Atmospheric Retrievals of the Young Giant Planet ROXs 42B b from Low- and
High-resolution Spectroscopy
Julie Inglis
1
, Nicole L. Wallack
2
, Jerry W. Xuan
3
, Heather A. Knutson
1
, Yayaati Chachan
4
,
5
,
11
, Marta L. Bryan
6
,
Brendan P. Bowler
7
, Aishwarya Iyer
8
,
12
, Tiffany Kataria
9
, and Björn Benneke
10
1
Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA;
jinglis@caltech.edu
2
Earth and Planets Laboratory, Carnegie Institution for Science, Washington, DC 20015, USA
3
Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA
4
Department of Physics and Trottier Space Institute, McGill University, 3600 rue University, H3A 2T8, Montreal, QC, Canada
5
Trottier Institute for Research on Exoplanets
(
iREx
)
, Université de Montréal, Canada
6
Department of Astronomy and Astrophysics, University of Toronto, M5S 3H4, Toronto, ON, Canada
7
Department of Astronomy, The University of Texas at Austin, Austin, TX 78712, USA
8
Goddard Space Flight Center, Greenbelt, MD 20771, USA
9
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
10
Department of Physics and Trottier Institute for Research on Exoplanets, Université de Montréal, Montreal, QC, Canada
Received 2023 November 22; revised 2024 January 19; accepted 2024 February 6; published 2024 April 15
Abstract
Previous attempts have been made to characterize the atmospheres of directly imaged planets at low resolution
(
R
∼
10
–
100 s
)
, but the presence of clouds has often led to degeneracies in the retrieved atmospheric abundances
with cloud opacity and temperature structure that bias retrieved compositions. In this study, we perform retrievals
on the ultrayoung
(
5 Myr
)
directly imaged planet ROXs 42B b with both a downsampled low-resolution
JHK
-
band spectrum from Gemini
/
NIFS and Keck
/
OSIRIS, and a high-resolution
K
-band spectrum from pre-upgrade
Keck
/
NIRSPAO. Using the atmospheric retrieval framework of
petitRADTRANS
, we analyze both data sets
individually and combined. We additionally
fi
t for the stellar abundances and other physical properties of the host
stars, a young M spectral type binary, using the SPHINX model grid. We
fi
nd that the measured C
/
O, 0.50
±
0.05,
and metallicity,
[
Fe
/
H
]
=
−
0.67
±
0.35, for ROXs 42B b from our high-resolution spectrum agree with those of
its host stars within 1
σ
. The retrieved parameters from the high-resolution spectrum are also independent of our
choice of cloud model. In contrast, the retrieved parameters from the low-resolution spectrum show strong
degeneracies between the clouds and the retrieved metallicity and temperature structure. When we retrieve both
data sets together, we
fi
nd that these degeneracies are reduced but not eliminated, and the
fi
nal results remain
highly sensitive to cloud modeling choices. We conclude that high-resolution spectroscopy offers the most
promising path for reliably determining atmospheric compositions of directly imaged companions independent of
their cloud properties.
Uni
fi
ed Astronomy Thesaurus concepts:
Exoplanet atmospheres
(
487
)
;
High resolution spectroscopy
(
2096
)
;
Atmospheric clouds
(
2180
)
;
Exoplanet atmospheric composition
(
2021
)
;
Exoplanet formation
(
492
)
1. Introduction
Directly imaged planets are a population of massive, self-
luminous companions, typically observed from orbital separa-
tions comparable to that of Saturn, to well beyond the orbital
distance of Neptune
(
10
–
100 s of au
)
. These companions are
typically young, with ages
100 Myr, and are often distin-
guished from brown dwarf companions
(
∼
13
–
80
M
J
)
as having
masses near or below the deuterium-burning limit at
∼
13
M
J
(
Bowler
2016
; Currie et al.
2022
)
. A more physically motivated
distinction between directly imaged planets and brown dwarfs
would be based on the formation process, as planets are
expected to form bottom-up from core accretion, while brown
dwarf companions form from gravitational collapse; however,
this is challenging to distinguish for individual objects
(
Pollack
et al.
1996
; Boss
1997
; Alibert et al.
2005
)
.
Population studies indicate that these lower-mass compa-
nions have properties that are distinct from those of massive
brown dwarf companions. Planetary-mass companions appear
to have a higher occurrence rate than brown dwarf companions
to the same stellar population, and tend to have lower orbital
eccentricities
(
Nielsen et al.
2019
; Wagner et al.
2019
; Bowler
et al.
2020a
; Nagpal et al.
2023
)
, and distinct stellar spin
–
orbit
orientations
(
Bowler et al.
