11institutetext: CENTRA, Faculdade de Ciências, Universidade de Lisboa, Ed.
C8, Campo Grande, P-1749-016 Lisboa, Portugal
11email<EMAIL_ADDRESS>22institutetext: European Southern
Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garching bei München, Germany
33institutetext: Instituto de Astrofísica e Ciências do Espaço, Faculdade de
Ciências, Universidade de Lisboa, Ed. C8, Campo Grande, 1749-016 Lisbon,
Portugal 44institutetext: Istituto Nazionale di Astrofisica (INAF) –
Osservatorio Astronomico di Palermo, Piazza del Parlamento 1, 90134 Palermo,
Italy 55institutetext: SUPA, School of Physics & Astronomy, University of St
Andrews, North Haugh, St Andrews, KY16 9SS, United Kingdom

# Spectral characterization of young LT dwarfs

L. Piscarreta 1122 K. Mužić 33 V. Almendros-Abad and A. Scholz 4455

(Received; accepted)

###### Abstract

Context. JWST and next-generation facilities are expected to uncover
populations of free-floating objects below the deuterium-burning limit in a
number of young clusters and star-forming regions. These young planetary-mass
brown dwarfs have spectral types L and T, shaped by molecular absorption and
modified by their low gravity, which makes them distinct from field objects.

Aims. We aim to provide a detailed characterization of near-infrared spectra
for young LT brown dwarfs, including robust spectral typing, calibrating
spectral indices, identifying possible binaries, and selecting suitable
spectral standards.

Methods. We process and analyze archival spectra from VLT/X-shooter for a
sample of 56 dwarfs with ages between 10 and 600 Myr and spectral types
between late-M and mid-T. We re-determine spectral types by comparing them
with a set of literature templates. We assess a large range of spectral
indices, calibrated using a specifically designed literature sample.

Results. We identify 15 spectral indices that are useful for spectral typing
for specific spectral ranges discussed here and provide the scaling relations
with spectral types. We also identify 6 spectral indices which can be used to
separate young L dwarfs from the field ones. The EWs of the alkali lines show
a correlation with age, increasing towards the objects with higher surface
gravity. From our sample, we confirm 3 that are likely to be binaries by their
anomalous spectra that appear to be better fitted by a combination of spectral
types. We identify 12 objects as preliminary near-infrared spectral standards
for young LT dwarfs.

Conclusions. This paper presents a significant step toward understanding the
spectral sequence and properties of young L and T dwarfs. The relations and
standards provided here will be useful for future spectroscopic work on young
brown dwarfs and giant planets.

###### Key Words.:

brown dwarfs – Techniques: spectroscopic

##  1 Introduction

The bottom of the initial mass function (IMF) is populated by brown dwarfs
(BDs), substellar objects with masses $\lesssim 80$ MJup. The lightest among
these are the so-called free-floating planetary-mass objects (PMOs) with
masses below the deuterium-burning limit at $\sim 12$ MJup, whose existence
have been confirmed by various deep surveys in nearby young star-forming
regions (SFRs; Luhman et al., 2009; Scholz et al., 2012; Peña Ramírez et al.,
2012; Lodieu et al., 2018; Miret-Roig et al., 2022; Bouy et al., 2022).
However, the details of the free-floating PMO formation process are still
largely unknown and represent one of the important missing pieces in our
understanding of star formation. Broadly speaking, populations of isolated
PMOs in star clusters may form by cloud fragmentation and core collapse (star-
like formation), or in protoplanetary disks (planet-like formation), followed
by ejection due to encounters with other stars or planet-planet interactions
(see Miret-Roig 2023 and references therein). The relative importance of these
two scenarios is not known, mainly due to the lack of observational
constraints - given their intrinsic faintness, studies of PMOs present a
challenging task for most of the current facilities. In total, only about a
few dozen young isolated PMOs have been spectroscopically confirmed so far,
with estimated masses above $\sim$5 MJup. This situation is expected to change
drastically in the near future with the advent of the James Webb Space
Telescope (JWST), which will provide, for the first time, a robust census of
young (1$-$3 Myr) free-floating PMOs in the 1-15 MJup range (Scholz et al.,
2022; Pearson & McCaughrean, 2023). These objects are expected to have
spectral types (SpTs) in the range between $\sim$L0 and early-to-mid T-types.
Evolutionary models predict that a Jupiter-mass object at 1-3 Myr should have
an effective temperature in the range 700 - 900 K, showing the typical T-type
features in the model atmospheres (Marley et al., 2021).

Spectral characteristics of BD atmospheres are strongly influenced by gravity,
which has been extensively used to remove field contaminants from
spectroscopic samples of BD candidates in star-forming regions (Bayo et al.
2011; Mužić et al. 2015; Esplin & Luhman 2020, to name only a few). In the
near-infrared (NIR), gravity-sensitive features include the alkali lines (K I,
Na I) and FeH absorption bands, which are less pronounced in young, low-
gravity atmospheres, as well as the broadband form of the H-band, shaped by
water absorption, which appears sharply triangular in young atmospheres as
opposed to a rounder shape in field dwarf atmospheres (Gorlova et al., 2003;
McGovern et al., 2004; Allers & Liu, 2013; Manjavacas et al., 2020; Almendros-
Abad et al., 2022). The assessment of youth (and therefore the membership in a
cluster or a SFR) and the SpT estimation are typically performed through a
comparison of candidate spectra with a set of spectral templates or with the
help of numerous spectral indices derived for both purposes (see Almendros-
Abad et al. 2022 and references therein). But, while the LT-type field
sequence has been robustly defined (Kirkpatrick et al., 2010; Burgasser et
al., 2006a), high-quality spectra of young objects are rare, making the
existing young set of templates sparse for the L-types (Luhman et al., 2017),
and basically non-existent for the T-types. On the other hand, L-type field
dwarfs exhibit significantly bluer colors than their young counterparts
(Faherty et al., 2016; Schneider et al., 2017), making them unsuitable for
spectral type derivation of young objects.

The current sample of spectroscopically confirmed L-type members in nearby
SFRs and young clusters with ages $\lesssim 5\,$Myr, apart from being small,
extends only down to SpTs L3-L4 (e.g. Alves de Oliveira et al., 2012; Mužić et
al., 2015), and typically suffer from significant extinction, which may
introduce additional uncertainties in the spectral fitting process. For both
their vicinity and lack of extinction, it is useful to turn to nearby young
moving groups (NYMGs) in order to search for a sample of relatively young
(10$-$600 Myr) objects that would span a large range of SpTs. Although due to
differences in age not all the LT objects in NYMGs will be in the planetary-
mass regime, they are still expected to share various spectral properties with
the younger objects at the same effective temperature. This kind of sample can
serve for the comparison with JWST spectra of young free-floating PMO
candidates, as well as with directly imaged giant planetary-mass companions
(Faherty et al., 2016).

This paper builds upon the analysis presented in Almendros-Abad et al. (2022),
who analyzed a large sample of NIR spectra of young and old cool dwarfs in the
spectral range of M0 to $\sim$L3. They inspected a number of SpT- and gravity-
sensitive spectral indices available in the literature and defined several new
ones. Using machine learning models, they confirmed that the broadband shape
of the $H-$band represents the most relevant feature when it comes to
distinguishing low- from high-gravity atmospheres, followed by the FeH
absorption bands and alkali lines in the $J-$band portion of the spectrum. The
main goal of this work is to extend the analysis of Almendros-Abad et al.
(2022) to later spectral types and provide ”prescriptions” to obtain an
accurate SpT and gravity classification for mid-to-late L dwarfs, and
eventually the T-dwarfs. To that end, we present a collection of NIR spectra
of LT members of various NYMGs, SFRs, and clusters with ages $\gtrsim 10$ Myr.
This is a starting point towards constructing a more complete set of templates
of young LT dwarfs.

There are several other works in the literature that also deal with
classification and youth assessment of the solar-neighbourhood L- (Allers &
Liu, 2013; Gagné et al., 2015b; Martin et al., 2017; Cruz et al., 2018) and
T-dwarfs (Zhang et al., 2021). However, the spectral-type coverage of the
proposed templates extends down to $\sim$L4, and is quite patchy at later
SpTs. Any new spectra are therefore helpful to fill-in the gaps. A large
fraction of the above mentioned spectral compendium come from the northern
facilities, it is then useful to turn to the South, where the sky is
particularly rich in NYMG members. Furthermore, a large fraction of the
available spectra have either very-low spectral resolution (R of a few
hundred), or a limited wavelength coverage (e.g. the $J$-band in Martin et al.
2017). A wide spectral coverage in the NIR is important for obtaining a proper
assessment of the extinction which is fundamental for the characterization of
new planetary-mass members of SFRs. At medium spectral resolutions, atomic and
molecular features are more easily separated, which in the first place
provides us with better line width measurements, and even increases the number
of lines that can be used for youth assessment. Also, medium-spectral
resolution enables an in-depth analysis of the objects’ atmospheric parameters
(e.g. effective temperature, gravity, metallicity), along with the assessment
of their cloud properties and disequilibrium chemistry (Petrus et al., 2023;
Hood et al., 2023). Although a retrieval-type analysis is out of the scope of
this paper, another goal of this work is to provide spectra as the basis for
future studies that will help improve the brown dwarf and planetary atmosphere
models.

In Sect. 2, we present our main dataset and complementary ones, along with the
details of the reduction process. We investigate the objects’ position in a
color-magnitude diagram (Sect. 3), derive their SpT and extinction (Sect. 4),
and evaluate various features related to gravity classification (Sect. 5). In
Sect. 6, we define a preliminary list of objects that can be used as standards
for spectral typing of young L and T dwarfs. The summary and conclusions are
presented in Sect. 7.

##  2 Dataset and data reduction

###  2.1 Sample selection

Young PMOs with ages of $\sim$1$-$5 Myr and masses $\sim$1$-$15 MJup should
have spectral classifications equal to $\sim$L0 or later (Scholz et al.,
2022). With this in mind, and in order to be complete, the selection criteria
for the dataset used in this work are objects located in NYMGs, nearby SFRs
and clusters, with NIR SpTs equal to M8 or later and with publicly available
spectra from the X-shooter spectrograph at ESO’s Very Large Telescope (VLT).
The sources were chosen from the list of UltraCoolDwarfs111Jonathan Gagné’s
List of Ultracool Dwarfs, as well as from Allers & Liu (2013); Best et al.
(2015); Burgasser et al. (2016); Kellogg et al. (2015); Manjavacas et al.
(2020); Marocco et al. (2015); Naud et al. (2014); Schneider et al. (2016) and
their NIR spectral classifications from the literature are between M8 and
T5.5. We find that 56 objects match the described criteria. Of these, 34
objects belong to NYMGs ($\beta$ Pictoris Moving Group, BPMG; AB Doradus
Moving Group, ABDMG; Argus, ARG; Carina-Near, CARN; Castor, CAS; Columba, COL;
Tucana-Horologium, THA; and TW Hydrae, TWA), and 22 objects to nearby SFRs and
clusters (Upper Scorpius, USCO; 32 Orionis, 32OR; Praesepe, PRA; and Pleiades,
PLE). Table 12 summarizes the details of our sample and Table 2 the
information regarding the mentioned regions.

Table 1: NYMGs, young clusters, and SFRs included in this work.

Region | Distance (pc) | Ref | Age (Myr) | Ref
---|---|---|---|---
ABDMG | $30^{+20}_{-10}$ | (1) | 149${}^{+51}_{-19}$ | (4)
ARG | 72.4 | (2) | 40$-$50 | (2)
BPMG | 30${}^{+20}_{-10}$ | (1) | 24$\pm$3 | (4)
CARN | 30$\pm$20 | (1) | 200$\pm$50 | (5)
CAS | 5$-$20 | (9) | 320$\pm$80 | (9)
COL | 50$\pm$20 | (1) | 42${}^{+6}_{-4}$ | (4)
THA | $46^{+8}_{-6}$ | (1) | 45$\pm$4 | (4)
TWA | 60$\pm$10 | (1) | 10$\pm$3 | (4)
32OR | 96$\pm$2 | (1) | $22^{+4}_{-3}$ | (4)
PLE | 134$\pm$9 | (1) | 112$\pm$5 | (6)
PRA | 187.35$\pm$3.89 | (8) |  $\sim$600 | (3)
USCO | 145$\pm$9 | (10) | 10$\pm$3 | (7)

222(1) Gagné et al. (2018); (2) Zuckerman (2019); (3) Kraus & Hillenbrand
(2007); (4) Bell et al. (2015); (5) Zuckerman et al. (2006); (6) Dahm (2015);
(7) Pecaut & Mamajek (2016); (8) Lodieu et al. (2019); (9) Ribas (2003) ; (10)
This work.

In the analysis presented in the following sections, we divide the sample into
four different classes based on age:

  * •

10 Myr $<$ Age $\leq$ 30 Myr: objects belonging to USCO, TWA, BPMG, and 32OR;

  * •

30 Myr $<$ Age $\leq$ 100 Myr: objects belonging to ARG, COL, and THA;

  * •

100 Myr $<$ Age $\lesssim$ 300 Myr: objects belonging to ABDMG, CARN, CAS, and
PLE. All the objects in this age class have ages between 100 and 200 Myr
except object #27 which is considered a member of the Castor Moving Group
($\sim$320 Myr) 333The age of the Castor Moving Group (CAS) is not that well
constrained and shows a large spread among its original and probable members
(Brandt et al., 2014; Mamajek et al., 2013). But most of the stars in CAS seem
to be older than 200 Myr (Zuckerman et al., 2013). In fact, it will be
noticeable in the posterior analysis that the object #27 has an age between
200 Myr and the oldest age class considered (PRA, age $\sim$600 Myr).;

  * •

Age $\sim$ 600 Myr: objects belonging to PRA.

###  2.2 Data reduction

X-shooter (Vernet et al., 2011) is an intermediate resolution spectrograph
that covers a wide wavelength range from $\sim$300 to 2500 nm, simultaneously,
with its three independent arms: UVB arm (300-550 nm), VIS arm (550-1000 nm),
and NIR arm (1000-2480 nm). The latter is of the utmost relevance for this
study, given the cool nature of the objects in our sample.

The publicly available data taken with X-shooter have been downloaded from the
ESO archive, along with the appropriate calibrations. The EsoReflex
environment (Freudling et al., 2013) was used to run version 3.5.3 of the
X-shooter pipeline (Modigliani et al., 2010) for the data reduction. The data
reduction steps encompass dark current subtraction, flat-field correction,
order tracing, wavelength calibration, sky subtraction, and flux calibration.
The final one-dimensional spectrum was extracted from the rectified and order-
merged 2D data product obtained from the pipeline. For that, we used the task
apall, implementing the optimal spectral extraction algorithm, from
IRAF444IRAF is distributed by the National Optical Astronomy Observatories,
which are operated by the Association of Universities for Research in
Astronomy, Inc., under cooperative agreement with the National Science
Foundation. (Image Reduction and Analysis Facility, Tody 1986). The noise of
the final 1D spectrum is extracted with the help of the 2D uncertainty map
supplied by the pipeline. We compared the IRAF extraction with the final 1D
extracted spectra obtained from the X-shooter pipeline and found that for the
majority of our sample, the IRAF extraction returned spectra with a better
signal-to-noise ratio (SNR). The telluric correction was performed using the
Molecfit software (Smette et al., 2015; Kausch et al., 2015). This tool
computes a synthetic transmission spectrum of the Earth’s atmosphere
considering the atmospheric conditions at the time of the observations.

For each object, the observing sequence typically provides several spectra,
which were individually corrected. For the objects that have been observed on
more than one night, we median-combined the telluric-corrected observations
from each night. In each of these cases, we inspected whether the SNR of the
combination improved that of an individual observation. If so, the final
spectrum is the median-combined spectrum, if not, we keep the observation with
a higher SNR.

In the NIR range, for spectra reduced and corrected for telluric absorption,
the dominant noise contribution comes from OH line residuals from the sky
subtraction process. We used the list of wavelengths corresponding to the sky
emission lines from EsoReflex to remove the residuals of OH line subtraction
above a defined threshold. The removed values were replaced by the mean flux
in a narrow window around that wavelength. The wavelength ranges 1.138-1.143
$\mu$m, 1.165-1.185 $\mu$m, and 1.235-1.260 $\mu$m were not corrected in order
not to interfere with the spectral lines present in this range: Na I doublet
at $\sim$1.14 $\mu$m and the K I doublets at 1.169, 1.177 $\mu$m and 1.243,
1.252 $\mu$m (Allers & Liu, 2013), respectively.

