# Discovery of the Remarkably Red L/T Transition Object VHS
J183135.58-551355.9

Thomas P. Bickle School of Physical Sciences, The Open University, Milton
Keynes, MK7 6AA, UK  Adam C. Schneider United States Naval Observatory,
Flagstaff Station, 10391 West Naval Observatory Rd., Flagstaff, AZ 86005, USA
Jonathan Gagné Planétarium Rio Tinto Alcan, Espace pour la Vie, 4801 av.
Pierre-de Coubertin, Montréal, Québec, Canada  Institute for Research on
Exoplanets, Université de Montréal, Département de Physique, C.P. 6128 Succ.
Centre-ville, Montréal, QC H3C 3J7, Canada  Jacqueline K. Faherty Department
of Astrophysics, American Museum of Natural History, Central Park West at 79th
Street, NY 10024, USA  Austin Rothermich Department of Astrophysics, American
Museum of Natural History, Central Park West at 79th Street, NY 10024, USA
Johanna M. Vos School of Physics, Trinity College Dublin, The University of
Dublin, Dublin 2, Ireland  Department of Astrophysics, American Museum of
Natural History, Central Park West at 79th Street, NY 10024, USA  Genaro
Suárez Department of Astrophysics, American Museum of Natural History, Central
Park West at 79th Street, NY 10024, USA  J. Davy Kirkpatrick IPAC, Mail Code
100-22, Caltech, 1200 E. California Blvd., Pasadena, CA 91125, USA  Aaron M.
Meisner NSF’s National Optical-Infrared Astronomy Research Laboratory, 950 N.
Cherry Ave., Tucson, AZ 85719, USA  Marc J. Kuchner Exoplanets and Stellar
Astrophysics Laboratory, NASA Goddard Space Flight Center, 8800 Greenbelt
Road, Greenbelt, MD 20771, USA  Adam J. Burgasser Department of Astronomy &
Astrophysics, University of California San Diego, La Jolla, CA 92093, USA
Federico Marocco IPAC, Mail Code 100-22, Caltech, 1200 E. California Blvd.,
Pasadena, CA 91125, USA  Sarah L. Casewell School of Physics and Astronomy,
University of Leicester, Leicester, LE1 7RH, UK  Dan Caselden Department of
Astrophysics, American Museum of Natural History, Central Park West at 79th
Street, NY 10024, USA  Daniella C. Bardalez Gagliuffi Department of Physics &
Astronomy, Amherst College, 25 East Drive, Amherst, MA 01003, USA  The
Backyard Worlds: Planet 9 Collaboration

###### Abstract

We present the discovery of VHS J183135.58$-$551355.9 (hereafter VHS
J1831$-$5513), an L/T transition dwarf identified as a result of its unusually
red near-infrared colors ($J-K_{\rm S}=3.633\pm 0.277$ mag; $J-W2=6.249\pm
0.245$ mag) from the VISTA Hemisphere Survey and CatWISE2020 surveys. We
obtain low resolution near-infrared spectroscopy of VHS J1831$-$5513 using
Magellan/FIRE to confirm its extremely red nature and assess features
sensitive to surface gravity (i.e., youth). Its near-infrared spectrum shows
multiple CH4 absorption features, indicating an exceptionally low effective
temperature for its spectral type. Based on proper motion measurements from
CatWISE2020 and a photometric distance derived from its $K_{\rm S}$-band
magnitude, we find that VHS J1831$-$5513 is a likely ($\sim$85$\%$
probability) kinematic member of the $\beta$ Pictoris moving group. Future
radial velocity and trigonometric parallax measurements will clarify such
membership. Follow-up mid-infrared or higher resolution near-infrared
spectroscopy of this object will allow for further investigation as to the
cause(s) of its redness, such as youth, clouds, and viewing geometry.

Brown Dwarfs; L Dwarfs; T Dwarfs; Stellar Associations; Moving Clusters

††facilities: Magellan/FIRE, Paranal/VISTA, WISE††software: FIREHOSE (Gagné et
al., 2015), SpeXtool v1 (Cushing et al., 2004), unTimely Catalog Explorer
(Kiwy, 2022), WiseView (Caselden et al., 2018)

##  1 Introduction

At young ages, brown dwarfs have not yet contracted to their final equilibrium
radii (Burrows et al., 1997) and have low masses for their effective
temperatures. They therefore have lower surface gravities and lower pressure
atmospheres than their field-age counterparts. This low pressure reduces
collision-induced absorption by H2 (Linsky, 1969; Borysow et al., 1997) and it
is hypothesized that it causes an excess of clouds and dust in their
photospheres (Cushing et al., 2008; Faherty et al., 2016), shifting emergent
flux to longer wavelengths (e.g., Faherty et al. 2012). Consequently, the
near-infrared colors of young brown dwarfs are notably redder than those of
field age objects of the same spectral type (Faherty et al., 2016; Liu et al.,
2016).

Young, red L and T dwarfs can act as valuable analogs for young, giant
exoplanets, possessing similar effective temperatures, masses, and atmospheric
properties (Liu et al., 2013; Faherty et al., 2016). The planets HR8799bcde
(Marois et al., 2008) and planetary-mass companions VHS 1256$-$1257 b (Gauza
et al., 2015), 2M1207b (Chauvin et al., 2004) and BD+60 1417b (Faherty et al.,
2021) are apt examples of this, all exhibiting near-infrared spectra
consistent with red, low-gravity, late-L dwarfs. Crucially, young free-
floating substellar objects can be studied without the interference of light
from a host star, providing convenient and effective laboratories for tests of
planetary theory (Faherty et al., 2016). This convenience does, however, come
at a cost; whereas companions can have properties (e.g., age and metallicity)
inferred from their host star under the assumption of common formation, the
properties of free-floating brown dwarfs are notoriously difficult to
determine. An age-mass-temperature degeneracy exists for brown dwarfs (Burrows
et al., 1997), making it challenging to pinpoint these three key properties
for isolated brown dwarfs. However, if a brown dwarf can be linked through
kinematics and age diagnostics to a known moving group with a well constrained
age, this degeneracy inherent in brown dwarfs can be broken, and properties
consistent throughout that group’s membership, such as age (e.g., Bell et al.
2015) and metallicity (e.g., Viana Almeida et al. 2009), may be attributed to
the object. When the age of an object is inferred, evolutionary models can be
used to estimate physical properties such as mass and effective temperature
(e.g., Filippazzo et al. 2015; Suárez et al. 2021). Such objects are vital
benchmarks for studying brown dwarf evolution, and at young ages and low
masses, can provide important empirical constraints to the initial mass
function (Gagné et al., 2017; Kirkpatrick et al., 2021, 2024).