2023
)
. The differing properties of
these two populations suggest that they likely have distinct
formation channels, but the nature of these formation channels
is currently debated. It has also been suggested that one or both
populations might not have formed in situ but instead migrated
away from their initial formation locations
(
Scharf &
Menou
2009
)
. However, Bryan et al.
(
2016
)
failed to
fi
nd
evidence for additional massive bodies in systems hosting
wide-separation directly imaged companions that could have
acted as scatterers, suggesting this is not the dominant
formation mechanism for these planets.
Numerous studies have explored how the elemental
abundances of giant planet atmospheres, which are often
parameterized as a carbon-to-oxygen ratio
(
C
/
O
)
and bulk
metallicity
(
e.g.,
[
Fe
/
H
]
)
, can encode information about their
formation and migration histories
(
e.g., Oberg et al.
2011
;
The Astronomical Journal,
167:218
(
19pp
)
, 2024 May
https:
//
doi.org
/
10.3847
/
1538-3881
/
ad2771
© 2024. The Author
(
s
)
. Published by the American Astronomical Society.
11
CITA National Fellow.
12
NASA Postdoctoral Fellow.
Original content from this work may be used under the terms
of the
Creative Commons Attribution 4.0 licence
. Any further
distribution of this work must maintain attribution to the author
(
s
)
and the title
of the work, journal citation and DOI.
1
Madhusudhan
2012
; Cridland et al.
2016
; Mordasini et al.
2016
; Turrini et al.
2021
)
. Companions that form via
gravitational instability, including cloud fragmentation and
disk instability, are expected to have envelope compositions
that are largely similar to those of their host stars,
(
analogous to
binary star formation
)
, although it has been shown that disk
structures can result in local enhancements of solid material
that can be incorporated during collapse
(
Boley & Duri-
sen
2010
; Boley et al.
2011
)
. Alternatively, core accretion
(
Pollack et al.
1996
; Lambrechts & Johansen
2012
)
is expected
to produce giant planets with a wide range of C
/
O and bulk
metallicity values. This is because the compositions of the solid
and gaseous components of the disk vary as a function of the
time and location within the disk, and different planets are
expected to accrete different quantities of solids versus gas
(
Oberg et al.
2011
; Turrini et al.
2021
; Chachan et al.
2023
)
.
However, as collapse from instability is more likely to occur
early in the disk
’
s lifetime
(
Boley
2009
)
, a newly formed planet
could still have access to a substantial reservoir of material in
the disk. If the planet is able to accrete additional material
following the initial collapse phase, a range of envelope
compositions may be possible for planets formed via disk
instability as well. Nonetheless, atmospheric composition could
still probe the formation and migration histories of directly
imaged planets and help distinguish between different forma-
tion scenarios.
Atmospheric characterization analyses of directly imaged
planets have historically made use of photometric and low-
resolution spectroscopic data sets
(
resolving power
R
∼
20
–
100
)
, which are compared to grids of self-consistent, one-
dimensional radiative
–
convective equilibrium forward models
(
e.g., the early studies of the HR 8799 planets: Barman et al.
2011
; Currie et al.
2011
; Galicher et al.
2011
; Marley et al.
2012
)
. These models have relatively limited degrees of
freedom, and often produce poor
fi
ts to these spectra. More
recently, a number of studies have begun to utilize spectral
inversion, or atmospheric retrieval, techniques to model the
atmospheres of isolated brown dwarfs
(
Burningham et al.
2017
;
Line et al.
2017
; Burningham et al.
2021
; Calamari et al.
2022
;
Lueber et al.
2022
; Hood et al.
2023
)
, directly imaged
companions
(
Mollière et al.
2020
; Ruf
fi
o et al.
2021
; Wang
et al.
2022
; Zhang et al.
2023
)
, and brown dwarf companions
(
Xuan et al.
2022
)
. These atmospheric retrievals can be used to
place constraints on the C
/
O ratios and metallicities of these
objects, as well as other physical quantities such as their radii,
surface gravities, and cloud properties.
Many of the directly imaged planets and brown dwarfs
examined in the literature lie in a temperature regime where
silicates are expected to condense in their upper atmospheres
(
Marley & Robinson
2015
)
. The presence of these clouds has a
strong effect on the observed shapes of their low-resolution
emission spectra
(
e.g., Burningham et al.
2017
)
. Previous
studies have explored a wide range of cloud models with
varying degrees of physical motivation and success at
reproducing the observed features. They also revealed that
low-resolution retrievals often exhibit strong degeneracies
between their retrieved cloud properties and other physical
parameters, such as effective temperature and metallicity. For
example, a retrieval analysis by Burningham et al.