We note that some spectra seem to present a slight discontinuity around
$\sim$2.27 $\mu$m, which coincides with one of the CO band-heads. This is
probably due to an illumination (vignetting) problem at the edge of the
X-shooter 11th order (Gonneau et al., 2016; Lodieu et al., 2018).

###  2.3 Complementary spectroscopic dataset

In several parts of the analysis presented in this paper, we use the sample of
approximately 2760 publicly available NIR spectra of cool dwarfs compiled by
Almendros-Abad et al. (2022) (hereafter AA22). The spectra span SpTs between
M0 and L5, and were obtained with a variety of telescopes and instruments.
This dataset is divided according to age into the following classes: young
($\lesssim 10\,$Myr), mid-gravity (objects belonging to NYMGs older than 10
Myr, or those classified as INT-G by Allers & Liu 2013), and field objects
(older objects with no youth spectroscopic features). The AA22 dataset was
complemented by the objects with the literature SpT later than L5 from the
SpeX Prism Spectral Library555SpeX Prism Library and the Montreal Spectral
Library666Montreal Spectral Library. In total, 98 spectra were included. To
have a homogeneous spectral classification for the entire complementary
sample, we re-derived the SpTs for the added objects using the same method as
in AA22, considering the T-type field templates from Burgasser et al. (2006a).
Of the 98 objects, 18 belong to the mid-gravity age class from AA22, whereas
the remaining is inserted in the field class. In several figures presented in
this paper, we maintain the same color coding for the three age classes as in
AA22: orange for the young objects, blue for the mid-gravity, and gray for the
field.

##  3 Color – absolute magnitude diagram

We start our analysis by examining the properties of our sample in the color-
absolute magnitude diagram. The magnitudes in the J-, H- and K-bands were
retrieved from 2MASS (Cutri et al., 2003) and complemented with catalogs from
several other authors (Luhman & Esplin, 2020; Bouy et al., 2022; Miret-Roig et
al., 2022; Medan et al., 2021; Faherty et al., 2016; Smart et al., 2017;
Burgasser et al., 2016; Liu et al., 2016; Marocco et al., 2015; Lodieu et al.,
2018; Bouy et al., 2015). The parallaxes are from Gaia EDR3 (Gaia
Collaboration et al., 2016, 2021) considering a matching radius of 2′′ and are
also complemented with measurements from several different authors (Liu et
al., 2016; Best et al., 2021; Galli et al., 2017; Manjavacas et al., 2019).
Only 28 of the initial 56 objects have trigonometric parallax measurements.
For objects located in USCO and PRA that do not have a parallax measurement,
we assumed the distance to be equal to the distance to the respective young
association. We calculate the mean distance to USCO using Gaia DR3 parallaxes
and the latest literature census of members of this region (Luhman, 2022). We
find a mean distance to USCO of 145$\pm$9 pc (see Table 2) which is in
agreement with previous works (145$\pm$2pc, Cook et al. 2017; 130$\pm$20pc,
Gagné et al. 2018). Object #63 is the only one with a parallax measurement but
no available 2MASS photometry. We implemented the magnitude system conversions
from Leggett et al. (2006) to convert the MKO magnitudes (Zhang et al., 2021)
to 2MASS.

Fig. 1 exhibits the 2MASS absolute magnitude in the J-band as a function of
(J-KS) for 44 of our initial 56 objects. We overplotted young (ages $\lesssim$
10 Myr) and field objects from AA22 and L dwarfs, with gravity classifications
of VL-G (very low-gravity) and FLD-G (field gravity), and T dwarfs from the
Database of Ultracool
Parallaxes777http://www.as.utexas.edu/~tdupuy/plx/Database_of_Ultracool_Parallaxes.html
(Dupuy & Liu, 2012; Liu et al., 2016; Dupuy & Kraus, 2013). The objects
belonging to the young class of AA22 and those with gravity classification
equal to VL-G are shown as orange dots whereas the FLD-G L dwarfs and T dwarfs
as gray dots. The information regarding magnitudes and parallaxes for the
objects in AA22 were also retrieved from 2MASS and Gaia EDR3, respectively,
considering the same matching radius as for our sample. For the case of the
remaining objects, their 2MASS absolute magnitudes in the J-band and their
(J-KS) colors are provided in the respective paper. Contrary to the objects in
our sample, these are corrected for extinction.

Figure 1: (MJ, J-KS) color-absolute magnitude diagram of our objects, very-low
gravity (orange circles), and field objects (gray circles) from the literature
(AA22; Database of Ultracool Parallaxes). Our sample is divided according to
the age of the association to which the objects probably belong. Green stars
represent objects in regions with ages $<$30 Myr, dark gray pentagons with
ages between 30$-$100 Myr (included), red diamonds with ages between 100$-$300
Myr (included), and white squares with ages $\sim$600 Myr. Data points where
the error bar is not visible mean that the bar is smaller than the marker
size. The three ellipses approximately highlight where the M, L, and T dwarfs
are located in this diagram. The arrow indicates what would be the effect of
an addition of 5 magnitudes of extinction.

The NIR colors of M- and L-type dwarfs are directly linked to their surface
temperature: L dwarfs have a lower surface temperature thus they will exhibit
redder colors. Moreover, young L dwarfs are typically redder than their field
counterparts of the same spectral type (Kirkpatrick et al., 2008; Cruz et al.,
2009; Faherty et al., 2016), thought to be a consequence of their lower
surface gravity leading to the formation of clouds in the upper layers of
their atmospheres (Madhusudhan et al., 2011), or, alternatively, of thermo-
chemical instabilities in cloudless atmospheres (Tremblin et al., 2016). As we
move towards the lower temperatures, into the T-dwarf sequence, we can observe
a dramatic shift towards bluer $J-K_{S}$ colors, often interpreted as a
transition towards ”cloudless” spectra, i.e. the clouds in these objects are
expected to form so deep in the atmosphere that they have little or no
influence on the final spectrum (Faherty et al., 2016).

The ellipses shown in Fig. 1 mark a rough location of different spectral
classes. We can observe that the majority of the objects with expected SpT
classifications of M and L appear to follow the young sequence. Nonetheless,
some objects appear to be more in agreement with the field sequence (e.g,
objects #2, #4, #27, #59, to name a few), which might suggest older ages.

##  4 Spectral type and extinction

In this section, we derive the spectral types for the objects in our sample.
To that end, we employ a comparison of the X-shooter spectra to a set of
spectral templates (Sect. 4.1), as well as a variety of SpT-sensitive indices
(Sect. 4.3). We also perform a methodical search for potential unresolved
binaries in our sample (Sect. 4.2).

###  4.1 Comparison to spectral templates

The first method we use to derive the SpT is a direct comparison of the
spectra with both young and field NIR spectral templates defined in the
literature. The young spectral standards are from Luhman et al. (2017),
whereas the field dwarf templates come from Kirkpatrick et al. (2010) and
Burgasser et al. (2006a). The L-type spectral sequence (Luhman et al., 2017)
has been constructed using the solar-neighborhood objects with an age of
$\lesssim$100 Myr, a subset of which have been associated with NYMGs. Table 2
summarizes the different sets of templates, along with the SpT ranges for
which they were defined. The regions affected by the telluric absorption were
excluded from the fitting process (1.3-1.5$\,\mu$m and 1.78-2.0$\,\mu$m), and
the spectra were resampled to have the same wavelength grid of the template
that they were being compared to.

Table 2: Sets of spectral templates used for the NIR SpT derivation.

Type | SpT Range | Ref
---|---|---
Young |  | M0 - L0 at each 0.5 subclass interval
---
L2, L4 and L7
Luhman et al. (2017)
Field | M0 - L9 at each 1 subclass interval | Kirkpatrick et al. (2010)
Field | T0 - T8 at each 1 subclass interval | Burgasser et al. (2006a)

In the fitting process, extinction may also be used as an additional free
parameter. Within our sample, this is only relevant for the objects belonging
to USCO, which suffer low, but non-negligible, amount of interstellar
reddening (Ardila et al., 2000; Rizzuto et al., 2015). In this case, the
extinction AV was varied between 0 to 2 mag (Lodieu et al., 2008), with a step
of 0.2 mag. We used the extinction law from Cardelli et al. (1989) with RV=3.1
to redden the spectral templates. For the remaining objects belonging to NYMGs
(located within the so-called Local Bubble, d$\lesssim$100 pc) and the two
open clusters (both PLE and PRA have low to negligible foreground reddening:
$E(B-V)_{PLE}=0.04$ mag, Breger 1986; $E(B-V)_{PRA}=0.027\pm 0.004$ mag,
Taylor 2006), we set AV=0 (Bell et al., 2015; Pecaut & Mamajek, 2013; Lodieu
et al., 2019).

Similarly to the method implemented in AA22, the fitting process has three
variables - SpT, extinction, and normalization wavelength. The latter is
searched on a grid from 1.55 to 1.78 $\mu$m with a step of 0.02 $\mu$m. For
objects in associations other than USCO, there are only two variables (SpT and
normalization wavelength). The best-fit template is the one that minimizes the
$\chi^{2}$ parameter, defined as:

$\centering\chi^{2}=\frac{1}{N-m}\sum\limits_{i=1}^{N}\frac{(O_{i}-T_{i})^{2}}{\sigma_{i}^{2}},\@add@centering$
(1)

where $N$ is the number of points included in the fit (number of wavelength
values), m is the number of free parameters ($m=3$ for USCO and $m=2$ for the
rest), $O$ and $\sigma$ are the object spectrum and its associated noise,
respectively, and $T$ is the template spectrum. All spectra were individually
compared with each one of the field and young templates. Next, we compare the
$\chi^{2}$ values of both comparisons and use the template (young or field)
associated with the lower $\chi^{2}$ value to derive the SpT and extinction,
where applicable. As an estimate of the uncertainty on the derived SpT, we use
the SpT step at which the correspondent set of templates is defined. In the
case of young templates, if the SpT derived is L0 or L2 we assumed an
uncertainty of $\pm$2.0 sub-SpTs, ${}^{+3.0}_{-2.0}$ sub-SpTs for L4 and
$\pm$3.0 sub-SpTs for L7, due to the lack of young L1, L3, L5, L6, L8, and L9
young templates.

In several cases, the attributed best-fit SpT in the M- and L-type spectral
range was that of a field template, which is somewhat unexpected given the
youth of the sample. For these objects, we performed an additional check in
order to visually inspect the quality of the best-fitted young and field
templates.

Fig. 2 shows the affected spectra, along with the best young (red) and field
templates (purple). A particularly useful feature to observe here is the
broad-band shape of the H-band, which has a well-defined triangular shape in
the young templates. Objects #57 and #58, located in PRA which is by far the
oldest region considered here, are better represented by the field templates.
Furthermore, field templates also appear to work well for the somewhat younger
sources, such as #27 located in CAS, and #59 and #60 in PLE. For these
objects, we retain the SpT attributed by the fitting process. The remaining
spectra visually appear to be better represented by the young templates, and
therefore we take the best-fit SpT derived using the young template as the
final one.

Figure 2: Comparison between the best-fitted young (red) and field (purple)
templates for dwarfs where the spectral classification by direct comparison
with templates yields a result of M or L field. The ID and young association
are shown above the correspondent spectrum (in black). All spectra are
normalized at 1.67 $\mu$m. An offset between the spectra was added for
clarity. Figure 3: Spectra of objects in the SpT range L0-L2 (in black)
compared with L0 (red) and L2 (purple) young templates. The spectra were
normalized at 1.67 $\mu$m. The ID of each object is listed on the left of the
respective spectrum. An offset between the spectra was added for clarity.
Figure 4: Spectra of objects in the SpT range L2-L4 (in black) compared with
L2 (red) and L4 (purple) young templates. The spectra were normalized at 1.67
$\mu$m. The ID of each object is listed on the left of the respective
spectrum. An offset between the spectra was added for clarity. Figure 5:
Spectra of objects in the SpT range L4-L7 (in black) compared with L4 (red)
and L7 (purple) young templates. The spectra were normalized at 1.67 $\mu$m.
The ID of each object is listed on the left of the respective spectrum. An
offset between the spectra was added for clarity. Figure 6: Spectrum of the
object #20 (PSO J318.5-22, in black) along with the L7 young template (in
red), L8 field template (in purple), and the spectrum of the object #56 (SIMP
J013656.5+093347.3, in gray) which was classified as T2 by direct comparison
with spectral templates. The latter is shown to underline the significant
change in the spectral morphology associated with the L/T transition. All
spectra are normalized at 1.67 $\mu$m.

The reason why these spectra originally appeared to be better fitted by the
field templates is probably the sparsity of the young template grid. For the
same reason, we decide to visually inspect the L-type objects to determine if
some of them have a SpT that would appear to be in between the SpTs defined by
the grid. In Fig. 3, we show a set of objects with SpTs in the range L0-L2,
and in Fig. 4 those with SpTs potentially in the range L2-L4. From Fig. 3, we
see that several spectra appear to be in between the L0 and L2 templates, and
we, therefore, re-assign them a SpT L1$\pm 1$ (objects #23, #24, #31, #34 and
#35; see Table 13). The range of L2-L4 (Fig. 4) is more difficult to judge
visually. In most cases, at least two bands are very well fitted by one of the
two templates, while the third one (most often the $K-$band) appears a bit
off. However, we can neither say that something in between would necessarily
provide a better fit. For these objects, we, therefore, retain the young SpT
as returned by the fitting procedure.

In Fig. 5, we show the objects best fitted by the young L4 or L7 templates.
Four of the shown objects (#21, #28, #42 and #62) are closer to the L4
templates, although most of them do not consistently follow the template shape
in all bands. In the case of object #21, its shape appears to be in between L4
and L7, but closer to L4. We, therefore, assign it a SpT of L5. Four objects
were classified as L7 young by direct comparison with spectral templates. The
spectra of objects #25 (2MASS J03552337+1133437), #47 (2MASS
J11193254-1137466) and #48 (2MASS J114724.10-204021.3) seem well fitted by a
L7 young template, although in the case of #25 both J- and K-bands appear
somewhat fainter relative to the H-band when compared to the template. As for
object #20 (PSO J318.5-22), Fig. 6 compares its spectrum (in black) with that
of object #56 (SIMP J013656.5+093347.3, in gray) which is classified as T2,
and that of an L7 young (in red) and an L8 field templates (in purple).
Compared to the young L7 template, object #20 appears to be of a slightly
later SpT, however, it is difficult to assign an exact SpT to it, given the
lack of appropriate comparison templates. The L-type field templates are too
blue compared to young L-types and thus completely inadequate for spectral
typing in this age regime. We show object #56 from our sample, which is a
$\sim 200$ Myr old T2 dwarf, to demonstrate the rapid change in the spectral
form at the LT transition. We assign this object a SpT L8$\pm$1, given that it
appears later than L7, but is also clearly not a T-dwarf.

Young, low-gravity mid-L and late-L dwarfs typically show redder near-infrared
colors than their older, higher-gravity counterparts with the same spectral
type (Faherty et al., 2016; Liu et al., 2016). For several T-dwarfs in their
sample, Zhang et al. (2021) report $J-K$ colors that are 0.4 - 0.8 mag higher
than what would be expected for field dwarfs. We observe a similar trend for 4
out of 5 T-dwarfs in our sample. Several of these objects also appear as
potential binary candidates (see Sect. 4.2). As we will discuss in that
section, it seems that the low-gravity behaviour in T-dwarfs may be mimicking
binarity when assessed using the field T-dwarf templates.

Finally, we do not perform a similar visual inspection for the L-type objects
located in USCO since they may have some degree of extinction, which makes it
more difficult to judge visually if some intermediate SpT would be more
appropriate (SpT$+$AV degeneracy). The final spectral classifications obtained
by comparison with spectral templates and posterior visual inspection, are
summarized in Table 13, column ”SpT Templates”.

Figure 7: Spectra of objects classified as T-type dwarfs along with their
best-fitted template (in red). The ID, derived SpT and region of each object
are shown next to the correspondent spectrum. All the spectra are normalized
at 1.57 $\mu$m. An offset between the spectra was added for clarity. Figure 8:
Comparison between the derived NIR SpT by direct comparison with spectral
templates (see Sect. 4.1) and the literature NIR SpT for the X-shooter
dataset. The solid black line indicates perfect agreement between
classifications. The black dotted lines represent the $\pm$2 sub-SpT range.
The ID of the objects for which their classifications do not agree within
$\pm$2 sub-SpTs is shown.

