# Precise Bolometric Luminosities and Effective Temperatures of 23 late-T and
Y dwarfs Obtained with JWST

Samuel A. Beiler Ritter Astrophysical Research Center, Department of Physics &
Astronomy, University of Toledo, 2801 W. Bancroft St., Toledo, OH 43606, USA
Michael C. Cushing Ritter Astrophysical Research Center, Department of Physics
& Astronomy, University of Toledo, 2801 W. Bancroft St., Toledo, OH 43606, USA
J. Davy Kirkpatrick IPAC, Mail Code 100-22, Caltech, 1200 E. California
Boulevard, Pasadena, CA 91125, USA  Adam C. Schneider United States Naval
Observatory, Flagstaff Station, 10391 West Naval Observatory Road, Flagstaff,
AZ 86005, USA  Sagnick Mukherjee Department of Astronomy and Astrophysics,
University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064,
USA  Mark S. Marley Lunar and Planetary Laboratory, University of Arizona,
1629 E. University Boulevard, Tucson, AZ 85721, USA  Federico Marocco IPAC,
Mail Code 100-22, Caltech, 1200 E. California Boulevard, Pasadena, CA 91125,
USA  Richard L. Smart Istituto Nazionale di Astrofisica, Osservatorio
Astrofisico di Torino, Strada Osservatorio 20, I-10025 Pino Torinese, Italy

###### Abstract

We present infrared spectral energy distributions of 23 late-type T and Y
dwarfs obtained with the James Webb Space Telescope. The spectral energy
distributions consist of NIRSpec PRISM and MIRI LRS spectra covering the
$\sim$1–12 $\mu$m wavelength range at $\lambda/\Delta\lambda\approx 100$ and
broadband photometry at 15, 18, and 21 $\mu$m. The spectra exhibit absorption
features common to these objects including H2O, CH4, CO, CO2, and NH3.
Interestingly, while the spectral morphology changes relatively smoothly with
spectral type at $\lambda<3$ $\mu$m and $\lambda>8$ $\mu$m, it shows no clear
trend in the 5 $\mu$m region where a large fraction of the flux emerges. The
broad wavelength coverage of the data enables us to compute the first accurate
measurements of the bolometric fluxes of cool brown dwarfs. Combining these
bolometric fluxes with parallaxes from Spitzer and HST, we also obtain the
first accurate bolometric luminosities of these cool dwarfs. We then used the
Sonora Bobcat solar metallicity evolutionary models to estimate the radii of
the dwarfs which results in effective temperature estimates ranging from
$\sim$1000 to 350 K with a median uncertainty of $\pm$20 K which is nearly an
order of magnitude improvement over previous work. We also discuss how various
portions of the spectra either do or do not exhibit a clear sequence when
ordered by their effective temperatures.

Brown dwarfs(185), Effective temperature(449), Fundamental parameters of
stars(555), Near infrared astronomy(1093), Spectroscopy(1558), Y dwarfs(1827),
James Webb Space Telescope(2291)

##  1 Introduction

Over the last two centuries, astronomers have advanced our understanding of
the life of stars, largely through measuring fundamental stellar parameters
such as mass ($M$), radius ($R$), and bolometric luminosity
($L_{\mathrm{bol}}$), as well as derived parameters such as effective
temperature ($T_{\mathrm{eff}}$=($L_{\mathrm{bol}}$/4$\pi\sigma R^{2}$)1/4). A
decades-long observational effort was needed to obtain these measurements for
a broad population, with stellar parallaxes requiring precise astrometric
observations (e.g. Bessel, 1838; Campbell, 1913), bolometric fluxes requiring
broad-wavelength spectral energy distributions (e.g. Wilsing et al., 1919;
Coblentz, 1922), and radii and masses requiring time series photometry and
spectroscopy of eclipsing spectroscopic binaries (e.g. Frost, 1896; Kuiper,
1938). Due to this effort, it is now possible to infer these properties for
any star with a known spectral type (e.g. Russell, 1914; Payne, 1924). With
this comes the ability to determine the mass function of stars, which is core
to our understanding of star formation, galactic evolution, and even the early
Universe (e.g. McKee & Ostriker, 2007; Hopkins, 2018; Smith, 2020; Kirkpatrick
et al., 2024). Large volume-limited samples of stars were painstakingly
compiled in the latter half of the 20th century, resulting in a stellar field
mass function that can be fit by a power law with a Salpeter slope at higher
masses, and a shallower power law or log normal at lower masses (e.g.
Salpeter, 1955; Bastian et al., 2010; Kroupa & Jerabkova, 2019).

A similar advancement has been underway for brown dwarfs since the discovery
of the first brown dwarfs Gl 229B, Teide 1, and PPl 15 (Nakajima et al., 1995;
Rebolo et al., 1995; Stauffer et al., 1994; Basri et al., 1996). However,
progress over these 30 years has been hampered by observational and
fundamental difficulties: 1) brown dwarfs do not obey a mass-luminosity
relation like their stellar counterparts, as without an internal heat source
they cool “inexorably like dying embers plucked from a fire” (Burrows et al.,
1997), 2) the brown dwarf binary fraction is only 5$-$20% compared to the
$\sim$50% for solar stars and higher for early spectral types (e.g. Fontanive
et al., 2018), making accurate radius and mass measurements difficult, and 3)
brown dwarfs emit a significant portion of their radiation in the near- and
mid-infrared ($>$1 $\mu$m). This last difficulty worsens for later spectral
types, with late-T and Y dwarfs ($T_{\mathrm{eff}}$$<$$\sim$1000 K) emitting
over 80% of their flux at wavelength redward of 3 $\mu$m, and doing so faintly
($M_{[4.5]}>13$). This observational difficulty has been overcome with ground
observations (e.g. Skemer et al., 2016; Morley et al., 2018; Miles et al.,
2020) and space telescopes like Spitzer Space Telescope (Werner et al., 2004),
WISE (Wright et al., 2010), and AKARI (Murakami et al., 2007), but only for a
handful of objects have sufficient spectral coverage for accurate bolometric
fluxes and luminosities. This has made estimating the effective temperatures
of these late objects difficult, resulting in uncertainties of order 20%
(Dupuy & Kraus, 2013; Kirkpatrick et al., 2021).

A lack of precise effective temperatures impacts our ability to construct a
reliable mass function. Since brown dwarfs have no mass-luminosity relation,
we cannot generate the mass function directly from the luminosities or
effective temperatures of a field population. Instead, the most commonly used
method is to construct a volume-limited luminosity (or effective temperature)
distribution, and then fit this distribution with simulated populations
created from an assumed mass function and birth rate, and evolved using
evolutionary model tracks (Burgasser, 2004; Filippazzo et al., 2015;
Kirkpatrick et al., 2021; Best et al., 2024; Kirkpatrick et al., 2024). From
previous work collecting a large sample of M, L, and T dwarfs with precise
luminosities and parallaxes, it has been shown that a power-law mass function
with $\alpha\approx$ 0.6 with a minimum formation mass best fits local volume-
limited samples (Kirkpatrick et al., 2021; Best et al., 2024; Kirkpatrick et
al., 2024; Raghu et al., 2024). Similar results have been found in young
clusters (e.g. Lodieu et al., 2007; Ramírez et al., 2012; Alves de Oliveira,
2013). However, due to the aforementioned lack of a large sample of late-T and
Y dwarfs with reliable effective temperatures, the low end of this mass
function is not well constrained. This includes limited constraints on the
minimum formation mass.

The James Webb Space Telescope (JWST, Gardner et al., 2023), with its
unprecedented sensitivity and broad spectral coverage, is a natural answer to
our observational difficulties. For the late-T and Y dwarfs, JWST observations
are capable of collecting $>$90% of the flux, which along with precise
parallaxes can lower the bolometric luminosity fractional uncertainty below 6%
(Beiler et al., 2023). These precise luminosities, along with theoretical
radii often determined from evolutionary models, allow for the calculation of
precise effective temperatures for objects with broad-wavelength JWST spectral
energy distributions. With a representative sample of objects with these
observations, it will be possible to improve the effective temperature
estimates of hundreds of ultracool objects within the current volume-limited
sample. This in turn will further our understanding of the substellar mass
function and ultracool atmospheres.

In this paper we present the spectral energy distributions of 23 late-T and Y
dwarfs, consisting of low resolution spectra from $\sim$1–12 $\mu$m and
photometry out to 21 $\mu$m, and determine $L_{\mathrm{bol}}$ and
$T_{\mathrm{eff}}$ for the sample. Beiler et al. (2023) previously presented
the spectral energy distribution of one of the objects from this sample (WISE
J0359$-$54). In $\S$2, we discuss our sample selection for this project, whose
observations and reduction we report in $\S$3 and $\S$4. These are the first
near-infrared spectra for two of our objects, which we classify in $\S$5. In
$\S$6 we remark on the spectral morphology of these broad-wavelength spectral
energy distributions and the large swath of molecular absorption features they
contain. We then calculate $F_{\mathrm{bol}}$, $L_{\mathrm{bol}}$, and
$T_{\mathrm{eff}}$ for our whole sample in $\S$7, and in $\S$8 we explore how
incomplete spectral energy distributions impact $T_{\mathrm{eff}}$and whether
we can correct for their incompleteness. With effective temperatures in hand,
we explore how absorption features change as a function of $T_{\mathrm{eff}}$
in $\S$9.

##  2 Sample Selection

We selected our sample for this program (GO 2302, PI Cushing) from the 243
brown dwarfs with a spectral type of T6 or later within a 20 pc radius of the
Sun (Kirkpatrick et al., 2019, 2021). We chose this spectral type cut-off so
that there is overlap between our sample and that of Filippazzo et al. (2015)
who derived effective temperatures for 198 M, L, and T dwarfs. As much as we
would like to observe all 243 of these brown dwarfs with JWST, such a proposal
is untenable so we selected a representative sample. We eliminated suspected
subdwarfs and binaries, and objects with a fractional parallax uncertainty
greater than 5%. This left us with 143 potential targets, which are shown in
Figure 1. We placed these objects in eight bins based on their absolute [4.5]
Spitzer magnitudes and selected three objects from each bin (shown as stars in
the figure) based on their [3.6]$-$[4.5] colors: one with a roughly average
color, one with a redder than average color, and one with a bluer than average
color. The properties of these 24 objects are given in Table 2. Hereafter we
will abbreviate the full designations of these objects as HHMM+DD.

Figure 1: The 143 potential targets (circles) from which we selected our
sample (stars). The potential targets have spectral types of T6 or later, fall
within 20 pc of the Sun, have fractional parallax uncertainties less than 5%,
and are not suspected of being binaries or subdwarfs. The potential targets
were divided into 8 bins in

absolute [4.5] magnitude, which are color coded and marked with vertical
lines. We selected 3 targets from each bin that span the [3.6]$-$[4.5] color
space. The targets marked as white stars had parts of their observations fail.

Table 1: Astrometric and Photometric Properties of Our Sample

Name | Spec. | $\varpi_{\mathrm{abs}}$ | IRAC [3.6] | IRAC [4.5] | W1 | W2 | F1000W | F1500W | F1800W | F2100W | Ref.${}^{\tablenotemark{b}}$
---|---|---|---|---|---|---|---|---|---|---|---
| type | (mas) | (mag) | (mag) | (mag) | (mag) | (mag)${}^{\tablenotemark{a}}$ | (mag)${}^{\tablenotemark{a}}$ | (mag)${}^{\tablenotemark{a}}$ | (mag)${}^{\tablenotemark{a}}$ |
WISE J024714.52+372523.5 | T8 | $64.8\pm 2.0$ | $16.70\pm 0.04$ | $14.55\pm 0.02$ | $17.74\pm 0.09$ | $14.58\pm 0.02$ | $13.15$ | $12.64$ | $12.62$ | $12.63$ | 14,14,3,5,9,1
WISEPA J031325.96+780744.2 | T8.5 | $135.6\pm 2.8$ | $15.31\pm 0.02$ | $13.27\pm 0.02$ | $15.98\pm 0.02$ | $13.22\pm 0.01$ | $11.62$ | $11.01$ | $10.92$ | $10.99$ | 13,13,2,5,9,1
WISE J035934.06$-$540154.6 | Y0 | $73.6\pm 2.0$ | $17.55\pm 0.07$ | $15.33\pm 0.02$ | $19.21\pm 0.22$ | $15.41\pm 0.03$ | $13.66$ | $12.84$ | $12.65$ | $12.62$ | 10,10,2,5,9,1
WISE J043052.92+463331.6 | T8 | $96.1\pm 2.9$ | $16.13\pm 0.03$ | $14.22\pm 0.02$ | $18.16\pm 0.17$ | $14.31\pm 0.02$ | $13.22$ | $12.51$ | $12.33$ | $12.40$ | 14,14,2,5,9,1
WISE J053516.80$-$750024.9 | Y1 | $68.7\pm 2.0$ | $17.75\pm 0.08$ | $15.01\pm 0.02$ | $18.37\pm 0.10$ | $15.00\pm 0.02$ | $13.39$ | $12.30$ | $12.04$ | $11.95$ | 10,10,2,5,9,1
WISE J073444.02$-$715744.0 | Y0 | $74.5\pm 1.7$ | $17.65\pm 0.08$ | $15.21\pm 0.02$ | $19.11\pm 0.21$ | $15.24\pm 0.02$ | $13.47$ | $12.63$ | $12.50$ | $12.51$ | 10,10,2,5,9,1
WISE J082507.35+280548.5 | Y0.5 | $152.6\pm 2.0$ | $17.33\pm 0.06$ | $14.65\pm 0.02$ | $18.30\pm 0.18$ | $14.65\pm 0.02$ | $12.44$ | $11.29$ | $11.07$ | $10.97$ | 11,11,2,5,9,1
ULAS J102940.52+093514.6 | T8 | $68.6\pm 1.7$ | $16.08\pm 0.03$ | $14.46\pm 0.02$ | $16.76\pm 0.04$ | $14.43\pm 0.02$ | $12.59$ | $12.25$ | $12.21$ | $12.33$ | 18,19,3,5,9,1
CWISEP J104756.81+545741.6 | Y1 | $68.1\pm 4.9$ | $18.73\pm 0.17$ | $16.26\pm 0.02$ |  $19.36$${}^{\tablenotemark{c}}$ | $16.18\pm 0.06$ | $14.15$ | $13.23$ | $13.10$ | $13.14$ | 7,1,1,7,9,1
WISE J120604.38+840110.6 | Y0 | $84.7\pm 2.1$ | $17.34\pm 0.06$ | $15.22\pm 0.02$ | $18.09\pm 0.09$ | $15.17\pm 0.02$ | $12.91$ | $12.20$ | $11.99$ | $11.98$ | 11,11,2,5,9,1
SDSSp J134646.45$-$003150.4 | T6.5 | $69.2\pm 2.3$ | $14.67\pm 0.02$ | $13.67\pm 0.02$ | $15.48\pm 0.02$ | $13.69\pm 0.01$ | $11.91$ | $11.71$ | $11.66$ | $11.65$ | 20,21,4,5,9,1
WISEPC J140518.40+553421.4 | Y0.5 | $158.2\pm 2.6$ | $16.88\pm 0.05$ | $14.06\pm 0.02$ | $18.27\pm 0.13$ | $14.10\pm 0.01$ | $12.53$ | $11.40$ | $11.16$ | $11.09$ | 12,11,2,5,9,1
CWISEP J144606.62$-$231717.8 | Y1 | $103.8\pm 5.0$ | $18.91\pm 0.04$ | $15.92\pm 0.02$ |  $19.65$${}^{\tablenotemark{c}}$ | $15.96\pm 0.07$ | $13.67$ | $12.46$ | $12.22$ | $12.18$ | 7,1,1,8,9,1
WISE J150115.92$-$400418.4 | T6 | $72.8\pm 2.3$ | $15.28\pm 0.02$ | $14.13\pm 0.02$ | $16.13\pm 0.03$ | $14.23\pm 0.02$ | $12.53$ | $12.32$ | $12.33$ | $12.29$ | 16,15,2,5,9,1
WISEPA J154151.66$-$225025.2 | Y1 | $166.9\pm 2.0$ | $16.66\pm 0.04$ | $14.23\pm 0.02$ | $17.61\pm 0.17$ | $14.22\pm 0.03$ | $11.98$ | $10.93$ | $10.71$ | $10.66$ | 12,11,2,5,9,1
SDSS J162414.37+002915.6 | T6 | $91.8\pm 1.2$ | $14.41\pm 0.02$ | $13.10\pm 0.02$ | $15.15\pm 0.02$ | $13.13\pm 0.01$ | $11.74$ | $11.53$ | $11.52$ | $11.58$ | 22,21,4,5,9,1
WISEPA J195905.66$-$333833.7 | T8 | $83.9\pm 2.0$ | $15.36\pm 0.02$ | $13.79\pm 0.02$ | $16.14\pm 0.03$ | $13.80\pm 0.01$ | $11.96$ | $11.77$ | $11.54$ | $11.55$ | 13,13,2,5,9,1
WISEPC J205628.90+145953.3 | Y0 | $140.8\pm 2.0$ | $16.03\pm 0.03$ | $13.92\pm 0.02$ | $17.50\pm 0.10$ | $13.93\pm 0.02$ | $11.74$ | $10.93$ | $10.79$ | $10.82$ | 12,12,2,5,9,1
WISE J210200.15$-$442919.5 | T9 | $92.9\pm 1.9$ | $16.32\pm 0.04$ | $14.22\pm 0.02$ | $16.70\pm 0.04$ | $14.16\pm 0.02$ | $12.59$ | $11.98$ | $11.95$ | $11.99$ | 10,10,6,5,9,1
WISEA J215949.54$-$480855.2 | T9 | $73.9\pm 2.6$ | $16.84\pm 0.05$ | $14.58\pm 0.02$ | $17.97\pm 0.12$ | $14.65\pm 0.02$ | $13.42$ | $12.72$ | $12.64$ | $12.67$ | 15,15,2,5,9,1
WISE J220905.73+271143.9 | Y0 | $161.7\pm 2.0$ | $17.82\pm 0.09$ | $14.74\pm 0.02$ | $18.52\pm 0.20$ | $14.74\pm 0.02$ | $12.67$ | $11.48$ | $11.22$ | $11.12$ | 13,17,2,5,9,1
WISEA J235402.79+024014.1 | Y1 | $130.6\pm 3.3$ | $18.11\pm 0.11$ | $15.01\pm 0.02$ | $18.05\pm 0.14$ | $15.02\pm 0.03$ | $13.44$ | $12.23$ | $11.99$ | $11.94$ | 11,11,2,5,9,1
WISEPA J201824.96$-$742325.9 | T7 | $83.2\pm 1.9$ | $15.28\pm 0.02$ | $13.55\pm 0.02$ | $16.46\pm 0.04$ | $13.60\pm 0.01$ | $12.51$ | $12.04$ | $12.00$ | $12.02$ | 13,13,5,5,9,1
WISEPA J041022.71+150248.5 | Y0 | $151.3\pm 2.0$ | $16.64\pm 0.04$ | $14.17\pm 0.02$ | $18.02\pm 0.17$ | $14.10\pm 0.02$ | $12.27$ | $11.35$ | $11.24$ | $11.21$ | 12,12,2,5,9,1