(
2017
)
found that their cloud-free models tended toward isothermal
pressure
–
temperature
(
P
–
T
)
pro
fi
les and high metallicities in
order to compensate for the effects of clouds. This degeneracy
has been noted in many subsequent studies, with a variety of
proposed solutions
(
e.g., Piette & Madhusudhan
2020
; Zhang
et al.
2023
)
. Lueber et al.
(
2022
)
found that their treatment of
cloud opacity also resulted in trade-offs with the retrieved
surface gravity and were unable to obtain good constraints on
the C
/
O ratios of many of the brown dwarfs in their sample.
On the other hand, Mollière et al.
(
2020
)
retrieved a C
/
O value
consistent with solar in their paper on HR 8799 e. This value
was independent of the cloud model used and did not correlate
with other physical parameters such as the vertical temperature
structure.
We can obtain a complementary perspective on the atmo-
spheres of these cloudy objects using high-resolution spectrosc-
opy. At high spectral resolution, the ratios of the line depths of
different molecular species can be used to constrain their
relative abundances in a way that is less biased by the presence
of continuum opacity sources from clouds. As the cores of
absorption lines are emitted higher up in the atmosphere than
the continuum
fl
ux, high-resolution spectroscopy also allows
observers to probe a much broader range of pressures,
including pressures that lie above the cloud tops. This can
increase the signal-to-noise ratio
(
S
/
N
)
of molecular detections
for cloudy objects
(
Gandhi et al.
2020
; Hood et al.
2020
)
.In
their recent study of the brown dwarf companion HD 4747 B,
Xuan et al.
(
2022
)
found that their retrieved abundances from
high-resolution spectroscopy were insensitive to their choice of
cloud model. Similarly, Wang et al.
(
2022
)
performed joint
retrievals on low- and high-resolution spectroscopy of
HR 8799 e and found that while clouds are likely present in
this planet
’
s atmosphere, they are located deeper in the
atmosphere than where the majority of the
fl
ux was emitted,
resulting in a minimal effect on their observed spectrum. They
obtained good constraints on the C
/
O, C
/
H, and O
/
H ratios,
retrieving values that were consistent with other studies of the
HR 8799 planets
(
e.g., Ruf
fi
o et al.
2021
)
and AF Lep b
(
Zhang
et al.
2023
)
.
ROXs 42B b is an ultrayoung directly imaged planetary
companion on a wide orbit around a low-mass binary star. Its
large separation
(
∼
1
′′
)
from its host stars makes it a favorable
target for atmospheric characterization. Its large orbital
separation and low-mass binary host make it an interesting
case study for formation. In this paper, we perform atmospheric
retrievals on low- and high-resolution spectroscopy of the
young companion ROXs 42B b. Bowler et al.
(
2014
)
published
a medium-resolution spectrum for this object spanning the
J
,
H
,
and
K
bands
(
1.1
–
2.4
μ
m
)
, while Bryan et al.
(
2018
)
published
a high-resolution
K
-band spectrum. However, neither of these
studies sought to interpret these data using atmospheric
retrieval modeling. We use the open-source radiative transfer
code
petitRADTRANS
(
Mollière et al.
2019
,
2020
)
in order
to constrain the properties of ROXs 42B b
’
s atmosphere,
including its C
/
O ratio and metallicity. We compare our
constraints from low-resolution-only
(
Section
5.1
)
, high-
resolution-only
(
Section
5.2
)
, and joint high- and low-
resolution retrievals
(
Section
5.3
)
to explore the advantages
and disadvantages of each data type in the context of
atmospheric characterization. Finally, we compare our
retrieved abundances for ROXs 42B b to those of its primary,
which is an unresolved binary, in Section
6
and discuss
implications for the formation of this system.
2
The Astronomical Journal,
167:218
(
19pp
)
, 2024 May
Inglis et al.
2. System Properties
ROXs 42B is a close binary system
13
in the
ρ
Ophiuchus
star-forming region
(
Bouvier & Appenzeller
1992
)
.A
candidate companion was
fi
rst identi
fi
ed around the binary by
Ratzka et al.
(
2005
)
. The companion was later con
fi
rmed by
Kraus et al.
(
2014
)
and Currie et al.
(
2014b
)
. Kraus et al.
(
2014
)
measured a projected separation of 1
17, which corresponds to
a separation of 175 au with the updated distance from Gaia
Collaboration
(
2022
)
. The primary binary, ROXs 42B AB, has
a
(
unresolved
)
spectral type of M0 and has been identi
fi
ed as a
young system based on weak H
α
emission, X-ray emission,
and possible lithium absorption in its optical spectrum
(
Bouvier
& Appenzeller
1992
)
. Isochronal
fi
tting gives an approximate
stellar age of
-
+
6.8
2.3
3.4
Myr
(
Kraus et al.
