was published before DR2. We
show in Figure 6 the distribution of the difference between the parallax
measurements ($\pi_{DR2}-\pi_{wt}$) for these 372 M dwarfs within 15 pc. We
note that the distribution is not Gaussian and shows a shoulder in the
negative half of the histogram. Because our sample size is relatively small,
we found that fitting a curve to the distribution and determining the peak
leads to offsets that were dependent on the bin size. We therefore report the
median offset, $-0.67^{+0.99}_{-1.79}$ mas. The uncertainty spans $\pm 34$% of
the parallax differences on either side of the median offset ($-2.46$ mas to
$0.32$ mas) and is asymmetric due to the asymmetric distribution. This
negative difference is in the sense that the DR2 parallaxes are slightly
smaller than parallaxes for the same objects available before the DR2, which
corresponds to distances slightly further away. This offset is similar to the
$-0.71\pm 0.06$ mas difference that Arenou et al. (2018) found in their
comparison of DR2 results to RECONS nearby star parallaxes. The RECONS group
conducted their own comparison of Gaia DR1 parallaxes to $Hipparcos$
parallaxes for stars within 25 pc (Jao et al., 2016) and find a distance-
dependent offset of $-0.24\pm 0.02$ mas in their analysis; an offset of
similar magnitude is also present in the DR2 data (Jao et al., in prep).
Another study compared the distances of eclipsing binaries at 30 pc $-$ 3 kpc
with $G<$ 12 mag to their distances derived from DR2 parallaxes and find an
offset of $-82\pm 33~{}\mu$as (Stassun & Torres, 2018). However, the results
of that study are not relevant here, as the stars presented in this work are
at closer distances and are thus more sensitive to the distance-dependent
offset discussed in Jao et al. (2016). We do not apply any correction to the
DR2 parallaxes listed here. The $-0.67$ mas difference we find will not
substantially affect any results based on the parallax, as it amounts to 0.3%
and 1% of the parallax at 5 and 15 pc, respectively. Future data releases from
Gaia will include longer baselines for the parallax determinations, which will
improve the parallax values. Outliers in Figure 6 at $\pm 20-30$ mas are LP
119-26, G 184-31, LTT 13861, and GJ 791.2AB. While GJ 791.2AB and LTT 13861AB
are known binaries with a subarcsecond separations between their components,
the other two could be unknown binaries.

As part of the DR2 catalog, astrometric quality flags are provided. For our
spectroscopic sample, we assess here two of these flags: the astrometric
excess noise (aen) and its significance. As discussed in Lindegren et al.
(2018) and Arenou et al. (2018), the astrometric excess noise is the goodness
of fit or the extra noise, in mas, that is needed to explain the residuals in
the astrometric solution for an object. We show in Figure 7 the DR2
astrometric excess noise as a function of the Gaia ($B_{p}-R_{p})$ color.
Illustrated is the increase in aen to roughly 1 mas with redder presumably
single stars. Binaries with angular separations $<$2″ are indicated; many are
elevated above the black points which symbolize presumably single stars. One
presumably single star lies among the known unresolved binaries and is
possibly an unresolved binary itself: LHS 246.

We also note that for M dwarfs in our selected mass range, the astrometric
excess noise significance values are generally large (10-100), as seen in
Figure 8. While it is noted that the aen significance should be less than 2.0
(Lindegren et al., 2018), most of these targets have robust distances via
ground-based parallaxes that agree with the DR2 parallaxes. We note binaries
with separations $<$2″. These all have significance values larger than 10, not
unexpectedly, as all were treated as single objects in the DR2 astrometric
reduction. Presumably, both the astrometric excess noise for these objects and
its significance will be reduced in future Gaia data releases.

Figure 6: Stacked histogram of the parallax differences between Gaia DR2
results and the weighted mean of parallaxes for the same 372 targets published
prior to DR2 in black (noted as ‘Lit’ for literature). The blue vertical line
indicates a median offset at -0.67 mas, meaning that DR2 parallaxes are
generally smaller (with corresponding distances that are further away) than
the parallaxes for the same objects published before the release of DR2 data.
In red are noted binaries with separations $<$ 2″.  Figure 7: Gaia DR2
astrometric excess noise (aen) as a function of Gaia ($B_{p}-R_{p}$) color for
the 379 M dwarfs with 5-parameter DR2 astrometric solutions. We indicate
binaries with separations $<$ 2″ in red, excluding 9 close binaries with
weighted mean DR2 parallaxes. The astrometric excess noise increases for
redder objects; many close binaries exhibit large astrometric excess noise,
due to their treatment as single objects in the DR2 reduction. We label one
subarcsecond-separation binary candidate.  Figure 8: Stacked histogram of the
significance of the Gaia DR2 astrometric excess noise for 379 M dwarfs (in
black), in logarithmic form. Most of these nearby M dwarfs have astrometric
excess noise with significance roughly $10-100$. We show the 56 binaries with
separations $<$ 2″ that have 5-parameter DR2 astrometric solutions in solid
red, not including 9 close binaries with weighted mean DR2 parallaxes. All the
binaries with separations $<$ 2″ have an astrometric excess noise significance
greater than 10, not an unexpected finding.