References. — (1) This Work, (2) Kirkpatrick et al. (2021), (3) Best et al.
(2020), (4) Tinney et al. (2003), (5) Kirkpatrick et al. (2019), (6) Tinney et
al. (2014), (7) Meisner et al. (2020a), (8) Marocco et al. (2020), (9)
CatWISE2020 Catalog (Eisenhardt et al., 2020), (10) Kirkpatrick et al. (2012),
(11) Schneider et al. (2015), (12) Cushing et al. (2011), (13) Kirkpatrick et
al. (2011), (14) Mace et al. (2013), (15) Tinney et al. (2018), (16) Tinney et
al. (2012), (17) Cushing (2014), (18) Burningham et al. (2013), (19) Thompson
et al. (2013), (20) Tsvetanov et al. (2000), (21) Burgasser et al. (2006),
(22) Strauss et al. (1999)

At the time of the proposal’s submission, CWISEP J1446$-$23 and CWISEP
J1047+54, two of our selected objects, did not meet our 5% parallax cutoff,
but were undergoing astrometric follow-up by some of the authors with the
Hubble Space Telescope (HST) to reach this level. With the follow up now
complete, we computed their parallaxes using data from WISE/NEOWISE, Spitzer,
and HST. The procedure resembles closely the one described in Kirkpatrick et
al. (2021), but with a few key differences, which we briefly summarize here.
We measure source positions in the HST drizzle images provided by MAST using
CASU imcore, a source detection routine. The x,y pixel coordinates measured by
imcore are converted to $\alpha,\delta$ using the drizzled image WCS, and then
matched to Gaia DR3 using a 3″ matching radius. The positions of matching Gaia
sources are propagated from the Gaia epoch (2016.0) to the epoch of the HST
observations ($\sim$2021) using their measured parallax and proper motion. We
then derived a six-parameter transformation between the HST and the Gaia
coordinates by projecting both coordinates onto a tangent plane whose tangent
point is defined by the CRVAL1 and CRVAL2 FITS header keywords. We then solved
for the six parameters of the transformation, which account for offsets,
rotation, and scaling, using the IDL routine regress. The residuals of the
transformation are added in quadrature to the measurement errors to compute
the final coordinate uncertainties. More details on the full reduction and
astrometric calibration of the HST data are given in Marocco et al. (in
prep.). The parallax and proper motions were computed using the calibrated
$\alpha,\delta$ values as described in Kirkpatrick et al. (2019). Comparing
the new values with the preliminary measurements from Kirkpatrick et al.
(2019), we see that the addition of just one HST measurement at the extreme of
the previously poorly sampled parallactic ellipse allowed us to dramatically
improve the quality of our fit. This results in fractional uncertainties of
4.8% and 7.2% for CWISEP J1446$-$23 and CWISEP J1047+54, respectively. These
newly calculated parallaxes are given in Table 1.

##  3 Observations

We observed our sample using JWST’s Near Infrared Spectrograph (NIRSpec,
Jakobsen et al., 2022) and Mid Infrared Instrument (MIRI, Rieke et al., 2015),
collecting low-resolution spectroscopy with both instruments and broadband
photometry with MIRI (GO 2302, PI Cushing). NIRSpec was used in fixed-slit
mode with the CLEAR/PRISM filter and the S200A1 slit ($0\farcs 2\times 3\farcs
2$) and SUBS200A1 subarray. This filter allowed us to obtain a spectrum from
0.6–5.3 $\mu$m with a resolving power of $R={\lambda}/{\Delta\lambda}=30-300$.
The observations were executed with the NRSRAPID readout pattern and a 5 point
dither. MIRI spectroscopy was carried out using the low-resolution
spectrometer (LRS) in slit mode ($0\farcs 51\times 4\farcs 7$) and the FULL
subarray. We used the FASTR1 readout mode and a 2-point “along slit nod”
dither. MIRI LRS allowed us to obtain a spectrum from $\sim$5–14 $\mu$m with a
resolving power of 50$-$200\. We chose to truncate the red edge of the
spectrum where the signal-to-noise ratio first falls below 10 past 12 $\mu$m.
We also collected photometry in four MIRI broadband filters: F1000W, F1500W,
F1800W, and F2100W ($\lambda_{\mathrm{pivot}}$= 9.954, 15.065, 17.987, 20.795
$\mu$m, respectively). For the observations we used the FASTR1 readout and a
4-point dither, with 5 as our selected starting dither position.

Exposure times for each object were chosen via the Exposure Time Calculator
using a model spectrum (Marley et al., 2021) scaled to the object’s [4.5]
magnitude. We required that the MIRI photometry achieve a signal-to-noise
ratio of 30 and the NIRSpec and MIRI LRS simulated observations achieve a
median signal-to-noise ratio of 30, allowing us to achieve
$\sigma_{F_{\mathrm{bol}}}/F_{\mathrm{bol}}\leq 0.03$. We also required a
signal-to-noise ratio of 10 at both 5 and 12 $\mu$m, as these points are where
we merge our spectra and photometry when we build the spectral energy
distributions. These signal-to-noise ratio requirements have all been
surpassed due to JWST surpassing pre-launch requirements. Details on
individual observations can be found in Table 2.

Table 2: Target Exposure Times Name | NIRSpec | MIRI LRS | MIRI F1000W | MIRI F1500W | MIRI F1800W | MIRI F2100W |
---|---|---|---|---|---|---|---
| Obs. Date | N$\times$Int | Obs. Date | N$\times$Int | Obs. Date | N$\times$Int | Obs. Date | N$\times$Int | Obs. Date | N$\times$Int | Obs. Date | N$\times$Int |
| (UT) | (s) | (UT) | (s) | (UT) | (s) | (UT) | (s) | (UT) | (s) | (UT) | (s) |
WISE J0247+37 | 2022-09-21 | 5$\times$ 10.93 | 2022-09-21 | 2$\times$ 249.75 | 2022-09-21 | 4$\times$ 13.88 | 2022-09-21 | 4$\times$ 13.88 | 2022-09-21 | 4$\times$ 33.30 | 2022-09-21 | 8$\times$ 76.31 |
WISEPA J0313+78 | 2022-09-17 | 5$\times$ 9.37 | 2022-09-17 | 2$\times$ 77.70 | 2022-09-17 | 4$\times$ 13.88 | 2022-09-17 | 4$\times$ 13.88 | 2022-09-17 | 4$\times$ 13.88 | 2022-09-17 | 4$\times$ 19.43 |
WISE J0359$-$54 | 2022-09-12 | 5$\times$ 17.16 | 2022-09-12 | 2$\times$1387.52 | 2022-09-12 | 4$\times$ 19.43 | 2022-09-12 | 4$\times$ 19.43 | 2022-09-12 | 4$\times$ 49.95 | 2022-09-12 | 12$\times$ 79.55 |
WISE J0430+46 | 2022-09-21 | 5$\times$ 9.37 | 2022-09-21 | 2$\times$ 180.38 | 2022-09-21 | 4$\times$ 13.88 | 2022-09-21 | 4$\times$ 13.88 | 2022-09-21 | 4$\times$ 19.43 | 2022-09-21 | 4$\times$ 52.73 |
WISE J0535$-$75 | 2022-09-19 | 5$\times$ 15.60 | 2022-09-13 | 2$\times$ 693.76 | 2022-09-19 | 4$\times$ 16.65 | 2022-09-19 | 4$\times$ 19.43 | 2022-09-19 | 4$\times$ 44.40 | 2022-09-19 | 12$\times$ 74.00 |
WISE J0734$-$71 | 2023-07-09 | 5$\times$ 17.16 | 2023-07-09 | 2$\times$1248.77 | 2023-07-09 | 4$\times$ 16.65 | 2023-07-09 | 4$\times$ 19.43 | 2023-07-09 | 4$\times$ 47.18 | 2023-07-09 | 12$\times$ 76.78 |
WISE J0825+28 | 2022-10-25 | 5$\times$ 12.48 | 2022-10-25 | 2$\times$ 416.26 | 2022-10-29 | 4$\times$ 13.88 | 2022-10-29 | 4$\times$ 13.88 | 2022-10-29 | 4$\times$ 19.43 | 2022-10-29 | 4$\times$ 44.40 |
ULAS J1029+09 | 2023-05-04 | 5$\times$ 10.93 | 2023-05-04 | 2$\times$ 208.13 | 2023-05-04 | 4$\times$ 13.88 | 2023-05-04 | 4$\times$ 13.88 | 2023-05-04 | 4$\times$ 27.75 | 2023-05-04 | 8$\times$ 65.21 |
CWISEP J1047+54 | 2022-11-25 | 5$\times$ 34.30 | 2022-11-11 | 10$\times$1681.12 | 2022-11-11 | 4$\times$ 41.63 | 2022-11-11 | 4$\times$ 44.40 | 2022-11-11 | 12$\times$ 62.90 | 2022-11-11 | 32$\times$ 105.10 |
WISE J1206+84 | 2022-10-03 | 5$\times$ 17.16 | 2022-10-17 | 2$\times$ 971.26 | 2023-02-27 | 4$\times$ 16.65 | 2022-10-29 | 4$\times$ 19.43 | 2022-10-29 | 4$\times$ 41.63 | 2023-02-27 | 8$\times$ 98.51 |
SDSSP J1346$-$00 | 2023-07-18 | 5$\times$ 9.37 | 2023-07-18 | 2$\times$ 61.05 | 2023-07-17 | 4$\times$ 13.88 | 2023-07-17 | 4$\times$ 13.88 | 2023-07-17 | 4$\times$ 19.43 | 2023-07-17 | 4$\times$ 49.95 |
WISEPC1405+55 | 2023-02-28 | 5$\times$ 9.37 | 2023-03-04 | 2$\times$ 194.25 | 2023-05-03 | 4$\times$ 13.88 | 2023-05-03 | 4$\times$ 13.88 | 2023-05-03 | 4$\times$ 13.88 | 2023-05-03 | 4$\times$ 24.98 |
CWISEP J1446$-$23 | 2023-02-03 | 5$\times$ 24.95 | 2023-02-25 | 6$\times$1181.24 | 2023-02-25 | 4$\times$ 30.52 | 2023-02-25 | 4$\times$ 27.75 | 2023-02-25 | 4$\times$ 80.48 | 2023-02-25 | 16$\times$ 79.78 |
WISE J1501$-$40 | 2023-02-25 | 5$\times$ 9.37 | 2023-03-07 | 2$\times$ 111.00 | 2023-03-05 | 4$\times$ 13.88 | 2023-03-05 | 4$\times$ 13.88 | 2023-03-05 | 4$\times$ 22.20 | 2023-03-05 | 4$\times$ 83.25 |
WISEPA J1541$-$22 | 2023-03-05 | 5$\times$ 9.37 | 2023-03-05 | 2$\times$ 208.13 | 2023-03-05 | 4$\times$ 13.88 | 2023-03-05 | 4$\times$ 13.88 | 2023-03-05 | 4$\times$ 13.88 | 2023-03-05 | 8$\times$ 26.36 |
SDSS J1624+00 | 2023-02-25 | 5$\times$ 9.37 | 2023-03-08 | 2$\times$ 41.63 | 2023-03-11 | 4$\times$ 13.88 | 2023-03-11 | 4$\times$ 13.88 | 2023-03-11 | 4$\times$ 13.88 | 2023-03-11 | 4$\times$ 24.98 |
WISEPA J1959$-$33 | 2022-09-23 | 5$\times$ 9.37 | 2022-09-28 | 2$\times$ 83.25 | 2022-09-28 | 4$\times$ 13.88 | 2022-09-28 | 4$\times$ 13.88 | 2022-09-28 | 4$\times$ 16.65 | 2022-09-28 | 4$\times$ 47.18 |
WISEPC J2056+14 | 2022-09-20 | 5$\times$ 9.37 | 2022-09-20 | 2$\times$ 138.75 | 2022-09-20 | 4$\times$ 13.88 | 2022-09-20 | 4$\times$ 13.88 | 2022-09-20 | 4$\times$ 13.88 | 2022-09-20 | 4$\times$ 24.98 |
WISE J2102$-$44 | 2022-09-19 | 5$\times$ 9.37 | 2022-09-19 | 2$\times$ 180.38 | 2022-09-19 | 4$\times$ 13.88 | 2022-09-19 | 4$\times$ 13.88 | 2022-09-19 | 4$\times$ 19.43 | 2022-09-19 | 4$\times$ 61.05 |
WISE J2209+27 | 2022-10-17 | 5$\times$ 10.93 | 2022-10-17 | 2$\times$ 513.38 | 2022-10-17 | 4$\times$ 13.88 | 2022-10-17 | 4$\times$ 13.88 | 2022-10-17 | 4$\times$ 19.43 | 2022-10-17 | 4$\times$ 41.63 |
WISEA J2354+02 | 2023-07-06 | 5$\times$ 14.04 | 2023-07-06 | 2$\times$ 582.76 | 2023-07-06 | 4$\times$ 16.65 | 2023-07-06 | 4$\times$ 13.88 | 2023-07-06 | 4$\times$ 24.98 | 2023-07-06 | 4$\times$ 83.25 |
WISEA J2018$-$74 | – | – | 2022-09-19 | 2$\times$ 61.05 | 2022-09-19 | 4$\times$ 13.88 | 2022-09-19 | 4$\times$ 13.88 | 2022-09-19 | 4$\times$ 16.65 | 2022-09-19 | 4$\times$ 38.85 |
WISEPA J0410+15 | – | – | – | – | 2022-09-22 | 4$\times$ 13.88 | 2022-09-22 | 4$\times$ 13.88 | 2022-09-22 | 4$\times$ 13.88 | 2022-09-22 | 4$\times$ 27.75 |

Two of our objects had issues with their target acquisition which resulted in
a portion of their observations failing, which is why they are colored red in
Figure 1. WISEPA J0410+15 (Y0) is missing both spectral observations due to an
error in the submitted proper motion that caused it to fall outside of the
acquisition area. Its photometry is reported in this paper, but this object is
not included in our analysis. WISEPA J2018$-$74 (T7) is missing its NIRSpec
observation due to an failed guide star acquisition. The reason for its
failure is unknown and the failure was not identified until after the period
to request repeating the observation had passed. We use a previously observed
near-infrared spectrum and Spitzer photometry as a replacement for the NIRSpec
data, and we calculate a correction for the lack of NIRSpec data in Section 8.
Guide star failures did occur for several of our other targets, again with no
clear cause, but the others were identified quickly and the observations were
repeated upon request.