2014
)
. Models suggest
individual component masses of 0.89
±
0.08 and 0.36
±
0.04
M
e
(
Kraus et al.
2014
)
. The absence of infrared excess
in either W3 or W4 in Wide-
fi
eld Infrared Survey Explorer
observations or a radio emission at 1.3 mm indicates that this
system does not contain a signi
fi
cant protoplanetary disk
(
Kraus et al.
2014
; Daemgen et al.
2017
)
. However, Spitzer
observations at 8
μ
m suggest that the companion, ROXs 42B b,
has excess infrared emission and might therefore host a
circumplanetary disk despite the lack of accretion signatures
(
Martinez & Kraus
2021
)
. ROXs 42B b is closest to a spectral
type of L0 but is also observed to have colors much redder than
fi
eld objects of a similar spectral type, which could be due to
circumstellar dust
(
Kraus et al.
2014
; Daemgen et al.
2017
)
.A
summary of measured parameters for this system used in this
paper is shown in Table
1
.
Evolutionary model
fi
ts of the photometry of ROXs 42B b
place approximate bounds on its mass of 10
±
4
M
J
for an
assumed age between 1 and 5 Myr
(
Kraus et al.
2014
)
using
models from Chabrier et al.
(
2000
)
. In a follow-up study,
Bowler et al.
(
2014
)
obtained medium-resolution near-infrared
(
NIR
)
JHK
-band spectra of the companion and found that the
shape of the
H
-band
fl
ux peak was best-matched by grid
models with low surface gravities, consistent with its relatively
young age. Published constraints on the effective temperature
of this object vary. Values from the photometric study of Currie
et al.
(
2014a
)
ranged from 1800 to 2200 K depending on the
models used and whether or not clouds were included. Currie
et al.
(
2014b
)
fi
t a low-resolution
K
-band spectrum from the
Very Large Telescope SINFONI and found a signi
fi
cantly
higher effective temperature range of 1800
–
2600 K, which also
varied depending on their treatment of clouds in the grid
models. There are currently no published constraints on ROXs
42B b
’
s atmospheric metallicity or C
/
O ratio due to the
limitations of
fi
ts to publicly available grid models
(
Currie et al.
2014a
; Daemgen et al.
2017
)
. Bryan et al.
(
2018
)
obtained a
high-resolution
K
-band spectrum for this object and used it to
measure a projected rotational velocity of
-
+
9
.5
2.3
2.1
km s
−
1
, but
this study assumed a solar composition atmosphere. To date,
the only published composition constraint for this object is an
upper limit on its CO
2
abundance from Daemgen et al.
(
2017
)
.
There are currently no published composition constraints for
the primary, ROXs 42B AB, either. Only a few directly imaged
planet hosts in the literature have measured abundances, e.g.,
HR 8799
(
Wang et al.
2020
)
. In most cases, the retrieved
chemical abundances are compared to solar values instead of
their stellar value. However, in order to make determinations
about the formation mechanisms of the companion, it is
necessary to have stellar properties to compare to our retrieved
Table 1
Summary of the Previously Derived System Parameters and Data Used in our
Analysis of ROXs 42B b Along with new Derived Parameters for the Host Star
from this Work using the SPHINX Model Grid from Iyer et al.
(
2023
)
Parameter
Value
References
Primary
(
ROXs 42B AB
)
RA
(
J2000
)
16 31 15.018
Gaia Collaboration
(
2022
)
Dec
(
J2000
)
−
24 32 43.715
Gaia Collaboration
(
2022
)
SpT
M0
±
1
Bowler et al.
(
2014
)
m
J
(
mag
)
9.91
±
0.02
Bowler et al.
(
2014
)
m
H
(
mag
)
9.02
±
0.02
Bowler et al.
(
2014
)
m
K
s
(
mag
)
8.67
±
0.02
Bowler et al.
(
2014
)
¢
m
L
(
mag
)
8.42
±
0.05
Daemgen et al.
(
2017
)
A
V
-
+
1
.7
1.2
0.9
Bowler et al.
(
2014
)
dist
(
pc
)
-
+
1
46.447
0.6627
0.6627
Gaia Collaboration
(
2022
)
Age
(
Myr
)
-
+
6.8
2.3
3.
4
Kraus et al.
2014
M
1
(
M
e
)
0.89
±
0.08
Kraus et al.
(
2014
)
M
2
(
M
e
)
0.36
±
0.04
Kraus et al.
(
2014
)
T
eff
(
K
)
3850
±
80
a
Kraus et al.
(
2014
)
binary sep
(
mas
)
≈
83
Kraus et al.
