# Ultracool Dwarfs Observed with the Spitzer Infrared Spectrograph - III. Dust
Grains in Young L Dwarf Atmospheres Are Heavier

Genaro Suárez,1,2 Stanimir Metchev,2,3
1Department of Astrophysics, American Museum of Natural History, Central Park
West at 79th St, New York, NY, 10024, USA
2Department of Physics and Astronomy, The University of Western Ontario, 1151
Richmond St, London, Ontario, N6A 3K7, Canada
3Institute for Earth and Space Exploration, The University of Western Ontario,
1151 Richmond St, London, Ontario, N6A 3K7, Canada
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Analysis of all archival 5–14 micron spectra of field ultracool dwarfs from
the Infrared Spectrograph on the Spitzer Space Telescope has shown that
absorption by silicates in the 8–11 micron region is seen in most L-type (1300
K to 2200 K) dwarfs. The absorption is caused by silicate-rich clouds in the
atmospheres of L dwarfs and is strongest at L4–L6 spectral types. Herein we
compare averages of the mid-infrared silicate absorption signatures of L3–L7
dwarfs that have low ($\lesssim$104.5 cm s-2) vs. high ($\gtrsim$105 cm s-2)
surface gravity. We find that the silicate absorption feature is sensitive to
surface gravity and indicates a difference in grain size and composition
between dust condensates in young and old mid-L dwarfs. The mean silicate
absorption profile of low-gravity mid-L dwarfs matches expectations for
$\sim$1 micron-sized amorphous iron- and magnesium-bearing pyroxene
(MgxFe1-xSiO3) grains. High-gravity mid-L dwarfs have silicate absorption
better represented by smaller ($\lesssim$0.1 $\mu$m) and more volatile
amorphous enstatite (MgSiO3) or SiO grains. This is the first direct
spectroscopic evidence for gravity-dependent sedimentation of dust condensates
in ultracool atmospheres. It confirms theoretical expectations for lower
sedimentation efficiencies in low-gravity atmospheres and independently
confirms their increased dustiness.

###### keywords:

brown dwarfs — stars: atmospheres — infrared: stars

††pubyear: 2015††pagerange: Ultracool Dwarfs Observed with the Spitzer
Infrared Spectrograph - III. Dust Grains in Young L Dwarf Atmospheres Are
Heavier–Ultracool Dwarfs Observed with the Spitzer Infrared Spectrograph -
III. Dust Grains in Young L Dwarf Atmospheres Are Heavier

orangergb0.98, 0.6, 0.01

##  1 Introduction

The atmospheres of L spectral type dwarfs have effective temperatures between
approximately 1300–2200 K (Kirkpatrick, 2005; Filippazzo et al., 2015). It is
observationally established, based both on their very red optical to near-
infrared colours (Knapp et al., 2004; Kirkpatrick, 2005) and on the direct
detection of silicates in mid-infrared spectra (Roellig et al., 2004; Cushing
et al., 2006; Looper et al., 2008; Suárez & Metchev, 2022), that these
atmospheres are dusty. Theoretically, silicon-bearing molecules such as quartz
(SiO2), pyroxene (MgxFe1-xSiO3), and olivine (MgxFe2-xSiO4), including the Mg-
rich endmembers enstatite (MgSiO3) and forsterite (Mg2SiO4), are expected to
start forming 0.1–1 $\mu$m-sized silicate dust condensates at $\leq$2000 K
(Burrows et al., 1997; Burrows et al., 2001; Ackerman & Marley, 2001; Lodders,
2002). The theory dictates that the silicate condensate clouds sediment to
deeper levels as the L-type substellar atmosphere cools, and at $\lesssim$1300
K effective temperatures the clouds drop below the altitude of the $\sim$0.1
bar pressure level of the mid-infrared photosphere (Luna & Morley, 2021). The
onset of dust cloud formation at warm temperatures and their later
sedimentation at cooler temperatures have been observationally confirmed from
5–14 $\mu$m mid-infrared spectra of L dwarfs (Suárez & Metchev, 2022).

In addition to being dependent on temperature, dust sedimentation in the
atmosphere is also a function of surface gravity. Cloud settling is less
efficient at lower gravity, which should lead to increased cloud vertical
depth and optically thicker cloud decks (Stephens et al., 2009; Madhusudhan et
al., 2011; Marley et al., 2012; Charnay et al., 2018). Indeed, unusually red
optical/near-infrared colours are a well-known trait of young L dwarfs (e.g.,
Kirkpatrick et al. 2006, 2008; Looper et al. 2008; Faherty et al. 2016), which
have lower surface gravity because of their larger radii at their earlier
evolutionary stages (e.g., Burrows et al. 1997). Indirect evidence of the
greater importance of dust in younger L-type atmospheres also comes from their
enhanced brightness variations (Metchev et al., 2015; Biller et al., 2015; Vos
et al., 2018; Vos et al., 2019; Bowler et al., 2020), understood to be caused
by the rotationally modulated visibility of large dust cloud features
(Burgasser et al., 2002; Artigau et al., 2009).

The role of gravity in sedimentation also dictates that heavier dust grains,
made of potentially more refractory compounds, should sediment first, leaving
lighter grains at higher altitudes (Ackerman & Marley, 2001; Cooper et al.,
2003). However, this has yet to be observationally demonstrated, and is the
main finding of the present study.

The physical properties and mineral composition of silicate dust in brown
dwarf atmospheres remain relatively unexplored. They require a population
analysis of high signal-to-noise ratio (SNR) mid-infrared spectra of these
objects that awaits observations with the James Webb Space Telescope (JWST).
To date, only a limited sample has been analysed based on low-resolution
spectra with the Spitzer Space Telescope Infrared Spectrograph (IRS; Houck et
al. 2004), and only during Spitzer’s 2003–2009 Cryogenic Mission. Namely,
theoretical modelling to match six moderate- to high-SNR L dwarf Spitzer IRS
spectra (Roellig et al., 2004; Cushing et al., 2006; Looper et al., 2008) has
shown that dust clouds in L dwarfs comprise a combination of amorphous
silicates (quartz, enstatite, and forsterite) and iron condensed in
$\lesssim$1 $\mu$m-sized grains (Cushing et al., 2006; Burningham et al.,
2021; Luna & Morley, 2021). For over a decade, this small sample of L dwarf
spectra has been the only source to probe cloud chemistry directly. Recently,
silicate absorption was also detected in the atmosphere of the late-L
planetary-mass companion VHS J125601.92$-$125723.9 b using JWST Mid-Infrared
Instrument (MIRI) spectra (Miles et al., 2022) and forsterite clouds have been
inferred in the IRS spectra of two young ($\sim 200$ Myr) early-T dwarf
atmospheres (Vos et al., 2022a).