##  4 Data Reduction

###  4.1 JWST Pipeline

We used the JWST Science Calibration Pipeline (Version 1.12.5) for the data
reduction, using the 11.17.6 Calibration Reference Data System (CRDS) version
and the 1193.pmap CRDS context to assign the reference files. There were three
issues we noted while processing the data:

1\. CWISEP J1047+54 is not identified by the “source_catalog” step in the
F2100W filter due to low signal, even though it could be seen by eye. This was
overcome by lowering the signal-to-noise threshold for detection
(“snr_threshold”) of this step from 3.0 to 1.0.

2\. The uncertainty due to the photometric zero point of the MIRI photometry
is not included in the pipeline. The current version of the pipeline for MIRI
photometry is accurate to 3% or better based on measured flux calibration
stars111https://www.stsci.edu/contents/news/jwst/2023/updates-to-the-miri-
imager-flux-calibration-reference-
files?page=3&filterUUID=0655d914-43ee-4d09-a91b-9f45be575098, so we adopt a 3%
uncertainty for our MIRI photometric points.

3\. There is a slight error in the wavelength calibration past 12 $\mu$m, the
nominal end of the MIRI LRS spectrum, but the error is small enough
(0.01$-$0.03 $\mu$m) and over a short enough range that we do not attempt
correction. This wavelength error is the residual from the wavelength error
that previously plagued the entire MIRI LRS spectrum (e.g. Beiler et al.,
2023) before a correction was added to the JWST pipeline after further
calibration observations. Further calibration will likely be required to
improve the wavelength calibration past 12 $\mu$m, but likely is not a high
priority since this range is outside of the nominal range of the MIRI LRS
spectrum.

###  4.2 Pipeline Calibration

The pre-flight goal for the precision of the absolute flux calibration of JWST
spectra was $\sim$10% (Gordon et al., 2022). We use our sample to get a sense
for the reliability of the pipeline’s baseline absolute flux calibration by
comparing synthetic photometry to previous observations.

####  4.2.1 NIRSpec

We generate synthetic WISE (W1 and W2) and Spitzer ([3.6] and [4.5])
photometry from the NIRSpec spectra following methods and using zero-points
from Reach et al. (2005), Cushing et al. (2006), and Jarrett et al. (2011).
Figure 2 shows the difference between the observed (found in Table 2) and
synthetic photometry, as a function of [4.5] apparent magnitude. Variability
is not a concern for these objects, as Brooks et al. (2023) detected no long-
term variability above 20 mmags for late-T and Y dwarfs at these wavelengths,
and Trucks (2019) observed a maximum short-term variability of 4.2%. With this
large sample we would also expect any variability to impact the scatter of the
data, but not the average offset. The deltas of the W2 and [4.5] filters,
which cover a similar wavelength range, are both evenly distributed around 0,
with a scatter of approximately twice the individual uncertainties (0.1 and
0.05 magnitudes of scatter respectively). The W1 deltas are also evenly
distributed around 0, but with a much larger scatter. These three trends point
to the pipeline calibration being well within the 10% pre-flight goal.

Figure 2: The difference between observed and synthetic magnitudes (Spitzer
and WISE) for our sample. Note the y-axis ranges are all different. Therefore
we added a solid line and dashed lines at 0 and $\pm$ 0.1 magnitudes
respectively for ease of comparison between the different photometric bands
while retaining the fine detail for each distribution. The [4.5], W1, and W2
synthetic photometries are consistent with observations with varying levels of
scatter, but the [3.6] synthetic photometry is systematically $\sim$0.3
magnitudes fainter than the observed magnitude. Since this is not the case for
the W1 photometry (which covers a similar wavelength range) or the [4.5]
Spitzer photometry, this is likely an issue with the observed [3.6]
magnitudes, possibly due to a light leak.

In contrast to the W1, W2, and [4.5] filters, the [3.6] filter stands out with
the synthetic photometric magnitudes being consistently $\sim$0.3 magnitudes
fainter than observed magnitudes. This has previously been seen in
observations of WISE J0359$-$54 (Beiler et al., 2023) and WISE
J085510.83$-$071442.5 (Luhman et al., 2023), with WISE J0855$-$07 showing a
$\sim$0.4 mag offset for the synthetic photometry of both NIRSpec PRISM and
G395M. The fault seems to be with the observed [3.6] magnitudes since this
offset is occurring for two different NIRSpec modes, is not occurring for W1
even though it covers a similar wavelength regime, and is the only one of the
filters we test with this issue.

To see if this issue extends beyond substellar observations, we found 6
objects selected as calibrators for JWST which have both available NIRSpec
PRISM/CLEAR spectra and [3.6] magnitudes (Krick et al., 2021). Their
observations and properties are listed in Table 3. These NIRSpec observations
were taken using a different subarray with a shorter height (32 vs 64 pixels),
which unfortunately means that there is some overlap between nods when
performing background subtraction. This results in a poor out-of-the-box flux
calibration, and as such we must first calibrate these 6 spectra to their
K-band magnitudes (Cutri et al., 2003; Lawrence et al., 2007; McMahon et al.,
2013; Dye et al., 2018), which we also list in Table 3. We then calculate
their synthetic [3.6] magnitudes and the deltas to observed values, and plot
them along with the data for our sample and WISE 0855 ([3.6] = 17.34,
[3.6]${}_{\mathrm{IRAC}}-[3.6]_{\mathrm{Sim}}=-0.41$, (Luhman et al., 2023))
in Figure 3. We plot these deltas as a function of [3.6] magnitude since some
of the calibrator stars lack [4.5] measurements. The uncertainties on the
deltas for the calibrator stars include the K-band magnitude uncertainties.

Table 3: Calibrator Star Observations and Properties Obj. Name | Spec. TypeaaAll spectral types and IRAC [3.6] magnitudes come from (Krick et al., 2021). | Program # | K-band (mag) | IRAC [3.6]aaAll spectral types and IRAC [3.6] magnitudes come from (Krick et al., 2021). (mag) | Mode | Slit | Subarray
---|---|---|---|---|---|---|---
2MASS J18022716+6043356 | A2V | 1536 | 11.83$\pm$0.018bb2MASS Ks magnitude from the Two Micron All Sky Survey (Cutri et al., 2003). | 11.828$\pm$0.008 | PRISM/CLEAR | S1600A1 | SUB512
2MASS J17571324+6703409 | A3V | 4496 | 11.16$\pm$0.023bb2MASS Ks magnitude from the Two Micron All Sky Survey (Cutri et al., 2003). | 11.150$\pm$0.005 | PRISM/CLEAR | S1600A1 | SUB512
G 191-B2B | DA1 | 1537 | 12.78$\pm$0.003ccUKIRT WFCAM K (MKO) magnitude from the UKIRT Hemisphere Survey (Dye et al., 2018). | 12.835$\pm$0.007 | PRISM/CLEAR | S1600A1 | SUB512
GD 153 | DA1 | 4497 | 14.31$\pm$0.062bb2MASS Ks magnitude from the Two Micron All Sky Survey (Cutri et al., 2003). | 14.370$\pm$0.007 | PRISM/CLEAR | S1600A1 | SUB512
LDS 749B | DBQ4 | 4497 | 15.11$\pm$0.012ddVISTA Ks (2MASS) magnitude from the VISTA Hemisphere Survey (Lawrence et al., 2007). | 15.092$\pm$0.057 | PRISM/CLEAR | S1600A1 | SUB512
2MASS J03323287$-$2751483 | F7V | 4498 | 15.06$\pm$0.012eeUKIRT WFCAM K (MKO) magnitude from the UKIRT Infrared Deep Sky Survey (McMahon et al., 2013). | 14.859$\pm$0.040 | PRISM/CLEAR | S1600A1 | SUB512
Figure 3: The difference between the observed and synthetic [3.6] magnitudes
for both our sample (blue) and 6 JWST calibrator stars (yellow). The
calibrator stars are near zero, distinct from the $\sim$0.3 magnitude
systematic offset of our sample. This means the [3.6] offset is likely due to
a trait inherent to ultracool objects, possibly their extreme red spectra in
this bandpass.

The differences for all the calibrator stars are near zero, which is different
from the systematic offset we are seeing in the late brown dwarfs. This means
the offset we are seeing is likely a result of the strange shape of brown
dwarf spectra within the [3.6] bandpass, which starts with near zero flux at
the blue edge and climbs steeply towards the red edge. As such, a light leak
or a small discrepancy in the red edge of the [3.6] transmission curve could
explain the trend we are seeing. Within this current range of spectral types,
the offset is not obviously a function of spectral type. Future NIRSpec
observations of M, L, and early T dwarfs would be useful in order to see how
this offset changes as a function of spectral type and morphology.

####  4.2.2 MIRI LRS

We also test the pipeline’s flux calibration of our MIRI LRS data using
synthetic F1000W photometry, which we generate following the procedure in
Gordon et al. (2022). These are plotted in Figure 4. We see a systematic
offset, with the simulated photometry being $\sim$0.04 magnitudes fainter than
the observed F1000W magnitude, just over the uncertainty of our photometric
observations. Unfortunately, F1000W is the only observed photometry whose
entire bandpass fits within the MIRI LRS spectral range, so we cannot
determine whether this is an issue with the photometric or spectroscopic
absolute flux calibration. The JWST spectral pipeline currently does not
include true pathloss correction based on the actual slit point, so this is
likely the culprit, and a 4% error is within expectations for the current
absolute flux calibration of MIRI LRS.

Figure 4: The difference of between the observed and synthetic F1000W
magnitudes for our sample, which show synthetic photometry is $\sim$0.04
magnitudes dimmer. This is likely due to the JWST spectral pipeline pathloss
correction step not accounting for the actual slit position.

###  4.3 Flux Calibration and Merging of Spectra

While the absolute flux calibration of JWST appears to be within the pre-
flight goal of $\sim$10%, higher precision calibration is needed to achieve
our desired relative precision of 3% on the bolometric flux measurement. We
therefore obtained photometry to improve the absolute calibration to at least
$\sim$5%. The NIRSpec spectra were absolutely calibrated with [4.5] photometry
(Kirkpatrick et al., 2021), and the MIRI LRS spectra were calibrated with MIRI
F1000W photometry. Both of these photometric values and uncertainties can be
found in Table 2. From these magnitudes we calculate the scaling factors
needed to convert our spectra and their uncertainties to absolute units of
Jansky (Reach et al., 2005; Gordon et al., 2022). It is worth noting Spitzer
and JWST photometry assume different nominal spectra, $\nu f_{\nu}$ = constant
and $f_{\lambda}$ = constant, respectively.

We create continuous $\sim$0.6–$\sim$13 $\mu$m spectra by merging the NIRSpec
and MIRI spectra at their overlap from 5 to 5.3 $\mu$m. The NIRSpec spectra
have a higher resolving power than the MIRI LRS spectra at these wavelengths
but a lower signal-to-noise ratio. To balance the trade-off between including
spectral features only visible in NIRSpec and including low signal-to-noise
data, we cut the NIRSpec spectra where they first drop below a signal-to-noise
ratio of 10; the precise wavelength at which this occurs varies across our
sample. We also trim the spectra longward of 12 $\mu$m at the shortest
wavelength point where the signal-to-noise ratio first drops below 10, and
similarly trim at the longest wavelength point with negative flux before the
$Y$ band ($<$0.96 $\mu$m). As such, the upper and lower wavelength bounds of
the merged spectra vary for each object. The final spectral energy
distributions for each object, including MIRI photometry, are plotted in
Figures 5$-$7. With these flux calibrated spectra, we are able to calculate
synthetic photometry for most of the JWST photometric filters. We report this
process and its results in Appendix A.

Figure 5: The reduced and calibrated spectral energy distributions of our
sample plotted in normalized fν, primarily ordered by spectral type and
secondarily ordered by [4.5] absolute magnitude. We removed points which are
consistent with 0 (f${}_{i}<\sigma_{i}$), and show the uncertainties of our
spectrum with the grey shaded bars. Note that WISEA J2018$-$74 lacks NIRSpec
data, and so we instead plot the near-infrared Magellan/FIRE spectrum from
(Burgasser et al., 2011) and Spitzer [3.6] and [4.5] photometry. Figure 6:
Same as Figure 5. Figure 7: Same as Figure 5.

##  5 Near-Infrared Spectral Typing

Two of our objects, CWISEP J1047+54 and CWISEP J1446$-$23, have no previous
near-infrared spectroscopic observations, and as such only have spectral type
estimates inferred from their Spitzer [3.6]$-$[4.5] colors (Y0 and $\geq$Y1
respectively, Meisner et al., 2020a). We determined the spectral types for
these two objects by comparing their near-infrared spectra to spectral
standards defined in Cushing et al. (2011) and Kirkpatrick et al. (2012).
Since the spectral standards have a higher resolution than our near-infrared
data, we convolve the standards down to the resolution of NIRSpec for ease of
comparison, which can be seen in Figures 8.

Figure 8: Near-infrared portion of the NIRSpec spectra of CWISEP J1047+54
(left, black) and CWISEP J1446$-$23 (right, black) compared to the spectral
standards (red), all of which are normalized to unity at the peak of the $J$
band and offset by constants. The spectra for the spectral standards come from
Lucas et al. (2010) (T dwarf) and Schneider et al. (2015) (Y dwarfs). We
classify both of our objects as a Y1 dwarfs.