##  4 Discussion and Conclusion

We have compiled a volume-complete list of M dwarf primary stars, as well as a
list of all the known M dwarf companions, with masses $0.1\leq
M/\hbox{M${}_{\odot}$}\leq 0.3$ that lie within 15 pc. This is only now
possible by augmenting the parallaxes from the Gaia DR2 and with those from
ground-based astrometry efforts. We now investigate the volume-completeness of
our sample and whether Eddington or Malmquist biases are present in the
sample.

We first compare the actual number of M dwarf primaries within 15 pc within
our mass range of interest to the expected number. As mentioned previously, we
extrapolate from the number of these types of M dwarf primary stars within 10
pc, assuming completeness within 10 pc and a constant stellar density to 15
pc. As noted by Henry et al. (2018), the 10 pc sample was considered to be at
least 90% complete before the release of parallaxes from the DR2, and the DR2
did not reveal any new M dwarf primaries within this mass range within 10 pc.
We therefore assume that the 10 pc sample is complete. There are 104 M dwarf
primaries within this mass range and within 10 pc presented here as part of
our spectroscopic sample, but there were 109 M dwarfs in the same mass range
presented in Winters et al. (2019a). There are two reasons for the slight
difference between the two numbers. The first is the availability of DR2
parallaxes, which resulted in some distance shifts for targets near the 10 pc
horizon, as well as some mass estimate changes, which affected the membership
of some stars. The second reason is that mass estimates differ slightly,
depending whether the estimate is from the $M_{V}$ magnitude (as used in
Winters et al., 2019a) or $M_{K}$ magnitude, although they agree within their
uncertainties. This change in the actual number from 109 to 104 M dwarf
primaries within our mass range of interest decreases the expected number
within 15 pc from $368\pm 19$ to $351\pm 19$. The 369 primaries in our sample
is in agreement with the expected 351 M dwarf primaries of this kind within 15
pc.

We next assess the completeness of both the M dwarf primary population and the
total number of M dwarfs with masses $0.1\leq M/\hbox{M${}_{\odot}$}~{}\leq
0.3$ within the 15 pc volume. In Figures 1 and 3, these groups are noted in
blue and green. We do this by comparing the stellar number density for stars
of these masses at the 15 pc volume horizon to that of the 10 pc volume. For
the 369 M dwarf primaries, the stellar number density at 15 pc is $0.026\pm
0.001$ stars per cubic pc, compared to the density of $0.025\pm 0.002$ stars
per cubic pc for the 104 primaries within 10 pc. These densities agree well.
In a similar fashion for the total number ($512$) of these kinds of M dwarfs
within 15 pc, we calculate a stellar number density of $0.036\pm 0.002$ stars
per cubic parsec, as compared to $0.037\pm 0.003$ stars per cubic parsec for
the 153 within the 10 pc volume. As with the primaries’ density comparison,
the densities for the total number of these kinds of M dwarfs within 10 pc and
15 pc are in agreement.

We now investigate whether Eddington and/or Malmquist biases affect various
groups of stars that we have presented. The Eddington bias is an over-
representation of fainter/more distant objects in samples because, due to
random observational errors, their magnitude/parallax uncertainties are larger
than those of brighter/nearer stars (Eddington, 1913). The classical Malmquist
bias affects magnitude-limited samples and results in the over-representation
of bright stars in samples (Malmquist, 1922). These biases could potentially
affect our sample in both distance and mass space.