In Fig. 8, we compare the SpTs derived in this section and those obtained from
the literature. The solid lines indicate a perfect agreement, while the dotted
lines mark $\pm 2$ sub-SpT uncertainty. We see that the majority of our
results agree well with the literature classification, except for 3 objects.
Object #16 belongs to USCO and its literature classification comes from Lodieu
et al. (2018), which does not consider extinction when deriving SpTs. The
effect of increasing the extinction in the spectra is similar to the effect of
decreasing the effective temperature, i.e. by ignoring the extinction, one
will obtain systematically later SpTs888This in fact is the case for all other
USCO objects as well, whose X-shooter spectra have first been analyzed in
Lodieu et al. (2018). For this reason, as a literature value in Table 13, we
prefer the classification from Luhman et al. (2018) which considers extinction
in their fitting process.. As for object #37 (J0357-4417), it is a known
unresolved binary system identified by Bouy et al. (2003). Marocco et al.
(2013) estimated the NIR SpTs of its components by fitting synthetic binary
templates and the best-retrieved fit was that of an L4.5+L5($\pm$1) composite.
On the other hand, in the optical, the SpTs derived for this object were M9+L1
(Martín et al., 2006). The difference between classifications was assigned to
the fact that the NIR composite templates were created from field dwarfs and
object #37 exhibits signs of youth. The assigned unresolved NIR SpT in the
literature was L2pec (Marocco et al., 2013), based on the best fit in the
J-band. Our composed SpT derivation is M9.5$\pm$0.5. Nonetheless, we note that
the template does not reproduce well the object’s spectrum (see Fig. 17).
Regarding the one object located below the lower dotted line (object #25), it
was classified as an L3 dwarf in Allers & Liu (2013) by combining the
information from direct comparison with spectral templates and index
classifications. However, when analyzing individually the comparison between
moderate resolution spectra and templates for the J- and K-bands separately,
they obtained the best match of L7 and L2, respectively. In this work, we
estimate a spectral classification of L7.0$\pm$1.0 by direct comparison with
spectral templates. Nonetheless, we note that although the H-band is well
fitted, both the J- and K- bands are redder than the template fitted. An
important point to note is that different normalization wavelengths can yield
slightly different spectral classifications. In this work, we use the H-band,
however, some other works, compare their template fittings by normalizing the
spectra in the J-band (e.g, Kirkpatrick et al. 2010).

###  4.2 Unresolved binaries

Figure 9: Spectral index criteria applied for unresolved binary candidates
selection defined in Burgasser et al. (2010). The top three panels and the
first bottom panel compare pairs of index values whereas the other panels
compare index ratios to the NIR SpT derived in Sect. 4.1. The objects from our
dataset are represented as black dots. Strong binary candidates are
highlighted with red diamonds and weak binary candidates with red circles.

Figure 10: Strong (objects #52, #55 and #63) and weak (objects #51 and #53)
binary candidates (in black) overplotted with the best-fitted individual
templates (magenta) and the best-fitted composite templates (green). The two
components of the synthetic binary templates are also plotted in yellow and
blue, respectively.

Some objects in our sample show peculiar spectra which do not provide a good
fit when compared to any of the spectral templates. One of the main reasons
that might explain the observed peculiarity of a spectrum is multiplicity. The
transition from L- to T-type objects supposes significant changes in spectral
properties, caused by pronounced, deep molecular absorption bands (e.g. CH4,
H2O) developing at the lower temperatures. Hence, a blended-light spectrum
from an L/T binary combination will appear peculiar when compared to spectra
of other ultracool dwarfs (e.g. Bardalez Gagliuffi et al., 2014; Ashraf et
al., 2022).

To test whether our sample harbors potential unresolved binaries, we used the
method defined in Burgasser et al. (2010), based on six different combinations
of index-index and index-SpT diagrams that segregate possible unresolved LT-
dwarf binaries. If an object matches two of the six criteria it is selected as
a weak binary candidate, whereas satisfying at least three criteria, places
the object among the strong candidates. This method is especially sensitive to
companions that differ in more than 1 SpT (i.e. a combination of an L-type and
a T-type object).

The selection process is shown in Fig. 9, where six criteria for identifying
potential binarity are delineated by dashed lines. We have identified five
binary candidates: objects #52 and #55 were selected by six indices and object
#63 by three indices therefore these are considered strong candidates; the
weak candidates are objects #51 and #53 which were selected by two indices
each. The strong and weak binary candidates are highlighted as red diamonds
and circles, respectively.

To estimate the SpT of both companions of the binary candidates, we use
synthetic binary templates, similar to the technique described in Day-Jones et
al. (2013). For this exercise, we combine the T-type templates with the L-type
field templates, since the young L-type templates do not have a complete
sequence. The templates were normalized to 1 at 1.28 $\mu$m and scaled to a
common flux level using the MJ-SpT relation from Faherty et al. (2016). Fig.
10 exhibits the best-fitted individual templates (in magenta) along with the
best-fitted composite templates (in green). The two different components of
the synthetic binary templates are shown in yellow and blue. Table 3
summarizes the SpTs derived by these two different comparisons, complemented
with the respective $\chi^{2}$ parameters.

The three strong binary candidates have previously been reported as such. The
object #52 has been disentangled into an L8+T7 binary system by Day-Jones et
al. (2013, BLRT15), in agreement with the SpTs estimated here. #55 has been
reported as an L6+T5 composite in Marocco et al. (2015, BLRT203), with both
SpTs slightly earlier than those found here. It was also selected as a strong
binary candidate by Zhang et al. (2021) with a composite spectral
classification of L7+T6. In their discovery paper, Naud et al. (2014)
identified the T-type companion to the young M3 star GU Psc (#63 here) as a
weak binary candidate, following the same set of criteria as we did. Its
spectrum appears to be more similar to the confirmed T1+T5 tight binary SDSS
J102109.69-030420.1 (Burgasser et al., 2006b) and a T2+T6 binary candidate
J121440.95+631643.4 (Geißler et al., 2011) than to any of the single
templates.

Similar to #63, the two weak candidates (#51 and #53) appear as composites of
two T-type objects999The disentanglement of these objects’ spectra into two
T-type objects is in agreement with the combined classifications estimated in
Zhang et al. (2021): object #51 was flagged as a weak binary candidate where
its combined SpT was estimated as T2+T3, and object #53 was flagged as a
strong candidate with T1.5+T3.5.. Particularly, in the case of object #53,
appearing to be a combination of two objects with similar SpTs (T2 and T4),
the improvement in the fit is only marginal, making its binary status highly
questionable. We decide to retain those three objects for the remainder of the
analysis since they represent one of the very few known T-type objects with
low surface gravity. Our understanding of these cool atmospheres at young ages
is rather limited, and, since all the claims of the composite nature of the
objects come from the field templates, one cannot exclude that their slight
peculiarity with respect to the standards may be related to the surface
gravity. Three out of five T-dwarfs in our sample appear redder than their
field counterpart(#51, #63 and #50). Objects #51 and #63 were selected as
binary candidates, along with object #53. The remaining object, #50, has a
later SpT (T5), which is not included in the binarity criteria of Burgasser et
al. (2010). Interestingly, high-resolution imaging reveals that binary
factions among the T-dwarfs are of the order 10% (Burgasser et al., 2003,
2006b; Fontanive et al., 2018), making it highly unlikely that at least 60% of
our sample of T-dwarfs, however small, should indeed be binaries. Considering
this, the lower surface gravity of the T dwarfs in our sample might be
mimicking binarity.

Table 3: SpT derived for the strong and weak binary candidates by direct
comparison with single and composite templates.

ID |  | Best fit single
---
template
$\chi^{2}_{single}$ |  | Best fit composite
---
template
$\chi^{2}_{comp}$
Strong Binary Candidates
#52 | L9 ($\pm$1) | 0.3285 | L7+T7 ($\pm$1) | 0.0696
#55 | T0 ($\pm$1) | 2.1397 | L8+T6 ($\pm$1) | 0.5694
#63 | T3 ($\pm$1) | 0.0786 | T2+T8 ($\pm$1) | 0.0327
Weak Binary Candidates
#51 | T3 ($\pm$1) | 1.4887 | T1+T4 ($\pm$1) | 0.4534
#53 | T3 ($\pm$1) | 0.4758 | T2+T4 ($\pm$1) | 0.4269

This selection method was defined to select binary candidates that straddle
the L/T transition. Consequently, there are other objects in our sample that
can be potential binary candidates but are not selected as such as a result of
their similar SpTs. As seen previously (see discussion in Sect. 4.1), object
#37 is an example of such. Another case is object #47 (J1119-1137), a tight
binary where the components have approximately equal magnitudes resulting in
an unresolved SpT of L7 (Best et al., 2017). As the spectral composition of
objects with L classifications does not result in such spectral morphological
changes as an L+T dwarfs composition, we do not perform a methodical search
for these. Object #37 and #47 are therefore also retained in the following
analysis such as the weak selected binary candidates.

###  4.3 Spectral type indices

Figure 11: Selected SpT indices from the literature versus the NIR SpT derived
by direct comparison with spectral templates. The classes young, mid-gravity
and field from the dataset of AA22 are represented as orange, blue and gray
circles, respectively. The black solid lines represent the sensitivity range
of each index (see Table 10). The red dashed line in the spectral index
$\omega_{D}$ represents the best fit if the sensitivity range is considered
from M4 down to T8. The black arrows demonstrate the effect of 5 magnitudes of
extinction on the index values.  Figure 12: Selected SpT indices from the
literature versus the NIR SpT derived by direct comparison with spectral
templates. The classes young, mid-gravity and field from the dataset of AA22
are represented as orange, blue and gray circles, respectively. The black
solid lines represent the sensitivity range of each index (see Table 10). The
black arrows demonstrate the effect of 5 magnitudes of extinction on the index
values.

An alternative way to derive SpT is by using spectral indices that correlate
well within a given SpT range. This approach is of great interest when, for
example, there is no access to the entire NIR wavelength range of the object’s
spectrum, leading to a decrease in the accuracy of the SpT derivation by
direct comparison with spectral templates. Moreover, quantifying specific
spectral features does not require an age estimate (if defined as gravity-
insensitive) and is less computationally costly. Therefore, it is of utmost
relevance to test several indices in order to inspect which are their
sensitivity ranges and whether they can be used for spectral classification.
One thing to consider is that the main disadvantage regarding the use of
spectral indices is the fact that the majority of them are extinction-
dependent. Hence, extinction needs to be estimated using another procedure.

In total 15 indices matched the criteria mentioned above: H2OB, K1, H2O-C,
H2O-H, H2O-1.5, $\omega_{0}$, $\omega_{D}$, sHJ, CH4A, CH4B, K2, CH4-B, CH4-C,
CH4-H and CH4-K. Figs. 11 and 12 show the indices selected along with their
sensitivity range (solid black line) and the effect that an additional
extinction of five magnitudes would have on the values of the indices (black
arrow). Table 10 summarizes the ranges of applicability, the type of
polynomial fit along with the respective coefficients, and the rmse of each
selected SpT index.

Table 4: Spectral type indices selected.

Index | Index | Sensitivity | Coefficientsa | Type | rmse
---|---|---|---|---|---
name | reference | range | c0 | c1 | c2 | c3 | of fit | (SpT)
H2OB | (1) | M5-L4 | 5.808 | 64.156 | -108.775 | 44.736 | 3rd degree | 0.99
|  | L9-T8 | 29.479 | -20.416 | – | – | linear | 1.00
K1 | (2) | M5-L3 | 6.707 | 23.623 | – | – | linear | 0.77
H2O-C | (3) | M4-L2 | 37.130 | -30.240 | – | – | linear | 0.79
H2O-H | (4) | M5-L3 | 38.348 | -33.438 | – | – | linear | 0.98
|  | T0-T8 | 31.521 | -19.174 | – | – | linear | 0.68
H2O (1.5 $\mu$m) | (5) | M5-L4 | -32.696 | 51.745 | -14.011 | – | 2nd degree | 0.97
$\omega_{D}$ | (6) | M4-L6 | 4.547 | 29.312 | -11.631 | – | 2nd degree | 0.94
|  | T1-T8 | 15.649 | 6.877 | -0.837 | – | 2nd degree | 0.66
sHJ | (7) | T2.5-T8 | 18.803 | 10.554 | -8.353 | 2.982 | 3rd degree | 0.25
CH4A | (1) | T0-T8 | 28.918 | -11.717 | 0.220 | – | 2nd degree | 0.37
CH4B | (1) | T0-T5 | 27.750 | -8.969 | – | – | linear | 0.56
$\omega_{0}$ | (6) | T1-T8 | 14.897 | 7.534 | -1.007 | – | 2nd degree | 0.60
K2 | (2) | T0-T8 | 18.861 | -5.297 | -0.108 | – | 2nd degree | 0.56
CH4-B | (3) | T3-T8 | 28.871 | -11.882 | 4.908 | – | 2nd degree | 0.23
CH4-C | (3) | T0-T5 | 26.477 | -8.668 | – | – | linear | 0.52
CH4-H | (4) | T3-T8 | 28.985 | -11.037 | 3.981 | – | 2nd degree | 0.27
CH4-K | (4) | T0-T6 | 27.176 | -9.550 | 0.473 | – | 2nd degree | 0.52

101010References: (1) McLean et al. (2003), (2) Tokunaga & Kobayashi (1999),
(3) Burgasser et al. (2002), (4) Burgasser et al. (2006a), (5) Geballe et al.
(2002), (6) Zhang et al. (2018), (7) Testi et al. (2001). a The spectral type
is calculated from the polynomial fits as: SpT = $\sum_{i=0}^{n}c_{i}\times$
(index)i (with $n=1$ for linear, $n=2$ for the second-degree and $n=3$ for the
third-degree polynomial fit).

We then proceeded to the computation of the selected indices for each object
of our sample. For the objects in USCO, we considered the extinction value
estimated in Sect. 4.1 to correct the spectra for reddening, using the
Cardelli extinction law with $R_{V}$=3.1. The SpT and its uncertainty were
calculated as the weighted mean and weighted standard deviation of the values
obtained from various indices, which depend on each index’s SpT range of
applicability. The final values have been rounded to the next 0.5 sub-SpT, and
are presented in Table 13, column ”SpT Indices”.

The plots shown in Figs. 11 and 12 show a good correlation with SpTs earlier
than $\sim$L6, and later than $\sim$T0. The LT transition range is not well
populated and also does not show good behavior in the sense that most indices
appear rather flat and/or with high dispersion. The only potentially valuable
index for this range may be $\omega_{D}$ (lower right panel of Fig. 11) which
has also the advantage of being extinction-independent. For this reason, we
try to fit a single polynomial to the entire range of the plot (red dashed
line). However, in the range L6-T1 we notice that basically all the points are
below the fit line, which means that the index tends to provide systematically
earlier SpTs in this spectral range. The SpT range L6-T0 is therefore not
included in any sensitivity range of the spectral type indices selected.

In Fig. 13 we compare the estimated SpTs obtained with both classification
methods: comparison with spectral templates and spectral indices. The
classifications seem to agree well within $\pm$2 sub-SpTs, except for 6
objects in our sample. Three of these six objects (IDs #20, #25, and #47) are
classified as late-L dwarfs (L8$\pm$1, L7$\pm$3, and L7$\pm$3, respectively)
by direct comparison with spectral templates and posterior visual inspection
but have an earlier SpT derived with the index classification method
(L4$\pm$3, L2.5$\pm$1.0, and L4.5$\pm$3.0, respectively). This is not
unexpected, given the behavior of the indices for the late-L types, as
discussed above. Objects #11 and #13 are located in USCO and exhibit
discrepant classifications by more than 2 sub-SpTs as well (L4${}^{+3}_{-2}$,
L2$\pm$2 using templates and M9$\pm$1, M9.5$\pm$1.0 using spectral types
indices, respectively). On the other hand, the SpT retrieved from the
comparison with spectral templates (L0$\pm$2) for object #38 is earlier than
the one computed using the spectral indices (L2.5$\pm$0.5). The spectrum of
object #11 is quite noisy in several regions important for index calculation,
which is probably responsible for the discrepancy. In the case of the objects
#13 and #38, we notice that the $J-$band part of the spectrum is not that well
reproduced by the best-fit spectral template fits.

Figure 13: Comparison between the derived NIR SpT using spectral indices (see
Sect. 4.3) and the SpT derived by direct comparison with spectral templates
(see Sect. 4.1). The solid black line indicates perfect agreement between
classifications. The black dotted lines represent the $\pm$2 sub-SpT range.
The ID of the objects for which their classifications do not agree within
$\pm$2 sub-SpTs is shown.