The study of Suárez & Metchev (2022) re-assessed all 113 Spitzer IRS
observations of $\geq$M5 ($T_{\rm eff}\leq 3000$ K) dwarfs outside of known
$\lesssim$10 Myr-old star-forming regions. A comparative analysis of the 69 L
dwarf spectra in the sample established many more instances of spectroscopic
silicate cloud detections beyond the six known prior. The study revealed that
silicate clouds first form, then thicken, and sediment out of the visible
atmosphere as the effective temperature decreases from $\approx$2000 K to
$\approx$1300 K. While the Suárez & Metchev (2022) analysis focused mostly on
$\gtrsim$500 Myr-old field dwarfs outside of known star-forming regions, it
also included four L3–L6.5-type dwarfs with spectroscopic and kinematic
evidence of youth (few tens of Myr). This sample of relatively young objects,
complemented with old counterparts, allows an investigation of the surface
gravity (or age) dependence of silicate absorption in ultracool atmospheres.

Herein we compare the silicate absorption in the mid-infrared Spitzer IRS
spectra of young, low-surface gravity mid-L dwarfs ($\log g\lesssim 4.5$; 1800
K $\gtrsim T_{\rm eff}\gtrsim$ 1200 K) to their older, higher-gravity ($\log
g{\gtrsim}5.0$) counterparts in the Spitzer IRS sample. Our analysis confirms
the theoretical expectations of gravity-dependent sedimentation of dust clouds
from Ackerman & Marley (2001); Cooper et al. (2003). Specifically, we find
that heavier dust grains have higher abundances in lower-gravity L-type
atmospheres than they do at higher surface gravity. In Section 2 we describe
the sample and the approach followed to compare silicate absorption profiles
in young and old ultracool atmospheres. An investigation of how the silicate
absorption depends on surface gravity is presented in Section 3. In Section 4
we compare observed silicate absorption profiles to theoretical expectations.
We summarise our conclusions in Section 5.

##  2 Sample and Methods

To assess the surface gravity dependence of the silicate absorption feature we
define sub-samples of young and old mid-L dwarfs with the strongest silicate
features. We then use a separate sub-sample of mid-L dwarfs with no
discernible silicate features to estimate the continuum for the silicate-rich
spectra. Table 1 lists the L3–L7 dwarfs in each sub-sample and their relevant
properties.

###  2.1 Selection of Mid-L Dwarfs with Silicate-rich and Silicate-poor
Spectra

To measure silicate absorption strengths we iterated on Suárez & Metchev
(2022), and defined a silicate index as the ratio of an interpolated continuum
to the median flux at 9.3 $\mu$m in a 0.6 $\mu$m-wide window. The interpolated
continuum was calculated as the best $\log F_{\nu}$ vs. $\log\lambda$ linear
fit to the fluxes in two regions that frame the silicate feature and are
mostly free of other molecular absorption: 7.2–7.7 $\mu$m and 13.0–14.0 $\mu$m
(Figure 1). We changed the central wavelength of the silicate absorption index
(to 9.3 $\mu$m from 9.0 $\mu$m) compared to Suárez & Metchev (2022) to better
match theoretical expectations from Luna & Morley (2021). The long-wavelength
continuum region was further moved to 13.0–14.0 $\mu$m vs. 11.2–11.8 $\mu$m to
exclude as much as possible of the red wing of the silicate feature for both
young and old dwarfs (Figure 1).

Figure 1: Silicate index measurements for the low-surface gravity ($\log
g=4.45\pm 0.21$; Filippazzo et al. 2015) L5$\gamma$ dwarf 2MASS
J03552337+1133437 (top spectrum) and the high-surface gravity ($\log g=5.13\pm
0.28$; Filippazzo et al. 2015) L6 dwarf 2MASS J21481628+4003593 (bottom
spectrum). The silicate index is defined as the ratio of the interpolated
continuum (black point; $C_{9.3}$) to the median flux (red point; $F_{9.3}$)
at 9.3 $\mu$m in a 0.6 $\mu$m-wide window (brown points in the central dark
grey vertical region). The interpolated continuum (black dashed curve with
uncertainties shown by the grey shaded region) is obtained as a linear $\log
F_{\nu}$ vs. $\log\lambda$ fit to the fluxes in the 7.2–7.7 $\mu$m and 13–14
$\mu$m continuum regions (grey points in the outer light grey vertical
regions). The $C_{9.3}/F_{9.3}$ silicate index is indicated in the legend.

(a)

(b)

Figure 2: (a): Silicate index as a function of spectral type for all 113 M5–T9
dwarfs with IRS spectra (black points) in Suárez & Metchev (2022). The black
dashed curve corresponds to the median silicate index in bins of two spectral
subtypes. The vertical red dashed lines delimit the L3–L7 spectral type range
(slightly shifted for clarity) within which we analyse young objects with
silicate-rich spectra (red circles), old objects with silicate-rich spectra
(blue squares), and objects with silicate-poor spectra (green diamonds). (b):
Silicate index excess ($\Delta$Si), defined as the difference between the
measured and the median (black dashed line) silicate index for each object
(Section 2.1). $\Delta{\rm Si}>0.10$ (above the black dash-dotted line) and
$\Delta{\rm Si}<-0.10$ (below the black dotted line) were used to select
silicate-rich and silicate-poor spectra. The rest of the symbols are the same
as in (a).

Figure 2a shows the updated silicate index measurements as a function of
spectral type for the M5–T8 dwarfs in Suárez & Metchev (2022). We adopt
optical spectral types for M and L dwarfs and infrared types for T dwarfs. The
dashed line traces the median silicate index value in two spectral subtype-
wide bins. As observed in Suárez & Metchev (2022), the L dwarfs show a
systematic excess in silicate index values above a declining trend from late-M
to T dwarfs. This indicates near-ubiquitous 8–11 $\mu$m silicate absorption in
L dwarfs. The updated definition of the silicate index with a redder central
wavelength and a wider continuum span compared to Suárez & Metchev (2022)
shows that silicate absorption is already detectable in the average L1 dwarf,
slightly earlier than the L2 onset noted in Suárez & Metchev (2022).

We define a silicate index excess ($\Delta$Si) for each ultracool dwarf as the
difference between its measured silicate index and the median index for its
spectral type (black dashed curve in Figure 2a). Figure 2b shows the silicate
excess as a function of spectral type for the full sample in Suárez & Metchev
(2022). We constrain our analysis to L3–L7 dwarfs, as they have the strongest
absorption on average, and their 8–11 $\mu$m silicate absorption is not
contaminated by the 7–9 $\mu$m methane absorption that sets in at spectral
type L8 (Suárez & Metchev, 2022). From all L3–L7 dwarfs, we select those with
$\Delta{\rm Si}>0.10$ and for which $\Delta{\rm Si}$ is positive by more than
twice its uncertainty (i.e., SNR ($\Delta{\rm Si})>2$) as mid-L dwarfs with
silicate-rich spectra. This selection includes three of the five mid-L dwarfs
previously known or suspected to have silicate absorption: 2MASS
J18212815+1414010 (L4.5), 2MASS J21481633+4003594 (L6), and 2MASS
J22244381$-$0158521 (L4.5; Cushing et al., 2006; Looper et al., 2008). The
remaining two—2MASS J00361617+1821104 (L3.5) and 2MASS J15074769$-$1627386
(L5; Cushing et al., 2006)—have silicate indices closer to the median silicate
index for their spectral subtypes. That is, they still likely have silicate
absorption, but it does not stand out in strength compared to other L dwarfs
of similar spectral types. (The sixth L dwarf with previously reported
silicate absorption is 2MASS J02550357$-$4700509 (L8; Roellig et al., 2004),
which is outside of the L3–L7 spectral type range considered here.)