We first investigate whether the Eddington bias affects the stars in our
sample in distance space, that is, whether more distant stars make up a
disproportionate part of our sample. We perform this analysis by comparing the
stellar density of the primary M dwarfs with masses $0.1\leq
M/\hbox{M${}_{\odot}$}\leq 0.3$ found within a 1-$\sigma_{\pi}$ volume shell
outside of 15 pc to that within the 15-pc volume, assuming a constant stellar
density. Within 15 pc, there is one primary star per 38.3 pc3. Using the
median parallax uncertainty of 0.0805 mas for the primary M dwarfs in our
sample, we calculate a volume of 51.4 pc3 between 15 pc and 15.017 pc. We thus
calculate that there are 1.3 primary stars within the 1-$\sigma$ volume shell
outside of 15 pc. We perform a similar analysis for the total number of stars
within our mass range of interest and the $413$ stars in our spectroscopic
sample, where the median parallax uncertainties are 0.0851 mas and 0.0805 mas,
respectively. We calculate that 1.9 and 1.5 stars, respectively, lie within
the 1-$\sigma_{\pi}$ volume shell outside of 15 pc for those two groups of
stars. We therefore conclude that the Eddington bias is not relevant for these
three samples (primaries, total, and spectroscopic) in distance space due to
the exquisite precision of the DR2 parallaxes.

We next address whether an Eddington bias is present in our sample in mass
space, that is, whether the faint, lowest mass primary M dwarfs in our sample
are over-represented. As noted above, the masses for most of these M dwarfs
are estimated using the MLR in the $M_{K}$ magnitude. Thus, the mass
uncertainties are a combination of the uncertainties in the 2MASS $K_{s}$
magnitude, the parallax, and the scatter in the MLR. The median uncertainty in
the $K_{s}$ magnitudes for the primaries in our sample is 0.021 mag, and as
noted above, the median parallax uncertainty for the primary stars is 0.0805
mas. Because these photometric and astrometric uncertainties are typically
small (0.2% for the faintest target with $K=10.66\pm 0.022$ mag, and 0.12% for
the most distant target at 15 pc), the mass uncertainties are dominated by the
0.014 M/M⊙ scatter in the MLR. We therefore compare the primary M dwarfs with
masses between $0.100-0.114$ M/M⊙, a range of $1-\sigma_{mass}$, within 15 pc
to the number of primary stars within this mass range within 10 pc. Within 10
pc are 10 such primaries; extrapolating to 15 pc and assuming a constant
stellar density leads us to expect $34\pm 6$ such objects. The 39 primary M
dwarfs in our sample with masses between $0.100-0.114$ M/M⊙ are comfortably
within the expected value, when considering the Poisson uncertainty. We thus
conclude that the lowest mass stars in our sample are not over-represented.

We also perform a similar analysis to determine whether the highest mass
primary stars are under- or over-represented in our sample. Because there are
only 2 primary stars with masses $0.286-0.300$ M/M⊙($1-\sigma_{mass}$) within
10 pc, we broaden our comparison range to $2-\sigma_{mass}$ ($0.272-0.300$
M/M⊙) for more reliable statistics. There are 11 primaries in this mass range
within 10 pc, from which we extrapolate an expected $37\pm 6$ primary stars.
The number of primaries in our sample within this mass range within 15 pc (32)
is within the expected range, illustrating that neither an Eddington nor a
Malmquist bias is present.

The sample of primary stars with masses $0.1\leq M/\hbox{M${}_{\odot}$}\leq
0.3$ within 15 pc that we present here is essentially volume-complete. While
there are likely a few additional secondary components to be found within this
mass range, we would overall be missing only a few percent of the population
of these M dwarfs. Some of these companions we will identify during our high-
resolution spectroscopic and speckle imaging surveys. Ultimately, future data
releases from Gaia will identify any primary stars within this mass range that
we may have missed. These would likely be the primaries of multiple systems
with companions at subarcsecond separations that have neither a DR2 parallax
nor a previous parallax from the literature. We thus conclude that, to the
best of our knowledge, the sample we present here is volume-complete.

These stars are attractive for both stellar astrophysics and exoplanetary
science. Thus, the existence of a vetted census of nearby, fully-convective M
dwarfs is a valuable resource for those studying them in their own right and
those searching them for planets.

A better understanding of the multiplicity statistics (separation, orbital
period, eccentricity, and mass ratio distributions) for this sample of fully-
convective stars is valuable for constraining star formation and evolution
scenarios. Determining whether a log-normal or a power-law model best fits the
orbital period distribution would constrain whether low-mass star formation
has a preferred spatial scale or follows a scale-free process in the formation
of binaries (Duchêne & Kraus, 2013). We have identified a number of candidate
multiple stars in our spectroscopic sample, which we list in Table 5. Results
from our complementary high-resolution spectroscopic and speckle imaging
surveys, in combination with Gaia imaging data and results from previous
multiplicity work, will provide a complete picture of the types and
separations of companions that are hosted by these fully-convective stars.
Moreover, the combination of precise astrometry data from Gaia with the RV
results from our spectroscopic survey will permit a probe of any multiplicity-
kinematics/age correlation that could constrain evolution models for low-mass
stars. A volume-complete sample eliminates the need for any corrections due to
incompleteness.