While targeted searches using the Two Micron All-Sky Survey (2MASS; Skrutskie
et al. 2006) have discovered unusually red, nearby L dwarfs (Kellogg et al.,
2015; Schneider et al., 2017), the detection limit of 2MASS ($J\approx 17$
mag) means that many low mass, red L/T dwarfs are missed. This restriction is
the primary reason that the number of spectroscopically confirmed free-
floating L/T dwarfs with extremely red colors ($J-K>2.2$ mag) remains low
($\sim$15). The advent of a new generation of surveys, such as the VISTA
Hemisphere Survey (VHS; McMahon et al. 2013), the UKIDSS Large Area Survey
(UKIDSS LAS; Lawrence et al. 2007) and UKIRT Hemisphere Survey (UHS; Dye et
al. 2018), which probe significantly deeper than 2MASS ($5\sigma$ J-band
depths of 20.2, 19.9 and 19.6 mag respectively), has brought the potential for
the discovery of objects with fainter $J$-band magnitudes than previously
possible (e.g., Schneider et al. 2023b). Consequently, these surveys are ideal
hunting grounds for young, red L and T dwarfs, the $J$-bands of which are
inherently suppressed. Reaching fainter $J$-band magnitudes also means that
redder objects than previously known have become detectable. Indeed, until
Schneider et al. (2023b)’s discovery of the reddest known free-floating L/T
dwarf CWISE J050626.96+073842.4 (CWISE J0506+0738; $(J-K)_{\rm MKO}$=2.974$\pm
0.039$ mag) using UHS, it had been approximately a decade since the discovery
of the previously reddest known objects PSO J318.5338$-$22.8603 ($(J-K)_{\rm
MKO}$=2.74$\pm 0.04$ mag; Liu et al. 2013) and ULAS J222711$-$004547
($(J-K)_{\rm MKO}$=2.79$\pm 0.06$ mag; Marocco et al. 2014). The discovery of
such extraordinarily red objects is important as it allows us to explore
parameters that influence the appearance of brown dwarfs such as youth,
metallicity, clouds, and viewing inclination (e.g., Looper et al. 2008; Vos et
al. 2017; Suárez & Metchev 2022; Suárez et al. 2023). It is also vital for
understanding the differences between free-floating planetary mass objects and
directly imaged exoplanets. Directly imaged exoplanets occupy a unique color-
magnitude sequence (e.g., Gratton et al. 2024), and the discovery of extremely
red, faint objects such as CWISE J0506+0738 (a strong candidate member of the
$\beta$ Pictoris Moving Group; Schneider et al. 2023b), serves to narrow the
color-magnitude gap.

In this work, we present VHS J1831$-$5513, an L/T transition dwarf with
anomalously red near-infrared colors. At $J-K_{\rm S}=3.633\pm 0.277$ mag, it
is potentially the reddest known free-floating substellar object, more so than
the current reddest spectroscopically confirmed object in the literature,
CWISE J0506+0738, by $\sim$0.66 mag. In Section 2 we discuss the discovery of
VHS J1831$-$5513\. In Section 3, we present Magellan/FIRE spectroscopic
follow-up data and in Section 4, we analyze and discuss those data. In Section
5, we evaluate young moving group membership, estimate physical properties,
and investigate the prospects for variability in VHS J1831$-$5513.

##  2 Identification of VHS J1831-5513

The unique color space occupied by young L dwarfs makes it possible to perform
targeted searches using a photometric approach; a particularly valuable
property given their typically low tangential velocities (Faherty et al.,
2009, 2012), which makes their discovery through proper motion-based searches
(e.g., Backyard Worlds; Kuchner et al. 2017; Humphreys et al. 2020)
challenging. Utilizing this principle, we performed a half-sky search of
CatWISE2020 (CatWISE; Marocco et al. 2021) and VHS for objects with extremely
red ($J-K_{\rm S}>2$ mag, $J-W2>4$ mag) near-infrared colors (Bickle et al.,
in prep). VHS J1831$-$5513 was discovered during a secondary search, which
used the CatWISE reject table instead of the main CatWISE catalog, in order to
collect any spuriously rejected candidates. VHS J1831$-$5513 was rejected by
CatWISE due to the overlap of a latent (a.k.a. charge persistence; Eisenhardt
et al. 2020) artifact in WISE. We used WiseView111http://byw.tools/wiseview
(Caselden et al., 2018), a tool designed to aid the visualisation of motion in
WISE time-resolved coadds, to vet VHS J1831$-$5513, and confirmed the presence
of an overlapping latent. We therefore checked the unTimely catalog (Meisner
et al., 2023; Kiwy, 2022) to investigate if its CatWISE photometry was
adversely affected. This showed that both the W1 and W2 bands were affected by
$\sim 0.1-0.2$ mag in the scan direction where the latent was present, but
both to a similar extent, so while the CatWISE W1-W2 color is not completely
unaffected, it is approximately accurate, with an offset from the average
unTimely W1-W2 color in the epochs where the latent is absent of only 0.012
mag. We also visually inspected the higher-resolution VHS imagery to confirm
there were no obvious contaminants or resolved companions affecting its near-
infrared colors. Once these checks were complete, and we were satisfied that
VHS J1831$-$5513 was a genuine extremely red candidate, it was added to our
list for follow-up spectroscopy.

##  3 Observations

We used the 6.5m Magellan Baade telescope and the Folded-port InfraRed
Echellette (FIRE; Simcoe et al. 2013) spectrograph to obtain near-infrared
spectra for VHS J1831$-$5513\. Observations were made on 2023 June 30 under
clear conditions. We operated FIRE in the low resolution prism mode using the
0$\farcs$8 slit (resolution $\lambda$/$\Delta\lambda\sim$100) covering the
full 0.8$-$2.5 $\micron$ wavelength range. The source was observed in an ABBA
pattern with 16 individual exposures of 120 seconds each, using the Sample Up
the Ramp (SUTR) read mode. Immediately after the science image we obtained a
Neon, Neon, Argon lamp and the A0 star HD 153842 for telluric, wavelength and
flux calibration. All data were reduced using a custom version of the FIREHOSE
(Gagné et al., 2015) package. The pipeline was modified such that boxcar
extractions were performed on A-B images to avoid large variations in the
slope of the resulting spectra, and subroutines from the SpeXtool v1 package
(Cushing et al., 2004; Vacca et al., 2003) were used to combine, mask, and
inspect the resulting spectra.