We select seven objects in the L3–L7 range with the most negative silicate
excess as a sub-sample representative of mid-L dwarfs with silicate-poor
spectra. Mirroring the selection of silicate-rich spectra, we select these to
have $\Delta{\rm Si}<-0.10$ and a $\Delta{\rm Si}$ value that is negative by
more than twice its uncertainty. It is highly likely that the atmospheres of
the mid-L dwarfs with silicate-poor spectra are still abundant in silicates.
However, the silicate condensates may have mostly settled to a layer below the
visible 8–11 $\mu$m photosphere. Hence, their spectra are representative of
the expected mid-infrared continuum and absorption by other non-silicate
species, such as water and methane.

###  2.2 Assignment of Surface Gravity

We use spectral features known to be associated with gravity, corroborated
with kinematic association, or lack thereof, to known young stellar moving
groups to assign mid-L dwarfs into categories of low- versus high-surface
gravity. We disfavour surface gravity determinations from photospheric model
fits to the low-resolution Spitzer IRS spectra themselves, or to broad
spectral energy distributions (SEDs) that are not constrained by age. Gravity
determinations from Spitzer IRS spectra do not conform well with results from
near-infrared spectra that contain pressure-sensitive lines or features (e.g.,
Suárez et al., 2021). Broad SEDs are excellent for bolometric luminosity
estimates, but are poor for determining surface gravities (Cushing et al.,
2008). They benefit from an evolutionary model-dependent radius or mass
estimate for improved effective temperature and surface gravity determination
(e.g., Cushing et al., 2008; Filippazzo et al., 2015).

There are four L3–L6.5 dwarfs among the 13 silicate-rich spectra with a
$\gamma$ spectroscopic designation indicative of low surface gravity and hence
youth. We extract these as a sub-sample of young silicate-rich mid-L spectra.
The remaining nine (L4–L6.5) dwarfs with silicate-rich spectra have no
previously published spectroscopic indications of youth. We assign these to
the sub-sample of old silicate-rich mid-L spectra. We verify the age
classification of our mid-L dwarfs with silicate-rich spectra by checking
whether any of them may be kinematically associated with known nearby young
stellar moving groups. Three of the $\gamma$-classified objects (2MASS
J03552337+1133437, 2MASS J14252798$-$3650229, and 2MASS J22443167+2043433) are
bona fide members of the 110–150 Myr-old (Luhman et al., 2005; Barenfeld et
al., 2013) AB Doradus moving group (Liu et al., 2013; Gagné et al., 2015; Vos
et al., 2018) and 2MASS J05012406$-$0010452 is a possible member of the
Columba or Carina moving groups (Gagné et al., 2015), which are coeval at
20–40 Myr (Torres et al., 2008). Conversely, the BANYAN $\Sigma$ algorithm
(Gagné et al., 2018) tool indicates that seven of the nine old silicate-rich
mid-L dwarfs have a $>$96% probability of being field objects. Only 2MASS
J17534518$-$6559559 (L4) and 2MASS J09201223+3517429 (L6.5) have 85% and 14%
probabilities of membership in the 40–50 Myr-old (Zuckerman, 2019) Argus and
110–150 Myr AB Doradus moving groups, respectively. However, kinematic
association with a young stellar moving group is not a sufficient indicator of
youth. Because of the lack of spectroscopic confirmation of low surface
gravity, we keep these two objects in our sample of old mid-Ls. Their IRS
spectra have low-SNR ($\approx$10 at 9 $\mu$m), and so do not significantly
contribute to our representation of old silicate-rich mid-L dwarfs (Section
2.4).

The above division in low vs. high surface gravity sub-samples is mostly
consistent with surface gravity determinations for the individual objects in
the published literature. The four young dwarfs all have $\log g\lesssim 4.5$
($g\lesssim 10^{4.5}$ cm s-2) from combined constraints on their bolometric
luminosities from trigonometric parallaxes and (photospheric model fits to)
SEDs, and on the ages for the respective parent associations (Filippazzo et
al., 2015; Gagné et al., 2015; Vos et al., 2018). The old dwarfs with gravity
estimates all have $\log g\gtrsim 5.0$ ($g\gtrsim 10^{5.0}$ cm s-2) (Cushing
et al., 2008; Gagné et al., 2015; Filippazzo et al., 2015; Dupuy & Liu, 2017;
Luna & Morley, 2021; Burningham et al., 2021). Some studies point to higher
$\log g$ values for two of the four young dwarfs (2MASS J22443167+2043433 in
Stephens et al. 2009; 2MASS J14252798$-$3650229 in Gagné et al. 2015), or to a
lower $\log g$ for one of the old dwarfs (2MASS J22244381$-$0158521; Cushing
et al., 2008; Stephens et al., 2009). All of the discrepant gravities were
obtained by fitting atmospheric models to broad SEDs without an age
constraint, and so are potentially less accurate. For instance, while Gagné et
al. (2015) find a field-like $\log g=5.0\pm 0.5$ for 2MASS J14252798$-$3650229
from an age-unconstrained photospheric model to the SED, they also note that
this object is a young $\gamma$-class L4 dwarf from analysis of narrower
spectral regions sensitive to surface gravity. Similarly, Cushing et al.
(2008) and Stephens et al. (2009) find a relatively low $\log g=4.5\pm 0.5$
from age-unconstrained photospheric model fits to the SED of 2MASS
J22244381$-$0158521\. However, when combined with an evolutionary model
appropriate for its otherwise field-age kinematics, the photospheric fit to
the SED results in a higher surface gravity ($\log g\geq 5.2$; Cushing et al.,
2008; Filippazzo et al., 2015).

Figure 2 highlights the selected sub-samples of mid-L dwarfs from Table 1
according to their silicate strength and surface gravity.

(a)

(b)

Figure 3: (a): Normalised comparison of four young silicate-rich (brown
curves), seven old silicate-rich (orange curves), and seven silicate-poor
(grey curves) L3–L6.5 spectra. The normalisation was performed to the median
flux in the 7.2–7.7 $\mu$m and 13.0–14.0 $\mu$m continuum windows (light grey
vertical regions) that surround the silicate absorption. The 9.0–9.6 $\mu$m
window (medium grey vertical region) denotes the range where silicate
absorption is on average the strongest. The weighted average of the silicate-
poor spectra is indicated by the black curve and its uncertainty by the
surrounding dark grey shaded region. The best second-order polynomial fit to
this combined spectrum in the 7.2–14.0 $\mu$m range is represented by the
black dashed curve. (b): The 7.2–14.0 $\mu$m sub-range of the same spectra as
in (a), divided by the polynomial fit to the average silicate-poor mid-L
continuum. By construction, the continuum-divided weighted average (black
curve) of silicate-poor spectra scatters around unity (dashed line; same as in
(a)).