Both objects are clearly Y dwarfs, as they exhibit strong $Y$-band peaks
compared to the T dwarf spectral standards. We classify both CWISEP J1047+54
and CWISEP J1446$-$23 as Y1 dwarfs primarily due to the narrowness of their
$J$-band peaks, however, it is difficult to precisely spectral type these
objects due to the low signal-to-noise ratio of the Y1 spectral standard and
the resolution of our data.

##  6 Prominent Absorption Bands

With such a broad spectral range we are able to see a plethora of molecular
absorption features, including water ($\mathrm{H}_{2}\mathrm{O}$), methane
($\mathrm{CH}_{4}$), ammonia ($\mathrm{NH}_{3}$), carbon monoxide
($\mathrm{CO}$), and carbon dioxide ($\mathrm{CO}_{2}$). These features have
been seen in previously published Spitzer, JWST, and ground-based observations
(Oppenheimer et al., 1998; Roellig et al., 2004; Schneider et al., 2015; Miles
et al., 2020; Suárez & Metchev, 2022; Beiler et al., 2023; Luhman et al.,
2023), but the ability to see them in a single spectrum is groundbreaking. Of
particular note is the absence of a resolved phosphine ($\mathrm{PH}_{3}$)
feature in any of our objects, which is in direct contradiction to the
predictions of atmospheric models with disequilibrium chemistry (e.g. Meisner
et al., 2023; Mukherjee et al., 2023b), as has been previously noted in Beiler
et al. (2023) and Luhman et al. (2023).

With this large sample that spans the spectral type regime, we can now see how
these features evolve as a function of spectral type. We plot a spectral
sequence in Figure 9, preferentially selecting objects with Spitzer colors and
M[4.5] typical of the 20 pc population. There is a clear sequence of the flux
decreasing shortward of 2 $\mu$m and narrowing of the $J$ and $H$ bands, which
we would expect given that this progression of features is what defines these
spectral types. The near-infrared peaks are disappearing for the later-type
objects as even the deeper layers probed by these atmospheric windows reach
temperatures where we start to see the collapse of the Wien tail. The
decreasing trend extends to 4 $\mu$m and is also the case in the valley
between the 5 and 10 $\mu$m peak. This is caused by the blackbody peak moving
redward for cooler objects and/or the increasing absorption from water and
methane.

Figure 9: A spectral sequence of representative objects, showing how varied
the spectra are for these late types, plotted both in absolute flux (left) and
normalized flux (right), and offset for clarity. The zero flux level for each
spectrum is marked by the dashed line at the left edge of each spectrum.

Similarly, past 8 $\mu$m we see a sequence in the ammonia features. The
absorption in this portion of the spectrum is increasing in later spectral
types, seen most clearly in the deepening of the ammonia $P$ and $R$ branches,
and the $Q$-branch doublet. However, as these features deepen, the normalized
flux actually increases as the blackbody peak moves closer to these
wavelengths.

This leaves the 5 $\mu$m peak, where there is almost no sequence. CO and CO2
both have strong bands in this regime, and small changes in a variety of
atmospheric parameters can have a large effect on these molecular bands. For
one, the atmospheric composition, specifically the metallicity and the C/O
ratio, affects the CO and CO2 abundances since they are 2- and 3-metal
molecules made of carbon and oxygen. Another factor in the lack of a clean
sequence around the 5 $\mu$m region is disequilibrium chemistry. At the higher
temperatures of L and early T dwarfs, carbon dioxide and carbon monoxide are
the dominant reservoirs of carbon over methane, which is why the earliest
objects have strong CO and CO2 bands. Yet even at the cooler temperatures of
later spectral types where CH4 is chemically favored, we still see significant
amounts of CO and CO2, as it is dredged from the deeper, warmer layers of the
atmosphere into the photosphere faster than it can be converted into CH4.
Having so many parameters that can affect the CO and CO2 abundances obfuscates
any trends that might occur as a function of spectral type. Surface gravity
also strongly impacts these species, as seen in Zahnle & Marley (2014). At the
temperatures of Y dwarfs, low-gravity objects will have enhanced CO and CO2
absorption compared to high-gravity objects of the same temperature.

One trend we do see in this wavelength range is the repression of the blue
edge of the 5 $\mu$m peak as we go to later spectral types, driven by the
increasing abundance of methane. The increased abundance of methane with later
spectral types is primarily tied to the decrease in effective temperature.

##  7 Bolometric Luminosities and Effective Temperatures

By design, we are able to collect a substantial fraction of the light emitted
by the objects in our sample due to the broad spectral coverage of JWST,
resulting in precise bolometric fluxes. Calculating $F_{\mathrm{bol}}$
($F_{\mathrm{bol}}=\int_{0}^{\infty}f_{\lambda}\,d\lambda$) requires
constructing a complete spectral energy distribution from 0 to $\infty$
$\mu$m. To do so, we linearly interpolate between zero flux at 0 $\mu$m to the
first data point of the NIRSpec spectrum, and then from the last data point
through the JWST photometric points at 15.065, 17.987, and 20.795 $\mu$m.
Longward of this last photometric point, the spectral energy distribution can
be approximated as a Rayleigh-Jeans tail,

$f_{\lambda}=\frac{2ck_{\mathrm{B}}T}{\lambda^{4}}=\frac{C_{\mathrm{RJ}}}{\lambda^{4}},$
(1)

where $c$ is the speed of light, $k_{\mathrm{B}}$ is the Boltzmann constant,
$T$ is temperature, and $C_{\mathrm{RJ}}$ is the proportionality constant. We
solve for $C_{\mathrm{RJ}}$ using the F2100W flux density at 20.795 $\mu$m,
which gives us a functional form that allows us to extend the spectral energy
distribution to $\infty$ $\mu$m.

To calculate $F_{\mathrm{bol}}$, we integrate this spectral energy
distribution. The regions of linear interpolation and the Rayleigh-Jeans tail
can be calculated analytically, while the spectrum is integrated numerically
using Simpson’s rule, which is reliable at the low resolution of our JWST
spectra. We estimate the uncertainty of $F_{\mathrm{bol}}$ by generating one
million spectral energy distributions from the uncertainty distributions on
each data point. This includes randomly sampling the absolution calibration
scaling factors derived from the Spitzer [4.5] and F1000W photometric points,
allowing the NIRSpec and MIRI LRS spectra (and their uncertainties) to scale
independently. We calculated $F_{\mathrm{bol}}$ for each of these million
spectral energy distributions, with the mean and standard deviation of the
resulting distributions reported in Table 4. Our $F_{\mathrm{bol}}$
measurements have fractional uncertainties under 2% (except for WISE
J2102$-$44, which has a fraction uncertainty of 2.2%), which is well within
our 3% goal.

We then calculate $L_{\mathrm{bol}}$ as $L_{\mathrm{bol}}=4\pi
d^{2}F_{\mathrm{bol}}$ using distances derived from the precise parallaxes
listed in Table 2. We report these bolometric luminosities in Table 4. With
such precise $F_{\mathrm{bol}}$ measurements, the parallax uncertainties
becomes the dominant term in the bolometric luminosity uncertainties.

We could now calculate the effective temperature of our sample if our objects
had known radii, since

$T_{\mathrm{eff}}=\left(\frac{L_{\mathrm{bol}}}{4\pi\sigma
R^{2}}\right)^{\frac{1}{4}}.$ (2)

It is currently unfeasible to make direct measurements of the radii of the
solivagant brown dwarfs that make up our sample. However, the radii of brown
dwarfs are $\sim 1\pm 0.1$ $\mathcal{R}_{\mathrm{J}}^{\mathrm{N}}$—the nominal
value for Jupiter’s equatorial radius of $7.1492\times 10^{7}$ m (Mamajek et
al., 2015)—across a wide range of ages and masses due to the competing effects
of Coulomb repulsion and electron degeneracy (e.g. Burrows et al., 2001). We
adopt this radius of 1 RJup for a nominal effective temperature
$T_{\mathrm{eff}}^{R_{\mathrm{Jup}}}$, which we report in Table 4.

Table 4: Effective Temperature with Various Radius Assumptions Name | SpT | $F_{\mathrm{bol}}$ | $L_{\mathrm{bol}}$ | $\mathrm{log}(L/\mathcal{L}_{\odot}^{N})^{\tablenotemark{a}}$ | $T_{\mathrm{eff}}^{R_{\mathrm{Jup}}}$ | $T_{\mathrm{eff}}^{\mathrm{uni}}$ | $T_{\mathrm{eff}}^{\mathrm{B24}}$
---|---|---|---|---|---|---|---
|  | (W m-2) | (W) |  | (K) | (K) | (K)
WISE J0247+37 | T8 | $1.930\pm 0.033\times 10^{-16}$ | $5.497\pm 0.355\times 10^{20}$ | $-5.843\pm 0.028$ | 623 | $669^{+22}_{-35}$ | $627^{+35}_{-40}$
WISEPA J0313+78 | T8.5 | $5.578\pm 0.078\times 10^{-16}$ | $3.625\pm 0.156\times 10^{20}$ | $-6.024\pm 0.019$ | 562 | $598^{+17}_{-27}$ | $560^{+29}_{-31}$
WISE J0359$-$54 | Y0 | $6.952\pm 0.124\times 10^{-17}$ | $1.536\pm 0.088\times 10^{20}$ | $-6.397\pm 0.025$ | 453 | $468^{+13}_{-23}$ | $443^{+23}_{-19}$
WISE J0430+46 | T8 | $1.781\pm 0.033\times 10^{-16}$ | $2.310\pm 0.144\times 10^{20}$ | $-6.219\pm 0.027$ | 502 | $525^{+16}_{-26}$ | $495^{+28}_{-23}$
WISE J0535$-$75 | Y1 | $9.170\pm 0.153\times 10^{-17}$ | $2.326\pm 0.139\times 10^{20}$ | $-6.216\pm 0.026$ | 503 | $526^{+16}_{-26}$ | $496^{+28}_{-23}$
WISE J0734$-$71 | Y0 | $8.568\pm 0.154\times 10^{-17}$ | $1.846\pm 0.091\times 10^{20}$ | $-6.317\pm 0.022$ | 475 | $493^{+14}_{-24}$ | $466^{+24}_{-20}$
WISE J0825+28 | Y0.5 | $1.786\pm 0.029\times 10^{-16}$ | $9.168\pm 0.293\times 10^{19}$ | $-6.621\pm 0.014$ | 398 | $406^{+10}_{-16}$ | $387^{+15}_{-15}$
ULAS J1029+09 | T8 | $3.316\pm 0.053\times 10^{-16}$ | $8.435\pm 0.438\times 10^{20}$ | $-5.657\pm 0.023$ | 694 | $756^{+23}_{-39}$ | $705^{+39}_{-49}$
CWISEP J1047+54 | Y1 | $3.886\pm 0.063\times 10^{-17}$ | $1.002\pm 0.145\times 10^{20}$ | $-6.582\pm 0.063$ | 407 | $415^{+20}_{-22}$ | $395^{+23}_{-21}$
WISE J1206+84 | Y0 | $1.154\pm 0.020\times 10^{-16}$ | $1.927\pm 0.100\times 10^{20}$ | $-6.298\pm 0.023$ | 480 | $499^{+14}_{-24}$ | $472^{+26}_{-20}$
SDSSp J1346$-$00 | T6.5 | $1.126\pm 0.016\times 10^{-15}$ | $2.816\pm 0.191\times 10^{21}$ | $-5.133\pm 0.030$ | 1011 | $1044^{+26}_{-55}$ | $976^{+58}_{-87}$
WISEPC J1405+55 | Y0.5 | $2.021\pm 0.033\times 10^{-16}$ | $9.657\pm 0.344\times 10^{19}$ | $-6.598\pm 0.015$ | 404 | $412^{+10}_{-17}$ | $392^{+16}_{-15}$
CWISEP J1446$-$23 | Y1 | $5.736\pm 0.092\times 10^{-17}$ | $6.366\pm 0.629\times 10^{19}$ | $-6.779\pm 0.043$ | 364 | $366^{+14}_{-14}$ | $351^{+16}_{-13}$
WISE J1501$-$40 | T6 | $6.993\pm 0.110\times 10^{-16}$ | $1.579\pm 0.101\times 10^{21}$ | $-5.385\pm 0.028$ | 811 | $897^{+27}_{-48}$ | $836^{+49}_{-68}$
WISEPA J1541$-$22 | Y1 | $2.671\pm 0.045\times 10^{-16}$ | $1.147\pm 0.033\times 10^{20}$ | $-6.523\pm 0.013$ | 421 | $432^{+11}_{-18}$ | $411^{+18}_{-17}$
SDSS J1624+00 | T6 | $1.595\pm 0.022\times 10^{-15}$ | $2.265\pm 0.066\times 10^{21}$ | $-5.228\pm 0.013$ | 888 | $987^{+22}_{-60}$ | $922^{+53}_{-78}$
WISEPA J1959$-$33 | T8 | $6.224\pm 0.090\times 10^{-16}$ | $1.058\pm 0.052\times 10^{21}$ | $-5.558\pm 0.021$ | 734 | $805^{+24}_{-43}$ | $750^{+42}_{-56}$
WISEPC J2056+14 | Y0 | $3.443\pm 0.056\times 10^{-16}$ | $2.077\pm 0.067\times 10^{20}$ | $-6.266\pm 0.014$ | 489 | $510^{+14}_{-25}$ | $481^{+26}_{-20}$
WISE J2102$-$44 | T9 | $2.434\pm 0.054\times 10^{-16}$ | $3.372\pm 0.157\times 10^{20}$ | $-6.055\pm 0.020$ | 552 | $585^{+17}_{-27}$ | $549^{+29}_{-30}$
WISEA J2159$-$48 | T9 | $1.371\pm 0.027\times 10^{-16}$ | $3.004\pm 0.221\times 10^{20}$ | $-6.105\pm 0.032$ | 536 | $565^{+20}_{-26}$ | $532^{+30}_{-28}$
WISE J2209+27 | Y0 | $1.449\pm 0.025\times 10^{-16}$ | $6.621\pm 0.207\times 10^{19}$ | $-6.762\pm 0.014$ | 367 | $371^{+9}_{-13}$ | $355^{+13}_{-11}$
WISEA J2354+02 | Y1 | $8.642\pm 0.154\times 10^{-17}$ | $6.067\pm 0.319\times 10^{19}$ | $-6.800\pm 0.023$ | 359 | $362^{+10}_{-12}$ | $347^{+13}_{-11}$
WISEA J2018$-$74 ${}^{\tablenotemark{b}}$ | T7 | $5.019\pm 0.136\times 10^{-16}$ | $8.677\pm 0.458\times 10^{20}$ | $-5.645\pm 0.023$ | 721 | $784^{+31}_{-50}$ | $733^{+47}_{-58}$

A more rigorous estimate of our objects’ radii can be made using the technique
of Saumon et al. (2000), which relies on evolutionary models. Evolutionary
models use our current understanding of substellar atmospheric and interior
physics to predict the relations between the fundamental parameters of brown
dwarfs including the age, radius, and luminosity. With these models, we can
estimate the radius distributions for our objects from our observed luminosity
and an age distribution.

Our objects have no age constraints due to not being a part of young moving
groups or binary systems, so we make the reasonable assumption of a field age
distribution. We report temperatures assuming two age distributions: 1) a
uniform 1$-$10 Gyr distribution as preferred by Kirkpatrick et al. (2024) and
2) an exponential distribution ($p_{\mathrm{age}}(t)=e^{-\beta t}$) where
$t\in[0,10]$ Gyr and $\beta=0.44$, as preferred by Best et al. (2024). This
exponential distribution is skewed younger, which results in larger radii and
cooler temperatures due to brown dwarfs contracting and cooling as they age.