##  5 Evaluation of youth-related features

Visual comparison of NIR spectra of young dwarfs to their field counterparts
has revealed a wealth of spectral (atomic and molecular) features that differ
with age, directly related to differences in surface gravity of these objects
(e.g Lucas et al., 2001; Gorlova et al., 2003; Luhman et al., 2017; Allers &
Liu, 2013). AA22 applied machine learning methods to the low-resolution
spectra in the range between M0 and L3, and find that the features with the
most importance when it comes to separating low-gravity young dwarfs from
their field counterparts are the broad-band shape of the H-band, FeH bands,
and the lines of the alkali elements (KI and NaI). In this section, we
evaluate and discuss various spectral indices sensitive to gravity and their
applicability to the spectral range $>$L3. We also measure the pseudo-
equivalent widths (pEWs) of various prominent alkali lines and study their
behavior with spectral type and age. In the following analysis, we assume the
spectral type of the sample to be that estimated by comparison with spectral
templates (see Sect. 4.1).

###  5.1 Gravity-sensitive NIR spectral indices

Figure 14: Selected gravity-sensitive spectral indices from the literature
versus the NIR SpT derived in Sect. 4.1. Our sample is divided into the
different age classes presented in Sect. 2.1 where the classes ¡30 Myr (USCO,
TWA, BPMG and 32OR), 30$-$100 Myr (ARG, COL and THA), 100$-$300 Myr (ABDMG,
CAS, CARN and PLE), and 600 Myr (PRA) are shown as green stars, black
pentagons, red diamonds, and white squares, respectively. The complementary
dataset is divided into young, mid-gravity, and field objects represented as
orange, blue, and gray dots, respectively.

The gravity-sensitive indices that we visually inspected from the literature
are listed in Table 15 along with their functional forms, spectral features
targeted and references. Some of the indices inspected in Sect. 4.3 also
demonstrated a gravity-sensitive behavior, such as sH2OJ, CH4 (1.6 $\mu$m),
WH, QH, sH2OH1, K2, CH4-B, CH4-C, CO, CH4-H and CH4-K. Where applicable, the
spectra were corrected for the extinction derived in Sect. 4.1 using
Cardelli’s extinction law with RV=3.1. Given the scarcity of low-gravity
objects in the late L and T-type regime, this discussion is limited to the
spectral types down to L7.

In Fig. 14, we show a set of gravity-sensitive indices, using the dataset from
AA22, along with the objects analyzed in this work. The orange dots show
objects that are typically younger ($<$10 Myr) than our sample, but we see
that they anyway separate well from the field objects. This means that some of
these indices will be useful to classify the young members of SFRs in future
deep spectroscopic surveys.

Both HPI and TLI-g are based on the H2O absorption in the H-band. HPI presents
a good correlation with SpT for the younger and field populations from SpT M6,
whilst being gravity-sensitive. The fact that a correlation with SpT exists
between the different age classes provides an easier way to separate them.
TLI-g shows a clear separation from, at least, M2 and the intermediate-gravity
objects populate the region between the young and field populations. Our
objects seem to overlap mostly with the intermediate-age class. The youngest
objects from our sample have at least 10 Myrs and the young class from AA22
has ages $\lesssim$10 Myrs. Therefore, the separation might remain if late-L
objects from SFRs with ages of only a few Myr follow the trend visible down to
L2 for young dwarfs. The objects in the $<$30 Myr age class later than L4 seem
to indicate that this may be so. Another water-based index, H2O-J, does not
appear gravity-sensitive in the M spectral range but shows a progressively
more gravity-sensitive behavior towards the late L-types.

The gravity-sensitive indices that measure the methane features, both in the
H- and K- bands, were defined as SpT indices to classify objects in the T
spectral sequence. Interestingly, they can have a dual role, because in
L-dwarfs the spectral regions considered to compute these indices are actually
quantifying the slope of the blue end of each band caused by the water
absorption features. The CH4-1.6 $\mu$m index considers both absorption peaks
in the H-band of T dwarfs enhanced by the methane absorption bands, as does
CH4-H but with the inverse formulation of CH4-1.6 $\mu$m. Both indices
increase monotonically through the T sequence and thus can be used to classify
T-type objects. However, for SpTs earlier than L6, they demonstrate a good
performance as gravity-sensitive indices. The young and field populations can
be easily separated since M0, having some overlap within M3 and M5, but for
SpTs$>$M6 the separation is very pronounced. WH measures the water absorption
feature on the blue side of the H-band and has a similar behavior to CH4-1.6
$\mu$m index. CH4-K measures the 2.2 $\mu$m methane absorption feature and it
does not exhibit a similar behavior as the other selected indices. It does not
perform so well in the separation of the different age classes for the early-
to mid-M sequence. However, for SpTs later than M8, the trend of the younger
and older objects starts to increase and decrease, respectively. This behavior
is interesting and could be extremely useful to disentangle young and field
populations in the L sequence.

An equivalent analysis of gravity-sensitive indices would be extremely
interesting for the T-dwarf range, in light of the upcoming JWST results. This
has, so far, been basically impossible given the lack of known young T-type
objects. We note that the T-dwarfs included in this study appear in agreement
with the field dwarf positions in plots like that shown in Fig. 14.

###  5.2 Pseudo-equivalent widths of alkali lines

Figure 15: Pseudo-equivalent widths of the alkali lines in the J-band as a
function of the SpT derived in Sect. 4.1. The sample is divided according to
the age classes defined in Sect. 2.1. The color and marker scheme for our
sample is the same as Fig. 14. The purple circles are field objects from
McLean et al. (2003) and Cushing et al. (2005). In the right panels of each
subfigure, there are the KDE for each age class (color-coded accordingly).
Figure 16: Pseudo-equivalent widths of the alkali lines as a function of the
age. The sample is divided according to the age classes defined in Sect. 2.1.
The color and marker scheme for our sample is the same as Fig. 14. The purple
circles are field objects from McLean et al. (2003) and Cushing et al. (2005).
In the right panels of each subfigure, there are the KDE for each age class
(color-coded accordingly).

The alkali lines (Na I and K I) are the dominant atomic spectral features in
the $J$-band spectra of ultracool dwarfs but are also found in the $H$\- and
$K$-bands. The strength of the absorption of the alkali lines is primarily
affected by the surface temperature of the object, but pressure broadening
plays a major role in creating their final shape. They have been found to be a
very good probe for differences in surface gravity for late-type objects
(Gorlova et al., 2003; Schlieder et al., 2012; Allers & Liu, 2013; Martin et
al., 2017; Manjavacas et al., 2020). In this section, we study the pseudo-
equivalent widths (pEW) of the alkali lines for the objects in our sample and
compare them with that of field objects. We focused on the K I doublets at
1.17, 1.24 and 1.51 $\mu$m and the Na I doublet at 1.14 $\mu$m. The Na I
doublet in the K-band (2.21 $\mu$m) basically disappears at L-types (McLean et
al., 2003; Cushing et al., 2005), which is our principal SpT range of interest
in this work, and thus was not considered.

The pEWs were measured using the same method as in Manara et al. (2013), which
integrates the Gaussian fit of the line, previously normalized to the local
pseudo-continuum at the edges of the line. The errors in the pEW measurements
are estimated from the propagation of 1$\sigma$ of the estimated continuum. We
visually checked that the extent of all the lines is correctly estimated, and
corrected them if needed. We also inspected the appearance of the alkali
lines. Some sources presented contamination from single-pixel spikes within
the extent of the line: the pEW of those lines is not considered. We also
measured the pEWs of the alkali lines for a sample of field dwarfs with SpTs
M6-T8 with a somewhat lower spectral resolution than that of X-shooter
(R$\approx$2000), coming from different public surveys (McLean et al., 2003;
Cushing et al., 2005).

In Fig. 15 we present the pEW of the alkali lines as a function of the SpT.
The sources from our X-shooter sample are separated into age classes following
the same color scheme used in the rest of this work. Field objects are
represented with purple circles. In order to get a clearer view of potential
trends in the data, on the right side of each plot we show the distribution
for each age class smoothed with a Kernel Density Estimator (KDE). In the
L-type range, our objects are clearly distinguished from the field ones,
having lower pEW values, as expected given their low-gravity nature. A similar
trend has previously been reported by Martin et al. (2017) down to L0 and
Manjavacas et al. (2020) down to L4, and here we show that the trend maintains
also for later L-types for most of the lines. The exception is the K I 1516.7
nm and Na I 1139 nm lines (the two rightmost panels of Fig. 15), where we see
that the distinction between the objects in our sample and the field dwarfs
maintains only down to $\sim$L4. Similar behavior for the Na I line can be
observed in Fig. 21 of Allers & Liu (2013). Regarding the K I 1516.7 nm line,
field sources with SpT earlier than L5 present larger pEW, whereas young
sources present very low pEWs ($<$1.5 $\AA$).

For the K I lines located in the J-band, we also observe that the youngest
objects in our sample ($<$30 Myr; green stars) have on average lower pEW than
the objects belonging to the next age group (30$-$100 Myr; grey pentagons),
which is in turn not well distinguished from even older objects in the
X-shooter sample. A similar observation has been previously made for the K I
lines, but also for other lines in the optical portion of the spectra by
Manjavacas et al. (2020). They found that the pEWs do not significantly change
after the age of PLE, meaning that low-mass stars and more massive BDs have
nearly approached their final radii after their first $\sim$100 Myr, which is
also in agreement with the evolutionary models (Baraffe et al., 2015).
However, although the trend of lower pEWs for young with respect to the field
dwarfs seems to maintain throughout the SpT L, we also observe a general drop
in pEW values for all objects with SpT in the range L6$-$L8, also seen in
plots of Allers & Liu (2013). At the transition from L to T-type field dwarfs,
we see either a plateau in pEW values or an increase, followed by a decrease
towards the later T-types.

Although we have only a few young T-dwarfs in our sample, it seems that they
maintain the trend of lower pEWs at least in two lines (K I at 1169.2 nm and
1177.8 nm). In other cases, the distinction from the field objects is not that
clear. Considering the field age class, the K I doublets in the J-band seem to
decrease drastically for later T-types (SpT $\gtrsim$ T4/T5). This behavior
was also observed in previous works (e.g, Martin et al. 2017). Clearly, it is
an imperative to populate this SpT region with younger T dwarfs to be able to
draw further conclusions. However, the considerable decrease of pEW values in
field late-T dwarfs might suggest that differences in surface gravity through
the K I doublets are no longer distinguishable for late T-types.

It is important to note that the K I 1243.7 nm line is partially blended with
a FeH feature that may affect the measurement of the pEWs. Given that the
field sources we have used present a lower spectral resolution, their pEWs may
artificially have larger values than those measured from the X-shooter
spectra. This is the reason why previous studies do not include this line in
the analysis (Allers & Liu, 2013; Martin et al., 2017).

Another way to observe the age trends is to plot the pEWs of the alkali lines
as a function of the age group, as shown in Fig. 16. For this exercise, we
remove all the objects in the T-type range. As expected from Fig. 15, the pEW
on average increases as a function of age (surface gravity), which can be
appreciated in the KDEs on the right-hand side of each panel, with the peaks
of the distribution shifting upwards with age.

##  6 Suggested low-gravity spectral standards

There is plenty of spectra of old field dwarfs, with comparable temperatures
and SpTs, which can be combined to create spectral templates. On the other
hand, spectra of young late-type objects are rare and have a heterogeneous
nature in the sense that they encompass a large spread of NIR colors for a
fixed optically-based SpT (Allers & Liu, 2013; Cruz et al., 2018). As a
result, a well-covered sequence of young LT templates is still lacking. The
sequence used for template fitting in this work is that of Luhman et al.
(2017), covering SpTs L0, L2, L4 and L7, at low spectral resolution. It is
important to work towards constructing a more complete sequence that will
allow the classification of the new ultracool spectra obtained by JWST and
other upcoming facilities.

With this in mind, in Table 11, we present preliminary spectral standards for
spectral classification of low-gravity LT dwarfs that should be used as a
starting point towards achieving a more accurate young template sequence. In
the selection process, we did not take into account objects in USCO, since
these can be affected by extinction, or in PRA, since this association is the
oldest in our sample. When more than one spectra seemed suitable as a
standard, preference was given to those located in the youngest regions
considered in this work. We also prioritized objects with similar SpTs
estimated by direct comparison with spectral templates and using spectral type
indices, within the respective error range. For some subtypes, there are more
than one spectral standards that agree with the selection criteria and thus
are proposed. In the end, the standard sequence suggested covers SpTs from L0
down to $\sim$T5 but the subtypes L3, L6, L9, T0, T1, and T4 are lacking since
none of the objects in our sample were classified as such.

We note that object #21 was classified visually as L5, as it appears to be
later than L4 and earlier than L7, but closer in shape to the former one.
Object #20 is clearly later than L7, but at the same time lacks T-type
characteristics, therefore we proposed the L8 classification. This
classification can be re-iterated once a larger number of spectra in this
spectral range are known. The object #53 (T3) was selected as a weak binary
candidate in Sect. 4.2, but we nevertheless decide to include it here because,
even if it is a spectral binary, the components seem to have a very similar
spectral type which will not translate into a peculiar unresolved spectrum.
The same argument goes to object #47 which, as already mentioned in Sect. 4.2,
it is a tight binary where the components have nearly equal luminosity (Best
et al., 2017).

Regarding ages, for L-types, all of the sources selected as possible spectral
standards are younger than $\sim$50 Myr. The proposed T3 standard, object #53,
also has comparable age (located in ARG, 40$-$50 Myr). For the remaining two
T-type dwarfs, older objects had to be selected: object #56 located in CARN
(200$\pm$50 Myr), and object #50 in ABDMG (149${}^{+51}_{-19}$ Myr). Ideally,
one would want a set of templates with ages below 10 Myr to classify the PMO
samples that JWST will detect but, at the moment, such data is lacking. What
we present here should be seen as a step towards classification of the young
late-L to T dwarfs in SFRs that should be revised once new data is acquired.

Table 5: Proposed low-gravity LT spectral standards.

SpT | ID | Name | Region
---|---|---|---
L0 | #33 | J0037-5846 | THA
L1 | #23 | J0045+1634 | ARG
| #34 | J0223-5815 | THA
| #35 | J0323-4631 | THA
L2 | #41 | J0153-6744 | THA
L4 | #42 | J0342-6817 | THA
L5 | #21 | J2154-1055 | ARG
L7 | #47a | J1119-1137 | TWA
L8 | #20 | PSO J318.5-22 | BPMG
T2 | #56 | J0136+0933 | CARN
T3 | #53b | PSO J168.18-27 | ARG
$\sim$T5 | #50 | J1110+0116 | ABDMG

111111a Known nearly-equal flux binary (Best et al., 2017). b Selected as weak
binary candidate in Sect. 4.2.

##  7 Summary and conclusions

We present NIR VLT/X-shooter archival spectra of 56 ultracool dwarfs, probable
members of several NYMGs, young clusters and SFRs, with SpTs in the range M8
to T6. The expected ages of the analyzed objects are between 10 and 600 Myr.
We re-determine their SpTs through a comparison with a set of literature young
and field templates, and a set of SpT-sensitive indices. With the help of a
complementary spectroscopic sample comprising more than 3000 MLT dwarfs of all
ages (from nearby SFRs to field), we identify 15 spectral indices that are
useful for spectral typing of LT dwarfs and provide their scaling relations
with SpT.

As one of the important goals of this paper is to provide means to distinguish
young from old LT dwarfs based on their NIR spectra, we identify several
spectral indices from the literature suitable for this purpose in the L-type
spectral range. In the future, it will be crucial to establish a similar
framework for the T-type objects, currently not possible due to the lack of
young objects in this spectral range. We find that the T-dwarf spectra in our
sample consistently show redder colors when compared to their field
counterparts, which has been interpreted as a signature of youth. Given their
peculiarity when compared to field objects, these spectra also tend to be
recognized as potential unresolved spectral binaries. We find the latter
interpretation unlikely, given the low prevalence of binaries in high spatial
resolution surveys of T-dwarfs, and conclude that the red colors are probably
caused by the effects of low surface gravity.

We also inspected the behavior of several alkali lines in the $J-$ and the
$H-$bands, observing the correlations of their widths with the SpT and age.
The pEWs of the K I lines in the $J-$band typically increase from M8 to
$\sim$L4, displaying a turnover towards later L-types. The K I line in the
$H-$band (1516.7 nm) and the Na I $J-$band line (1139 nm) show a constant
decrease in pEWs with increasing SpT. These observations are particularly
valid for the field dwarfs, while the pEWs of the objects in our sample which
are significantly younger have lower values, and do not show strong trends
among them. The pEWs of the alkali lines show clear trends with age, as a
consequence of changes in the surface gravity.