The final reduced spectrum is shown in Figure 1, in which prominent absorption
features and telluric bands are labeled. We caution that due to the nonlinear
response of the detector, the slope after the $\sim$2.3 $\micron$ CO edge may
be unreliable as response decreases rapidly towards the edge of the detector.

Figure 1: Magellan/FIRE spectrum of VHS J1831$-$5513 (black), Gaussian
smoothed using a width of 15 pixels. Key molecular absorption features are
labeled. Original resolution data are plotted in grey and flux uncertainty is
shown in blue.

##  4 Analysis

Table 1: Properties of VHS J1831$-$5513

Parameter | Value | References
---|---|---
$\alpha$ [J2000] (°) | 277.898262 | 1
$\delta$ [J2000] (°) |  $-$55.232219 | 1
$\mu_{\alpha}$aaProper motion values corrected for CatWISE2020 systematic offsets. (mas yr-1) | 1.43$\pm 9.6$ | 2
$\mu_{\delta}$aaProper motion values corrected for CatWISE2020 systematic offsets. (mas yr-1) |  $-$84.24$\pm 10.4$ | 2
J (mag) | 20.175$\pm 0.229$ | 1
$K_{s}$ (mag) | 16.542$\pm 0.048$ | 1
W1 (mag) | 14.735$\pm 0.018$ | 2
W2 (mag) | 13.926$\pm 0.016$ | 2
d${}_{\text{phot}}$bbPhotometric distance estimated using the VHS $K_{s}$ magnitude and the absolute magnitude-spectral type relation of Dupuy & Liu (2012). (pc) | 55.4$\pm 5.5$ | 3
Spectral Type [NIR] | L8$\gamma$-T0$\gamma$ | 3

Notes:

References. — (1) VHS DR6 (McMahon et al., 2013) (2) CatWISE2020 Reject Table
(Marocco et al., 2021) (3) This work

###  4.1 Spectral Type

The left panel of Figure 2 compares the near-infrared spectrum of VHS
J1831$-$5513 to several field-age L/T transition spectral standards (Burgasser
et al., 2006; Kirkpatrick et al., 2010; Cruz et al., 2018). The extremely red
spectral slope and low gravity features (e.g., steep H-band slope) in the
near-infrared spectrum of VHS J1831$-$5513 leads to poor fits to the spectral
standards over the 1–2.4$\micron$ range as a whole, as is the case for many
other young, red objects (e.g., Faherty et al. 2013; Liu et al. 2013;
Schneider et al. 2016, 2023b). The best fit over the $J$-band is the L9
standard 2MASS J02550357$-$4700509 (Kirkpatrick et al., 2010). Although
progress is being made in the spectral classification of young L and T dwarfs
(e.g., Piscarreta et al. 2024), there is not yet a unified approach tailored
to young objects, nor a complete set of young L/T transition spectral
standards. The diversity seen in the near-infrared slopes and molecular
absorption features within the known young populations remains a challenge for
the development of a uniform classification technique of young objects. The
right panel of Figure 2 compares VHS J1831$-$5513 to the young, red objects
WISEA J114724.10$-$204021.3 (WISEA J1147$-$2040; L7$\gamma$; Schneider et al.
2016), PSO J318.5338$-$22.8603 (PSO J318.5$-$22; L7 VL-G; Liu et al. 2013) and
CWISE J050626.96+073842.4 (L8-T0$\gamma$; Schneider et al. 2023b). These
comparisons highlight the extremely red near-infrared slope of VHS
J1831$-$5513, which is noticeably redder than many members of the young
planetary-mass population, and is matched only by CWISE J0506+0738, the
reddest free-floating L/T dwarf currently known.

Figure 2: Left: Smoothed Magellan/FIRE spectrum of VHS J1831$-$5513 (black)
compared to the spectral standards (red, labeled) 2MASS J08251968+2115521 (L7)
from Cruz et al. (2018), 2MASS J16322911+1904407 (L8) and 2MASS
J02550357$-$4700509 (L9) from Kirkpatrick et al. (2010), and SDSS
J120747.17+024424.8 (T0) and SDSS J083717.21$-$000018.0 (T1) from Burgasser et
al. (2006). Right: VHS J1831$-$5513 compared to the young, planetary-mass
objects WISEA J1147$-$2040 (Schneider et al., 2016), PSO J318.5$-$22 (Liu et
al., 2013) and CWISE J0506+0738 (Schneider et al., 2023b). All spectra are
normalized between 1.27 and 1.29 $\micron$.

Like CWISE J0506+0738, the spectrum of VHS J1831$-$5513 displays likely CH4
absorption features at the H-band peak and on the red side of the K-band peak.
These features also occur in the spectrum of another young, planetary-mass L
dwarf, VHS 1256$-$1257 b. The left column of Figure 3 compares the H\- and
K-bands of the Magellan/FIRE spectrum of VHS J1831$-$5513 and the James Webb
Space Telescope (JWST) spectrum of VHS 1256$-$1257 b (Miles et al., 2023). The
two objects have several likely CH4 absorption features in common, as
highlighted in the left column of Figure 3. The wavelengths of these features
coincide with CH4 absorption bands that begin to form in model spectra of low
gravity objects at effective temperatures $\lesssim 1500$ K and become more
prominent as the temperature decreases. The right column of Figure 3 shows
Sonora Bobcat (Marley et al., 2021) models at solar metallicity and a constant
surface gravity (log(g)$=3.5$), with temperatures ranging from 1100K to 1500K.
Highlighted are the locations of the absorption features that occur in the
spectra of both VHS J1831$-$5513 and VHS 1256$-$1257 b.

Figure 3: Left column: Comparison between the H\- (top) and K\- (bottom) bands
of VHS J1831$-$5513 (black - smoothed; grey - original resolution) and the
young, planetary-mass companion VHS 1256-1257 b (red; Miles et al. 2023). CH4
absorption features that appear in both objects are marked by blue bands.
Right column: Sonora Bobcat (Marley et al., 2021) models at solar metallicity
and log(g) = 3.5, with a range of effective temperatures. The blue bands
represent the locations of the absorption features in the corresponding band
of the left column.