(
2014
)
fl
ux ratio
(
Δ
K
)
≈
1.1
Kraus et al.
(
2014
)
R
1
(
R
e
)
1.51
±
0.02
This work
R
2
(
R
e
)
1.39
±
0.02
This work
T
eff,1
(
K
)
3650
±
20
This work
T
eff,2
(
K
)
2600
±
20
This work
log
g
1
(
cgs
)
4.12
±
0.1
This work
log
g
2
(
cgs
)
4.26
±
0.1
This work
M
1
(
[
M
e
)
1.12
±
0.13
This work
M
2
(
M
e
)
1.29
±
0.26
This work
C
/
O
0.54
±
0.01
This work
[
Fe
/
H
]
−
0.30
±
0.03
This work
A
V
2.1
±
0.1
This work
Companion
(
ROXs 42B b
)
SpT
L1
±
1
Bowler et al.
(
2014
)
m
J
(
mag
)
16.91
±
0.11
Kraus et al.
(
2014
)
m
H
(
mag
)
15.88
±
0.05
Kraus et al.
(
2014
)
m
K
s
(
mag
)
15.01
±
0.06
Kraus et al.
(
2014
)
¢
m
L
(
mag
)
13.97
±
0.06
Daemgen et al.
(
2017
)
m
Br
α
(
mag
)
13.90
±
0.08
Daemgen et al.
(
2017
)
m
M
s
(
mag
)
14.01
±
0.23
Daemgen et al.
(
2017
)
sep
(
′′
)
1.170
Kraus et al.
(
2014
)
sep
(
au
)
175
Kraus et al.
(
2014
)
b
M
(
M
J
)
10
±
4
Kraus et al.
(
2014
)
Age
(
Myr
)
3
±
2
Bryan et al.
(
2018
)
vsini
-
+
9
.5
2.3
2.1
Bryan et al.
(
2018
)
1800
–
2600 K
Currie et al.
(
2014b
)
(
K
band
)
T
eff
1950
–
2000
Currie et al.
(
2014a
)
(
photometry
)
1600
–
2000 K
Daemgen et al.
(
2017
)
(
photometry
)
Notes.
a
The reported
T
eff
corresponds to the primary, brighter component in the
binary, calculated using the reported
K
-band
fl
ux ratio in Ratzka et al.
(
2005
)
.
b
Calculated using the separation measured by Kraus et al.
(
2014
)
and the
updated distance from Gaia Collaboration
(
2022
)
.
13
ROXs 42A and ROXs 42C are two nearby stars located within the error
circle of the Einstein Observatory which
fi
rst identi
fi
ed the Rho Ophiuchus
X-ray source, ROXs 42
(
Montmerle et al.
1983
)
. While ROXs 42C has a
similar age to ROXs 42B, it has a very different mass and is widely separated
from ROXs 42B, so it is unlikely to be af
fi
liated, while ROXs 42A is likely a
fi
eld star
(
Bouvier & Appenzeller
1992
)
.
3
The Astronomical Journal,
167:218
(
19pp
)
, 2024 May
Inglis et al.
abundances for the companion. In Section
6
,we
fi
t the optical
SuperNova Integral Field Spectrograph
(
SNIFS
)
spectrum of
the
(
unresolved
)
primary ROXs 42B AB from Bowler et al.
(
2014
)
using the SPHINX M dwarf model grid from Iyer et al.
(
2023
)
to constrain the abundances of the host binary.
3. Archival Data Used in this Study
3.1. Low-resolution Spectroscopy of ROXs 42B b
Bowler et al.
(
2014
)
published a medium-resolution
(
R
∼
1000
)
spectrum of ROXs 42B b. The
H
-band data in
this study were taken on UT 2012 May 9, and the
J
-band data
were taken on UT 2012 May 14 and July 4 using ALTAIR, the
facility AO system, and the Near-Infrared Integral Field
Spectrometer
(
NIFS; McGregor et al.
2003
)
, an image-slicer
integral
fi
eld spectrograph with a resolution of
R
∼
5000. The
K
-band data were taken with the OH-Suppressing Infrared
Imaging Spectrograph
(
OSIRIS; Larkin et al.
2006
)
on Keck II
on UT 2011 August 20. The OSIRIS measurements used
NGSAO, with an average seeing of
∼
0
6. The data were then
binned and smoothed from their original resolution to
R
∼
1000
to increase the S
/
N per resolution element. Details about the
data reduction can be found in Bowler et al.
(
2014
)
. In this
study, we further binned the data to a resolution of
R
=
300 for
the retrievals. This allowed us to use the correlated-k opacities
from
petitRADTRANS
, rather than substantially downsam-
pling the line-by-line opacities, which would result in
inaccuracies, and reduced the run times for our retrievals.