For this work, we draw one million ages and luminosities from their respective
distributions, and use the Sonora Bobcat solar metallicity evolutionary model
(Marley et al., 2021), part of new generation of self-consistent atmospheric
and evolutionary models that include updated opacities and atmospheric
chemistry. We perform a linear interpolation across the luminosity-age-radius
grid for pairs of ages and luminosities to arrive at a radius distribution.
The evolutionary model isochrones are plotted in Figure 10, more finely
sampled at low ages and more sparsely at older ages. Also plotted are the
drawn radii for two example objects: SDSS J1624+00, one of our more luminous
objects, and WISE J2209+27, one of our dimmer objects. Counter-intuitively,
for our sample the more luminous objects have a smaller radius, as the
evolutionary model isochrones have a local radius minimum at
$\mathrm{log}(L/\mathcal{L}_{\odot}^{N})$ $\sim$ $-$4.5.

Figure 10: The Sonora Bobcat solar-metallicity evolutionary model isochrones
(grey and black) plotted in luminosity-age-radius space, which we use to
estimate the radii of our objects. The 0.001, 0.01, 0.1, 1, and 10 Gyr
isochrones are plotted in black, and the model isochrones are more finely
sampled at low ages and more sparsely sampled at older ages. Also shown are
drawn radii points of two objects: SDSS J1624+00 (uniform age distribution in
yellow, exponential age distribution in pink), one of our more luminous
objects, and WISE J2209+27 (uniform in green, exponential in purple), one of
our dimmer objects. The exponential age distribution does extend to the 10
Gyr, but it is hidden by the uniform age distribution points. There is a local
minima in the evolutionary model grid at
$\mathrm{log}(L/\mathcal{L}_{\odot}^{N})$ $\sim$ $-$4.5 that results in the
more luminous objects in our sample having smaller radii than our dimmer
objects. For each distribution, the plotted points are only 1000 of the one
million randomly selected points, as this is sufficient to show the coverage
of the distributions.

We translate the radius and luminosity distributions into a temperature
distribution using Eq. 2. We summarize the temperature distributions with
their mean values and uncertainties that contain 34.1% of the distribution
above and below the mean respectively, which we report in Table 4. Our hottest
object is SDSSp J1346$-$00 at $\sim 1000$ K, and our coldest objects are WISEA
J2354+02 and CWISEP J1446$-$23 at $\sim 360$ K.

We also tested uniform age distributions that extended down to 0.5 Gyr to see
how this would vary $T_{\mathrm{eff}}$. This resulted in 1$-$5 K colder
temperatures, with larger differences for hotter objects. Uncertainties also
increase by 1$-$12 K, with the larger increases once again coming from the
hotter objects. The changes are a result of including even younger objects,
which extends the tail of the radius distributions to larger radii. The
fractional change in the mean $T_{\mathrm{eff}}$ is under 1% for all objects,
so we feel confident moving forward with our uniform 1$-$10 Gyr age
distribution.

As examples, we plot the radius and temperature distributions SDSS J1624+00
and WISE J2209+27, in Figures 11 and 12. Note that due to their inverse
relation, a larger radius results in cooler temperature, and vice versa. We
see step-like and spiky features in the uniform age and exponential age radius
distributions respectively due to our choice of linear interpolation and the
sparseness of the evolutionary model age sampling at older ages. These two
factors result in large age ranges between isochrones where the interpolated
surface has a constant slope and therefore results in a roughly constant
probability density for a given range of radii. A cubic interpolation was
attempted, but this results in both oscillatory artifacts and false peaks in
the interpolated surface, especially at younger ages, that have a much
stronger impact on the radius distribution than the linear interpolations
artifacts. The linear interpolation, while not creating a smooth radius
distribution, is sufficiently accurate for our work.

Figure 11: Left: the distribution of a million radii drawn from Sonora Bobcat
solar metallicity models using the luminosity of SDSS J1624+00 ($2.265\pm
0.064\times 10^{21}$ W) and either a 1$-$10 Gyr uniform age distribution
(gold) or a negative exponential age distribution (purple, described more
fully in Section 7). The mean radius for each distribution is plotted as
dashed vertical line, as well as 1 RJup. The bump from 1.07$-$1.25 RJup is due
to deuterium burning which occurs at $\sim$0.4 Gyr for this luminosity. The
different age distributions have a large disparity in their predicted radii
with the young ages of the exponential age distribution allowing for radii up
to 1.6 RJup. Right: the effective temperature distributions calculated using
the radius distributions on the left and the luminosity. The mean effective
temperature for each distribution is plotted as dashed vertical line, as well
as the nominal effective temperature, which assumes R = 1 RJup. The bump from
820$-$850 K is tied to deuterium burning. There is a significant difference in
the mean $T_{\mathrm{eff}}$ values of the two age assumptions, but an even
larger difference in the broadness of the $T_{\mathrm{eff}}$ distribution.
Figure 12: The same as Figure 11, but for WISE J2209+27 ($6.621\pm 0.208\times
10^{19}$ W). Here the deuterium burning bump is from 1.02$-$1.06 RJup and
360$-$370 K, and occurs at $\sim$4 Gyr for this luminosity. For the colder
objects, the two age assumptions have a similar spread in bulk of their
distributions, though the exponential age distribution results in longer
tails, especially at the young age, high radius end.

In comparing the temperature distributions for these two objects, we see that
for the hotter object, the exponential age distribution results in a much
wider range of radii and therefore also a wider range of effective
temperatures. At the hot end, this distribution results in $\sim$7%
uncertainty, but falls to $\sim$3% for the colder objects. On the other hand,
the uniform age distribution is consistently $\sim$3% across our sample.

No matter our choice of age distribution, the radius estimation ends up
dominating the effective temperature uncertainty for all objects (with the
exception of CWISEP J1446$-$23 and CWISEP J1047+54 whose higher parallax
uncertainties result in $\sigma_{L_{\mathrm{bol}}}$ equally contributing to
$\sigma_{T_{\mathrm{eff}}}$). A marginal improvement in the precision of
$T_{\mathrm{eff}}$ could be made with further astrometric follow-up or by
expanding the spectral energy distributions. However, even if we knew our
bolometric luminosity to infinite precision, we would still be unable to lower
our fractional $T_{\mathrm{eff}}$ uncertainty below 2.5% without stronger age
constraints or direct radius measurements.

Previous effective temperature estimates for these objects can be found in
Kirkpatrick et al. (2021), assigned either from measured values in Filippazzo
et al. (2015) or the $T_{\mathrm{eff}}$ versus MH or spectral type relations.
With the broad spectral coverage of JWST, we are able to significantly reduce
the uncertainly on $T_{\mathrm{eff}}$, in some cases by a factor of 7. The
previous estimates were accurate, despite their low precision, as all but two
of our objects fall within $1\sigma$ of the Kirkpatrick et al. (2021)
temperatures. As for systematic differences, the uniform age distribution
tends to result in higher $T_{\mathrm{eff}}$ than those of Kirkpatrick et al.
(2021), while the exponential age distribution results in a slightly lower
temperature in comparison.

The temperatures in Kirkpatrick et al. (2021) are largely derived from the
previous work of Filippazzo et al. (2015), who constructed spectral energy
distributions and calculated $T_{\mathrm{eff}}$ for a large sample of late M
to T dwarfs using a technique similar to ours. We constructed our sample to
overlap in parameter space with Filippazzo et al. (2015) and also included two
objects from their sample, allowing us to compare effective temperature
values. Figure 13 shows the Filippazzo et al. (2015) temperatures and our
uniform age distribution temperatures as a function of spectral type, M[4.5],
and MH. CWISEP J1446$-$23 and CWISEP J1047+54 do not have $H$-band photometry,
and so are not included in this plot.

Figure 13: Our effective temperatures (black) and effective temperatures from
Filippazzo et al. (2015) (orange) plotted as a function of spectral type,
[4.5] absolute magnitude, and $H$-band absolute magnitude (where available).
The samples overlap over a small range of parameters (including two shared
objects), and where this happens our objects tend to have hotter effective
temperatures. Objects that fall outside the population trends are labelled.

Looking at where the two samples overlap, we see that our $T_{\mathrm{eff}}$
values tend to the hotter side of the Filippazzo et al. (2015) distribution.
For two overlapping objects SDSS J1624+00 and SDSSp J1346$-$00, our effective
temperatures are 51 and 33 K hotter, respectively. This is true, even though
the Filippazzo luminosities are brighter. We measure
$\mathrm{log}(L/\mathcal{L}_{\odot}^{N})$ as $-$5.227$\pm$0.013 and
$-$5.133$\pm$0.030 respectively, compared to Filippazzo’s measurements of
$-$5.19$\pm$0.01 and $-$5.06$\pm$0.03. This means that the difference must be
in the assumed radii.

Filippazzo et al. calculated their radii by assuming an age of 0.5$-$10 Gyr
for both objects, and using the evolutionary models from Saumon & Marley
(2008) and Baraffe et al. (2003) arrived at a range of possible radii, which
they reported as $0.94\pm\sim 0.16$ $R_{\mathrm{Jup}}$, compared to our value
of $\sim 0.81\pm 0.05$ $R_{\mathrm{Jup}}$. The difference primarily arises
from Filippazzo et al. selecting a radius range from the evolutionary models,
which creates a bias towards the larger radii at the tail of the distribution,
while we draw a distribution from the evolutionary models, which favors the
smaller radii. This explains why our effective temperatures are systematically
hotter than those of Filippazzo et al. (2015). The different choices of
evolutionary models compounds this effect, as when we draw radii for these two
objects from the Saumon & Marley (2008) hybrid evolutionary models, we find
our radii increases by 0.02 $R_{\mathrm{Jup}}$. Similarly, our choice of
1$-$10 Gyr shifts our radii distribution smaller, but this is also a secondary
effect, as even if we assumed a uniform age of 0.1$-$10 Gyr, our mean radii
would only increase by 0.02 $R_{\mathrm{Jup}}$. Both choices impact the
reported radii, but even combined they cannot account for the 0.13
$R_{\mathrm{Jup}}$ difference.

The brighter luminosities reported by Filippazzo et al. are also interesting
in and of themselves. Updated parallaxes have remained within 1% of the old
values, so differences in distance are not the culprit, and both of these
objects had coverage out to 12 $\mu$mthrough WISE photometry or Spitzer
InfraRed Spectrograph (IRS) spectra, so an overestimated Rayleigh-Jeans tail
is not the issue. The likely cause of the discrepancy is the region from 2$-$6
$\mu$m, which Filippazzo et al. (2015) only sampled with Spitzer and WISE
photometry. The linear interpolation through these points, especially across
deep absorption features, could easily result in the luminosity difference we
are seeing in these objects. The systematically brighter [3.6] magnitudes that
we noted in Section 4.2 would also exacerbate this issue. This shows once
again how essential a complete spectral energy distribution is to calculating
the effective temperatures of these cold objects.

##  8 Incomplete Spectral Energy Distributions

Few substellar objects will have their full spectral energy distributions
observed with JWST, so it is useful to see how the effective temperatures
computed using incomplete spectral energy distributions compare to our
reported values. We look at six incomplete spectral energy distribution
variations, which are constructed from:

1\. JWST NIRSpec and MIRI LRS spectra,

2\. JWST NIRSpec spectra,

3\. JWST NIRSpec spectra and all four MIRI photometric points,

4\. Previous near-infrared spectra, W1, W2, and [4.5] photometric points, and
JWST MIRI LRS spectra,

5\. Previous near-infrared spectra, W1, W2, and [4.5] photometric points, JWST
MIRI LRS spectra, and our MIRI photometric points,

6\. Previous near-infrared spectra and W1, W2, and [4.5] photometric points.

When the NIRSpec spectrum is not included, we replaced it with previous ground
or Hubble observations, and Spitzer [4.5] and WISE W1 and W2 photometry when
available, as these observations are nearly ubiquitous for cold objects. The
references for the near-infrared spectra are found in Table 5. The Spitzer
[3.6] photometric point was omitted due to the systematic offset we noted in
Section 4.2, and points are also omitted in cases where they overlap with a
spectrum (such as the case for the W2 point when MIRI LRS is included). A
handful of our objects do have Spitzer IRS and M band spectra, but we chose to
not include these in our variant spectral energy distributions to make the
results more universally applicable.

When both NIRSpec and MIRI LRS are included, they are merged as before, but
when only one is included we trim the spectrum to eliminate low signal-to-
noise pixels or detector edge effects. For the NIRSpec data, we trim the
spectrum at the first point past 4 $\mu$m with a signal-to-noise ratio below
10 (cut-off wavelengths range from 4.94$-$5.29 $\mu$m). The MIRI LRS data
nominally covers down to 5 $\mu$m, but we find that the spectra are reliable
only down to 4.5 $\mu$m, so we make our cut there.

Table 5: Near-Infrared Spectral Reference Object Name | Reference
---|---
WISE J0247+37 | Mace et al. (2013)
WISEPA J0313+78 | Kirkpatrick et al. (2011)
WISE J0359$-$54 | Kirkpatrick et al. (2012)
WISE J0430+46 | Mace et al. (2013)
WISE J0535$-$75 | Schneider et al. (2015)
WISE J0734$-$71 | Kirkpatrick et al. (2012)
WISE J0825+28 | Schneider et al. (2015)
ULAS J1029+09 | Thompson et al. (2013)
WISE J1206+84 | Schneider et al. (2015)
SDSSP J1346$-$00 | Burgasser et al. (2006)
WISEPC1405+55 | Schneider et al. (2015)
WISE J1501$-$40 | Tinney et al. (2018)
WISEPA J1541$-$22 | Cushing et al. (2011)
SDSS J1624+00 | Burgasser et al. (2006)
WISEPA J1959$-$33 | Zhang et al. (2021)
WISEA J2018$-$74 | Burgasser et al. (2011)
WISEPC J2056+14 | Cushing et al. (2011)
WISE J2102$-$44 | Tinney et al. (2018)
WISEA J2159$-$48 | Tinney et al. (2018)
WISE J2209+27 | Schneider et al. (2015)
WISEA J2354+02 | Schneider et al. (2015)

In building these incomplete spectral energy distributions, we adopt a similar
strategy as our full one. We linearly interpolate to zero flux at zero microns
to the bluest point, attached a Rayleigh-Jeans tail to the reddest point, and
in between, linearly interpolate through photometric points. These regions are
all integrated analytically, whereas the spectra are integrated numerically
using Simpson’s Rule. We generate 100,000 spectral energy distributions (high-
resolution near-infrared data makes generating one million difficult) based on
the uncertainties on each data point from which we calculate
$F_{\mathrm{bol}}$, from which we calculate $L_{\mathrm{bol}}$ with the
distance. For this comparison, since we only care about the difference in
temperature between the complete and partial spectral energy distributions, we
only calculate radii and temperatures based on the uniform age distribution.
We plot the difference between the effective temperatures from the complete
and partial spectral energy distributions
($T_{\mathrm{eff}}$${}^{\mathrm{full}}-$$T_{\mathrm{eff}}$partial) in Figure
14, with each panel showing a different partial spectral energy distribution.
This is done as a function of [4.5] absolute magnitude, which roughly
corresponds to spectral type.

Figure 14: The difference in effective temperatures derived from various
partial spectral energy distributions and those from the full distribution as
a function of the absolute [4.5] magnitude. For ease of comparison, we include
dashed lines at 0 K and dotted lines at $\pm$20 K. Linear fits are shown for
each data set (solid line), with the covariance errors plotted as the shaded
region. More detail on how we build the spectral energy distributions can be
found in Section 8.

The only partial distribution that results in consistently hotter effective
temperatures is the one that includes MIRI photometric points but not the MIRI
LRS spectra, which is expected as linearly interpolating from the 5 $\mu$m
peak to the 10 $\mu$m photometric point significantly overestimates the flux
in this regime. This partial distribution also show almost no dependence on
[4.5] absolute magnitude (fits listed in Table 6).