Unlike CWISE J0506+0738 and VHS 1256$-$1257 b, VHS J1831$-$5513 displays a
prominent absorption feature at the peak of the J-band, centered at $\sim$1.3
$\micron$. This feature is not reproduced by the Sonora models and, to our
knowledge, no feature centered at this wavelength has previously been noted in
other L dwarfs. In T dwarfs, a 1.3 $\micron$ CH4 band is responsible for the
gradually increasing downward slope on the red side of the J-band peak,
starting in early T dwarfs and progressing through later subtypes. It
eventually merges with the 1.4 $\micron$ H2O band to produce the
characteristic, thin J-band peak of late-T dwarfs (Burgasser et al., 2002).
Given the presence of likely CH4 absorption elsewhere in the spectrum of VHS
J1831$-$5513, the observed 1.3 $\micron$ feature may also be the result of CH4
absorption. Given that such absorption has only been seen in T dwarfs, this
would be suggestive of VHS J1831$-$5513 being narrowly on the T side of the
L/T transition. However, we caution that CH4 is not known to exhibit any sharp
features in this area, and this would therefore be a very unusual presentation
for CH4 absorption. There is a known telluric O2 feature close to the
wavelength in question (though not at the exact wavelength) which may cause
contamination (Kausch et al. 2015 and references therein). We therefore
inspected the raw science and telluric data to check if the feature was the
result of poor telluric correction, but no obvious cause was found. The
feature also does not appear in any of the other spectra taken with the
instrument on the night. For now, we are uncertain of the feature’s cause, and
characterize it as an unknown absorber. Future acquisition of higher
resolution, higher signal-to-noise (S/N) spectra will allow this feature to be
investigated further using the spectral inversion (retrieval) technique, which
has been effectively utilized in recent studies to constrain cloud properties
and elemental abundances of substellar objects (e.g., Burningham et al. 2021;
Calamari et al. 2022; Vos et al. 2023; Hood et al. 2023; Adams et al. 2023;
Whiteford et al. 2023).

Considering the L9 standard being the best J-band fit, the deep 1.1 $\micron$
H2O band, and the H\- and K-band CH4 absorption features, we assigned a
preliminary spectral type of L8-T0 (v. red), prior to gravity assessment.

###  4.2 Gravity

Although the extremely red near-infrared colors of VHS J1831$-$5513 are a
potential indicator of youth, a small population of field gravity objects are
also known to possess red colors (e.g., Marocco et al. 2014), possibly due to
an excess of sub-micron sized dust grains in their photospheres (Hiranaka et
al., 2016). A near equator-on inclination angle has also been found to be a
cause of red colors among field objects (Vos et al., 2017; Guerra Toro et al.,
2022; Suárez et al., 2023), indicating that red colors in brown dwarfs are
more complex diagnostically than previously thought. Hence, other spectral
diagnostics must be performed to confirm youth.

Youth in brown dwarfs and planetary-mass objects can also be inferred through
evidence of low surface gravity, as young objects are still contracting
(Burrows et al., 1997) and have larger radii than equivalent temperature field
objects. Intermediate and low surface gravity objects, suffixed $\beta$ and
$\gamma$ respectively (Kirkpatrick 2005; or INT-G and VL-G per Allers & Liu
2013 indices), can be discerned from field gravity objects by utilizing
morphological differences in their optical and near-infrared spectra. Gravity-
sensitive indices are well established for early-to-mid type L dwarfs (Lucas
et al., 2001; McGovern et al., 2004; Kirkpatrick et al., 2006; Cruz et al.,
2009; Allers & Liu, 2013; Martin et al., 2017; Cruz et al., 2018). Some rely
on the weakening of atomic lines in the spectra of lower gravity objects.
Others measure the shape of spectral regions, the morphologies of which are
particularly affected by the strength of H2 collision-induced absorption
(CIA), which is reduced in lower gravity objects. However, most gravity-
sensitive indices do not function well for late type L dwarfs ($>$L5).

One index that may function for objects as late in type as VHS J1831$-$5513 is
the H-slope index (Schneider et al., 2023b). Low gravity (young) objects have
more peaked H-bands caused by reduced H2 CIA in their low-pressure
photospheres. H-slope aims to quantify this by using a linear least-squares
fit between 1.45-1.64 $\micron$ to measure the slope of the blue side of the
H-band, where the unit is normalized flux/wavelength. Schneider et al. (2023b)
found that for L7-T0 dwarfs, typical field gravity objects have H-slope values
ranging from 2-4, and low gravity objects have values between 3-5. VHS
J1831$-$5513 has an H-slope value of 5.068, considerably higher than those of
field objects, and even slightly exceeding the top end of the young
population. This result is extremely similar to that of the spectrum of CWISE
J0506+0738, which returns an H-slope value of 5.043222Schneider et al. (2023b)
reported an H-slope value of 4.38 for CWISE J0506+0738, calculated before
rescaling to correct for Keck/NIRES interband flux calibration issues. Our
value for CWISE J0506+0738 is calculated using its spectrum rescaled to its
photometric $J-K$ color..

The H2(K) index (Canty et al., 2013) has also been shown to differentiate low
gravity and field gravity objects at late-L subtypes (Schneider et al., 2014).
Like the H-cont and H-slope indices, it utilizes the reduced H2 CIA that
occurs in lower gravity objects, but in the K-band. To do this, it measures
the slope between 2.17 $\micron$ and 2.24 $\micron$ by calculating the ratio
of the median fluxes in 0.02 $\micron$ ranges centered at those wavelengths in
the unsmoothed spectrum of an object. For L7-T0 spectral types, typical index
scores for field gravity objects are $1.05\leqslant$H2(K)$\leqslant 1.2$,
whereas low gravity objects score much lower than their field gravity
counterparts of the same spectral type (Schneider et al., 2014). VHS
J1831$-$5513 returns a score of H2(K)=1.045, over 1$\sigma$ below the field
sequence at L7, and significantly further below for later spectral types
($\sim$3$\sigma$ below for L8), where the field sequence sees a rapid increase
(see fig. 10 of Schneider et al. 2014).

We caution that as most of these indices predate the discovery that
inclination angle is correlated with cloud opacity (Vos et al., 2017; Guerra
Toro et al., 2022; Suárez et al., 2023), they are not designed to account for
this, and as such, it is possible that the viewing geometry of VHS
J1831$-$5513 may interfere with the gravity assessment they provide. The
existence of such contamination and extent to which this may impact the index
scores is yet to be fully tested.