While medium-resolution data have been suggested as a way to
overcome the degeneracies of low-resolution data
(
e.g., Hood
et al.
2023
)
,we
fi
nd that running our retrievals at
R
∼
1000
results in unphysical solutions due to the low S
/
N and opacity
sampling. These issues vanish when we bin to a slightly lower
resolution. We
fi
nd no substantial differences to our retrieved
parameters for a resolution of
R
∼
100
–
600, only a difference
in run time. We opt for
R
∼
300 to optimize between resolution
and run time.
3.2. High-resolution Spectroscopy of ROXs 42B b
Bryan et al.
(
2018
)
obtained a high-resolution
K
-band
spectrum of ROXs 42B b on UT 2015 June 1 and 2, using the
pre-upgrade NIRSPEC instrument
(
R
∼
25,000
)
on Keck II.
The target was observed using a 0
041
×
2
26 slit in adaptive
optics
(
AO
)
mode in order to minimize blending with the
primary star. For ROXs 42B b, both the companion and
primary
(
separation
∼
1
2
)
were observed simultaneously in
the slit, with their light spatially separated on the detector. The
host star
’
s spectrum was then used to derive a wavelength
solution and telluric correction for the lower S
/
N planetary
data. Details on the observations and data reduction can be
found in Bryan et al.
(
2018
)
. We used two spectral orders
spanning
λ
=
2.27
–
2.38
μ
m in our retrieval because they
contain absorption lines from both water and CO, including
two strong CO band heads. The other spectral orders had less
accurate telluric corrections and wavelength solutions, and we
therefore follow the example of Bryan et al.
(
2018
)
and exclude
them from our analysis.
In Figure
1
we show the cross-correlation function for our
continuum-normalized, radial-velocity-corrected high-resolu-
tion spectrum compared to single molecular template spectra.
We detect H
2
O and CO, which are expected to be the dominant
near-infrared absorbers in an atmosphere of this temperature, at
greater than 8
σ
. We do not detect CH
4
or OH, which are
predicted to have much lower abundances.
3.3. SNIFS Optical Spectrum of ROXs 42B AB
In order to derive an estimate for the abundances of the
binary host stars, we use a low-resolution optical spectrum
obtained on UT 2012 May 20 by SNIFS at the University of
Hawai
’
i 2.2 m telescope and published in Bowler et al.
(
2014
)
.
SNIFS is an integral
fi
eld unit with simultaneous coverage of
the blue
(
3000
–
5200
Å
)
and red
(
5200
–
9500
Å
)
optical regions
at a resolving power of
R
∼
1300. Additional details about the
data reduction can be found in Bowler et al.
2014
. In this study,
Figure 1.
Cross-correlation functions
(
CCFs
)
showing detections of CO and H
2
O using two orders
(
2.27
–
2.38
μ
m
)
from the high-resolution NIRSPEC
K
-band
spectrum. The signi
fi
cance is computed by dividing the CCF by the standard deviation of the out-of-peak baseline.
4
The Astronomical Journal,
167:218
(
19pp
)
, 2024 May
Inglis et al.
we binned the SNIF optical spectrum to a resolution of
R
∼
100
for comparison with the SPHINX model grid, which has a
native resolution of
R
∼
250
(
Iyer et al.
2023
)
.
4. Atmospheric Retrieval Setup
We use the retrieval framework implemented in
peti-
tRADTRANS
(
Mollière et al.
2019
,
2020
)
to model our low-
and high-resolution spectra. We use a retrieval setup similar to
the one described in Mollière et al.
(
2020
)
, which we describe
in more detail below.
Following previous studies
(
Burningham et al.
2017
;
Mollière et al.
2020
; Xuan et al.
2022
, etc.
)
, we assume that
the atmosphere of ROXs 42B b is in local chemical
equilibrium, with the exception of potential quenched carbon
chemistry. We use
petitRADTRANS
to calculate layer-
dependent chemical abundances by interpolating tables gener-
ated by easyCHEM, a Gibbs Free Energy minimizer
(
Mollière
et al.
2019
)
. We parameterize the bulk chemistry using a C
/
O
ratio and metallicity,
[
Fe
/
H
]
, which together set the abun-
dances for all of the individual species. We perform initial
fi
ts
to test for the potential presence of disequilibrium chemistry by
fi
tting for a carbon quench pressure, which
fi
xes the
abundances of carbon monoxide, water, and methane to a
constant value at pressures lower than the quench pressure. We
fi
nd that the quench pressure either tends to very low values or
is completely unconstrained, and therefore exclude it from our
fi
nal
fi
ts. This is not surprising, as methane is expected to have
a very low abundance throughout ROXs 42B b
’
s atmosphere,
and it is primarily the measured ratio of CH
4
to CO that
constrains the quench pressure when the atmosphere is not in
chemical equilibrium
(
Fortney et al.