Table 5: Candidate Multiple Systems

Name | RA | DEC | Flag
---|---|---|---
| (hh:mm:ss) | (dd:mm:ss) |
LP 119-26 | 05:16:53.5 |  $+$56:40:19 | $\Delta\pi$
LEP J0617+8353 | 06:17:05.3 |  $+$83:53:35 | 2p
LHS 246 | 08:25:52.8 |  $+$69:02:01 | aen
LP 549-6 | 09:58:56.5 |  $+$05:58:00 | 2p
LHS 296 | 11:01:19.7 |  $+$03:00:17 | 2p
GJ 1227 | 18:22:27.1 |  $+$62:03:02 | 2p
GJ 1230B | 18:41:09.8 |  $+$24:47:20 | elev
G 184-31 | 18:49:54.5 |  $+$18:40:29 | $\Delta\pi$
LHS 3746 | 22:02:29.4 |  $-$37:04:51 | 2p
GJ 896B | 23:31:52.6 |  $+$19:56:14 | elev

Note. — Flag Description: ‘2p’ indicates that only a 2-parameter DR2
astrometric solution is available for the object; ‘aen’ indicates that the DR2
astrometric excess noise for this object is similar to that of known
subarcsecond binaries, as illustrated in Figure 7; ‘$\Delta\pi$’ indicates
that the difference between the object’s DR2 and pre-DR2 parallaxes is larger
or smaller than $\pm 20$ mas, respectively, as shown in Figure 6; ‘elev’ means
that the object is elevated above the main sequence in the HR Diagram in
Figure 5 due to overluminosity.

One of the motivations for planet searches around nearby low-mass stars is to
find nearby transiting planets whose atmospheres are most accessible for
study. Due to the efforts of MEarth (Nutzman & Charbonneau, 2008; Irwin et
al., 2015) and $TESS$ (Ricker et al., 2015), there are currently six systems
among the $413$ nearby, M dwarfs presented here that are known to host
transiting planets: GJ 1214b (Charbonneau et al., 2009), GJ 1132bc (Berta-
Thompson et al., 2015; Bonfils et al., 2018), LHS 1140bc (Dittmann et al.,
2017; Ment et al., 2019), LTT 1445Ab (Winters et al., 2019a), LHS 3844b
(Vanderspek et al., 2019), 2MA 0505-4756b (TOI-540b; Ment et al., 2020). Along
with the planets orbiting the 0.08 M/M⊙ ultra-cool dwarf TRAPPIST-1 (Gillon et
al., 2017), these are some of the most promising small exoplanets for
atmospheric studies in the near future with large telescopes.

Acknowledgments

We are grateful to Matthew Payne for valuable conversations and suggestions
that helped improve the analysis and interpretation of the results presented
here. We also thank Eliot Haley Vrijmoet for early access to his excellent M
dwarf astrometry paper. We thank the referee for their insightful comments and
suggestions that improved the manuscript. We thank Emily Pass for help with
refining the sample.

This work is made possible by a grant from the John Templeton Foundation. The
opinions expressed in this publication are those of the authors and do not
necessarily reflect the views of the John Templeton Foundation. This material
is based upon work supported by the National Science Foundation under grant
AST-1616624, and work supported by the National Aeronautics and Space
Administration under Grant No. 80NSSC18K0476 issued through the XRP Program.
The RECONS team is indebted to long-term support from the NSF, most recently
under grant AST-1715551.

We thank the members of the SMARTS Consortium, who have enabled the operations
of the small telescopes at CTIO since 2003, as well as observers and observer
support at CTIO, specifically Arturo Gomez, Mauricio Rojas, Hernan Tirado,
Joselino Vasquez, Alberto Miranda, and Edgardo Cosgrove.

Data products from the Two Micron All Sky Survey, which is a joint project of
the University of Massachusetts and the Infrared Processing and Analysis
Center/California Institute of Technology, funded by the National Aeronautics
and Space Administration (NASA) and the NSF have been used extensively, as
have the SIMBAD database and the Aladin and Vizier interfaces, operated at
CDS, Strasbourg, France. This work has made ample use of the Smithsonian
Astrophysical Observatory/NASA Astrophysics Data System. This work has made
use of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This research has made use
of the Washington Double Star Catalog maintained at the U.S. Naval
Observatory.

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