Considering the extremely red near-infrared slope, the H-slope and H2(K)
indicators, and the probable kinematic match to the $\sim$22 Myr $\beta$
Pictoris Moving Group (Zuckerman et al., 2001; Shkolnik et al., 2017)
discussed later, we conclude that VHS J1831$-$5513 has low surface gravity,
and tentatively classify it as L8$\gamma$-T0$\gamma$. Both a higher S/N
spectrum and the future development of gravity-sensitive indices applicable to
L/T transition objects will contribute to a higher confidence gravity
assessment for VHS J1831$-$5513.

##  5 Discussion

###  5.1 Moving Group Membership

Young moving groups typically retain similar 3D velocities for a few hundred
Myr, and their population encompasses the whole range of masses from
planetary-mass to stars (Zuckerman & Song, 2004; Torres et al., 2008; Malo et
al., 2013; Gagné et al., 2014; Faherty et al., 2016). Young moving groups are
coeval, so objects that are found to be a member of a group can be assigned
the age of that group and become key benchmarks for its population.

To determine if VHS J1831$-$5513 is a member of a known young moving group, we
used the BANYAN $\Sigma$ algorithm (Gagné et al., 2018c), which uses Bayes’
theorem to select the best-matching XYZUVW model among 27 young associations
and the distribution of nearby field stars, while optionally marginalizing
over missing radial velocities or distances with an exact, analytical solution
to the marginalization integrals. BANYAN $\Sigma$ requires minimum inputs of
position and proper motions, and can optionally use distance and heliocentric
radial velocity with respective uncertainties. If distance and/or radial
velocity are not provided, it calculates and provides optimal values for
these, assuming membership in each of the 27 groups.

The long time baseline of CatWISE (12 epochs over 8 years) means that it can
provide proper motion measurements with reasonable confidence ($\pm\sim$10 mas
yr-1 for a W$1=14$ mag source; Marocco et al. 2021). We therefore use the
CatWISE proper motion data for the BANYAN $\Sigma$ input. However, CatWISE has
known systematic astrometric
offsets333https://irsa.ipac.caltech.edu/data/WISE/CatWISE/gator_docs/CatWISE2020_Table1_20201012.tbl
compared to Gaia DR2. We therefore applied the offsets for the CatWISE tile in
which VHS J1831$-$5513 is located, and used the corrected proper motion values
for our BANYAN $\Sigma$ input. When only provided with the position and proper
motions of VHS J1831$-$5513, with respective uncertainties, BANYAN $\Sigma$
gives a 79.7% membership probability for the $\sim$22 Myr $\beta$ Pictoris
Moving Group (BPMG; Zuckerman et al. 2001; Shkolnik et al. 2017), an 8.6%
probability for the $\sim$45 Myr Argus Association (ARG; Torres et al. 2008;
Zuckerman 2019), a 2% probability for the $\sim$130 Myr AB Doradus Moving
Group (ABDMG; Zuckerman et al. 2004; Gagné et al. 2018b), and a 9.8%
probability of VHS J1831$-$5513 not being a member of any known group.

VHS J1831$-$5513 is too faint at optical wavelengths to be detected by the
Gaia mission (Gaia Collaboration et al., 2023), and in surveys where it is
detected, insufficient astrometric data of adequate precision to determine a
parallax exist. We instead calculated a photometric distance for VHS
J1831$-$5513\. As has been noted in previous works, objects with unusual near-
infrared colors do not conform well to standard absolute magnitude relations
(Faherty et al., 2013, 2016; Filippazzo et al., 2015; Liu et al., 2016). In
investigating this, Schneider et al. (2023b) compared the parallactic
distances of several very red, free-floating objects to their J, K, W1, and W2
photometric distances, and showed that for those objects, the K-band
photometric distance provided the best match on average to the measured
parallax. We therefore used the VHS Ks-band magnitude to calculate a
photometric distance for VHS J1831$-$5513 using the absolute magnitude-
spectral type relations in Dupuy & Liu (2012). Using a spectral type of L9$\pm
1$, we determine a Ks-band photometric distance for VHS J1831$-$5513 of
55.4$\pm 5.5$ pc. This distance agrees well with the optimal kinematic
distances for BPMG (51.5$\pm 5.1$ pc) and ARG (54.8$\pm 5.8$ pc) membership
provided by BANYAN $\Sigma$. Adding this photometric distance to the existing
position and proper motion parameters, BANYAN $\Sigma$ gives an 85.2%
membership probablity for BPMG, 9.7% for ARG, 0.4% for ABDMG and 4.6% for no
group. While promising, this is not a conclusive indicator of BPMG membership,
as a probability of $>90\%$ is typically used as a cutoff to select high
probability group members (Gagné et al., 2015). Regardless, the indications of
low surface gravity in its spectrum and the fairly low precision proper motion
measurements from CatWISE for VHS J1831$-$5513 merit further investigation of
a $\sim 85\%$ membership probability. A summary of the BANYAN $\Sigma$ results
are provided in Table 2.

In light of its positive spectral indicators of youth and its best BANYAN
$\Sigma$ kinematic match, we find that VHS J1831$-$5513 is most likely a
member of the BPMG. A higher precision proper motion measurement, as well as
future radial velocity and trigonometric parallax measurements are required to
confirm or refute this membership.

Table 2: BANYAN $\Sigma$ Membership Results

Input Data | Group Membership Probability (%)aaABDMG = AB Doradus Moving Group (Zuckerman et al., 2004); ARG = Argus Association (Torres et al., 2008); BPMG = $\beta$ Pictoris Moving Group (Zuckerman et al., 2001); Field = Not a member of any known group. | dopt (pc)bbOptimal distance to VHS J1831$-$5513, assuming membership of individual groups.
---|---|---
$\mu$ | BPMG (79.7), ARG (8.6), ABDMG (2), Field (9.8) | BPMG (51.5$\pm$5.1), ARG (54.8$\pm$5.8), ABDMG (67.1$\pm$6)
$\mu$ \+ dphot | BPMG (85.2), ARG (9.7), ABDMG (0.4), Field (4.6) | -

Notes:

###  5.2 Physical Properties

Under the assumption that it is a member of the BPMG, certain physical
properties of VHS J1831$-$5513 can be inferred. Viana Almeida et al. (2009)
found that the BPMG has approximately solar metallicity, so we assume solar
metallicity for our analysis. Firstly, we estimated the bolometric luminosity
of VHS J1831$-$5513\. To do this, we used the Sanghi et al. (2023) empirical
bolometric correction-spectral type polynomial relations for young objects, in
combination with the absolute VHS $K_{\rm S}$-band magnitude based on our
previously calculated photometric distance. We estimate a bolometric
luminosity for VHS J1831$-$5513 of log$(L_{bol}/L_{\odot})=-4.57\pm 0.09$.
Note that several assumptions are made when determining this value, such as
our photometric distance being accurate and the Sanghi et al. (2023) relations
being applicable to such an unusually red object. A more accurate bolometric
luminosity can be determined with a measured parallax and broader wavelength
coverage.