###  2.3 Continuum Removal

Figure 3a illustrates the difference in the silicate absorption feature
between the selected sub-samples of silicate-poor and silicate-rich mid-L
spectra. The full 5.2–14.2 $\mu$m spectra are shown scaled to the same average
flux in the 7.2–7.7 $\mu$m and 13.0–14.0 $\mu$m continuum regions. The
weighted average of the silicate-poor mid-L spectra (black curve), obtained
using the inverse squared values of the errors on the scaled flux as weights,
traces the mid-infrared continuum in the near-total absence of silicate
absorption. It does not exhibit a significant scatter and is well-represented
by a second-order polynomial fit (black dashed curve) between 7.2–14.0 $\mu$m.
The silicate-rich spectra exhibit characteristic broad absorption from 8
$\mu$m out to 11–13 $\mu$m.

To isolate the silicate absorption signature in silicate-rich mid-L dwarfs
from that of other potential continuum absorbers, we divide all normalised IRS
spectra by the quadratic fit to the weighted average silicate-poor mid-L
continuum. The continuum-divided mid-L spectra are shown in Figure 3b, where
we have narrowed the rendering to the 7.2–14.0 $\mu$m range that spans the
$\sim$8–13 $\mu$m silicate absorption. The underlying assumption for the
continuum removal is that any non-silicate absorbers (such as water or
methane) are present at similar strength in the silicate-poor and silicate-
rich mid-L spectra. While that appears to mostly be the case, given the
similarity among the continuum-divided mid-L spectra outside the silicate
absorption region (Figure 3b), there remain some systematic differences.
Namely, the spectra of mid-L dwarfs with enhanced silicate absorption
generally have higher fluxes at $<$7.5 $\mu$m and lower fluxes at $\gtrsim$13
$\mu$m compared to the silicate-poor spectra. The culprit for the short-
wavelength difference is likely water absorption. Mid-L dwarfs with higher
silicate content in the upper atmosphere likely have some of the gas-phase
water column blocked, and hence exhibit weaker water absorption. At long
wavelengths the culprit is likely silicates themselves. The absorption
signatures of the nine-micron amorphous pyroxene (including enstatite)
features may extend beyond 13 $\mu$m (Luna & Morley, 2021).

Despite the systematics at the edges, the continuum-divided silicate-rich
spectra do isolate the main part of the silicate feature well. A difference in
the red wing of this feature is discernible in Figure 3b between the young
(brown) and old (orange) silicate-rich mid-L spectra, with the young mid-L
spectra consistently tracking below the old spectra at $>$10 $\mu$m. However,
most of the individual spectra are too noisy to assess this difference. We
proceed by scaling and averaging the silicate absorption profiles themselves.

###  2.4 Scaling and Averaging of Silicate Absorption Profiles

With the continua of the silicate-rich spectra factored out, we scale the
strengths of the silicate absorption profiles to each other to account for
differences in the silicate column density among objects. We use the flux
median of the silicate-rich spectra within a 0.6 $\mu$m-wide region centred on
9.3 $\mu$m (Cushing et al., 2006; Luna & Morley, 2021) to scale all absorption
profiles to the same depth (Figure 4a). We can apply such scaling without fear
of contamination from non-silicate absorbers, because we have already removed
their effect after dividing by the silicate-poor continuum. In so far as the
silicate species are similar among the different mid-L dwarfs, their
normalised absorption profiles will also be similar as a function of
wavelength, save for a multiplicative constant. However, small departures from
similarities, as expected among different amorphous sub-types of silicates,
are enhanced.

We take the weighted average of the scaled spectra for each of the sub-samples
and obtain population-averaged silicate absorption profiles for young and old
mid-L spectra. As for the combination of the silicate-poor spectra (Section
2.3), we use the inverse squared values of the errors on the scaled flux as
weights. The combined spectra are shown in Figure 4a by red and blue curves,
with correspondingly shaded one-sigma uncertainty regions. Figure 4a also
includes the weighted average for continuum-divided silicate-poor mid-L
spectra (in black) as an estimate of the accuracy of the continuum removal
process. Because the continuum in the silicate absorption region was
determined from the silicate-poor spectra, the continuum-divided weighted
average of the silicate-poor spectra scatters around unity.

(a)

(b)

Figure 4: (a) Continuum-divided 7.2–14.0 $\mu$m subsections of the mid-L dwarf
IRS spectra from Figure 3b with the strength of the silicate absorption in
silicate-rich spectra scaled to the same median flux in a 0.6 $\mu$m-wide
window centred on 9.3 $\mu$m (vertical grey band). Weighted averages of these
mid-L spectra are shown as follows: young silicate-rich spectra (red), old
silicate-rich spectra (blue), silicate-poor spectra (black). The uncertainties
of the weighted-average spectra are shown by shaded regions of the
corresponding colour. The vertical red dashed and blue dotted lines mark the
wavelengths of strongest silicate absorption in young and old silicate-rich
mid-L spectra, respectively (see Section 2.4). Spectra of individual objects
follow the same colour scheme as in Figure 3. (b) Inverse of fluxes in panel
(a). This representation allows a direct comparison with flux ratio
predictions for condensate cloud vs. grey cloud models in Figure 7 of Luna &
Morley (2021).

##  3 Results: Gravity-dependent Silicate Absorption

Figure 4a shows that young silicate-rich mid-L spectra have a distinct
absorption profile compared to old silicate-rich mid-L spectra. We observe
three main differences.

1\. Silicate absorption strength peaks at a 0.4 $\mu$m longer wavelength in
young mid-L dwarfs. While the silicate absorption profiles for both the young
and the old silicate-rich mid-L subsets were normalised to the same flux at
9.3 $\mu$m, Figure 4a shows that the central wavelengths at which each of the
profiles is the deepest are different. We estimate these central wavelengths
by fitting a third-order polynomial to each continuum-divided weighted-average
silicate-rich spectrum over the 8.0–11.5 $\mu$m wavelength range. We find that
silicate absorption peaks at 9.5$\pm$0.1 $\mu$m in young silicate-rich mid-L
spectra and at 9.1$\pm$0.1 $\mu$m in old silicate-rich mid-L spectra, as shown
by the red vertical dashed line and the blue vertical dotted line in Figure
4a. We estimate the central wavelength uncertainties from $10^{4}$ Monte Carlo
realizations of each scaled and averaged spectrum. We consider the flux at
each wavelength as a Gaussian random variate centred on the weighted average
flux, and a standard deviation equal to the flux uncertainty. The central
wavelength was measured in each realisation as explained above. The quoted
uncertainty on the central wavelength is the 68% confidence interval on the
central wavelengths from the Monte Carlo simulation.