Finally, we identify 12 objects as preliminary spectral standards for young L
and T dwarfs, which should be useful for spectral typing of the objects
identified with the new facilities, such as the JWST. More high-quality
spectra of young ultracool dwarfs, in particular those with SpTs in the late
L- and the T-type regime are needed to establish a complete set of templates
for the characterization of young brown dwarfs and PMOs.

###### Acknowledgements.

We are grateful to Carlo Manara for providing the code to calculate the
pseudo-equivalent widths of the alkali lines. L.P., K.M., and V.A. acknowledge
funding by the Science and Technology Foundation of Portugal (FCT), grants
PTDC/FISAST/7002/2020, UIDB/00099/2020, PTDC/FIS-AST/28731/2017,
IF/00194/2015, SFRH/BD/143433/2019, 2022.03809.CEECIND, UIDB/04434/2020 and
UIDP/04434/2020. L.P. acknowledges financial support from the CSIC project
JAEICU-21-ICE-09, from Centro Superior de Investigaciones Científicas (CSIC)
under the PIE project 20215AT016, and the program Unidad de Excelencia María
de Maeztu CEX2020-001058-M. 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 benefitted
from the SpeX Prism Spectral Libraries, maintained by Adam Burgasser at
http://www.browndwarfs.org/spexprism. This research has benefitted from the
Montreal Brown Dwarf and Exoplanet Spectral Library, maintained by Jonathan
Gagné.

## References

  * Allers et al. (2007) Allers, K. N., Jaffe, D. T., Luhman, K. L., et al. 2007, Astrophysical Journal, 657, 511
  * Allers & Liu (2013) Allers, K. N. & Liu, M. C. 2013, ApJ, 772, 79
  * Almendros-Abad et al. (2022) Almendros-Abad, V., Mužić, K., Moitinho, A., Krone-Martins, A., & Kubiak, K. 2022, Astronomy and Astrophysics, 657, A129
  * Alves de Oliveira et al. (2012) Alves de Oliveira, C., Moraux, E., Bouvier, J., & Bouy, H. 2012, A&A, 539, A151
  * Ardila et al. (2000) Ardila, D., Martín, E., & Basri, G. 2000, AJ, 120, 479
  * Artigau et al. (2006) Artigau, É., Doyon, R., Lafrenière, D., et al. 2006, ApJ, 651, L57
  * Ashraf et al. (2022) Ashraf, A., Bardalez Gagliuffi, D. C., Manjavacas, E., et al. 2022, ApJ, 934, 178
  * Baraffe et al. (2015) Baraffe, I., Homeier, D., Allard, F., & Chabrier, G. 2015, A&A, 577, A42
  * Bardalez Gagliuffi et al. (2014) Bardalez Gagliuffi, D. C., Burgasser, A. J., Gelino, C. R., et al. 2014, ApJ, 794, 143
  * Bayo et al. (2011) Bayo, A., Barrado, D., Stauffer, J., et al. 2011, A&A, 536, A63
  * Bell et al. (2015) Bell, C. P. M., Mamajek, E. E., & Naylor, T. 2015, Monthly Notices of the RAS, 454, 593
  * Best et al. (2017) Best, W. M. J., Liu, M. C., Dupuy, T. J., & Magnier, E. A. 2017, ApJ, 843, L4
  * Best et al. (2015) Best, W. M. J., Liu, M. C., Magnier, E. A., et al. 2015, ApJ, 814, 118
  * Best et al. (2021) Best, W. M. J., Liu, M. C., Magnier, E. A., & Dupuy, T. J. 2021, AJ, 161, 42
  * Bouy et al. (2015) Bouy, H., Bertin, E., Sarro, L. M., et al. 2015, A&A, 577, A148
  * Bouy et al. (2003) Bouy, H., Brandner, W., Martín, E. L., et al. 2003, AJ, 126, 1526
  * Bouy et al. (2022) Bouy, H., Tamura, M., Barrado, D., et al. 2022, A&A, 664, A111
  * Brandt et al. (2014) Brandt, T. D., Kuzuhara, M., McElwain, M. W., et al. 2014, ApJ, 786, 1
  * Breger (1986) Breger, M. 1986, ApJ, 309, 311
  * Burgasser et al. (2010) Burgasser, A. J., Cruz, K. L., Cushing, M., et al. 2010, Astrophysical Journal, 710, 1142
  * Burgasser et al. (2006a) Burgasser, A. J., Geballe, T. R., Leggett, S. K., Kirkpatrick, J. D., & Golimowski, D. A. 2006a, ApJ, 637, 1067
  * Burgasser et al. (2002) Burgasser, A. J., Kirkpatrick, J. D., Brown, M. E., et al. 2002, Astrophysical Journal, 564, 421
  * Burgasser et al. (2006b) Burgasser, A. J., Kirkpatrick, J. D., Cruz, K. L., et al. 2006b, ApJS, 166, 585
  * Burgasser et al. (2003) Burgasser, A. J., Kirkpatrick, J. D., Reid, I. N., et al. 2003, ApJ, 586, 512
  * Burgasser et al. (2016) Burgasser, A. J., Lopez, M. A., Mamajek, E. E., et al. 2016, ApJ, 820, 32
  * Canty et al. (2013) Canty, J. I., Lucas, P. W., Roche, P. F., & Pinfield, D. J. 2013, Monthly Notices of the RAS, 435, 2650
  * Cardelli et al. (1989) Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, Astrophysical Journal, 345, 245
  * Cook et al. (2017) Cook, N. J., Scholz, A., & Jayawardhana, R. 2017, AJ, 154, 256
  * Covey et al. (2010) Covey, K. R., Lada, C. J., Román-Zúñiga, C., et al. 2010, Astrophysical Journal, 722, 971
  * Cruz et al. (2009) Cruz, K. L., Kirkpatrick, J. D., & Burgasser, A. J. 2009, AJ, 137, 3345
  * Cruz et al. (2018) Cruz, K. L., Núñez, A., Burgasser, A. J., et al. 2018, AJ, 155, 34
  * Cushing et al. (2005) Cushing, M. C., Rayner, J. T., & Vacca, W. D. 2005, ApJ, 623, 1115
  * Cushing et al. (2000) Cushing, M. C., Tokunaga, A. T., & Kobayashi, N. 2000, Astronomical Journal, 119, 3019
  * Cutri et al. (2003) Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, VizieR Online Data Catalog, II/246
  * Dahm (2015) Dahm, S. E. 2015, The Astrophysical Journal, 813, 108
  * Day-Jones et al. (2013) Day-Jones, A. C., Marocco, F., Pinfield, D. J., et al. 2013, Monthly Notices of the RAS, 430, 1171
  * Dupuy & Kraus (2013) Dupuy, T. J. & Kraus, A. L. 2013, Science, 341, 1492
  * Dupuy & Liu (2012) Dupuy, T. J. & Liu, M. C. 2012, ApJS, 201, 19
  * Dupuy et al. (2018) Dupuy, T. J., Liu, M. C., Allers, K. N., et al. 2018, AJ, 156, 57
  * Esplin & Luhman (2020) Esplin, T. L. & Luhman, K. L. 2020, AJ, 159, 282
  * Faherty et al. (2012) Faherty, J. K., Burgasser, A. J., Walter, F. M., et al. 2012, ApJ, 752, 56
  * Faherty et al. (2016) Faherty, J. K., Riedel, A. R., Cruz, K. L., et al. 2016, ApJS, 225, 10
  * Fontanive et al. (2018) Fontanive, C., Biller, B., Bonavita, M., & Allers, K. 2018, MNRAS, 479, 2702
  * Freudling et al. (2013) Freudling, W., Romaniello, M., Bramich, D. M., et al. 2013, A&A, 559, A96
  * Gagné et al. (2015a) Gagné, J., Burgasser, A. J., Faherty, J. K., et al. 2015a, ApJ, 808, L20
  * Gagné et al. (2017) Gagné, J., Faherty, J. K., Burgasser, A. J., et al. 2017, ApJ, 841, L1
  * Gagné et al. (2014a) Gagné, J., Faherty, J. K., Cruz, K., et al. 2014a, ApJ, 785, L14
  * Gagné et al. (2015b) Gagné, J., Faherty, J. K., Cruz, K. L., et al. 2015b, ApJS, 219, 33
  * Gagné et al. (2014b) Gagné, J., Lafrenière, D., Doyon, R., et al. 2014b, ApJ, 792, L17
  * Gagné et al. (2014c) Gagné, J., Lafrenière, D., Doyon, R., Malo, L., & Artigau, É. 2014c, ApJ, 783, 121
  * Gagné et al. (2015c) Gagné, J., Lafrenière, D., Doyon, R., Malo, L., & Artigau, É. 2015c, ApJ, 798, 73
  * Gagné et al. (2018) Gagné et al., J. 2018, Astrophysical Journal, 856, 23
  * Gaia Collaboration et al. (2021) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649, A1
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1
  * Galli et al. (2017) Galli, P. A. B., Moraux, E., Bouy, H., et al. 2017, A&A, 598, A48
  * Geballe et al. (2002) Geballe, T. R., Knapp, G. R., Leggett, S. K., et al. 2002, Astrophysical Journal, 564, 466
  * Geißler et al. (2011) Geißler, K., Metchev, S., Kirkpatrick, J. D., Berriman, G. B., & Looper, D. 2011, ApJ, 732, 56
  * Gonneau et al. (2016) Gonneau, A., Lançon, A., Trager, S. C., et al. 2016, A&A, 589, A36
  * Gorlova et al. (2003) Gorlova, N. I., Meyer, M. R., Rieke, G. H., & Liebert, J. 2003, ApJ, 593, 1074
  * Hood et al. (2023) Hood, C. E., Fortney, J. J., Line, M. R., & Faherty, J. K. 2023, ApJ, 953, 170
  * Kausch et al. (2015) Kausch, W., Noll, S., Smette, A., et al. 2015, A&A, 576, A78
  * Kellogg et al. (2015) Kellogg, K., Metchev, S., Geißler, K., et al. 2015, AJ, 150, 182
  * Kirkpatrick et al. (2008) Kirkpatrick, J. D., Cruz, K. L., Barman, T. S., et al. 2008, ApJ, 689, 1295
  * Kirkpatrick et al. (2010) Kirkpatrick, J. D., Looper, D. L., Burgasser, A. J., et al. 2010, Astrophysical Journals, 190, 100
  * Knapp et al. (2004) Knapp, G. R., Leggett, S. K., Fan, X., et al. 2004, AJ, 127, 3553
  * Kraus & Hillenbrand (2007) Kraus, A. L. & Hillenbrand, L. A. 2007, The Astronomical Journal, 134, 2340
  * Leggett et al. (2006) Leggett, S. K., Currie, M. J., Varricatt, W. P., et al. 2006, MNRAS, 373, 781
  * Liu et al. (2013a) Liu, M. C., Dupuy, T. J., & Allers, K. N. 2013a, Astronomische Nachrichten, 334, 85
  * Liu et al. (2016) Liu, M. C., Dupuy, T. J., & Allers, K. N. 2016, Astrophysical Journal, 833, 96
  * Liu et al. (2013b) Liu, M. C., Magnier, E. A., Deacon, N. R., et al. 2013b, ApJ, 777, L20
  * Lodieu et al. (2008) Lodieu, N., Hambly, N. C., Jameson, R. F., & Hodgkin, S. T. 2008, MNRAS, 383, 1385
  * Lodieu et al. (2019) Lodieu, N., Pérez-Garrido, A., Smart, R. L., & Silvotti, R. 2019, A&A, 628, A66
  * Lodieu et al. (2018) Lodieu, N., Zapatero Osorio, M. R., Béjar, V. J. S., & Peña Ramírez, K. 2018, MNRAS, 473, 2020
  * Lucas et al. (2001) Lucas, P. W., Roche, P. F., Allard, F., & Hauschildt, P. H. 2001, MNRAS, 326, 695
  * Luhman (2022) Luhman, K. L. 2022, AJ, 163, 24
  * Luhman & Esplin (2020) Luhman, K. L. & Esplin, T. L. 2020, AJ, 160, 44
  * Luhman et al. (2018) Luhman, K. L., Herrmann, K. A., Mamajek, E. E., Esplin, T. L., & Pecaut, M. J. 2018, AJ, 156, 76
  * Luhman et al. (2009) Luhman, K. L., Mamajek, E. E., Allen, P. R., & Cruz, K. L. 2009, ApJ, 703, 399
  * Luhman et al. (2017) Luhman, K. L., Mamajek, E. E., Shukla, S. J., & Loutrel, N. P. 2017, Astronomical Journal, 153, 46
  * Madhusudhan et al. (2011) Madhusudhan, N., Burrows, A., & Currie, T. 2011, ApJ, 737, 34
  * Mamajek et al. (2013) Mamajek, E. E., Bartlett, J. L., Seifahrt, A., et al. 2013, AJ, 146, 154
  * Manara et al. (2013) Manara, C. F., Beccari, G., Da Rio, N., et al. 2013, A&A, 558, A114
  * Manjavacas et al. (2019) Manjavacas, E., Apai, D., Zhou, Y., et al. 2019, AJ, 157, 101
  * Manjavacas et al. (2020) Manjavacas, E., Lodieu, N., Béjar, V. J. S., et al. 2020, MNRAS, 491, 5925
  * Marley et al. (2021) Marley, M. S., Saumon, D., Visscher, C., et al. 2021, ApJ, 920, 85
  * Marocco et al. (2013) Marocco, F., Andrei, A. H., Smart, R. L., et al. 2013, AJ, 146, 161
  * Marocco et al. (2015) Marocco, F., Jones, H. R. A., Day-Jones, A. C., et al. 2015, MNRAS, 449, 3651
  * Martin et al. (2017) Martin, E. C., Mace, G. N., McLean, I. S., et al. 2017, ApJ, 838, 73
  * Martín et al. (2006) Martín, E. L., Brandner, W., Bouy, H., et al. 2006, A&A, 456, 253
  * McGovern et al. (2004) McGovern, M. R., Kirkpatrick, J. D., McLean, I. S., et al. 2004, ApJ, 600, 1020
  * McLean et al. (2003) McLean, I. S., McGovern, M. R., Burgasser, A. J., et al. 2003, Astrophysical Journal, 596, 561
  * Medan et al. (2021) Medan, I., Lépine, S., & Hartman, Z. 2021, AJ, 161, 234
  * Miret-Roig (2023) Miret-Roig, N. 2023, Ap&SS, 368, 17
  * Miret-Roig et al. (2022) Miret-Roig, N., Bouy, H., Raymond, S. N., et al. 2022, Nature Astronomy, 6, 89
  * Modigliani et al. (2010) Modigliani, A., Goldoni, P., Royer, F., et al. 2010, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7737, Observatory Operations: Strategies, Processes, and Systems III, ed. D. R. Silva, A. B. Peck, & B. T. Soifer, 773728
  * Mužić et al. (2015) Mužić, K., Scholz, A., Geers, V. C., & Jayawardhana, R. 2015, ApJ, 810, 159
  * Naud et al. (2014) Naud, M.-E., Artigau, É., Malo, L., et al. 2014, ApJ, 787, 5
  * Peña Ramírez et al. (2012) Peña Ramírez, K., Béjar, V. J. S., Zapatero Osorio, M. R., Petr-Gotzens, M. G., & Martín, E. L. 2012, ApJ, 754, 30
  * Pearson & McCaughrean (2023) Pearson, S. G. & McCaughrean, M. J. 2023, arXiv e-prints, arXiv:2310.01231
  * Pecaut & Mamajek (2013) Pecaut, M. J. & Mamajek, E. E. 2013, ApJS, 208, 9
  * Pecaut & Mamajek (2016) Pecaut, M. J. & Mamajek, E. E. 2016, Monthly Notices of the RAS, 461, 794
  * Petrus et al. (2023) Petrus, S., Chauvin, G., Bonnefoy, M., et al. 2023, A&A, 670, L9
  * Ribas (2003) Ribas, I. 2003, A&A, 400, 297
  * Rizzuto et al. (2015) Rizzuto, A. C., Ireland, M. J., & Kraus, A. L. 2015, MNRAS, 448, 2737
  * Rojas-Ayala et al. (2012) Rojas-Ayala, B., Covey, K. R., Muirhead, P. S., & Lloyd, J. P. 2012, Astrophysical Journal, 748, 93
  * Schlieder et al. (2012) Schlieder, J. E., Lépine, S., Rice, E., et al. 2012, AJ, 143, 114
  * Schneider et al. (2017) Schneider, A. C., Windsor, J., Cushing, M. C., Kirkpatrick, J. D., & Shkolnik, E. L. 2017, AJ, 153, 196
  * Schneider et al. (2016) Schneider, A. C., Windsor, J., Cushing, M. C., Kirkpatrick, J. D., & Wright, E. L. 2016, ApJ, 822, L1
  * Scholz et al. (2012) Scholz, A., Jayawardhana, R., Muzic, K., et al. 2012, Astrophysical Journal, 756, 24
  * Scholz et al. (2022) Scholz, A., Muzic, K., Jayawardhana, R., Quinlan, L., & Wurster, J. 2022, PASP, 134, 104401
  * Slesnick et al. (2004) Slesnick, C. L., Hillenbrand, L. A., & Carpenter, J. M. 2004, Astrophysical Journal, 610, 1045
  * Smart et al. (2017) Smart, R. L., Marocco, F., Caballero, J. A., et al. 2017, MNRAS, 469, 401
  * Smette et al. (2015) Smette, A., Sana, H., Noll, S., et al. 2015, A&A, 576, A77
  * Taylor (2006) Taylor, B. J. 2006, AJ, 132, 2453
  * Testi et al. (2001) Testi, L., D’Antona, F., Ghinassi, F., et al. 2001, Astrophysical Journall, 552, L147
  * Tody (1986) Tody, D. 1986, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 627, Instrumentation in astronomy VI, ed. D. L. Crawford, 733
  * Tokunaga & Kobayashi (1999) Tokunaga, A. T. & Kobayashi, N. 1999, Astronomical Journal, 117, 1010
  * Tremblin et al. (2016) Tremblin, P., Amundsen, D. S., Chabrier, G., et al. 2016, ApJ, 817, L19
  * Ujjwal et al. (2020) Ujjwal, K., Kartha, S. S., Mathew, B., Manoj, P., & Narang, M. 2020, AJ, 159, 166
  * Vernet et al. (2011) Vernet, J., Dekker, H., D’Odorico, S., et al. 2011, A&A, 536, A105
  * Weights et al. (2009) Weights, D. J., Lucas, P. W., Roche, P. F., Pinfield, D. J., & Riddick, F. 2009, Monthly Notices of the RAS, 392, 817
  * Zhang et al. (2021) Zhang, Z., Liu, M. C., Best, W. M. J., Dupuy, T. J., & Siverd, R. J. 2021, ApJ, 911, 7
  * Zhang et al. (2018) Zhang, Z., Liu, M. C., Best, W. M. J., et al. 2018, Astrophysical Journal, 858, 41
  * Zuckerman (2019) Zuckerman, B. 2019, Astrophysical Journal, 870, 27
  * Zuckerman et al. (2006) Zuckerman, B., Bessell, M. S., Song, I., & Kim, S. 2006, The Astrophysical Journal, 649, L115
  * Zuckerman et al. (2013) Zuckerman, B., Vican, L., Song, I., & Schneider, A. 2013, ApJ, 778, 5