To test this value, we also derive a bolometric correction for VHS 1256-1257b
using the bolometric luminosity from Miles et al. (2023) and photometry from
the Ultracoolsheet (Best et al. 2024 and references therein), and apply it to
VHS J1831$-$5513\. VHS 1256-1257b is known to be red and young, and the broad
wavelength coverage provided by the JWST observations of this object allows
for a precise determination of its L${}_{\text{bol}}$ value. This yields a
value of log$(L_{bol}/L_{\odot})=-4.51\pm 0.09$ for VHS J1831$-$5513.

We used the Sonora Bobcat (Marley et al., 2021) and Diamondback (Morley et
al., 2024) evolutionary models at solar metallicity to estimate the mass and
radius of VHS J1831$-$5513 using the age of BPMG ($22\pm 6$ Myr; Shkolnik et
al. 2017) and the bolometric luminosity derived from the Sanghi et al. (2023)
relations. Using the Sonora Bobcat models, assuming BPMG membership, we infer
a radius of $1.32^{+0.03}_{-0.02}$ $R_{\text{Jup}}$ and a mass of $7\pm 1$
$M_{\text{Jup}}$. Using the calculated bolometric luminosity, derived radius,
and the Stefan-Boltzmann law, we estimate an effective temperature for VHS
J1831$-$5513 of $T_{\text{eff}}=1130\pm 60$ K. From the Sonora Diamondback
models, taking the same age and bolometric luminosity, we infer a radius of
$1.42^{+0.04}_{-0.03}$ $R_{\text{Jup}}$, a mass of $6.5\pm 1.5$
$M_{\text{Jup}}$ and an effective temperature of $T_{\text{eff}}=1085\pm 60$
K.

While both models suggest a similar mass and effective temperature for VHS
J1831$-$5513, the radius is notably different. The Diamondback values are
preferred, as the model incorporates silicate clouds, as well as gravity-
dependent cloud clearing, which appears to occur at the L/T transition (Marley
et al., 2010). In both cases, the mass is well below the deuterium burning
limit of $\sim$13 $M_{\text{Jup}}$ (Spiegel et al. 2011 and references
therein) and the effective temperature is $\sim$150-200 K cooler than an L9 at
field age (Kirkpatrick et al., 2021), which is consistent with previous
findings that young objects are cooler than field age objects of equivalent
spectral type (Filippazzo et al., 2015; Faherty et al., 2016; Liu et al.,
2016; Suárez et al., 2021). An insufficient number of L/T transition objects
are currently known in BPMG to infer the temperature at which the L/T
transition occurs in the group. However, the temperature at which the L/T
transition occurs decreases with age, and Gagné et al. (2018a) found that the
L/T transition for ABDMG is $\sim$1150 K, suggesting that if VHS J1831$-$5513
is a true member of BPMG, the L/T transition may occur at a similar
temperature in the two groups, despite the $\sim$100 Myr age difference.

VHS J1831$-$5513 is notably $\sim$100 K cooler than PSO J318.5$-$22 (Miles et
al., 2018) which displays no corresponding near-infrared CH4 absorption
features. It is however, an extremely similar effective temperature to CWISE
J0506+0738 ($T_{\text{eff}}=1140\pm 80$ K; Schneider et al. 2023b), which
exhibits likely CH4 absorption at both the H\- and K-band peaks. This
temperature similarly bolsters the empirical temperature constraint provided
by CWISE J0506+0738 for the introduction of CH4 absorption into the near
infrared spectra of young L/T transition objects.

BANYAN $\Sigma$ returns a non-zero probability of VHS J1831$-$5513 being a
member of ABDMG, which has very similar UVW and distance values among its
membership to that of BPMG. These similarities are known to confuse membership
assignment for some objects between the two groups (Gagné et al., 2018c). In
case of the unlikely event that VHS J1831$-$5513 is an ABDMG member, we
repeated the analysis using the age of the ABDMG ($133^{+15}_{-20}$ Myr; Gagné
et al. 2018b). Assuming ABDMG membership, the Marley et al. (2021) models
suggest a radius of $1.23^{+0.13}_{-0.11}$ $R_{\text{Jup}}$, an effective
temperature of $1170\pm 50$ K and a mass of $12\pm 0.2$ $M_{\text{Jup}}$ for
VHS J1831$-$5513\. This would still place VHS J1831$-$5513 below the deuterium
burning limit, solidifying its status as a planetary-mass object. We reiterate
that the scenario where VHS J1831$-$5513 is a member of ABDMG is unlikely, and
BPMG is the strong favorite for membership.

###  5.3 Prospects for Variability

Young L and T dwarfs are known to exhibit stronger photometric and
spectrophotometric variability than field age objects, driven by rotational
modulations of condensate clouds in their atmospheres (Biller et al., 2015,
2018; Metchev et al., 2015; Lew et al., 2016; Schneider et al., 2018; Vos et
al., 2018, 2019, 2020, 2022; Eriksson et al., 2019; Miles-Páez et al., 2019;
Bowler et al., 2020; Manjavacas et al., 2021). Furthermore, the L/T transition
has been shown to have a higher variability occurrence rate than other
spectral types (Radigan, 2014). Indeed, Liu et al. (2024) determined that the
variability rate of young objects at the L/T transition is $64^{+23}_{-22}\%$,
compared to $31^{+12}_{-9}\%$ outside the L/T transition. Variable L dwarfs
are more likely to have cloudier atmospheres (Suárez & Metchev, 2022) and
redder colors (Ashraf et al., 2022) than non-variable counterparts.
Additionally, both variability amplitude and infrared colors have been found
to be correlated with inclination angle, with equator-on objects having higher
amplitudes and redder colors than those which are viewed pole-on (Vos et al.,
2017). Near-infrared colors also depend on cloud thickness, where redder L
dwarfs have higher cloud opacity than bluer objects (Suárez & Metchev, 2022).