Table 6: Linear Fits and Covariance Matricies of Difference in Temperatures Between Complete and Various Partial Spectral Energy Distributions  NIRSpec | LRS | Phot. | $c_{1}$ | $c_{0}$ | $Cov$
---|---|---|---|---|---
X | X | – | 5.5 |  $-$70.4 | $\begin{pmatrix}1.0&-15.1\\\ -15.1&226.2\end{pmatrix}$
X | – | – | 16.1 |  $-$181.3 | $\begin{pmatrix}19.9&-301.9\\\ -301.9&4585.8\end{pmatrix}$
X | – | X | 1.5 |  $-$44.6 | $\begin{pmatrix}2.8&-41.1\\\ -41.1&616.2\end{pmatrix}$
– | X | – |  $-$5.9 | 104.0 | $\begin{pmatrix}18.9&-284.5\\\ -284.5&4286.3\end{pmatrix}$
– | X | X |  $-$10.4 | 159.9 | $\begin{pmatrix}15.6&-234.2\\\ -234.2&3521.2\end{pmatrix}$
– | – | – | 5.2 |  $-$21.6 | $\begin{pmatrix}39.5&-597.3\\\ -597.3&9052.9\end{pmatrix}$

The strongest dependence on [4.5] absolute magnitude comes from the spectral
energy distribution with only the NIRSpec spectrum. For the hottest objects in
our sample, NIRSpec plus a Rayleigh-Jeans tail mostly replicates the flux, but
as we look at cooler objects and the peak of the blackbody curve moves
redward, more and more flux is coming out at wavelengths not probed by
NIRSpec. This $\sim$75 K offset for the coldest objects is one of the primary
reasons why MIRI LRS data is so important for understanding Y dwarf
atmospheres. The MIRI photometry is not quite as essential, but without it the
coldest objects would be systematically off by $\sim 1\sigma$ ($\sim$20 K).

We have particular interest in the partial spectral energy distribution which
includes the MIRI data but not the NIRSpec spectrum, as this is the data we
have available for WISEPA J2018$-$74\. From this partial spectral energy
distribution we calculate $F_{\mathrm{bol}}$ and $L_{\mathrm{bol}}$ (reported
in Table 4), which results in an effective temperature of 761${}^{+23}_{-42}$
K for our uniform age distribution, and 710 ${}^{+39}_{-50}$ K for our
exponential distribution. WISEPA J2018$-$74 has a [4.5] absolute magnitude of
13.15$\pm$0.05 which, given the fits listed in Table 6, requires a temperature
correction of 23 $\pm$ 8 K. We therefore report the effective temperature of
WISEPA J2018$-$74 as 784${}^{+31}_{-50}$ K for our uniform age distribution,
and 733 ${}^{+47}_{-58}$ K for our exponential distribution. This is the
reported temperature in Table 4.

##  9 Evolution of Absorption Features with Effective Temperature

We now order our objects by their effective temperatures, as shown across
Figures 15$-$19, and observe trends in their spectral morphology. The objects
selected for the spectral type sequence in Figure 9 happen to be ordered by
effective temperature, but we can see in Figure 15 that the near-infrared
spectral type ordering does not map directly to effective temperature. There
is still a correlation, as the near-infrared region is primarily shaped by
methane and water, whose abundances are strongly dependent on temperature.
However there are some objects that buck the spectral type ordering. WISE
J0535$-$75 (Y1) is the most discrepant, with a temperature hotter than any
other Y dwarf and one T8. This T8, WISE J0430+46, is also out of place. It is
colder than any of the T9 dwarfs, and is almost 150 K colder than the other T8
dwarfs. These objects are not poorly spectral typed, as when this sample is
ordered by their spectral types, there is a clear sequence in the near-
infrared. The problem is that for these cold objects, this region no longer
dominates the spectral energy distribution, and as such the near-infrared does
not correlate as strongly with $T_{\mathrm{eff}}$ as it does for hotter
objects.

Figure 15: Our sample of objects, sorted by effective temperature, zoomed in
on the near-infrared portion of the spectra. Each object is normalized across
this shown portion of the spectra, and offset to the red dashed line. Figure
16: Same as Figure 15, but zoomed in on the 3 $\mu$m ammonia feature. Figure
17: Same as Figure 15, but zoomed in on the 5 $\mu$m peak. Figure 18: Same as
Figure 15, but zoomed in on the valley between the 5 and 10 $\mu$m peaks.
Figure 19: Same as Figure 15, but zoomed in on the 10 $\mu$m peak.

One would hope that since the 5 $\mu$m peak is where a significant portion of
our sample’s flux is emitted there would be a clear sequence in this
wavelength range. However, as seen in Figure 17, the 5 $\mu$m region does not
follow a temperature sequence, nor could we identify one by eye. This lack of
a sequence is especially true amongst the Y dwarf. The spectral diversity is
due to the same significant atmospheric degeneracies we discussed in regards
to the spectral type sequence. Given the spectral diversity and apparent
sensitivity of this wavelength range, this spectral region is ripe for further
study and will be useful in refining our knowledge of atmospheric physics and
chemistry. One prime example of this is how the lack of any phosphine
absorption in any of our objects and other published ultracool dwarfs (aside
from one reported detection of PH3 in a spectrum with a signal-to-noise ratio
of $\sim$5 Burgasser et al. (2023)) is challenging our current understanding
of phosphorus chemistry in these atmospheres.

One possibility for this spectral diversity is that we are probing variation
in the surface gravities of these objects. Zahnle & Marley (2014) showed how
the carbon species are particularly sensitive to gravity and predicted that
CO2 could be detectable down to 500 K in low-gravity objects. We do see
multiple detections in Y dwarfs below 400 K, which generally have low surface
gravities predicted by evolutionary models (e.g. Marley et al., 2021). The
lower gravities of the Y dwarfs also mean that if the variation in gravity
remains the same, it would result in a high fractional change in the
population, thus creating the greater diversity that we see among the Y
dwarfs. Further work will need to be done examining this possible connection
between the carbon-bearing species and surface gravity.

There are two objects in particular that stand out due to the features of the
carbon-bearing species: CWISEP J1047+54 and WISE J0535$-$75\. CWISEP J1047+54
is a Y1 dwarf exhibiting abnormally strong CO2 and CO features compared to
other Y1’s. Along with this, it also exhibits a steeper slope on the blue edge
of the 5 $\mu$m peak, likely caused by weaker CH4 absorption. This may be
explained by extreme disequilibrium chemistry, low gravity, or a low C/O ratio
causing the oxygen bearing molecules to be favored. On the other extreme is
WISE J0535$-$75, a Y1 dwarf with no discernible CO2 band and an almost
undetectable CO band, possibly due to a low metallicity or high surface
gravity. These features result in both objects being distinct in [4.5] vs
[3.6]$-$[4.5] color-magnitude space when compared to the rest of the 20 pc
sample because of their extreme colors (CWISEP J1047+54 is extremely blue and
WISE J0535$-$75 is extremely red). This may mean Spitzer colors are useful for
identifying objects with interesting chemistries.

One major molecule not seen in this wavelength range is NH3, but it can be
seen in the NIRSpec portion of the spectrum. A tentative detection of ammonia
at 3 $\mu$m was claimed in Beiler et al. (2023), and we can confirm it with
this full sample, as it is seen in a majority of our objects. The depth of the
feature generally increases with temperature, though the low signal-to-noise
ratio makes it difficult to determine the depth for the coldest objects.

The ammonia sequence is more apparent in the mid-infrared regime, where the
8$-$12 $\mu$m ammonia band absorption increases as effective temperature
drops. Only WISE J0535$-$75 breaks the sequence, having stronger absorption
than objects with similar temperatures. That said, the spectral morphology of
this wavelength range appears to be the most strongly correlated with
effective temperature. This region is almost entirely shaped by ammonia, whose
abundance is not strongly affected by disequilibrium chemistry, C/O, or M/H
(Mukherjee et al., 2023a). Instead, due to being quenched deep in the
convective layer, the ammonia abundance and absorption is primarily dependent
on effective temperature. This makes the spectral morphology of this region a
great tracer of effective temperature.

##  10 Conclusion

We present 0.6$-$22 $\mu$m spectral energy distributions of 23 late-T and Y
dwarfs, consisting of JWST NIRSpec PRISM, MIRI LRS, and MIRI photometry. With
this large sample, we test the absolute calibration of the JWST pipeline by
comparing synthetic photometry with previous observations. The NIRSpec data
matches most previous observations, though it reveals a systematic offset
($\sim$0.3 mag) between the Spitzer observed and synthetic [3.6] magnitudes
that only occurs for late brown dwarfs. This was previously noted in two Y
dwarfs, and this large sample confirms that the offset is a systematic issue.
We propose that this is caused by the uncommon red shape of the brown dwarf
spectrum in this band and/or a light leak. The MIRI LRS data shows a
$\sim$0.04 mag offset when compared to the observed F1000W photometry, which
we attribute to the pathloss correction step of the JWST pipeline not
accounting for actual slit pointing.

With these broad wavelength spectral energy distributions and precise
parallaxes, we are able to calculate the bolometric luminosities of our sample
with a precision of $\sim$6%. From this we calculate $T_{\mathrm{eff}}$ using
three different radii assumptions, including a naive assumption of 1 RJup and
two based on evolutionary models and age distributions endorsed by Kirkpatrick
et al. (2021) and Best et al. (2024), respectively. This resulted in effective
temperatures ranging from $\sim$1000-350 K for spectral types from T6 to Y1.
These effective temperatures are approaching the limit of precision achievable
with current evolutionary models and age estimates, and extends the population
of brown dwarfs with precise effective temperatures into the Y dwarf regime.
We also investigate how partial spectral energy distributions systematically
affect the derived effective temperatures for these late-type brown dwarfs,
and provide corrections as a function of [4.5] absolute magnitude.

Our spectral energy distributions also reveal a plethora of absorption
features from a variety of molecules, and with this large sample we can see
how these features evolve as a function of spectral type and effective
temperature. We note the extreme diversity of the spectral morphology from
3.5$-$5.5 $\mu$m, which appears to be sensitive to atmospheric properties.
This includes a surprising lack of PH3, as has been seen in other JWST
observations, and strong CO and CO2 absorption even in the Y dwarfs. The
diversity of the 5 $\mu$m peak is in direct contrast to the 8$-$12 $\mu$m
regime, whose spectral morphology (shaped largely by NH3) appears to correlate
with effective temperature. We also confirm the NH3 detection at 3 $\mu$m that
was tentatively noted in Beiler et al. (2023). Given that these broad
wavelength spectral energy distributions cover a wide range of molecular
features, probe various layers of the photosphere, and display significant
diversity, this sample is ideal for both forward model and retrieval fits.

## Acknowledgments

This work is based [in part] on observations made with the NASA/ESA/CSA James
Webb Space Telescope. The data were obtained from the Mikulski Archive for
Space Telescopes at the Space Telescope Science Institute, which is operated
by the Association of Universities for Research in Astronomy, Inc., under NASA
contract NAS 5-03127 for JWST. The specific observations analyzed can be
accessed via https://doi.org/10.17909/dwnb-jv28 (catalog 10.17909/dwnb-jv28).
These observations are associated with program #2302. Support for program
#2302 was provided by NASA through a grant from the Space Telescope Science
Institute, which is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS 5-03127. This research has
benefited from the Y Dwarf Compendium maintained by Michael Cushing at
https://sites.google.com/view/ydwarfcompendium. This research has made use of
the Spanish Virtual Observatory (https://svo.cab.inta-csic.es) project funded
by MCIN/AEI/10.13039/501100011033/ through grant PID2020-112949GB-I00.

##  Appendix A Synthetic JWST Photometry of Our Sample

We provide synthetic JWST vega magnitudes for our sample of complete spectral
energy distributions in all filters that fall entirely within our observed
wavelength range in Tables 7-9. All values were calculated following the
process from Gordon et al. (2022). The NIRCam zero points used are the average
zero point across all detectors listed in the JWST User
Documentation222https://jwst-
docs.stsci.edu/files/182256933/224166043/1/1695068757137/NRC_ZPs_1126pmap.txt.
No table is currently published for the MIRI photometry. Instead we used
publicly available Stage 3 data products from JWST Program 1040, which report
flux and vega magnitudes, to derive the zero points for filters F560W, F770W,
and F1130W (113.69, 64.03, and 23.83 Jy, respectively). The coronagraphic
filters do not have any such available observations, so the calculated SVO
zero points were used333http://svo2.cab.inta-csic.es/svo/theory/fps3/.