2\. Silicate absorption in young mid-L dwarfs is nearly twice as broad. When
scaled to the same absorption depth at 9.3 $\mu$m, the equivalent width of the
silicate absorption in young mid-L dwarfs is 1.0$\pm$0.1 $\mu$m, whereas for
the old mid-L dwarfs it is 0.6$\pm$0.1 $\mu$m. We estimate the uncertainties
on the equivalent widths from the same Monte Carlo simulation used for the
uncertainties on the central wavelengths of the silicate absorption above. The
absorption feature in young mid-L dwarfs spans almost the entire plotted range
in Figure 4a, from $\sim$7.5 $\mu$m to $>$13.0 $\mu$m. In old mid-L dwarfs the
silicate absorption strength tapers off beyond $\approx$11.5 $\mu$m. Low-level
silicate absorption in old mid-L dwarfs may still be present at $>$11.5
$\mu$m, as in young mid-L dwarfs. However, even in our weighted-averaged
spectra the difference from the silicate-poor 11.5–13.0 $\mu$m continuum is
marginal.

3\. Silicate absorption in young mid-L dwarfs is more asymmetric towards
longer wavelengths. Young mid-L dwarfs with silicate-rich spectra have a
flatter silicate absorption profile for wavelengths longer than the feature
peak compared to a sharper absorption profile in old mid-L dwarfs with
silicate-rich spectra. The difference is most pronounced in the 10–12 $\mu$m
wavelength range, where the scaled and averaged silicate absorption profile in
young mid-L dwarfs is significantly stronger than in old mid-L dwarfs.
Conversely, over 7.5–9.0 $\mu$m the absorption profiles are fully consistent
with each other.

Overall, the silicate absorption profile in young ($\sim$20–150 Myr; $\log
g{\lesssim}4.5$) silicate-rich mid-L spectra is redder, broader, and more
asymmetric than in old ($\gtrsim$500 Myr; $\log g{\gtrsim}5.0$) silicate-rich
mid-L spectra. This constitutes the first observational evidence for a surface
gravity dependence of the mid-infrared silicate absorption in ultracool dwarf
spectra.

##  4 Discussion

Prior to Suárez & Metchev (2022), the existing Spitzer IRS spectra of the six
L dwarfs inferred to show silicate absorption (Roellig et al., 2004; Cushing
et al., 2006; Looper et al., 2008) offered the only opportunity to analyse the
composition of silicates in brown dwarf atmospheres. The consensus picture
from that sample is that the mid-infrared silicate absorption in L dwarfs is
dominated by $\sim$0.1–1.0 $\mu$m amorphous enstatite or quartz grains that
reside in optically thin cloud slabs near the top of the atmosphere, at
temperatures of $\sim$1100 K and pressures of $\lesssim$0.01 bar (Burningham
et al. 2021; Luna & Morley 2021, and references therein). This silicate cloud
layer may overlay a deeper iron cloud deck (Burningham et al., 2021). A
similar multi-layer scenario, comprising a patchy forsterite cloud above a
deeper, optically thick iron deck, represents well the silicate absorption
inferred in two young early-T dwarfs (Vos et al., 2022a).

The mid-infrared atmospheric modelling of silicates presented in Luna & Morley
(2021) is the broadest to date. They model five of the six L3.5–L6 dwarfs with
previously detected silicate absorption from Spitzer IRS. By virtue of the
similarity in spectral types, the best-fit models in Luna & Morley (2021) all
have similar fundamental parameters: four objects are inferred to have an
effective temperature of $T_{\rm eff}=1800$ K and a surface gravity of $\log
g=5$ and one has $T_{\rm eff}=1700$ K and $\log g=4$. The one object (2MASS
J1507476$-$162738; L5) with a low-gravity best-fit model for the mid-infrared
spectrum is unlikely to be young, however. It has no spectroscopic signatures
of youth in $R{\sim}900$ optical (Reid et al., 2000) or $R{\sim}2000$ near-
infrared (Rayner et al., 2009) spectra, and the BANYAN $\Sigma$ algorithm
yields a 99.9% probability of being an old field object. Filippazzo et al.
(2015) find a semi-empirical surface gravity of $\log g{=}5.18$, based on an
assumed $>$500 Myr age and evolutionary models. As we have shown in Suárez et
al. (2021), $R{\sim}100$ Spitzer IRS spectra by themselves, as analysed in
Luna & Morley (2021), may yield substantially less accurate results for
effective temperature and surface gravity when fit by photospheric models
compared to $R{\approx}2300$ near-infrared spectra. Hence this object has a
likely higher gravity than inferred from the model best fit to the IRS
spectrum in Luna & Morley (2021). Overall, the small number of previously
known silicate-rich L-dwarf IRS spectra analysed in Luna & Morley (2021) and
the similarity in effective temperatures and surface gravities, do not allow a
differentiation among the mid-infrared silicate absorption feature as a
function of fundamental parameters.

However, Luna & Morley (2021) do produce detailed predictions for the
spectroscopic signatures of silicate condensates that can be compared to
anticipated spectra from JWST. The recognition of a much larger sample of L
dwarfs with detectable silicate absorption in Spitzer IRS spectra (Suárez &
Metchev, 2022), and the gravity-dependent sub-sampling that we have performed
here, allow a first look at systematic effects as a function of surface
gravity.

###  4.1 Dust Clouds in Young Atmospheres are Dominated by Heavier Grains

We use the Luna & Morley (2021) predictions to extract differences in silicate
composition, grain size, or crystallinity that match the observed
spectroscopic differences between low- and high-surface gravity mid-L dwarfs
(Section 3). Specifically, we use the predictions for the mid-infrared
silicate flux ratio $F_{\rm ratio}$ from Figure 7 in Luna & Morley (2021),
wherein $F_{\rm ratio}$ is defined as the wavelength-dependent ratio of the
grey-cloud ($F_{\rm grey}$) to the condensate-cloud ($F_{\rm cloud}$) model
atmosphere. In so far as the grey-cloud model is representative of our
featureless silicate-poor mid-L spectra, the Luna & Morley (2021) $F_{\rm
ratio}$ metric is similar to the inverse of our continuum-divided spectra
(Figure 4a). We plot this inverse in Figure 4b. The only difference is that in
Luna & Morley (2021) the grey-cloud and condensate-cloud models are not scaled
to each other in the silicate-free wavelength regions, while we have scaled
both silicate-poor and silicate-rich mid-L spectra to the same average
continuum (Figure 3).

A comparison between our Figure 4b and Figure 7 of Luna & Morley (2021)
reveals that the redder and more rounded 9.5 $\mu$m silicate absorption
profile in young low-gravity mid-L dwarfs is likely caused by 1 $\mu$m
amorphous magnesium- and iron-bearing pyroxene (MgxFe1-xSiO3) grains. Pyroxene
is the only iron-bearing silicate modelled in Luna & Morley (2021) with a
profile as asymmetric as the observed one, including a steeper slope over
8.0–9.5 $\mu$m and a flatter slope over 9.5–13 $\mu$m. An admixture of larger
($>$1 $\mu$m) amorphous enstatite grains is also possible, given the inverse
dependence of peak wavelength on dominant grain size (Luna & Morley, 2021).
However, the grains could not be as large as 10 $\mu$m, as they would lack the
characteristic absorption features and would instead behave as a source of
grey opacity (Cushing et al., 2006; Luna & Morley, 2021).