##  Appendix A Additional tables

In Table 12 we summarize basic observational parameters of our sample
presented in Sect. 2.

Table 13 shows the spectral classification results discussed in Sect. 4.

Table 6: The objects in our dataset, along with some basic observational
parameters.

ID | Name | RA | DEC | Date observation | ESO PROG ID | EXPTIME | NEXP | Slit (′′) | R ($\lambda/\Delta\lambda$)a
---|---|---|---|---|---|---|---|---|---
2 | UScoJ160606-233513 | 16:06:06.29 | -23:35:13.3 | 2014-07-04 | 093.C-0769(A) | 197 | 16 | 1.2 | 4300
3 | UScoJ160723-221102 | 16:07:23.82 | -22:11:02.0 | 2014-04-22 | 093.C-0769(A) | 197 | 8 | 1.2 | 4300
|  |  |  | 2016-07-25 | 097.C-0592(A) | 290 | 8 | 0.9 | 5600
4 | UScoJ160737-224247 | 16:07:37.99 | -22:42:47.0 | 2014-07-04 | 093.C-0769(A) | 197 | 14 | 1.2 | 4300
|  |  |  | 2014-08-02 | 093.C-0769(A) | 197 | 32 | 1.2 | 4300
5 | UScoJ160818-223225 | 16:08:18.43 | -22:32:25.0 | 2014-07-02 | 093.C-0769(A) | 197 | 28 | 1.2 | 4300
|  |  |  | 2014-07-03 | 093.C-0769(A) | 197 | 14 | 1.2 | 4300
|  |  |  | 2014-07-04 | 093.C-0769(A) | 197 | 14 | 1.2 | 4300
6 | UScoJ160828-231510 | 16:08:28.47 | -23:15:10.4 | 2014-06-15 | 093.C-0769(A) | 197 | 14 | 1.2 | 4300
|  |  |  | 2014-06-20 | 093.C-0769(A) | 197 | 14 | 1.2 | 4300
7 | UScoJ161302-212428 | 16:13:02.32 | -21:24:28.5 | 2015-04-13 | 095.C-0812(A) | 300 | 4 | 1.2 | 4300
8 | UScoJ160918-222923 | 16:09:18.69 | -22:29:23.9 | 2015-04-13 | 095.C-0812(A) | 300 | 16 | 1.2 | 4300
9 | VISTAJ1559-2214 | 15:59:36.38 | -22:14:15.9 | 2015-04-13 | 095.C-0812(A) | 300 | 4 | 1.2 | 4300
10 | VISTAJ1614-2331 | 16:14:22.56 | -23:31:17.8 | 2015-04-14 | 095.C-0812(A) | 300 | 6 | 1.2 | 4300
11 | VISTAJ1611-2215 | 16:11:44.37 | -22:15:44.6 | 2015-04-12 | 095.C-0812(A) | 300 | 8 | 1.2 | 4300
12 | VISTAJ1607-2146 | 16:07:31.61 | -21:46:54.4 | 2015-04-14 | 095.C-0812(A) | 300 | 8 | 1.2 | 4300
13 | VISTAJ1604-2241 | 16:04:13.04 | -22:41:03.4 | 2015-04-13 | 095.C-0812(A) | 300 | 8 | 1.2 | 4300
14 | VISTAJ1614-2211 | 16:14:07.56 | -22:11:52.2 | 2015-04-12 | 095.C-0812(A) | 300 | 10 | 1.2 | 4300
15 | VISTAJ1605-2403 | 16:05:39.09 | -24:03:32.8 | 2015-04-12 | 095.C-0812(A) | 300 | 10 | 1.2 | 4300
16 | VISTAJ1604-2134 | 16:04:20.04 | -21:34:53.0 | 2015-04-13 | 095.C-0812(A) | 300 | 10 | 1.2 | 4300
17 | VISTAJ1601-2212 | 16:01:36.92 | -22:12:02.7 | 2015-04-13 | 095.C-0812(A) | 300 | 10 | 1.2 | 4300
18 | VISTAJ1615-2229 | 16:15:12.70 | -22:29:49.2 | 2015-04-14 | 095.C-0812(A) | 300 | 10 | 1.2 | 4300
19 | J0032-4405 | 00:32:55.80 | -44:05:05.8 | 2016-07-16 | 097.C-0592(A) | 300 | 6 | 0.9 | 5600
20 | PSO J318.5-22 | 21:14:08.02 | -22:51:35.8 | 2018-06-20 | 0101.C-0290(A) | 300 | 12 | 0.6 | 8100
|  |  |  | 2018-06-27 | 0101.C-0290(A) | 300 | 12 | 0.6 | 8100
21 | J2154-1055 | 21:54:34.50 | -10:55:30.8 | 2013-08-22 | 091.C-0462(B) | 290 | 10 | 0.9 | 5600
23 | J0045+1634 | 00:45:21.42 | 16:34:44.7 | 2018-10-09 | 0102.C-0121(A) | 234 | 12 | 0.6 | 8100
24 | J0518-2756 | 05:18:46.20 | -27:56:45.8 | 2018-11-27 | 0102.C-0121(A) | 234 | 12 | 0.6 | 8100
25 | 2MASS J03552337+1133437 | 03:55:23.60 | 11:33:34.3 | 2019-09-10 | 0103.C-0231(A) | 175 | 12 | 0.6 | 8100
26 | 2MASS J14252798-3650229 | 14:25:27.98 | -36:50:23.0 | 2018-06-19 | 0101.C-0290(A) | 234 | 12 | 0.6 | 8100
27 | J0339-3525 (LP 944-20) | 03:39:35.25 | -35:25:43.6 | 2013-10-18 | 092.D-0128(A) | 225 | 20 | 0.4 | 11600
28 | 2MASS J03264225-2102057 | 03:26:42.25 | -21:02:05.8 | 2018-10-21 | 0102.C-0121(A) | 234 | 12 | 0.6 | 8100
29 | 2MASS J22064498-4217208 | 22:06:44.98 | -42:17:21.1 | 2013-08-22 | 091.C-0462(B) | 290 | 6 | 0.9 | 5600
31 | J2322-6151 | 23:22:53.00 | -61:51:27.5 | 2018-06-26 | 0101.C-0290(A) | 234 | 12 | 0.6 | 8100
32 | J0006-6436 | 00:06:57.93 | -64:36:54.2 | 2016-07-22 | 097.C-0592(A) | 300 | 4 | 0.9 | 5600
33 | J0037-5846 | 00:37:43.06 | -58:46:22.8 | 2016-08-11 | 097.C-0592(A) | 290 | 8 | 0.9 | 5600
|  |  |  | 2013-08-22 | 091.C-0462(B) | 290 | 10 | 0.9 | 5600
34 | J0223-5815 | 02:23:54.65 | -58:15:06.6 | 2016-08-23 | 097.C-0592(A) | 300 | 6 | 0.9 | 5600
|  |  |  | 2016-08-26 | 097.C-0592(A) | 300 | 6 | 0.9 | 5600
35 | J0323-4631 | 03:23:10.01 | -46:31:23.6 | 2016-08-10 | 097.C-0592(A) | 290 | 8 | 0.9 | 5600
|  |  |  | 2013-08-22 | 091.C-0462(B) | 290 | 6 | 0.9 | 5600
36 | J0141-4633 | 01:41:58.23 | -46:33:57.3 | 2016-08-20 | 097.C-0592(A) | 300 | 6 | 0.9 | 5600
37 | J0357-4417 | 03:57:26.96 | -44:17:30.5 | 2013-08-22 | 091.C-0462(B) | 290 | 4 | 0.9 | 5600
38 | J0117-3403 | 01:17:47.49 | -34:03:25.8 | 2016-08-18 | 097.C-0592(A) | 290 | 8 | 0.9 | 5600
39 | J0241-0326 | 02:41:11.51 | -03:26:58.8 | 2013-08-22 | 091.C-0462(B) | 290 | 8 | 0.9 | 5600
40 | J0004-6410 | 00:04:02.88 | -64:10:35.8 | 2013-08-22 | 091.C-0462(B) | 290 | 10 | 0.9 | 5600
41 | 2MASS J01531463-6744181 | 01:53:14.63 | -67:44:18.1 | 2018-10-17 | 0102.C-0121(A) | 234 | 12 | 0.6 | 8100
|  |  |  | 2018-10-18 | 0102.C-0121(A) | 234 | 12 | 0.6 | 8100
42 | 2MASS J03421621-6817321 | 03:42:16.21 | -68:17:32.1 | 2018-10-08 | 0102.C-0121(A) | 234 | 24 | 0.6 | 8100
46 | J1207-3900 | 12:07:48.35 | -39:00:04.5 | 2015-05-31 | 095.C-0147(A) | 900 | 4 | 1.2 | 4300
|  |  |  | 2015-06-01 | 095.C-0147(A) | 900 | 4 | 1.2 | 4300
|  |  |  | 2018-04-28 | 0101.C-0290(A) | 234 | 12 | 0.6 | 8100
47 | 2MASS J11193254-1137466 | 11:19:32.54 | -11:37:46.6 | 2019-04-15 | 0103.C-0231(A) | 300 | 12 | 0.6 | 8100
48 | 2MASS J114724.10-204021.3 | 11:47:24.10 | -20:40:21.3 | 2018-06-16 | 0101.C-0290(A) | 300 | 12 | 0.6 | 8100
49 | WISE J052857.69+090104.2 | 05:28:57.68 | 09:01:04.4 | 2018-10-22 | 0102.C-0121(A) | 234 | 12 | 0.6 | 8100
|  |  |  | 2018-10-26 | 0102.C-0121(A) | 234 | 24 | 0.6 | 8100
50 | SDSSp J111010.01+011613.1 | 11:10:10.01 | 01:16:13.1 | 2018-04-29 | 0101.C-0290(A) | 234 | 12 | 0.6 | 8100
|  |  |  | 2018-05-27 | 0101.C-0290(A) | 234 | 12 | 0.6 | 8100
|  |  |  | 2018-05-28 | 0101.C-0290(A) | 234 | 12 | 0.6 | 8100
51 | SDSS J152103.24+013142.7 | 15:21:03.27 | 01:31:42.7 | 2011-06-09 | 087.C-0639(A) | 290 | 4 | 0.9 | 5600
52 | ULAS J004757.41+154641.4 | 00:47:57.43 | 15:46:41.2 | 2011-09-21 | 087.C-0639(B) | 490 | 4 | 0.9 | 5600
53 | PSO J168.1800-27.2264 | 11:12:43.25 | -27:13:36.1 | 2014-03-12 | 092.C-0229(B) | 600 | 6 | 1.2 | 4300
55 | ULAS J131610.13+031205.5 | 13:16:10.13 | 03:12:05.6 | 2011-06-06 | 087.C-0639(A) | 390 | 4 | 0.9 | 5600
56 | SIMP J013656.5+093347.3 | 01:36:56.56 | 09:33:47.3 | 2018-11-16 | 0102.C-0121(A) | 234 | 12 | 0.6 | 8100
57 | 2MASS J08370450+2016033 | 08:37:04.49 | 20:16:03.2 | 2017-01-01 | 098.C-0277(A) | 300 | 8 | 1.2 | 4300
58 | UGCS J084510.65+214817.0 | 08:45:10.66 | 21:48:17.1 | 2017-01-02 | 098.C-0277(A) | 300 | 10 | 1.2 | 4300
59 | 2MASS J03463425+2350036 | 03:46:34.25 | 23:50:03.6 | 2016-11-11 | 098.C-0277(A) | 300 | 10 | 1.2 | 4300
60 | 2MASS J03541027+2341402 | 03:54:10.27 | 23:41:40.2 | 2016-11-03 | 098.C-0277(A) | 300 | 14 | 1.2 | 4300
61 | 2MASS J00464841+0715177 | 00:46:48.42 | 07:15:17.8 | 2019-07-15 | 0103.C-0231(A) | 175 | 12 | 0.6 | 8100
62 | 2MASS J05120636-2949540 | 05:12:06.37 | -29:49:54.0 | 2018-10-31 | 0102.C-0121(A) | 234 | 12 | 0.6 | 8100
63 | Gu Psc b | 01:12:36.54 | 17:04:29.9 | 2018-11-14 | 0102.C-0121(A) | 234 | 12 | 0.6 | 8100
|  |  |  | 2018-11-25 | 0102.C-0121(A) | 234 | 12 | 0.6 | 8100
|  |  |  | 2018-11-26 | 0102.C-0121(A) | 234 | 12 | 0.6 | 8100

121212a Spectral resolutions as presented in the X-shooter’s Characteristics
Webpage
(https://www.eso.org/sci/facilities/paranal/instruments/xshooter/inst.html)
depending on wavelength and slit width.

Table 7: Spectral classification results.