2020
; Xuan et al.
2022
)
.
4.1. Opacities
We use the pre-tabulated correlated-k and line-by-line
opacities from
petitRADTRANS
(
Mollière et al.
2019
)
to
model our low and high-resolution spectra, respectively. We
include opacities from CO, H
2
O, FeH, CO
2
, OH, H
2
S, PH
3
,
Na, and K in our models. For completeness, we included the
opacities of CH
4
, HCN, and NH
3
in our initial
fi
ts, but found
that this had no effect on our retrieved posteriors for either the
low- or high-resolution
fi
ts. This is not surprising, as these
molecules are all predicted to have very low abundances in the
relatively hot atmosphere of ROXs 42B b. We
fi
nd similar
results for tests including VO and TiO. We
fi
nd that the alkali
species, Na and K, are particularly important for
fi
tting our
low-resolution data, as their absorption wings can affect the
continuum shape at the blue edge of the
J
band. We use the
same baseline list from the VALD opacity database
(
Piskunov
et al.
1995
)
and try three different treatments of the wings,
including the long wing treatment from Burrows & Volobuyev
(
2003
)
, custom pressure broadening
(
for details see Mollière
et al.
2019
)
, and a Lorentz pro
fi
le
(
Schweitzer et al.
1996
)
to
quantify the effect of this choice on our retrieved abundances.
We found that the differences were negligible and used the
custom pressure broadening in our
fi
nal
fi
ts. To cut down on
computation time for our high-resolution retrievals, we down-
sampled our opacities by a factor of 4
(
native resolution of 10
6
,
new resolution of
R
=
250,000
)
. This new resolution is still
10
×
the resolution of our data. We con
fi
rm that this resolution
is suf
fi
cient for our data by generating synthetic data using
petitRADTRANS
, and we retrieve data at both native and
downsampled resolutions. We
fi
nd no signi
fi
cant differences in
the retrieved posterior distributions.
4.2. Temperature Structure
We adopt the six-parameter spline pressure
–
temperature
pro
fi
le from Mollière et al.
(
2020
)
. This spline pro
fi
le splits the
atmosphere into three layers. The lowest layer of the
atmosphere is located beneath the radiative
–
convective bound-
ary. In this region, the temperature pro
fi
le is set equal to the
moist adiabat corresponding to the assumed atmospheric
temperature and composition. The middle layer, which extends
from the radiative
–
convective boundary to the point where the
optical depth
τ
=
0.1, is a radiative photosphere where the
temperature structure is set based on the optical depth and the
classical Eddington approximation. The uppermost layer
begins at
τ
=
0.1 and extends to a pressure of 10
−
6
bars. In
this layer, the temperature is set using a cubic spline anchored
by four equidistant points in log
(
P
)
. This allows for a more
complicated temperature structure than is permitted by the
Eddington approximation, which forces the temperature at
pressures above the photosphere to be isothermal. In our
fi
ts,
we penalize combinations of parameters that result in
temperature inversions, which we do not expect to be present
given ROXs 42B b
’
s wide orbital separation.
4.3. Clouds
Previous studies of isolated brown dwarfs and directly
imaged planets with effective temperatures similar to that of
ROXs 42B b have consistently found that clouds are required
in order to accurately model their low-resolution spectra
(
e.g.,
Burningham et al.
2017
; Mollière et al.
2020
; Burningham
et al.
2021
; Lueber et al.
2022
)
. Both Bowler et al.
(
2014
)
and
Currie et al.
(
2014a
)
found evidence for the presence of clouds
in the atmosphere of ROXs 42B b when comparing to grid
models. Spitzer mid-infrared spectroscopy of isolated brown
dwarfs with spectral types similar to that of ROXs 42B b
indicates that absorption from silicate grains is ubiquitous in
these atmospheres
(
Suárez & Metchev
2022
)
. There are many
cloud models of varying complexity in the literature, ranging
from one-parameter opaque cloud decks to multiple cloud
decks of different scale heights, pressure bases, and scattering
properties. We consider two different cloud models in our
retrievals: a simple, three-parameter gray cloud deck, and the
more complicated, physically motivated EddySed cloud model
(
Ackerman & Marley
2001
; Mollière et al.
2020
)
.