Conversely, the $\approx$9.1 $\mu$m peak and the narrower profile of silicate
absorption in old high-gravity mid-L dwarfs points to the presence of
$\lesssim$0.1 $\mu$m amorphous enstatite (MgSiO3) or SiO grains. Figure 7 of
Luna & Morley (2021) shows 0.1 $\mu$m amorphous enstatite grains peaking in
absorption strength around 9.2 $\mu$m in a 1800 K atmosphere, vs. a peak at
9.4 $\mu$m for larger 1 $\mu$m grains. One-micron amorphous SiO grains exhibit
a similar absorption peak and profile as 1 $\mu$m amorphous enstatite grains,
and are also expected to peak closer to 9.1 $\mu$m if smaller in size.
Contributions from other species are likely secondary. Thus, a contribution
from amorphous or crystalline quartz (SiO2), which peaks in strength at
$\approx$8.8 $\mu$m is possible, but not likely, given the sharpness of the
SiO2 absorption feature (Luna & Morley, 2021). A more accurate determination
of the silicate and iron content and grain size of dust clouds in brown dwarf
atmospheres awaits JWST MIRI observations, which will bring broader wavelength
coverage at higher SNR and spectral resolution.

While the comparison to model predictions is not conclusive about the
composition and size of the silicate grains in low- vs. high-gravity mid-L
dwarfs, there is one consistent difference between the two. The types of
grains that fit better the redder and broader silicate absorption observed in
young low-gravity mid-L dwarfs are heavier than the grains that fit better the
bluer and narrower silicate absorption profiles of old high-gravity mid-L
dwarfs.

###  4.2 Lower-gravity Ultracool Atmospheres Have Lower Sedimentation
Efficiency

The preceding spectroscopic analysis established that silicate grains in low-
gravity atmospheres are both larger ($\sim$1 $\mu$m) and composed of a heavier
molecule (MgxFe1-xSiO3) compared to silicates in high-gravity atmospheres,
which have sizes of $\lesssim$0.1 $\mu$m and are dominated by MgSiO3 or SiO.
For example, for a typical $x=0.4$ pyroxene (Mg0.4Fe0.6SiO3) has a molecular
weight of 23.9 g mol-1 per constituent atom, which is heavier than enstatite
(MgSiO3, 20.1 g mol-1 atom-1) or SiO (22.0 g mol-1 atom-1). Iron-rich pyroxene
condensates are also more refractory than enstatite or SiO condensates, and so
settle at lower altitudes in brown dwarf atmospheres (e.g., Ackerman & Marley
2001; Cooper et al. 2003; Lodders 2003; Woitke et al. 2020). We have thus
found spectroscopic evidence that the settling of dust condensates in
ultracool atmospheres depends on surface gravity.

This confirms the very well-established theoretical expectation that low-
gravity atmospheres have lower sedimentation efficiencies (Ackerman & Marley,
2001; Cooper et al., 2003), and that correspondingly the settling of dust
clouds in low-gravity atmospheres happens at lower temperatures (Stephens et
al., 2009; Madhusudhan et al., 2011; Marley et al., 2012; Charnay et al.,
2018), leading to dustier atmospheres in young objects.

Table 1: Sub-samples of mid-L dwarfs with silicate-rich and silicate-poor
spectra.

Designation | Short Name |  SpT${}_{\textrm{opt}}$ | Ref. |  SpT${}_{\textrm{IR}}$ | Ref. | Silicate Index |  $\Delta$Sia
---|---|---|---|---|---|---|---
Young silicate-rich mid-L spectra
2MASS J03552337+1133437b | 0355+1133 |  L5$\gamma$ | Cruz et al. (2009) |  L4$\gamma$ | Bardalez Gagliuffi et al. (2019) |  1.29$\pm$0.02 |  0.19$\pm$0.02
2MASS J05012406$-$0010452c |  0501$-$0010 |  L4$\gamma$ | Cruz et al. (2009) |  L4$\gamma$ | Gagné et al. (2015) |  1.35$\pm$0.08 |  0.20$\pm$0.08
2MASS J14252798$-$3650229b |  1425$-$3650 | L3 | Reid et al. (2008) |  L4$\gamma$ | Gagné et al. (2015) |  1.32$\pm$0.04 |  0.20$\pm$0.04
2MASS J22443167+2043433b | 2244+2043 | L6.5 | Kirkpatrick et al. (2008) |  L6–L8$\gamma$ | Gagné et al. (2015) |  1.37$\pm$0.07 |  0.38$\pm$0.07
Old silicate-rich mid-L spectra
2MASS J00043484$-$4044058 |  0004$-$4044 | L5 | Kirkpatrick et al. (2001) | L4.5 | Knapp et al. (2004) |  1.36$\pm$0.11 |  0.25$\pm$0.11
2MASS J01443536$-$0716142 |  0144$-$0716 | L5 | Liebert et al. (2003) | L5 | Marocco et al. (2013) |  1.29$\pm$0.05 |  0.18$\pm$0.05
2MASS J09201223+3517429d | 0920+3517 | L6.5 | Kirkpatrick et al. (2000) | T0p | Burgasser et al. (2006) |  1.31$\pm$0.14 |  0.32$\pm$0.14
2MASS J12392727+5515371 | 1239+5515 | L5 | Kirkpatrick et al. (2000) | L5 | Schneider et al. (2014) |  1.48$\pm$0.12 |  0.37$\pm$0.12
2MASS J14482563+1031590 | 1448+1031 | L4 | Wilson et al. (2003) | L5.5 | Schneider et al. (2014) |  1.26$\pm$0.05 |  0.10$\pm$0.05
2MASS J17534518$-$6559559 |  1753$-$6559 | L4 | Reid et al. (2008) | L4 | Marocco et al. (2013) |  1.37$\pm$0.09 |  0.22$\pm$0.09
2MASS J18212815+1414010 | 1821+1414 | L4.5 | Looper et al. (2008) | L5p | Kirkpatrick et al. (2010) |  1.25$\pm$0.01 |  0.11$\pm$0.01
2MASS J21481633+4003594 | 2148+4003 | L6 | Looper et al. (2008) | L6.5p | Kirkpatrick et al. (2010) |  1.44$\pm$0.01 |  0.40$\pm$0.01
2MASS J22244381$-$0158521 |  2224$-$0158 | L4.5 | Kirkpatrick et al. (2000) | L3.5 | Knapp et al. (2004) |  1.38$\pm$0.06 |  0.24$\pm$0.06
Silicate-poor mid-L spectra
2MASS J07003664+3157266 | 0700+3157 | L3.5 | Thorstensen & Kirkpatrick (2003) |  $\cdots$ |  $\cdots$ |  1.02$\pm$0.04 | $-0.11\pm 0.04$
2MASS J09083803+5032088 | 0908+5032 | L5 | Cruz et al. (2003) | L9 | Knapp et al. (2004) |  0.89$\pm$0.04 | $-0.21\pm 0.04$
2MASS J10365305$-$3441380 |  1036$-$3441 | L6 | Gizis (2002) | L6.5 | Burgasser et al. (2010) |  0.83$\pm$0.05 | $-0.20\pm 0.05$
2MASS J11263991$-$5003550 |  1126$-$5003 | L4.5 | Burgasser et al. (2008) | L6.5p | Burgasser et al. (2008) |  1.01$\pm$0.04 | $-0.13\pm 0.04$
2MASS J13314894$-$0116500 |  1331$-$0116 | L6 | Hawley et al. (2002) | L6 | Marocco et al. (2015) |  0.86$\pm$0.06 | $-0.18\pm 0.06$
2MASS J15150083+4847416 | 1515+4847 | L6 | Cruz et al. (2007) | L6.5 | Cruz et al. (2003) |  0.88$\pm$0.04 | $-0.15\pm 0.04$
2MASS J16262034+3925190 | 1626+3925 | sdL4 | Burgasser et al. (2007) | sdL | Burgasser (2004) |  0.95$\pm$0.06 | $-0.20\pm 0.06$