Table 7: Synthetic JWST Photometry of Our Sample Obj. Name | Parallax | F090W | F115W | F140M | F150W | F150W2 | F162M | F164N | F182M | F187N | F200W | F210M
---|---|---|---|---|---|---|---|---|---|---|---|---
WISE J0247+37 | 68.4$\pm$2.0 | 21.62 | 18.63 | 20.87 | 18.75 | 18.74 | 18.07 | 19.30 | 20.07 | 20.36 | 18.92 | 18.13
WISEPA J0313+78 | 135.6$\pm$2.8 | 20.80 | 17.95 | 20.37 | 18.17 | 18.16 | 17.48 | 18.96 | 19.66 | 19.81 | 18.38 | 17.59
WISE J0359$-$54 | 73.6$\pm$2.0 | 23.17 | 21.78 | 25.17 | 22.07 | 21.96 | 21.28 | 23.06 | 23.64 | $\cdots$ | 22.17 | 21.30
WISE J0430+46 | 96.1$\pm$2.9 | 21.52 | 19.54 | 21.69 | 19.63 | 19.72 | 18.90 | 19.60 | 21.09 | 23.03 | 20.51 | 19.90
WISE J0535$-$75 | 68.7$\pm$2.0 | 24.11 | 22.74 | $\cdots$ | 22.76 | 22.89 | 22.01 | 22.43 | 23.31 | 23.02 | 23.08 | 22.81
WISE J0734$-$71 | 74.5$\pm$1.7 | 23.15 | 20.73 | 23.30 | 21.09 | 21.01 | 20.37 | 22.14 | 22.49 | 22.99 | 21.40 | 20.62
WISE J0825+28 | 152.6$\pm$2.0 | 23.19 | 22.64 | $\cdots$ | 23.34 | 22.97 | 22.62 | $\cdots$ | 23.52 | $\cdots$ | 22.55 | 21.78
ULAS J1029+09 | 68.6$\pm$1.7 | 20.56 | 17.85 | 19.83 | 18.01 | 17.90 | 17.35 | 18.34 | 18.91 | 19.25 | 17.81 | 17.07
CWISEP J1047+54 | 68.1$\pm$4.9 | 23.64 | 21.45 | 26.03 | 22.10 | 21.87 | 21.30 | 24.64 | 24.18 | 24.43 | 22.17 | 21.28
WISE J1206+84 | 84.7$\pm$2.1 | 23.41 | 20.76 | 23.76 | 21.27 | 21.04 | 20.50 | 22.36 | 22.34 | 22.27 | 21.09 | 20.33
SDSSp J1346$-$00 | 69.2$\pm$2.3 | 18.91 | 16.27 | 17.79 | 16.37 | 16.26 | 15.72 | 16.27 | 16.83 | 17.05 | 16.11 | 15.46
WISEPC J1405+55 | 158.2$\pm$2.6 | 22.30 | 21.31 | $\cdots$ | 21.66 | 21.56 | 20.83 | 22.58 | 23.44 | $\cdots$ | 21.96 | 21.05
CWISEP J1446$-$23 | 103.8$\pm$5.0 | 24.55 | 23.13 | $\cdots$ | 23.79 | 23.40 | 22.88 | 24.22 | 25.52 | 24.11 | 23.31 | 22.48
WISE J1501$-$40 | 72.8$\pm$2.3 | 19.36 | 16.72 | 18.40 | 16.90 | 16.77 | 16.25 | 16.83 | 17.48 | 17.82 | 16.68 | 16.01
WISEPA J1541$-$22 | 166.9$\pm$2.0 | 22.99 | 21.40 | 23.70 | 22.07 | 21.78 | 21.41 | $\cdots$ | 23.02 | $\cdots$ | 21.82 | 21.09
SDSS J1624+00 | 91.8$\pm$1.2 | 18.40 | 15.85 | 17.47 | 15.97 | 15.87 | 15.30 | 15.77 | 16.56 | 16.91 | 15.88 | 15.24
WISEPA J1959$-$33 | 83.9$\pm$2.0 | 19.91 | 17.19 | 19.20 | 17.35 | 17.23 | 16.68 | 17.70 | 18.15 | 18.34 | 17.13 | 16.39
WISEPC J2056+14 | 140.8$\pm$2.0 | 22.21 | 19.60 | 23.07 | 20.05 | 19.89 | 19.26 | 20.74 | 21.55 | 21.04 | 20.21 | 19.44
WISE J2102$-$44 | 92.9$\pm$1.9 | 21.35 | 18.72 | 21.17 | 18.95 | 18.88 | 18.24 | 19.69 | 20.39 | 24.03 | 18.99 | 18.18
WISEA J2159$-$48 | 73.9$\pm$2.6 | 21.97 | 19.44 | 21.43 | 19.59 | 19.64 | 18.86 | 19.89 | 21.33 | 22.23 | 20.35 | 19.58
WISE J2209+27 | 161.7$\pm$2.0 | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | 24.44 | 21.80 | $\cdots$ | $\cdots$ | $\cdots$ | 22.79
WISEA J2354+02 | 130.6$\pm$3.3 | 23.60 | 22.95 | $\cdots$ | 23.43 | 23.38 | 22.27 | 22.78 | 24.04 | $\cdots$ | 23.32 | 22.84
WISEA J2018$-$74 | 83.2$\pm$1.9 | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$
Table 8: Synthetic JWST Photometry of Our Sample Obj. Name | Parallax | F212N | F250M | F277W | F300M | F322W2 | F323N | F335M | F356W | F360M | F405N | F410M
---|---|---|---|---|---|---|---|---|---|---|---|---
WISE J0247+37 | 68.4$\pm$2.0 | 17.82 | 19.91 | 18.53 | 17.71 | 17.19 | 20.39 | 18.96 | 16.63 | 16.78 | 14.51 | 14.65
WISEPA J0313+78 | 135.6$\pm$2.8 | 17.36 | 18.90 | 17.48 | 16.59 | 16.04 | 18.49 | 17.89 | 15.46 | 15.60 | 13.37 | 13.46
WISE J0359$-$54 | 73.6$\pm$2.0 | 21.43 | 21.31 | 20.10 | 19.23 | 18.25 | 20.15 | 19.68 | 17.62 | 17.82 | 15.49 | 15.52
WISE J0430+46 | 96.1$\pm$2.9 | 19.56 | 20.07 | 18.84 | 17.96 | 16.81 | 19.58 | 18.65 | 16.14 | 16.29 | 14.16 | 14.25
WISE J0535$-$75 | 68.7$\pm$2.0 | $\cdots$ | 22.51 | 20.58 | 19.61 | 18.34 | 23.35 | 20.54 | 17.68 | 17.88 | 15.50 | 15.44
WISE J0734$-$71 | 74.5$\pm$1.7 | $\cdots$ | 22.03 | 20.00 | 19.05 | 18.24 | 21.43 | 20.37 | 17.63 | 17.83 | 15.42 | 15.47
WISE J0825+28 | 152.6$\pm$2.0 | 21.65 | 21.94 | 20.17 | 19.19 | 18.06 | $\cdots$ | 20.20 | 17.42 | 17.65 | 15.17 | 15.10
ULAS J1029+09 | 68.6$\pm$1.7 | 16.79 | 18.73 | 17.65 | 16.90 | 16.62 | 18.62 | 18.14 | 16.11 | 16.22 | 14.12 | 14.35
CWISEP J1047+54 | 68.1$\pm$4.9 | 21.00 | 22.87 | 21.21 | 20.26 | 19.32 | $\cdots$ | 21.78 | 18.74 | 19.09 | 16.26 | 16.42
WISE J1206+84 | 84.7$\pm$2.1 | 20.00 | 21.06 | 19.60 | 18.68 | 17.95 | 20.15 | 19.80 | 17.35 | 17.56 | 15.18 | 15.31
SDSSp J1346$-$00 | 69.2$\pm$2.3 | $\cdots$ | 16.83 | 16.10 | 15.53 | 15.23 | 16.85 | 16.43 | 14.75 | 14.83 | 12.99 | 13.27
WISEPC J1405+55 | 158.2$\pm$2.6 | $\cdots$ | 22.21 | 20.01 | 18.86 | 17.51 | 20.82 | 19.69 | 16.85 | 17.12 | 14.57 | 14.49
CWISEP J1446$-$23 | 103.8$\pm$5.0 | 22.24 | 23.13 | 21.48 | 20.49 | 19.47 | 22.50 | 22.04 | 18.86 | 19.21 | 16.41 | 16.41
WISE J1501$-$40 | 72.8$\pm$2.3 | 15.73 | 17.50 | 16.75 | 16.15 | 15.85 | 17.47 | 17.05 | 15.36 | 15.43 | 13.58 | 13.85
WISEPA J1541$-$22 | 166.9$\pm$2.0 | $\cdots$ | 21.48 | 19.58 | 18.51 | 17.56 | 19.60 | 19.40 | 16.93 | 17.16 | 14.71 | 14.68
SDSS J1624+00 | 91.8$\pm$1.2 | $\cdots$ | 16.53 | 15.85 | 15.27 | 14.92 | 16.43 | 16.05 | 14.42 | 14.49 | 12.70 | 12.90
WISEPA J1959$-$33 | 83.9$\pm$2.0 | 16.13 | 17.84 | 17.00 | 16.35 | 15.87 | 17.56 | 17.26 | 15.35 | 15.45 | 13.37 | 13.62
WISEPC J2056+14 | 140.8$\pm$2.0 | 19.22 | 20.08 | 18.45 | 17.50 | 16.77 | 19.42 | 18.60 | 16.16 | 16.32 | 14.04 | 14.13
WISE J2102$-$44 | 92.9$\pm$1.9 | $\cdots$ | 19.67 | 18.35 | 17.51 | 16.95 | 19.75 | 18.69 | 16.38 | 16.53 | 14.27 | 14.38
WISEA J2159$-$48 | 73.9$\pm$2.6 | $\cdots$ | 20.31 | 19.18 | 18.33 | 17.36 | 22.87 | 19.52 | 16.74 | 16.96 | 14.59 | 14.69
WISE J2209+27 | 161.7$\pm$2.0 | $\cdots$ | $\cdots$ | 21.22 | 19.98 | 18.40 | 20.19 | 21.77 | 17.75 | 18.12 | 15.26 | 15.20
WISEA J2354+02 | 130.6$\pm$3.3 | 21.75 | 25.59 | 21.30 | 20.23 | 18.61 | 21.73 | 22.49 | 17.97 | 18.38 | 15.48 | 15.41
WISEA J2018$-$74 | 83.2$\pm$1.9 | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$
Table 9: Synthetic JWST Photometry of Our Sample  Obj. Name | Parallax | F430M | F444W | F460M | F466N | F470N | F480M | F560W | F770W | F1065C | F1130W | F1140C
---|---|---|---|---|---|---|---|---|---|---|---|---
WISE J0247+37 | 68.4$\pm$2.0 | 14.44 | 14.60 | 14.72 | 14.56 | 14.64 | 14.60 | 15.23 | 14.85 | 13.38 | 12.61 | 12.82
WISEPA J0313+78 | 135.6$\pm$2.8 | 13.19 | 13.33 | 13.39 | 13.26 | 13.31 | 13.24 | 13.86 | 13.39 | 11.85 | 11.02 | 11.23
WISE J0359$-$54 | 73.6$\pm$2.0 | 15.17 | 15.40 | 15.60 | 15.39 | 15.52 | 15.34 | 16.11 | 15.33 | 13.86 | 12.95 | 13.17
WISE J0430+46 | 96.1$\pm$2.9 | 14.07 | 14.24 | 14.35 | 14.28 | 14.30 | 14.35 | 15.27 | 14.64 | 13.41 | 12.58 | 12.80
WISE J0535$-$75 | 68.7$\pm$2.0 | 14.96 | 15.12 | 14.94 | 14.90 | 14.90 | 14.90 | 16.06 | 15.14 | 13.61 | 12.61 | 12.82
WISE J0734$-$71 | 74.5$\pm$1.7 | 15.11 | 15.30 | 15.39 | 15.25 | 15.28 | 15.17 | 15.95 | 15.30 | 13.71 | 12.80 | 13.00
WISE J0825+28 | 152.6$\pm$2.0 | 14.60 | 14.77 | 14.75 | 14.61 | 14.69 | 14.52 | 15.36 | 14.33 | 12.62 | 11.63 | 11.84
ULAS J1029+09 | 68.6$\pm$1.7 | 14.45 | 14.44 | 14.82 | 14.60 | 14.64 | 14.55 | 14.52 | 14.22 | 12.76 | 12.11 | 12.32
CWISEP J1047+54 | 68.1$\pm$4.9 | 16.21 | 16.32 | 16.85 | 16.49 | 16.75 | 16.33 | 16.90 | 16.24 | 14.42 | 13.39 | 13.58
WISE J1206+84 | 84.7$\pm$2.1 | 15.13 | 15.26 | 15.81 | 15.55 | 15.67 | 15.27 | 15.44 | 14.75 | 13.12 | 12.25 | 12.45
SDSSp J1346$-$00 | 69.2$\pm$2.3 | 13.72 | 13.56 | 14.25 | 14.03 | 14.06 | 13.92 | 13.45 | 13.26 | 12.05 | 11.51 | 11.73
WISEPC J1405+55 | 158.2$\pm$2.6 | 13.97 | 14.18 | 14.08 | 14.01 | 14.04 | 13.98 | 15.18 | 14.35 | 12.77 | 11.72 | 11.93
CWISEP J1446$-$23 | 103.8$\pm$5.0 | 15.89 | 16.04 | 16.18 | 15.96 | 16.09 | 15.81 | 16.66 | 15.71 | 13.91 | 12.83 | 13.04
WISE J1501$-$40 | 72.8$\pm$2.3 | 14.18 | 14.05 | 14.51 | 14.30 | 14.37 | 14.27 | 14.09 | 13.89 | 12.66 | 12.11 | 12.33
WISEPA J1541$-$22 | 166.9$\pm$2.0 | 14.20 | 14.34 | 14.33 | 14.16 | 14.25 | 14.07 | 14.87 | 13.88 | 12.16 | 11.19 | 11.41
SDSS J1624+00 | 91.8$\pm$1.2 | 13.01 | 13.05 | 13.42 | 13.25 | 13.27 | 13.25 | 13.24 | 13.04 | 11.85 | 11.34 | 11.55
WISEPA J1959$-$33 | 83.9$\pm$2.0 | 13.77 | 13.75 | 14.27 | 14.12 | 14.02 | 13.91 | 13.75 | 13.44 | 12.12 | 11.52 | 11.74
WISEPC J2056+14 | 140.8$\pm$2.0 | 13.85 | 13.99 | 14.23 | 13.98 | 14.16 | 13.87 | 14.29 | 13.59 | 11.95 | 11.06 | 11.27
WISE J2102$-$44 | 92.9$\pm$1.9 | 14.14 | 14.28 | 14.42 | 14.25 | 14.38 | 14.23 | 14.74 | 14.40 | 12.87 | 11.98 | 12.19
WISEA J2159$-$48 | 73.9$\pm$2.6 | 14.44 | 14.63 | 14.67 | 14.61 | 14.60 | 14.66 | 15.61 | 15.11 | 13.64 | 12.80 | 13.01
WISE J2209+27 | 161.7$\pm$2.0 | 14.62 | 14.86 | 15.03 | 14.78 | 14.95 | 14.67 | 15.62 | 14.62 | 12.90 | 11.82 | 12.03
WISEA J2354+02 | 130.6$\pm$3.3 | 14.88 | 15.13 | 15.16 | 15.03 | 15.09 | 15.01 | 16.27 | 15.36 | 13.68 | 12.58 | 12.79
WISEA J2018$-$74 | 83.2$\pm$1.9 | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | 14.34 | 13.93 | 12.69 | 12.02 | 12.23