ID | Name | Region | SpT Literature | Referencesa | SpT Templatesf | AV | Templates Set | SpT Indices
---|---|---|---|---|---|---|---|---
2 | UScoJ160606-233513 | USCO | M8.5$\pm$0.5 |  Luhman et al. (2018)e | M8.5$\pm$0.5 | 1.4 | Young | M9.5$\pm$0.5
3 | UScoJ160723-221102 | USCO | M8.5$\pm$0.5 | Luhman et al. (2018) | M7.0$\pm$0.5 | 1.4 | Young | M8.5$\pm$0.5
4 | UScoJ160737-224247 | USCO | M9.0$\pm$0.5 | Luhman et al. (2018) | M9.0$\pm$0.5 | 1.6 | Young | L0.5$\pm$0.5
5 | UScoJ160818-223225 | USCO | M9.25$\pm$0.5 | Luhman et al. (2018) | M9.5$\pm$0.5 | 0.0 | Young | L1.0$\pm$0.5
6 | UScoJ160828-231510 | USCO | M9.0$\pm$0.5 | Luhman et al. (2018) | M9.0$\pm$0.5 | 1.0 | Young | M9.0$\pm$0.5
7 | UScoJ161302-212428 | USCO | M9.5$\pm$0.5 | Luhman et al. (2018) | M9.0$\pm$0.5 | 1.8 | Young | L0.0$\pm$1.0
8 | UScoJ160918-222923 | USCO | L1.0$\pm$0.5 | Luhman et al. (2018) | L2.0$\pm$2.0 | 0.0 | Young | L2.0$\pm$0.5
9 | VISTAJ1559-2214 | USCO | M9.5$\pm$0.5 | Luhman et al. (2018) | M9.5$\pm$0.5 | 0.0 | Young | M9.5$\pm$1.0
10 | VISTAJ1614-2331 | USCO | M9.5$\pm$0.5 | Luhman et al. (2018) | M9.5$\pm$0.5 | 0.4 | Young | L1.5$\pm$1.0
11 | VISTAJ1611-2215 | USCO | L3.0$\pm$0.5 | Luhman et al. (2018) | L4.0${}^{+3}_{-2}$ | 0.6 | Young | M9.0$\pm$1.0
12 | VISTAJ1607-2146 | USCO | L1.0$\pm$0.5 | Luhman et al. (2018) | L0.0$\pm$2.0 | 1.6 | Young | L1.5$\pm$1.0
13 | VISTAJ1604-2241 | USCO | L1.0$\pm$0.5 | Luhman et al. (2018) | L2.0$\pm$2.0 | 1.0 | Young | M9.5$\pm$1.0
14 | VISTAJ1614-2211 | USCO | L1.0$\pm$0.5 | Luhman et al. (2018) | L0.0$\pm$2.0 | 1.4 | Young | M9.5$\pm$0.5
15 | VISTAJ1605-2403 | USCO | L1.0$\pm$0.5 | Luhman et al. (2018) | L2.0$\pm$2.0 | 0.4 | Young | L1.5$\pm$0.5
16 | VISTAJ1604-2134 | USCO | L6.0$\pm$1.0 | Lodieu et al. (2018) | L2.0$\pm$2.0 | 0.4 | Young | L1.0$\pm$0.5
17 | VISTAJ1601-2212 | USCO | L4.0$\pm$0.5 | Luhman et al. (2018) | L4.0${}^{+3}_{-2}$ | 1.6 | Young | L2.0$\pm$1.0
18 | VISTAJ1615-2229 | USCO | L4.0$\pm$0.5 | Luhman et al. (2018) | L4.0${}^{+3}_{-2}$ | 1.2 | Young | L3.0$\pm$1.0
19 | J0032-4405 | ABDMG | L0.0$\pm$1.0 |  Ujjwal et al. (2020); Allers & Liu (2013) | L0.0$\pm$2.0 |  | Young | L1.0$\pm$0.5
20 | PSO J318.5-22 | BPMG | L7.0$\pm$1.0 | Liu et al. (2013b) | L8.0$\pm$1.0 |  | Young | L4.0$\pm$3.0
21 | J2154-1055 | ARG | L5.0 $\beta$/$\gamma$ | Gagné et al. (2014b, 2015b) | L5.0$\pm$1.0 |  | Young | L4.5$\pm$3.0
23 | J0045+1634 | ARG | L2.0$\pm$1.0 | Gagné et al. (2014c); Allers & Liu (2013) | L1.0$\pm$1.0 |  | Young | L1.5$\pm$1.0
24 | J0518-2756 | COL | L1.0$\pm$1.0 | Gagné et al. (2014c); Allers & Liu (2013) | L1.0$\pm$1.0 |  | Young | L1.0$\pm$0.5
25 | 2MASS J03552337+1133437 | ABDMG | L3.0$\pm$1.0 | Liu et al. (2013a); Allers & Liu (2013) | L7.0$\pm$3.0 |  | Young | L2.5$\pm$1.0
26 | 2MASS J14252798-3650229 | ABDMG | L4.0 $\gamma$ | Gagné et al. (2015b) | L2.0$\pm$2.0 |  | Young | L4.0$\pm$0.5
27 | J0339-3525 | CAS | L0.0$\pm$1.0 |  Ribas (2003), Gagné et al. (2014c); Allers & Liu (2013) | M9.0$\pm$1.0 |  | Field | M9.5$\pm$0.5
28 | 2MASS J03264225-2102057 | ABDMG | L5.0$\beta\gamma$ | Faherty et al. (2016) | L4.0${}^{+3}_{-2}$ |  | Young | L5.0$\pm$3.5
29 | 2MASS J22064498-4217208 | ABDMG | L4.0 $\gamma$ | Faherty et al. (2016) | L2.0$\pm$2.0 |  | Young | L3.0$\pm$0.5
31 | J2322-6151 | THA | L3.0 $\gamma$ | Gagné et al. (2014c); Faherty et al. (2016) | L1.0$\pm$1.0 |  | Young | L2.5$\pm$0.5
32 | J0006-6436 | THA | M8.0 $\gamma$ | Gagné et al. (2014c, 2015b) | M9.0$\pm$0.5 |  | Young | L0.0$\pm$0.5
33 | J0037-5846 | THA | L0.0 $\gamma^{b}$ | Gagné et al. (2014c); Cruz et al. (2009) | L0.0$\pm$2.0 |  | Young | L1.0$\pm$1.0
34 | J0223-5815 | THA | L0.0 $\gamma^{b}$ | Gagné et al. (2014c); Cruz et al. (2009) | L1.0$\pm$1.0 |  | Young | L0.5$\pm$0.5
35 | J0323-4631 | THA | L0.0 $\gamma$ | Gagné et al. (2014c); Faherty et al. (2016) | L1.0$\pm$1.0 |  | Young | L0.5$\pm$0.5
36 | J0141-4633 | THA | L0.0$\pm$1.0 | Gagné et al. (2014c); Allers & Liu (2013) | L0.0$\pm$2.0 |  | Young | L1.5$\pm$1.0
37 | J0357-4417 | THA | L2.0$\pm$0.5 pecc | Gagné et al. (2014c); Marocco et al. (2013) | M9.5$\pm$0.5 |  | Young | L0.5$\pm$0.5
38 | J0117-3403 | THA | L1.0$\pm$1.0 | Gagné et al. (2014c); Allers & Liu (2013) | L0.0$\pm$2.0 |  | Young | L2.5$\pm$0.5
39 | J0241-0326 | THA | L1.0$\pm$1.0 | Gagné et al. (2014c); Allers & Liu (2013) | L0.0$\pm$2.0 |  | Young | L1.0$\pm$0.5
40 | J0004-6410 | THA | L1.0 $\gamma$ | Kirkpatrick et al. (2010); Faherty et al. (2016) | L2.0$\pm$2.0 |  | Young | L2.0$\pm$1.0
41 | 2MASS J01531463-6744181 | THA | L3.0 $\beta$ | Faherty et al. (2016) | L2.0$\pm$2.0 |  | Young | L3.5$\pm$0.5
42 | 2MASS J03421621-6817321 | THA | L4.0$\gamma^{b}$ | Gagné et al. (2014c, 2015b) | L4.0${}^{+3}_{-2}$ |  | Young | L3.0$\pm$1.0
46 | J1207-3900 | TWA | L1.0$\pm$1.0 | Gagné et al. (2014a) | M9.5$\pm$0.5 |  | Young | L1.0$\pm$0.5
47 | 2MASS J11193254-1137466 | TWA | L7.0 | Kellogg et al. (2015) | L7.0$\pm$3.0 |  | Young | L4.5$\pm$3.0
48 | 2MASS J114724.10-204021.3 | TWA | L7.0$\pm$1.0 | Schneider et al. (2016) | L7.0$\pm$3.0 |  | Young | L6.0$\pm$3.5
49 | WISE J052857.69+090104.2 | 32OR | L1.0 | Burgasser et al. (2016) | L0.0$\pm$2.0 |  | Young | L1.0$\pm$0.5
50 | SDSSp J111010.01+011613.1 | ABDMG | T5.5 | Gagné et al. (2015a); Burgasser et al. (2006a) | T5.0$\pm$1.0 |  | Field | T5.5$\pm$0.5
51 | SDSS J152103.24+013142.7 | ARG | T2.0$\pm$0.5 | Zhang et al. (2021); Knapp et al. (2004) | T3.0$\pm$1.0 |  | Field | T2.5$\pm$0.5
53 | PSO J168.1800-27.2264 | ARG | T2.5$\pm$0.5 | Zhang et al. (2021); Best et al. (2015) | T3.0$\pm$1.0 |  | Field | T3.0$\pm$0.5
56 | SIMP J013656.5+093347.3 | CARN | T2.5$\pm$0.5 | Gagné et al. (2017); Artigau et al. (2006) | T2.0$\pm$1.0 |  | Field | T2.0$\pm$0.5
57 | 2MASS J08370450+2016033 | PRA | L0.0 | Manjavacas et al. (2020) | L1.0$\pm$1.0 |  | Field | M9.5$\pm$0.5
58 | UGCS J084510.65+214817.0 | PRA | L1.5 | Manjavacas et al. (2020) | L1.0$\pm$1.0 |  | Field | L0.0$\pm$0.5
59 | 2MASS J03463425+2350036 | PLE | L1.0 | Manjavacas et al. (2020) | L1.0$\pm$1.0 |  | Field | L1.0$\pm$0.5
60 | 2MASS J03541027+2341402 | PLE | L3.0 | Manjavacas et al. (2020) | L2.0$\pm$1.0 |  | Field | L2.5$\pm$0.5
61 | 2MASS J00464841+0715177 | BPMG | L0.0 $\delta$ | Gagné et al. (2015b) | M9.5$\pm$0.5 |  | Young | L1.0$\pm$0.5
62 | 2MASS J05120636-2949540 | BPMGd | L5.0 $\beta$ | Gagné et al. (2015b) | L4.0${}^{+3}_{-2}$ |  | Young | L5.0$\pm$3.5
63 | Gu Psc b | ABDMG | T3.5$\pm$1.0 | Naud et al. (2014) | T3.0$\pm$1.0 |  | Field | T3.0$\pm$0.5

131313a The first reference is the membership (region) reference whilst the
second is the SpT reference. If there is only one reference it means that both
the region and SpT information were retrieved from that work. b Literature SpT
based on optical data. c Known unresolved binary, the SpT given is the
unresolved classification. d Uncertain membership. Object discussed in
Appendix C. e Combined spectral type, derived from a mixture of their own
classification (optical or NIR) and literature. f Final SpT classification
adopted throughout the analysis (see Sect. 4.1).

##  Appendix B X-shooter spectra

In Fig. 17 we show the remaining X-shooter spectra not present in the paper,
along with their best-fitted spectral template (see Sect. 4.1). All the
retrieved best-fits were accomplished with young templates (in red).

Figure 17: Remaining spectra of our sample along their best-fitted template in
red (see Sect. 4.1). For all of the objects presented here, the best-fit was
accomplished with a young template. The ID, young association, final SpT and
extinction derived (for objects in USCO) are shown above the correspondent
spectrum (in black). All spectra are normalized at 1.67 $\mu$m. An offset
between the spectra was added for clarity.

##  Appendix C Discussion on specific objects

In this section, we present a short discussion on the membership of some
specific objects. To do that, we use the Bayesian Analysis for Nearby Young
Associations (BANYAN) $\Sigma$, a tool that determines the membership
probability of an object belonging to a nearby young association (Gagné et al.
2018). It requests as mandatory inputs the coordinates (RA and DEC, in decimal
degrees), the proper motion (in mas/yr), and respective errors, both in right
ascension (RA) and declination (DEC). Optionally, the radial velocity (in
km/s) and parallax (in mas) of the objects, along with the associated errors,
can also be given. If such information is lacking, the membership probability
will still be computed and the algorithm will estimate the most likely
distance to the object and the radial velocity that it should have if it was a
member of a specific nearby young association.

###  C.1 Object #19 (J0032-4405)

As stated by Dupuy et al. (2018), object #19 has two parallax values in the
literature: the one from Faherty et al. (2012) which was considered in Gagné
et al. (2014c) and results in membership to BPMG, and the one from Faherty et
al. (2016) which leads to ABDMG.

In the color-absolute magnitude diagram (see Fig. 1), object #19 is in-between
both the young and the field sequences although it appears to be more in
agreement with the field sequence. When comparing with spectral templates, the
best fit was initially achieved with an L2 field template (see Sect. 4.1).
However, after visual inspection (see Fig. 2), we maintained the
classification obtained by the best young template (L0$\pm$2) since it
appeared to better reproduce the K-band. Nonetheless, we recognize that a
subtle ”shoulder” at $\sim$1.57$\mu$m is noticeable, which is typical of
intermediate-gravity objects (Allers & Liu 2013) and thus suggests a slightly
older age than some other objects of the sample. Moreover, in the TLI-g
diagram in Fig. 14 object #19 is clearly in agreement with the mid-gravity age
class of AA22 if we consider its SpT to be L0 (considering a young template)
but even more so if we consider its SpT to be L2 (first estimate obtained with
the best-fit being a field template in Sect. 4.1). Finally, its alkali lines
are broader than those of the age class $<$30 Myr which is where the objects
located in BPMG are included. Hence, all points towards a membership to ABDMG.

To re-analyze the nature of object #19, we implemented the BANYAN $\Sigma$
tool considering the parallax and proper motion values from Gaia DR3
($\pi=28.9542\pm 0.4217^{\prime\prime}$, $\mu_{\alpha}=127.841\pm 0.284$
mas/yr, $\mu_{\delta}=-96.832\pm 0.314$ mas/yr) and the radial velocity of
Faherty et al. (2016) ($r_{V}=12.95\pm 1.92$ km/s). The result corroborates a
membership to ABDMG ($\sim$150 Myr) with a probability of 99.4%, where the
remaining 0.6% suggest the field population. This result is in agreement with
previous works such as Ujjwal et al. (2020).

###  C.2 Object #62 (2MASS J05120636-2949540)

The derived SpT for object #62 was L4${}^{+3}_{-2}$, considering a young
template (see Sect. 4.1). Throughout this work, we considered that object #62
was a member of BPMG (age 24$\pm$2 Myr, Bell et al. 2015). However, it shows
high pEWs values for the alkali lines compared to the remaining objects within
the $<$30 Myr age class. Its values seem to be more in agreement with those of
the objects located in the age class 100$-$300 Myr. It is important to state
that this object’s spectrum has an artifact in the range of calculation of the
1243.7 nm K I line, therefore, it was not included in the panels corresponding
to this line in Figs. 15 and 16.

Regarding the gravity-sensitive indices, object #62 has not a trivial
behavior. In some indices, such as HPI, it has a value that is in agreement
with the mid-gravity class, towards the young sequence. On the other hand, its
TLI-g and CH4-K index values still agree better with the intermediate-gravity
age class but this time towards the overlapping region with the field objects
of AA22. This behavior might suggest that object #62 does not belong to BPMG,
which is among the youngest NYMGs in our sample.

We implemented the BANYAN $\Sigma$ tool considering: $\mu_{\alpha}=-5.0\pm
5.1$ mas/yr, $\mu_{\delta}=84.5\pm 6.6$ mas/yr, $r_{v}=19.8\pm 1.5$ km/s
(Gagné et al. 2015c), and $\pi=49.6\pm 2.8^{\prime\prime}$ (Best et al. 2021).
The algorithm presented a membership probability that completely favors the
field population. We conclude that object #62 might not be as young as members
of BPMG. But since it exhibits signs of youth (e.g, triangular H-band), it
does not seem to be as old as objects from the field population. Therefore,
its membership is uncertain; it may belong to an yet undefined young
association, or be an isolated object that was formed in a protoplanetary disk
and ejected early in its evolution.

##  Appendix D NIR spectral indices

In Table LABEL:tab_app:spec_indices we summarize the functional forms of all
the SpT indices inspected in Sect. 4.3 along with the respective references
and targeted spectral features. Some of these indices demonstrated a gravity-
sensitive behavior in a specific SpT range, but they were all defined in the
literature to be spectral indices that correlate well with SpT for a specific
range initially designated.

There are spectral indices in the literature that were, in fact, defined to be
gravity-sensitive, and the information regarding those is presented in Table
15.