  * aSilicate index excess defined as the difference between the measured silicate index value for each dwarf and the median index for its spectral type (Section 2.1 and Figure 2a).
bMember of the 110–150 Myr-old (Luhman et al., 2005; Barenfeld et al., 2013)
AB Doradus moving group. References are Liu et al. (2013); Gagné et al.
(2015); Vos et al. (2018) for 0355+1133, 1425$-$3650, and 2244+2043,
respectively.
cMember of either the Columba or Carina moving groups (Gagné et al., 2015),
which are coeval groups at 20–40 Myr (Torres et al., 2008).
dClose binary system with the individual components having near-infrared
spectral types of L5.5 and L9 (Dupuy & Liu, 2012). The binary is not resolved
in the Spitzer observations and, therefore, the IRS spectrum is likely
dominated by the brighter L5.5 dwarf.

##  5 Conclusion

We have established that the mid-infrared silicate absorption in the spectra
of mid-L dwarfs is sensitive to surface gravity (Section 3). It is broader,
redder, and more asymmetric for young $\log g{\lesssim}4.5$ mid-L dwarfs than
for their older $\log g{\gtrsim}5.0$ counterparts. Comparisons to theoretical
spectra reveal that the silicate grains in young mid-L dwarfs are heavier
(Section 4.1). They are larger ($\sim$1 $\mu$m) and dominated by silicates
that are more refractory (magnesium- and iron-bearing pyroxene) than grains in
the atmospheres of older mid-L dwarfs ($\lesssim$0.1 $\mu$m in size and
dominated by enstatite or SiO). This result directly confirms that dust cloud
sedimentation in low-gravity substellar atmospheres is suppressed (Section
4.2), as already anticipated by their redder optical and near-infrared
photospheric colours (Kirkpatrick, 2005; Filippazzo et al., 2015) and by their
enhanced photometric variability (e.g., Metchev et al. 2015; Biller et al.
2015). The surface gravity dependence of the condensate physics and chemistry
enhances the empirical context for JWST studies of brown dwarf and
exoplanetary atmosphere.

## Acknowledgements

We thank the referee Denise C. Stephens for a helpful report that
significantly improved the quality of this paper. We thank Marina Gemma for
discussions and suggestions on the use of appropriate nomenclature for dust
grains. G.S. acknowledges support from NSF award #2009177. Support for this
work was provided by the Canadian Space Agency under the Flights and Fieldwork
for the Advancement of Science and Technology programme (reference no.
19FAWESB40). The spectra presented here are obtained entirely with the Spitzer
Space Telescope, which was operated by the Jet Propulsion Laboratory,
California Institute of Technology under a contract with NASA.

## Data Availability

The spectra used in this analysis form part of the uniformly reprocessed set
of Spitzer IRS spectra of 113 M5–T9 dwarfs published and available in Suárez &
Metchev (2022) and on Genaro Suárez’
homepage111https://gsuarezcastro.wixsite.com/gsuarez/research.