Suárez et al. (2023) further demonstrated a correlation between infrared
color, cloud opacity, and viewing inclination for L dwarfs, finding that
equator-on objects exhibit more clouds and, therefore, are redder than objects
viewed close to pole-on. This indicates that equatorial latitudes are cloudier
than polar latitudes and the color diversity of brown dwarfs is strongly
influenced by their viewing geometry.

The VHS photometry of VHS J1831$-$5513 indicates a color of $J-K_{\rm
S}=3.633\pm 0.277$ mag. However, visual inspection and comparison of its
Magellan/FIRE spectrum showed that its spectrum is not as red as CWISE
J0506+0738 (see Figure 2), which has a color of $(J-K)_{\rm MKO}$=2.974$\pm
0.039$ mag (Schneider et al., 2023b). We therefore extracted synthetic
photometry from the spectrum of VHS J1831$-$5513 using a custom code with
filter profiles from SVO (Rodrigo et al., 2012; Rodrigo & Solano, 2020). This
gives a color of $(J-K_{\rm S})_{\text{synth}}=2.914\pm 0.008$ mag, which is
discrepant from the VHS color by 0.719 mag (3.07$\sigma$). The photometric and
synthetic colors of VHS J1831$-$5513 are compared to the photometric colors of
CWISE J0506+0738 and other L and T dwarfs in Figure 4.

Figure 4: Color-color diagrams comparing VHS J1831$-$5513 (blue square) to L
and T dwarfs with photometry from Schneider et al. (2023a) (yellow to red
circles) and CWISE J0506+0738 (green diamond; Schneider et al. 2023b). VHS
J1831$-$5513 is plotted using its VHS and CatWISE photometry, and represents a
significant outlier from even the reddest known objects. The blue lines in the
left and right plots indicate the synthetic $J-K_{\rm S}$ color calculated
from the Magellan/FIRE spectrum of VHS J1831$-$5513, which is still an outlier
from the bulk of the brown dwarf population, but is similar to that of CWISE
J0506+0738, the reddest known L/T transition dwarf.

The VHS J\- and $K_{\rm S}$-band exposures were taken $\sim$6 minutes apart,
so can be treated as near-simultaneous; the shortest known variability period
of a brown dwarf is $\sim$1.08 hr (Tannock et al., 2021; Vos et al., 2022),
and young brown dwarfs are known to be slow rotators (Schneider et al., 2018;
Vos et al., 2022). Thus, such a short time difference should be insufficient
to cause a significant enough photometric change to explain the observed color
discrepancy in VHS J1831$-$5513.

While we cannot definitively rule out that the sole cause of the color
discrepancy is the low S/N of the VHS J-band detection (S/N$\approx$4.6), we
note that VHS J1831$-$5513 possesses exceptionally red near-infrared colors,
which is suggestive of an extreme atmosphere, potentially viewed near equator-
on. Complex clouds, disequilibrium chemistry, and powerful atmospheric
dynamics may be expected in such a young, red atmosphere (Showman & Kaspi,
2013; Suárez & Metchev, 2023; Suárez et al., 2023), and can affect the
emergent flux observed from the object. It is therefore possible that cloud-
driven variability in VHS J1831$-$5513 may contribute to the observed
$(J-K_{\rm S})$ color discrepancy. The $\sim$9 yr difference between the VHS
images being taken and the Magellan/FIRE spectrum being collected is easily
sufficient for variability to have played a role in causing the discrepancy
between the two.

Pressure plays a key role in the behavior of clouds within the atmospheres of
substellar objects (Buenzli et al., 2012; Yang et al., 2016). With the J\- and
$K_{\rm S}$-bands probing different atmospheric depths, they may exhibit
different variability amplitudes, as has been observed in other L/T transition
objects, which show higher amplitudes in the J-band than the $K_{\rm S}$-band
(Artigau et al., 2009; Radigan et al., 2012; Vos et al., 2019). VHS
1256$-$1257 b, an object similar in nature to VHS J1831$-$5513, is highly
variable in the J-band, with both Bowler et al. (2020) and Zhou et al. (2020)
finding a 1.27 $\micron$ variability amplitude of $\sim$25$\%$, and Zhou et
al. (2022) finding a broader J-band variation of up to $38\%$ on a $\sim$1
year timescale, the highest ever observed in a substellar object. In the same
vein, phase shifts between J\- and $K_{\rm S}$ light curves can also affect
the $J-K_{\rm S}$ color of L/T transition dwarfs (e.g., McCarthy et al. 2024;
Plummer et al. 2024). Future time-resolved monitoring will provide insight
into whether differing variability amplitudes and/or a phase shift between the
J\- and KS-bands of VHS J1831$-$5513 exist, and if so, to what extent they
impact its $J-K_{\rm S}$ color.

The correlation between near infrared color, viewing inclination, and cloud
opacity in Suárez et al. (2023) is helpful to understand the appearance of
objects like VHS J1831$-$5513\. This may indicate that its extremely red near-
infrared colors and potentially the CH4 features in its Magellan/FIRE
spectrum, are explained, at least partially, by unusually thick clouds as a
consequence of the object being viewed equator-on. We note, however, that the
Suárez et al. (2023) study focused on L3–L7 dwarfs and did not take into
account objects as late in type as VHS J1831$-$5513\. L7 marks the peak for
$J-K$ colors on the field sequence as objects at later types rapidly get bluer
as condensates sink below the photosphere. While the trends between near-
infrared color and inclination in Vos et al. (2017) and Vos et al. (2020) are
observed into the L/T transition, it is an evolutionary stage in which marked
changes, both chemical and physical, occur in the atmospheres of brown dwarfs,
so further investigation is needed to determine if the trends identified in
Suárez et al. (2023) are applicable to the L/T transition.

The only multi-epoch survey to detect VHS J1831$-$5513 is the WISE mission.
However, because of the latent artifact contamination described in Section 2,
we were unable to confidently explore the variability properties of VHS
J1831$-$5513 using the WISE data. Nonetheless, VHS 1831$-$5513 is highly
likely to exhibit detectable variability given its red infrared colors, young
age, possible near equator-on inclination angle and cloudy atmosphere, and its
position at the L/T transition (Radigan, 2014; Vos et al., 2017, 2019; Suárez
& Metchev, 2022), making it a promising target for future variability studies.