Table 8: Spectral type indices inspected. Index | Reference | Formula | Feature Measured
---|---|---|---
H2O | (1) | $\frac{\langle F_{\lambda=1.550-1.560}\rangle}{\langle F_{\lambda=1.492-1.502}\rangle}$ |  $\sim$1.50-1.57 $\mu$m H2O absorption
TLI-K | (2) | $\frac{\langle F_{\lambda=1.97-1.99}\rangle}{\langle F_{\lambda=2.22-2.24}\rangle}$ |  $\sim$1.97 $\mu$m Ca lines
TLI-J | (2) | $\frac{\langle F_{\lambda=1.20-1.21}\rangle}{\langle F_{\lambda=1.27-1.29}\rangle}$ |  $\sim$1.2 $\mu$m FeH absorption band
sHJ | (3) | $\frac{\langle F_{\lambda=1.265-1.305}\rangle-\langle F_{\lambda=1.6-1.7}\rangle}{0.5(\langle_{\lambda=1.265-1.305}\rangle+\langle F_{\lambda=1.6-1.7}\rangle)}$ | continuum slope
sKJ | (3) | $\frac{\langle F_{\lambda=1.265-1.305}\rangle-\langle F_{\lambda=2.12-2.16}\rangle}{0.5(\langle F_{\lambda=1.265-1.305}\rangle+\langle F_{\lambda=2.12-2.16}\rangle)}$ | continuum slope
sH2OJ | (3) | $\frac{\langle F_{\lambda=1.265-1.305}\rangle-\langle F_{\lambda=1.09-1.13}\rangle}{0.5(\langle F_{\lambda=1.265-1.305}\rangle+\langle F_{\lambda=1.09-1.13}\rangle)}$ | 1.1 $\mu$m H2O absorption
sH2OH1 | (3) | $\frac{\langle F_{\lambda=1.6-1.7}\rangle-\langle F_{\lambda=1.45-1.48}\rangle}{0.5(\langle F_{\lambda=1.6-1.7}\rangle+\langle F_{\lambda=1.45-1.48}\rangle)}$ |  $\sim$1.40 $\mu$m H2O absorption
sH2OH2 | (3) | $\frac{\langle F_{\lambda=1.6-1.7}\rangle-\langle F_{\lambda=1.77-1.81}\rangle}{0.5(\langle F_{\lambda=1.6-1.7}\rangle+\langle F_{\lambda=1.77-1.81}\rangle)}$ |  $\sim$1.85 $\mu$m H2O absorption
sH2OK | (3) | $\frac{\langle F_{\lambda=2.12-2.16}\rangle-\langle F_{\lambda=1.96-1.99}\rangle}{0.5(\langle F_{\lambda=2.21-2.16}\rangle+\langle F_{\lambda=1.96-1.99}\rangle)}$ |  $\sim$2.4 $\mu$m H2O absorption
H2O-1.2 | (4) | $\frac{\langle F_{\lambda=1.26-1.29}\rangle}{\langle F_{\lambda=1.13-1.16}\rangle}$ |  $\sim$1.15 $\mu$m H2O absorption
H2O-1.5 | (4) | $\frac{\langle F_{\lambda=1.57-1.59}\rangle}{\langle F_{\lambda=1.46-1.48}\rangle}$ |  $\sim$1.4 $\mu$m H2O absorption
H2O-2.0 | (4) | $\frac{\langle F_{\lambda=2.09-2.11}\rangle}{\langle F_{\lambda=1.975-1.995}\rangle}$ |  $\sim$2.0 $\mu$m H2O absorption
CH4-1.6 | (4) | $\frac{\langle F_{\lambda=1.56-1.60}\rangle}{\langle F_{\lambda=1.635-1.675}\rangle}$ |  $\sim$1.6 $\mu$m CH4 absorption
CH4-2.2 | (4) | $\frac{\langle F_{\lambda=2.08-2.12}\rangle}{\langle F_{\lambda=2.215-2.255}\rangle}$ |  $\sim$2.2 $\mu$m CH4 absorption
J-FeH | (5) | $\frac{\langle F_{\lambda=1.195-1.205}\rangle}{\langle F_{\lambda=1.18-1.19}\rangle}$ | 1.2 $\mu$m FeH absorption
H2OA | (5) | $\frac{\langle F_{\lambda=1.338-1.348}\rangle}{\langle F_{\lambda=1.308-1.318}\rangle}$ |  $\sim$1.343 $\mu$m H2O absorption
H2OB | (5) | $\frac{\langle F_{\lambda=1.451-1.461}\rangle}{\langle F_{\lambda=1.565-1.575}\rangle}$ |  $\sim$1.456 $\mu$m H2O absorption
H2OC | (5) | $\frac{\langle F_{\lambda=1.783-1.793}\rangle}{\langle F_{\lambda=1.717-1.727}\rangle}$ |  $\sim$1.788 $\mu$m H2O absorption
H2OD | (5) | $\frac{\langle F_{\lambda=1.951-1.977}\rangle}{\langle F_{\lambda=2.062-2.088}\rangle}$ |  $\sim$1.964 $\mu$m H2O absorption
CH4A | (5) | $\frac{\langle F_{\lambda=1.725-1.735}\rangle}{\langle F_{\lambda=1.585-1.595}\rangle}$ |  $\sim$1.730 $\mu$m CH4 absorption
CH4B | (5) | $\frac{\langle F_{\lambda=2.195-2.205}\rangle}{\langle F_{\lambda=2.095-2.105}\rangle}$ |  $\sim$2.2 $\mu$m CH4 absorption
CO | (5) | $\frac{\langle F_{\lambda=2.295-2.305}\rangle}{\langle F_{\lambda=2.280-2.290}\rangle}$ |  $\sim$2.295 $\mu$m CO band
H2O-1 | (6) | $\frac{\langle F_{\lambda=1.335-1.345}\rangle}{\langle F_{\lambda=1.295-1.305}\rangle}$ |  $\sim$1.34 $\mu$m H2O absorption
H2O-2 | (6) | $\frac{\langle F_{\lambda=2.035-2.045}\rangle}{\langle F_{\lambda=2.145-2.155}\rangle}$ |  $\sim$2.0 $\mu$m H2O absorption
FeH | (6) | $\frac{\langle F_{\lambda=1.1935-1.2065}\rangle}{\langle F_{\lambda=1.2235-1.2365}\rangle}$ | 1.2 $\mu$m FeH absorption
H2O-K2 | (7) | $\frac{\langle F_{\lambda=2.07-2.09}\rangle/\langle F_{\lambda=2.235-2.255}\rangle}{\langle F_{\lambda=2.235-2.255}\rangle/\langle F_{\lambda=2.36-2.38}\rangle}$ |  $\sim$2.07-2.38 $\mu$m H2O absorption
H2O-H | (8) | $\frac{\langle F_{\lambda=1.595-1615}\rangle/\langle F_{\lambda=1.68-1.7}\rangle}{\langle F_{\lambda=1.68-1.7}\rangle/\langle F_{\lambda=1.76-1.78}\rangle}$ | H-band H2O absorption
H2O-K | (8) | $\frac{\langle F_{\lambda=2.18-2.2}\rangle/\langle F_{\lambda=2.27-2.29}\rangle}{\langle F_{\lambda=2.27-2.29}\rangle/\langle F_{\lambda=2.36-2.38}\rangle}$ | K-band H2O absorption
Q | (9) | $\frac{\langle F_{\lambda=2.07-2.13}\rangle}{\langle F_{\lambda=2.267-2.285}\rangle}\left[\frac{\langle F_{\lambda=2.4-2.5}\rangle}{\langle F_{\lambda=2.267-2.285}\rangle}\right]^{1.22}$ | 1.7-2.1 $\mu$m and $>$2.4 $\mu$m H2O absorption
WH | (10) | $\frac{\langle F_{\lambda=1.552-1.572}\rangle}{\langle F_{\lambda=1.655-1.675}\rangle}$ | H2O absorption
WK | (10) | $\frac{\langle F_{\lambda=2.04-2.06}\rangle}{\langle F_{\lambda=2.18-2.2}\rangle}$ | H2O absorption
QH | (10) | $\frac{\langle F_{\lambda=1.552-1.572}\rangle}{\langle F_{\lambda=1.655-1.675}\rangle}\left[\frac{\langle F_{\lambda=1.73-1.75}\rangle}{\langle F_{\lambda=1.655-1.675}\rangle}\right]^{1.581}$ | H2O absorption
QK | (10) | $\frac{\langle F_{\lambda=2.04-2.06}\rangle}{\langle F_{\lambda=2.182-2.202}\rangle}\left[\frac{\langle F_{\lambda=2.33-2.35}\rangle}{\langle F_{\lambda=2.182-2.202}\rangle}\right]^{1.14}$ | H2O absorption
$\omega_{0}$ | (11) | $\left(\frac{W_{H2O}}{-0.0105}^{*}-\frac{W_{H2O-1}}{-0.0102}^{*}\right)\left(\frac{1}{-0.0105}+\frac{1}{-0.0102}\right)^{-1}$ |  $\sim$1.50-1.57 $\mu$m H2O absorption
$\omega_{D}$ | (11) | $\left(\frac{W_{H2OD}}{0.0099}^{*}-\frac{W_{H2O-1}}{-0.0102}\right)\left(\frac{1}{0.0099}+\frac{1}{-0.0102}\right)^{-1}$ |  $\sim$1.964 $\mu$m H2O absorption
$\omega_{2}$ | (11) | $\left(\frac{W_{H2O-2}}{0.0098}^{*}-\frac{W_{H2O-1}}{-0.0102}\right)\left(\frac{1}{0.0098}+\frac{1}{-0.0102}\right)^{-1}$ |  $\sim$2.0 $\mu$m H2O absorption
K1 | (12) | $\frac{\langle F_{\lambda=2.10-2.18}\rangle-\langle F_{\lambda=1.96-2.04}\rangle}{0.5(\langle F_{\lambda=2.10-2.18}\rangle+\langle F_{\lambda=1.96-2.04}\rangle)}$ | 2.0 to 2.14 $\mu$m H2O absorption
K2 | (12) | $\frac{\langle F_{\lambda=2.20-2.28}\rangle-\langle F_{\lambda=2.10-2.18}\rangle}{0.5(\langle F_{\lambda=2.20-2.28}\rangle+\langle F_{\lambda=2.10-2.18}\rangle)}$ | 2.14 to 2.24 $\mu$m H2 absorption
H2O-A | (13) | $\frac{\langle F_{1.12-1.17}\rangle}{\langle F_{1.25-1.28}\rangle}$ | 1.15 $\mu$m H2O/CH4
H2O-B | (13) | $\frac{{\langle}F_{1.505-1.525}{\rangle}}{{\langle}F_{1.575-1.595}{\rangle}}$ | 1.4 $\mu$m H2O
H2O-C | (13) | $\frac{{\langle}F_{2.00-2.04}{\rangle}}{{\langle}F_{2.09-2.13}{\rangle}}$ | 1.9 $\mu$m H2O
CH4-A | (13) | $\frac{{\langle}F_{1.295-1.325}{\rangle}}{{\langle}F_{1.25-1.28}{\rangle}}$ | 1.3 $\mu$m CH4
CH4-B | (13) | $\frac{{\langle}F_{1.64-1.70}{\rangle}}{{\langle}F_{1.575-1.595}{\rangle}}$ | 1.6 $\mu$m CH4
CH4-C | (13) | $\frac{{\langle}F_{2.225-2.275}{\rangle}}{{\langle}F_{2.09-2.13}{\rangle}}$ | 2.2 $\mu$m CH4
H/J | (13) | $\frac{{\langle}F_{1.50-1.75}{\rangle}}{{\langle}F_{1.20-1.325}{\rangle}}$ | NIR color
K/H | (13) | $\frac{{\langle}F_{2.00-2.30}{\rangle}}{{\langle}F_{1.50-1.75}{\rangle}}$ | NIR color
CO | (13) | $\frac{{\langle}F_{2.325-2.375}{\rangle}}{{\langle}F_{2.09-2.13}{\rangle}}$ | 2.3 $\mu$m CO
2.11/2.07 | (13) | $\frac{{\langle}F_{2.10-2.12}{\rangle}}{{\langle}F_{2.06-2.08}{\rangle}}$ | K-band shape/CIA H2
K shape | (13) | $\frac{\langle F_{2.12-2.13}\rangle-\langle F_{2.15-2.16}\rangle}{\langle F_{2.17-2.18}\rangle-\langle F_{2.19-2.20}\rangle}$ | K-band shape/CIA H2
H2O-J | (14) | $\frac{{\langle}F_{1.14-1.165}{\rangle}}{{\langle}F_{1.26-1.285}{\rangle}}$ | 1.15 $\mu$m H2O
H2O-H | (14) | $\frac{{\langle}F_{1.48-1.52}{\rangle}}{{\langle}F_{1.56-1.60}{\rangle}}$ | 1.40 $\mu$m H2O
H2O-K | (14) | $\frac{{\langle}F_{1.975-1.995}{\rangle}}{{\langle}F_{2.08-2.10}{\rangle}}$ | 1.90 $\mu$m H2O
CH4-J | (14) | $\frac{{\langle}F_{1.315-1.34}{\rangle}}{{\langle}F_{1.26-1.285}{\rangle}}$ | 1.32 $\mu$m CH4
CH4-H | (14) | $\frac{{\langle}F_{1.635-1.675}{\rangle}}{{\langle}F_{1.56-1.60}{\rangle}}$ | 1.65 $\mu$m CH4
CH4-K | (14) | $\frac{{\langle}F_{2.215-2.255}{\rangle}}{{\langle}F_{2.08-2.12}{\rangle}}$ | 2.20 $\mu$m CH4
K/J | (14) | $\frac{{\langle}F_{2.060-2.10}{\rangle}}{{\langle}F_{1.25-1.29}{\rangle}}$ | J$-$K colour
H-dip | (15) | $\frac{{\langle}F_{1.61-1.64}{\rangle}}{{\langle}F_{1.56-1.59}{\rangle}+{\langle}F_{1.66-1.69}{\rangle}}$ | 1.65$\mu$m CH4
Table 8: continued.

141414(1) Allers et al. (2007); (2) Almendros-Abad et al. (2022); (3) Testi et
al. (2001); (4) Geballe et al. (2002); (5) McLean et al. (2003); (6) Slesnick
et al. (2004); (7) Rojas-Ayala et al. (2012); (8) Covey et al. (2010); (9)
Cushing et al. (2000); (10) Weights et al. (2009); (11) Zhang et al. (2018);
(12) Tokunaga & Kobayashi (1999); (13) Burgasser et al. (2002); (14) Burgasser
et al. (2006a); (15) Burgasser et al. (2010). * $W_{index}=-2.5\log{(index)}$,
where index are the H2O (Allers et al. 2007), H2O-D (McLean et al. 2003),
H2O-2 and H2O-1 (Slesnick et al. 2004) spectral indices.

Table 9: Gravity-sensitive spectral indices inspected.

Index | Reference | Formula | Feature Measured
---|---|---|---
FeHJ | (1) | $\left(\frac{\lambda_{1.200}-\lambda_{1.192}}{\lambda_{1.208}-\lambda_{1.192}}F_{1.208}+\frac{\lambda_{1.208}-\lambda_{1.200}}{\lambda_{1.208}-\lambda_{1.192}}F_{1.192}\right)/F_{1.200}$ | 1.2 $\mu$m FeH absorption
KIJ | (1) | $\left(\frac{\lambda_{1.244}-\lambda_{1.220}}{\lambda_{1.270}-\lambda_{1.220}}F_{1.270}+\frac{\lambda_{1.270}-\lambda_{1.244}}{\lambda_{1.270}-\lambda_{1.220}}F_{1.220}\right)/F_{1.244}$ | 1.244, 1.253$\mu$m KI doublet
H-cont | (1) | $\left(\frac{\lambda_{1.560}-\lambda_{1.470}}{\lambda_{1.670}-\lambda_{1.470}}F_{1.670}+\frac{\lambda_{1.670}-\lambda_{1.560}}{\lambda_{1.670}-\lambda_{1.470}}F_{1.470}\right)/F_{1.560}$ | H-band shape
VOz | (1) | $\left(\frac{\lambda_{1.058}-\lambda_{1.035}}{\lambda_{1.087}-\lambda_{1.035}}F_{1.087}+\frac{\lambda_{1.087}-\lambda_{1.058}}{\lambda_{1.087}-\lambda_{1.035}}F_{1.035}\right)/F_{1.058}$ | 1.06 $\mu$m VO absorption
TLI-g | (2) | $\frac{\langle F_{\lambda=1.56-1.58}\rangle}{\langle F_{\lambda=1.625-1.635}\rangle}$ | 1.5-1.565 $\mu$m H2O absorption
H2(K) | (3) | $\frac{\langle F_{\lambda=2.16-2.18}\rangle}{\langle F_{\lambda=2.23-2.25}\rangle}$ | K-band peak
HPI | (4) | $\frac{\langle F_{\lambda=1.675-1.685}\rangle}{\langle F_{\lambda=1.495-1.505}\rangle}$ | H-band peak for young objects
151515(1) Allers & Liu (2013); (2) Almendros-Abad et al. (2022); (3) Canty et
al. (2013); (4) Scholz et al. (2012)