## References

  * Ackerman & Marley (2001) Ackerman A. S., Marley M. S., 2001, ApJ, 556, 872
  * Artigau et al. (2009) Artigau É., Bouchard S., Doyon R., Lafrenière D., 2009, ApJ, 701, 1534
  * Bardalez Gagliuffi et al. (2019) Bardalez Gagliuffi D. C., et al., 2019, ApJ, 883, 205
  * Barenfeld et al. (2013) Barenfeld S. A., Bubar E. J., Mamajek E. E., Young P. A., 2013, ApJ, 766, 6
  * Biller et al. (2015) Biller B. A., et al., 2015, ApJ, 813, L23
  * Bowler et al. (2020) Bowler B. P., Zhou Y., Morley C. V., Kataria T., Bryan M. L., Benneke B., Batygin K., 2020, ApJ, 893, L30
  * Burgasser (2004) Burgasser A. J., 2004, ApJ, 614, L73
  * Burgasser et al. (2002) Burgasser A. J., Marley M. S., Ackerman A. S., Saumon D., Lodders K., Dahn C. C., Harris H. C., Kirkpatrick J. D., 2002, ApJ, 571, L151
  * Burgasser et al. (2006) Burgasser A. J., Geballe T. R., Leggett S. K., Kirkpatrick J. D., Golimowski D. A., 2006, ApJ, 637, 1067
  * Burgasser et al. (2007) Burgasser A. J., Cruz K. L., Kirkpatrick J. D., 2007, ApJ, 657, 494
  * Burgasser et al. (2008) Burgasser A. J., Looper D. L., Kirkpatrick J. D., Cruz K. L., Swift B. J., 2008, ApJ, 674, 451
  * Burgasser et al. (2010) Burgasser A. J., Cruz K. L., Cushing M., Gelino C. R., Looper D. L., Faherty J. K., Kirkpatrick J. D., Reid I. N., 2010, ApJ, 710, 1142
  * Burningham et al. (2021) Burningham B., et al., 2021, MNRAS, 506, 1944
  * Burrows et al. (1997) Burrows A., et al., 1997, ApJ, 491, 856
  * Burrows et al. (2001) Burrows A., Hubbard W. B., Lunine J. I., Liebert J., 2001, Reviews of Modern Physics, 73, 719
  * Charnay et al. (2018) Charnay B., Bézard B., Baudino J. L., Bonnefoy M., Boccaletti A., Galicher R., 2018, ApJ, 854, 172
  * Cooper et al. (2003) Cooper C. S., Sudarsky D., Milsom J. A., Lunine J. I., Burrows A., 2003, ApJ, 586, 1320
  * Cruz et al. (2003) Cruz K. L., Reid I. N., Liebert J., Kirkpatrick J. D., Lowrance P. J., 2003, AJ, 126, 2421
  * Cruz et al. (2007) Cruz K. L., et al., 2007, AJ, 133, 439
  * Cruz et al. (2009) Cruz K. L., Kirkpatrick J. D., Burgasser A. J., 2009, AJ, 137, 3345
  * Cushing et al. (2006) Cushing M. C., et al., 2006, ApJ, 648, 614
  * Cushing et al. (2008) Cushing M. C., et al., 2008, ApJ, 678, 1372
  * Dupuy & Liu (2012) Dupuy T. J., Liu M. C., 2012, ApJS, 201, 19
  * Dupuy & Liu (2017) Dupuy T. J., Liu M. C., 2017, ApJS, 231, 15
  * Faherty et al. (2016) Faherty J. K., et al., 2016, ApJS, 225, 10
  * Filippazzo et al. (2015) Filippazzo J. C., Rice E. L., Faherty J., Cruz K. L., Van Gordon M. M., Looper D. L., 2015, ApJ, 810, 158
  * Gagné et al. (2015) Gagné J., et al., 2015, ApJS, 219, 33
  * Gagné et al. (2018) Gagné J., et al., 2018, ApJ, 856, 23
  * Gizis (2002) Gizis J. E., 2002, ApJ, 575, 484
  * Hawley et al. (2002) Hawley S. L., et al., 2002, AJ, 123, 3409
  * Houck et al. (2004) Houck J. R., et al., 2004, ApJS, 154, 18
  * Kirkpatrick (2005) Kirkpatrick J. D., 2005, ARA&A, 43, 195
  * Kirkpatrick et al. (2000) Kirkpatrick J. D., et al., 2000, AJ, 120, 447
  * Kirkpatrick et al. (2001) Kirkpatrick J. D., Dahn C. C., Monet D. G., Reid I. N., Gizis J. E., Liebert J., Burgasser A. J., 2001, AJ, 121, 3235
  * Kirkpatrick et al. (2006) Kirkpatrick J. D., Barman T. S., Burgasser A. J., McGovern M. R., McLean I. S., Tinney C. G., Lowrance P. J., 2006, ApJ, 639, 1120
  * Kirkpatrick et al. (2008) Kirkpatrick J. D., et al., 2008, ApJ, 689, 1295
  * Kirkpatrick et al. (2010) Kirkpatrick J. D., et al., 2010, ApJS, 190, 100
  * Knapp et al. (2004) Knapp G. R., et al., 2004, AJ, 127, 3553
  * Liebert et al. (2003) Liebert J., Kirkpatrick J. D., Cruz K. L., Reid I. N., Burgasser A., Tinney C. G., Gizis J. E., 2003, AJ, 125, 343
  * Liu et al. (2013) Liu M. C., Dupuy T. J., Allers K. N., 2013, Astronomische Nachrichten, 334, 85
  * Lodders (2002) Lodders K., 2002, ApJ, 577, 974
  * Lodders (2003) Lodders K., 2003, ApJ, 591, 1220
  * Looper et al. (2008) Looper D. L., et al., 2008, ApJ, 686, 528
  * Luhman et al. (2005) Luhman K. L., Stauffer J. R., Mamajek E. E., 2005, ApJ, 628, L69
  * Luna & Morley (2021) Luna J. L., Morley C. V., 2021, ApJ, 920, 146
  * Madhusudhan et al. (2011) Madhusudhan N., Burrows A., Currie T., 2011, ApJ, 737, 34
  * Marley et al. (2012) Marley M. S., Saumon D., Cushing M., Ackerman A. S., Fortney J. J., Freedman R., 2012, ApJ, 754, 135
  * Marocco et al. (2013) Marocco F., et al., 2013, AJ, 146, 161
  * Marocco et al. (2015) Marocco F., et al., 2015, MNRAS, 449, 3651
  * Metchev et al. (2015) Metchev S. A., et al., 2015, ApJ, 799, 154
  * Miles et al. (2022) Miles B. E., et al., 2022, arXiv e-prints, p. arXiv:2209.00620
  * Rayner et al. (2009) Rayner J. T., Cushing M. C., Vacca W. D., 2009, ApJS, 185, 289
  * Reid et al. (2000) Reid I. N., Kirkpatrick J. D., Gizis J. E., Dahn C. C., Monet D. G., Williams R. J., Liebert J., Burgasser A. J., 2000, AJ, 119, 369
  * Reid et al. (2008) Reid I. N., Cruz K. L., Kirkpatrick J. D., Allen P. R., Mungall F., Liebert J., Lowrance P., Sweet A., 2008, AJ, 136, 1290
  * Roellig et al. (2004) Roellig T. L., et al., 2004, ApJS, 154, 418
  * Schneider et al. (2014) Schneider A. C., Cushing M. C., Kirkpatrick J. D., Mace G. N., Gelino C. R., Faherty J. K., Fajardo-Acosta S., Sheppard S. S., 2014, AJ, 147, 34
  * Stephens et al. (2009) Stephens D. C., et al., 2009, ApJ, 702, 154
  * Suárez & Metchev (2022) Suárez G., Metchev S., 2022, MNRAS, 513, 5701
  * Suárez et al. (2021) Suárez G., Metchev S., Leggett S. K., Saumon D., Marley M. S., 2021, ApJ, 920, 99
  * Thorstensen & Kirkpatrick (2003) Thorstensen J. R., Kirkpatrick J. D., 2003, PASP, 115, 1207
  * Torres et al. (2008) Torres C. A. O., Quast G. R., Melo C. H. F., Sterzik M. F., 2008, in Reipurth B., ed., , Vol. 5, Handbook of Star Forming Regions, Volume II. p. 757
  * Vos et al. (2018) Vos J. M., Allers K. N., Biller B. A., Liu M. C., Dupuy T. J., Gallimore J. F., Adenuga I. J., Best W. M. J., 2018, MNRAS, 474, 1041
  * Vos et al. (2019) Vos J. M., et al., 2019, MNRAS, 483, 480
  * Vos et al. (2022a) Vos J. M., et al., 2022a, arXiv e-prints, p. arXiv:2212.07399
  * Vos et al. (2022b) Vos J. M., Faherty J. K., Gagné J., Marley M., Metchev S., Gizis J., Rice E. L., Cruz K., 2022b, ApJ, 924, 68
  * Wilson et al. (2003) Wilson J. C., Miller N. A., Gizis J. E., Skrutskie M. F., Houck J. R., Kirkpatrick J. D., Burgasser A. J., Monet D. G., 2003, in Martín E., ed., IAU Symposium Vol. 211, Brown Dwarfs. p. 197
  * Woitke et al. (2020) Woitke P., Helling C., Gunn O., 2020, A&A, 634, A23
  * Zuckerman (2019) Zuckerman B., 2019, ApJ, 870, 27