## References

  * Alves de Oliveira (2013) Alves de Oliveira, C. 2013, Memorie della Societa Astronomica Italiana, 84, 905, doi: 10.48550/arXiv.1307.5397
  * Baraffe et al. (2003) Baraffe, I., Chabrier, G., Barman, T. S., Allard, F., & Hauschildt, P. H. 2003, Astronomy & Astrophysics, 402, 701, doi: 10.1051/0004-6361:20030252
  * Basri et al. (1996) Basri, G., Marcy, G. W., & Graham, J. R. 1996, The Astrophysical Journal, 458, 600, doi: 10.1086/176842
  * Bastian et al. (2010) Bastian, N., Covey, K. R., & Meyer, M. R. 2010, Annual Review of Astronomy and Astrophysics, 48, 339, doi: 10.1146/annurev-astro-082708-101642
  * Beiler et al. (2023) Beiler, S. A., Cushing, M. C., Kirkpatrick, J. D., et al. 2023, The Astrophysical Journal Letters, 951, L48, doi: 10.3847/2041-8213/ace32c
  * Bessel (1838) Bessel, F. W. 1838, Monthly Notices of the Royal Astronomical Society, 4, 152, doi: 10.1093/mnras/4.17.152
  * Best et al. (2020) Best, W. M. J., Liu, M. C., Magnier, E. A., & Dupuy, T. J. 2020, The Astronomical Journal, 159, 257, doi: 10.3847/1538-3881/ab84f4
  * Best et al. (2024) Best, W. M. J., Sanghi, A., Liu, M. C., Magnier, E. A., & Dupuy, T. J. 2024, A Volume-Limited Sample of Ultracool Dwarfs. II. The Substellar Age and Mass Functions in the Solar Neighborhood, doi: 10.48550/arXiv.2401.09535
  * Brooks et al. (2023) Brooks, H., Kirkpatrick, J. D., Meisner, A. M., et al. 2023, Long-term 4.6$\mu$m Variability in Brown Dwarfs and a New Technique for Identifying Brown Dwarf Binary Candidates, arXiv.  http://arxiv.org/abs/2304.05630
  * Burgasser (2004) Burgasser, A. J. 2004, The Astrophysical Journal Supplement Series, 155, 191, doi: 10.1086/424386
  * Burgasser et al. (2006) Burgasser, A. J., Geballe, T. R., Leggett, S. K., Kirkpatrick, J. D., & Golimowski, D. A. 2006, The Astrophysical Journal, 637, 1067, doi: 10.1086/498563
  * Burgasser et al. (2011) Burgasser, A. J., Cushing, M. C., Kirkpatrick, J. D., et al. 2011, The Astrophysical Journal, 735, 116, doi: 10.1088/0004-637X/735/2/116
  * Burgasser et al. (2023) Burgasser, A. J., Gerasimov, R., Bezanson, R., et al. 2023, UNCOVER: JWST Spectroscopy of Three Cold Brown Dwarfs at Kiloparsec-scale Distances, arXiv.  http://arxiv.org/abs/2308.12107
  * Burningham et al. (2013) Burningham, B., Cardoso, C. V., Smith, L., et al. 2013, Monthly Notices of the Royal Astronomical Society, 433, 457, doi: 10.1093/mnras/stt740
  * Burrows et al. (2001) Burrows, A., Hubbard, W. B., Lunine, J. I., & Liebert, J. 2001, Reviews of Modern Physics, 73, 719, doi: 10.1103/RevModPhys.73.719
  * Burrows et al. (1997) Burrows, A., Marley, M., Hubbard, W. B., et al. 1997, The Astrophysical Journal, 491, 856, doi: 10.1086/305002
  * Campbell (1913) Campbell, W. W. 1913, Stellar motions, with special reference to motions determined by means of the spectrograph.  https://ui.adsabs.harvard.edu/abs/1913smsr.book.....C
  * Coblentz (1922) Coblentz, W. W. 1922, Proceedings of the National Academy of Science, 8, 49, doi: 10.1073/pnas.8.3.49
  * Cushing (2014) Cushing, M. C. 2014, in 50 Years of Brown Dwarfs: From Prediction to Discovery to Forefront of Research, ed. V. Joergens, Astrophysics and Space Science Library (Cham: Springer International Publishing), 113–140, doi: 10.1007/978-3-319-01162-2_7
  * Cushing et al. (2006) Cushing, M. C., Roellig, T. L., Marley, M. S., et al. 2006, The Astrophysical Journal, 648, 614, doi: 10.1086/505637
  * Cushing et al. (2011) Cushing, M. C., Kirkpatrick, J. D., Gelino, C. R., et al. 2011, The Astrophysical Journal, 743, 50, doi: 10.1088/0004-637X/743/1/50
  * Cutri et al. (2003) Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, VizieR Online Data Catalog, 2246, II/246.  https://ui.adsabs.harvard.edu/abs/2003yCat.2246....0C
  * Dupuy & Kraus (2013) Dupuy, T. J., & Kraus, A. L. 2013, Science, 341, 1492, doi: 10.1126/science.1241917
  * Dye et al. (2018) Dye, S., Lawrence, A., Read, M. A., et al. 2018, Monthly Notices of the Royal Astronomical Society, 473, 5113, doi: 10.1093/mnras/stx2622
  * Eisenhardt et al. (2020) Eisenhardt, P. R. M., Marocco, F., Fowler, J. W., et al. 2020, The Astrophysical Journal Supplement Series, 247, 69, doi: 10.3847/1538-4365/ab7f2a
  * Filippazzo et al. (2015) Filippazzo, J. C., Rice, E. L., Faherty, J., et al. 2015, The Astrophysical Journal, 810, 158, doi: 10.1088/0004-637X/810/2/158
  * Fontanive et al. (2018) Fontanive, C., Biller, B., Bonavita, M., & Allers, K. 2018, Monthly Notices of the Royal Astronomical Society, 479, 2702, doi: 10.1093/mnras/sty1682
  * Frost (1896) Frost, E. B. 1896, The Astrophysical Journal, 3, 232, doi: 10.1086/140205
  * Gardner et al. (2023) Gardner, J. P., Mather, J. C., Abbott, R., et al. 2023, Publications of the Astronomical Society of the Pacific, 135, 068001, doi: 10.1088/1538-3873/acd1b5
  * Gordon et al. (2022) Gordon, K. D., Bohlin, R., Sloan, G. C., et al. 2022, The Astronomical Journal, 163, 267, doi: 10.3847/1538-3881/ac66dc
  * Hopkins (2018) Hopkins, A. M. 2018, Publications of the Astronomical Society of Australia, 35, e039, doi: 10.1017/pasa.2018.29
  * Jakobsen et al. (2022) Jakobsen, P., Ferruit, P., Alves de Oliveira, C., et al. 2022, Astronomy & Astrophysics, 661, A80, doi: 10.1051/0004-6361/202142663
  * Jarrett et al. (2011) Jarrett, T. H., Cohen, M., Masci, F., et al. 2011, The Astrophysical Journal, 735, 112, doi: 10.1088/0004-637X/735/2/112
  * Kirkpatrick et al. (2011) Kirkpatrick, J. D., Cushing, M. C., Gelino, C. R., et al. 2011, The Astrophysical Journal Supplement Series, 197, 19, doi: 10.1088/0067-0049/197/2/19
  * Kirkpatrick et al. (2012) Kirkpatrick, J. D., Gelino, C. R., Cushing, M. C., et al. 2012, The Astrophysical Journal, 753, 156, doi: 10.1088/0004-637X/753/2/156
  * Kirkpatrick et al. (2019) Kirkpatrick, J. D., Martin, E. C., Smart, R. L., et al. 2019, The Astrophysical Journal Supplement Series, 240, 19, doi: 10.3847/1538-4365/aaf6af
  * Kirkpatrick et al. (2021) Kirkpatrick, J. D., Gelino, C. R., Faherty, J. K., et al. 2021, The Astrophysical Journal Supplement Series, 253, 7, doi: 10.3847/1538-4365/abd107
  * Kirkpatrick et al. (2024) Kirkpatrick, J. D., Marocco, F., Gelino, C. R., et al. 2024, The Astrophysical Journal Supplement Series, 271, 55, doi: 10.3847/1538-4365/ad24e2
  * Krick et al. (2021) Krick, J. E., Lowrance, P., Carey, S., et al. 2021, The Astronomical Journal, 161, 177, doi: 10.3847/1538-3881/abe390
  * Kroupa & Jerabkova (2019) Kroupa, P., & Jerabkova, T. 2019, Nature Astronomy, 3, 482, doi: 10.1038/s41550-019-0793-0
  * Kuiper (1938) Kuiper, G. P. 1938, The Astrophysical Journal, 88, 472, doi: 10.1086/143999
  * Lawrence et al. (2007) Lawrence, A., Warren, S. J., Almaini, O., et al. 2007, Monthly Notices of the Royal Astronomical Society, 379, 1599, doi: 10.1111/j.1365-2966.2007.12040.x
  * Lodieu et al. (2007) Lodieu, N., Dobbie, P. D., Deacon, N. R., et al. 2007, Monthly Notices of the Royal Astronomical Society, 380, 712, doi: 10.1111/j.1365-2966.2007.12106.x
  * Lucas et al. (2010) Lucas, P. W., Tinney, C. G., Burningham, B., et al. 2010, Monthly Notices of the Royal Astronomical Society: Letters, 408, L56, doi: 10.1111/j.1745-3933.2010.00927.x
  * Luhman et al. (2023) Luhman, K. L., Tremblin, P., de Oliveira, C. A., et al. 2023, JWST/NIRSpec Observations of the Coldest Known Brown Dwarf, arXiv.  http://arxiv.org/abs/2311.17316
  * Mace et al. (2013) Mace, G. N., Kirkpatrick, J. D., Cushing, M. C., et al. 2013, The Astrophysical Journal Supplement Series, 205, 6, doi: 10.1088/0067-0049/205/1/6
  * Mamajek et al. (2015) Mamajek, E. E., Torres, G., Prsa, A., et al. 2015, IAU 2015 Resolution B2 on Recommended Zero Points for the Absolute and Apparent Bolometric Magnitude Scales, arXiv.  http://arxiv.org/abs/1510.06262
  * Marley et al. (2021) Marley, M. S., Saumon, D., Visscher, C., et al. 2021, The Astrophysical Journal, 920, 85, doi: 10.3847/1538-4357/ac141d
  * Marocco et al. (2020) Marocco, F., Kirkpatrick, J. D., Meisner, A. M., et al. 2020, The Astrophysical Journal, 888, L19, doi: 10.3847/2041-8213/ab6201
  * McKee & Ostriker (2007) McKee, C. F., & Ostriker, E. C. 2007, Annual Review of Astronomy and Astrophysics, 45, 565, doi: 10.1146/annurev.astro.45.051806.110602
  * McMahon et al. (2013) McMahon, R. G., Banerji, M., Gonzalez, E., et al. 2013, The Messenger, 154, 35.  https://ui.adsabs.harvard.edu/abs/2013Msngr.154...35M
  * Meisner et al. (2023) Meisner, A. M., Leggett, S. K., Logsdon, S. E., et al. 2023, The Astronomical Journal, 166, 57, doi: 10.3847/1538-3881/acdb68
  * Meisner et al. (2020a) Meisner, A. M., Caselden, D., Kirkpatrick, J. D., et al. 2020a, The Astrophysical Journal, 889, 74, doi: 10.3847/1538-4357/ab6215
  * Meisner et al. (2020b) Meisner, A. M., Faherty, J. K., Kirkpatrick, J. D., et al. 2020b, The Astrophysical Journal, 899, 123, doi: 10.3847/1538-4357/aba633
  * Miles et al. (2020) Miles, B. E., Skemer, A. J. I., Morley, C. V., et al. 2020, The Astronomical Journal, 160, 63, doi: 10.3847/1538-3881/ab9114
  * Morley et al. (2018) Morley, C. V., Skemer, A. J., Allers, K. N., et al. 2018, The Astrophysical Journal, 858, 97, doi: 10.3847/1538-4357/aabe8b
  * Mukherjee et al. (2023a) Mukherjee, S., Batalha, N. E., Fortney, J. J., & Marley, M. S. 2023a, The Astrophysical Journal, 942, 71, doi: 10.3847/1538-4357/ac9f48
  * Mukherjee et al. (2023b) Mukherjee, S., Fortney, J., Morley, C., et al. 2023b, The Sonora Substellar Atmosphere Models. IV. Elf Owl: Atmospheric Mixing and Chemical Disequilibrium with Varying Metallicity and C/O Ratios (Y- type Models), Zenodo, doi: 10.5281/zenodo.10381250
  * Murakami et al. (2007) Murakami, H., Baba, H., Barthel, P., et al. 2007, Publications of the Astronomical Society of Japan, 59, S369, doi: 10.1093/pasj/59.sp2.S369
  * Nakajima et al. (1995) Nakajima, T., Oppenheimer, B. R., Kulkarni, S. R., et al. 1995, Nature, 378, 463, doi: 10.1038/378463a0
  * Oppenheimer et al. (1998) Oppenheimer, B. R., Kulkarni, S. R., Matthews, K., & Kerkwijk, M. H. v. 1998, The Astrophysical Journal, 502, 932, doi: 10.1086/305928
  * Payne (1924) Payne, C. H. 1924, Harvard College Observatory Circular, 252, 1.  https://ui.adsabs.harvard.edu/abs/1924HarCi.252....1P
  * Raghu et al. (2024) Raghu, Y., Kirkpatrick, J. D., Marocco, F., et al. 2024, Simulating Brown Dwarf Observations for Various Mass Functions, Birthrates, and Low-mass Cutoffs, arXiv.  http://arxiv.org/abs/2406.09690
  * Ramírez et al. (2012) Ramírez, K. P., Béjar, V. J. S., Osorio, M. R. Z., Petr-Gotzens, M. G., & Martín, E. L. 2012, The Astrophysical Journal, 754, 30, doi: 10.1088/0004-637X/754/1/30
  * Reach et al. (2005) Reach, W., Megeath, S., Cohen, M., et al. 2005, Publications of the Astronomical Society of the Pacific, 117, 978, doi: 10.1086/432670
  * Rebolo et al. (1995) Rebolo, R., Osorio, M. R. Z., & Martín, E. L. 1995, Nature, 377, 129, doi: 10.1038/377129a0
  * Rieke et al. (2015) Rieke, G. H., Wright, G. S., Böker, T., et al. 2015, Publications of the Astronomical Society of the Pacific, 127, 584, doi: 10.1086/682252
  * Roellig et al. (2004) Roellig, T. L., Cleve, J. E. V., Sloan, G. C., et al. 2004, The Astrophysical Journal Supplement Series, 154, 418, doi: 10.1086/421978
  * Russell (1914) Russell, H. N. 1914, Popular Astronomy, 22, 331.  https://ui.adsabs.harvard.edu/abs/1914PA.....22..331R
  * Salpeter (1955) Salpeter, E. E. 1955, The Astrophysical Journal, 121, 161, doi: 10.1086/145971
  * Saumon et al. (2000) Saumon, D., Geballe, T. R., Leggett, S. K., et al. 2000, The Astrophysical Journal, 541, 374, doi: 10.1086/309410
  * Saumon & Marley (2008) Saumon, D., & Marley, M. S. 2008, The Astrophysical Journal, 689, 1327, doi: 10.1086/592734
  * Schneider et al. (2015) Schneider, A. C., Cushing, M. C., Kirkpatrick, J. D., et al. 2015, The Astrophysical Journal, 804, 92, doi: 10.1088/0004-637X/804/2/92
  * Skemer et al. (2016) Skemer, A. J., Morley, C. V., Allers, K. N., et al. 2016, The Astrophysical Journal Letters, 826, L17, doi: 10.3847/2041-8205/826/2/L17
  * Smith (2020) Smith, R. J. 2020, Annual Review of Astronomy and Astrophysics, 58, 577, doi: 10.1146/annurev-astro-032620-020217
  * Stauffer et al. (1994) Stauffer, J. R., Hamilton, D., & Probst, R. G. 1994, The Astronomical Journal, 108, 155, doi: 10.1086/117053
  * Strauss et al. (1999) Strauss, M. A., Fan, X., Gunn, J. E., et al. 1999, The Astrophysical Journal, 522, L61, doi: 10.1086/312218
  * Suárez & Metchev (2022) Suárez, G., & Metchev, S. 2022, Monthly Notices of the Royal Astronomical Society, stac1205, doi: 10.1093/mnras/stac1205
  * Thompson et al. (2013) Thompson, M. A., Kirkpatrick, J. D., Mace, G. N., et al. 2013, Publications of the Astronomical Society of the Pacific, 125, 809, doi: 10.1086/671426
  * Tinney et al. (2003) Tinney, C. G., Burgasser, A. J., & Kirkpatrick, J. D. 2003, The Astronomical Journal, 126, 975, doi: 10.1086/376481
  * Tinney et al. (2014) Tinney, C. G., Faherty, J. K., Kirkpatrick, J. D., et al. 2014, The Astrophysical Journal, 796, 39, doi: 10.1088/0004-637X/796/1/39
  * Tinney et al. (2012) —. 2012, The Astrophysical Journal, 759, 60, doi: 10.1088/0004-637X/759/1/60
  * Tinney et al. (2018) Tinney, C. G., Kirkpatrick, J. D., Faherty, J. K., et al. 2018, The Astrophysical Journal Supplement Series, 236, 28, doi: 10.3847/1538-4365/aabad3
  * Trucks (2019) Trucks, J. L. 2019, PhD thesis.  https://ui.adsabs.harvard.edu/abs/2019PhDT.......103T
  * Tsvetanov et al. (2000) Tsvetanov, Z. I., Golimowski, D. A., Zheng, W., et al. 2000, The Astrophysical Journal, 531, L61, doi: 10.1086/312515
  * Werner et al. (2004) Werner, M. W., Roellig, T. L., Low, F. J., et al. 2004, The Astrophysical Journal Supplement Series, 154, 1, doi: 10.1086/422992
  * Wilsing et al. (1919) Wilsing, J., Scheiner, J., & Munch, W. 1919, Publikationen des Astrophysikalischen Observatoriums zu Potsdam, 74.  https://ui.adsabs.harvard.edu/abs/1919POPot..74.....W
  * Wright et al. (2010) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, The Astronomical Journal, 140, 1868, doi: 10.1088/0004-6256/140/6/1868
  * Zahnle & Marley (2014) Zahnle, K. J., & Marley, M. S. 2014, The Astrophysical Journal, 797, 41, doi: 10.1088/0004-637X/797/1/41
  * Zhang et al. (2021) Zhang, Z., Liu, M. C., Marley, M. S., Line, M. R., & Best, W. M. J. 2021, The Astrophysical Journal, 921, 95, doi: 10.3847/1538-4357/ac0af7