##  6 Conclusion

We have presented the discovery of VHS J1831$-$5513, an extremely red, young
L/T transition object, identified through a search of the CatWISE reject and
VHS catalogs. We obtained Magellan/FIRE near-infrared spectroscopy of VHS
J1831$-$5513, which shows that it is an $\sim$L8$\gamma$-T0$\gamma$ dwarf with
likely CH4 absorption at the H\- and K-band peaks. The presence of CH4 in the
atmosphere of VHS J1831$-$5513 indicates a $T_{\rm eff}$ at the L/T
transition. We find that its spectral morphology is similar to those of other
young, red late-type L dwarfs, including the planetary mass companion VHS
1256$-$1257 b, with which it shares a number of individual CH4 absorption
features. VHS J1831$-$5513 also exhibits a 1.3 $\micron$ absorption feature,
the cause of which is unclear. This feature must be investigated further,
potentially at higher resolution, in order to confidently assert its cause.

Using the BANYAN $\Sigma$ Bayesian algorithm, we determine that VHS
J1831$-$5513 is a likely member of the $\sim$22 Myr BPMG based on its
kinematics. This membership assignment is supported by its low gravity score
in pressure-sensitive indices and its red near-infrared slope. Future
trigonometric parallax, radial velocity, and higher precision proper motion
measurements will help to test this membership. Using the age of BPMG, we
inferred physical properties for VHS J1831$-$5513\. Its estimated mass of
$6.5\pm 1.5$ $M_{\text{Jup}}$ places it among the lowest mass free-floating
BPMG members known (alongside CWISE J0506+0738 at $7\pm 2$ $M_{\text{Jup}}$;
Schneider et al. 2023b), contributing to empirical constraints on the group’s
initial mass function. Its estimated effective temperature of
$T_{\text{eff}}=1085\pm 60$ K is well below that of field-age objects of
similar spectral types, consistent with previous findings for other young
brown dwarfs. Given the spectroscopic evidence of the presence of CH4 in its
atmosphere, this temperature estimate also places empirical constraints on the
temperature at which CH4 begins to appear in the near-infrared spectra of
young L/T transition dwarfs.

The extremely red near-infrared colors and potentially near equator-on
inclination angle of VHS J1831$-$5513 make it highly likely to be extremely
cloudy. This, in combination with its young age, and position at the L/T
transition, suggests that VHS J1831$-$5513 is highly likely to be variable,
and is therefore an excellent prospective target for future photometric and
spectrophotometric monitoring. A significant ($\sim$3.1$\sigma$) $J-K_{\rm S}$
color discrepancy noticed between its Magellan/FIRE spectrum and VHS
photometry may also indicate that it has a significant difference between its
J\- and $K_{\rm S}$-band variability amplitudes or a potential phase shift
between its J\- and $K_{\rm S}$ light curves, making it a yet more intriguing
target for variability monitoring.

The discoveries of VHS J1831$-$5513 in this work and CWISE J0506+0738 in
Schneider et al. (2023b) hint at the existence of a population of
exceptionally red L/T transition objects which, until the introductions of
newer near-infrared surveys with deeper detection thresholds, were simply too
faint to be detected in the J-band by the previous generation of near-infrared
survey instruments (e.g., 2MASS). Future targeted searches of these catalogs
are warranted to discover more examples of such extraordinarily red objects.
This also highlights the importance of the upcoming Euclid mission (Laureijs
et al., 2011), which has an expected 5$\sigma$ point source J-band depth of
$\sim$24.5 mag (Euclid Collaboration et al., 2022), and so will be able to
detect not only intrinsically fainter red objects, but red objects at further
distances, expanding the census of known red objects and enabling a better
understanding of their space density, a key component for exploring the mass
functions of nearby associations.

VHS J1831$-$5513 is an excellent prospective JWST target to facilitate
atmospheric retrieval studies with high resolution data. This would also
represent an excellent opportunity to probe the L/T transition at young ages;
an area not yet fully understood, primarily due to the paucity of known young
L/T transition objects.

The Backyard Worlds: Planet 9 team would like to thank the many Zooniverse
volunteers who have participated in this project. We would also like to thank
the Zooniverse web development team for their work creating and maintaining
the Zooniverse platform and the Project Builder tools. This research was
supported by NASA grant 2017-ADAP17-0067. This material is supported by the
National Science Foundation under grant No. 2007068, 2009136, and 2009177. JF
acknowledges the Heising Simons Foundation as well as NSF award #1909776, and
NASA Award #80NSSC22K0142. J. M. V. acknowledges support from a Royal Society
- Science Foundation Ireland University Research Fellowship
(URF$\backslash$1$\backslash$221932). This research made use of the Montreal
Open Clusters and Associations (MOCA) database, operated at the Montréal
Planétarium (J. Gagné et al., in preparation). This paper includes data
gathered with the 6.5 meter Magellan Telescopes located at Las Campanas
Observatory, Chile. This publication makes use of data products from the Wide-
field Infrared Survey Explorer, which is a joint project of the University of
California, Los Angeles, and the Jet Propulsion Laboratory/ California
Institute of Technology, funded by the National Aeronautics and Space
Administration. CatWISE was funded by NASA under Proposal No. 16-ADAP16-0077
issued through the Astrophysics Data Analysis Program, and uses data from the
NASA-funded WISE and NEOWISE projects. This work uses data obtained as part of
the VISTA Hemisphere Survey, ESO Progam, 179.A-2010 (PI: McMahon). This
research has made use of the Spanish Virtual Observatory
(https://svo.cab.inta-csic.es) project funded by
MCIN/AEI/10.13039/501100011033/ through grant PID2020-112949GB-I00. This work
has benefitted from The UltracoolSheet at http://bit.ly/UltracoolSheet,
maintained by Will Best, Trent Dupuy, Michael Liu, Aniket Sanghi, Rob Siverd,
and Zhoujian Zhang, and developed from compilations by Dupuy & Liu (2012,
ApJS, 201, 19), Dupuy & Kraus (2013, Science, 341, 1492), Deacon et al. (2014,
ApJ, 792, 119), Liu et al. (2016, ApJ, 833, 96), Best et al. (2018, ApJS, 234,
1), Best et al. (2021, AJ, 161, 42), Sanghi et al. (2023, ApJ, 959, 63), and
Schneider et al. (2023, AJ, 166, 103).

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