For our gray cloud model, we consider a simple cloud deck
with a wavelength-independent opacity and parameterize the
opacity by the cloud base pressure,
P
base
, the opacity at the
cloud base,
κ
0
, and the pressure scaling power law,
γ
,as
follows:
⎜⎟
⎛
⎝
⎞
⎠
kk
=
g
()()
P
P
P
.1
0
base
In addition to this simple cloud prescription, we also carry
out
fi
ts using the EddySed cloud model from Ackerman &
Marley
(
2001
)
as implemented in
petitRADTRANS
(
Mollière
et al.
2020
)
. In this cloud model, the location of the cloud base
is set by where the condensation curve of a given cloud species
intersects with the atmospheric pressure
–
temperature pro
fi
le.
The vertical extent and number density of the clouds are
calculated using parameters representing the vertical mixing,
5
The Astronomical Journal,
167:218
(
19pp
)
, 2024 May
Inglis et al.
K
zz
, and the sedimentation ef
fi
ciency
f
sed
. In addition, we
fi
t for
a multiplicative factor that scales the abundance of each cloud
species relative to the equilibrium chemistry-predicted value at
the cloud base,
X
species
.
We use a Mie scattering model to calculate the wavelength-
dependent opacity from each cloud species in the EddySed
model. We determine which cloud species to include in our
model by comparing likely
P
–
T
pro
fi
les for ROXs 42B b to
condensation curves for a wide range of potential cloud
species. Based on this, we
fi
nd that iron
(
Fe
)
, enstatite
(
MgSiO
3
)
, forsterite
(
Mg
2
SiO
4
)
, quartz
(
SiO
2
)
, and corundum
(
Al
2
O
3
)
are all possible cloud species that could condense in
the atmosphere of ROXs 42B b. Signatures of silicate clouds
have been observed in Spitzer IRS data of similar spectral type
brown dwarfs
(
e.g., Cushing et al.
2006
; Burgasser et al.
2008
;
Burningham et al.
2021
)
. Visscher et al.
(
2010
)
predict that the
formation of quartz clouds will be repressed in favor of
enstatite due to the high abundance of Mg, though this has been
shown to not always be true by Burningham et al.
(
2021
)
,
whose retrievals favored enstatite clouds over deeper quartz
clouds. On the other hand, Gao et al.
(
2020
)
predict that
fosterite should be the dominant silicate species to condense
from equilibrium chemistry and cloud microphysics. However,
the cross sections of quartz, forsterite, and enstatite clouds have
a nearly identical slope at near-infrared wavelengths with no
unique features to differentiate them
(
Wakeford & Sing
2015
)
,
so we choose to focus on enstatite clouds for this study. We
explore multiple combinations of cloud species including
Al
2
O
3
, Fe, and MgSiO
3
, as well as different cloud particle
properties
(
amorphous versus crystalline
)
for the solid species
in our retrieval, which changes the refractive indices and
resulting scattering cross sections. We
fi
nd that our choice of
amorphous versus crystalline structure has a negligible impact
on our retrieved posterior probability distributions, so we use
amorphous Mie scattering particles for our
fi
nal models. This is
consistent with model
fi
ts to mid-infrared Spitzer IRS spectra
of brown dwarfs, which are best reproduced by amorphous
silicate cloud particles
(
Luna & Morley
2021
; Suárez &
Metchev
2023
)
.
4.4. Additional Fit Parameters
We also
fi
t for the surface gravity, parameterized as log
(
g
)
.
In the low-resolution retrievals, we additionally
fi
t for a
fl
ux
scaling parameter in order to match the overall
fl
ux level. Our
high-resolution spectrum is continuum normalized, and so is
not sensitive to the absolute
fl
ux level.
petitRADTRANS
computes the
fl
ux density emitted at the surface of the planet.
To obtain the observed
fl
ux, we must multiply this quantity by
Table 2
Summary of all Fitted Parameters in Our High-resolution
(
HR
)
and Low-resolution
(
LR
)
petitRADTRANS
Retrievals and our Adopted Priors
Parameter
Prior
Description
Retrieval
R
P
(
1, 3
)
R
J
planet radius in Jupiter radii
LR
log
g
(
2, 5.5
)
log of the planet surface gravity
LR,HR
v
sin
i
(
0, 20
)
km s
−
1
projected rotational velocity of the planet
HR
rv
(
−
10, 10
)
km s
−
1
apparent radial velocity of the planet
HR
A
v
(
0, 5
)
optical extinction coef
fi
cient
LR
b
error in
fl
ation term
LR,HR
scale K
(
0.9, 1.1
)
scale factor for the
K
band
LR
scale H
(
0.9, 1.1
)
scale factor for the
H
band
LR
Temperature Model Parameters
T
1
,
T
2
,
T
3
(
0.1, 1
)
anchor points for the spline pressure
–
temperature pro
fi
le
(
as fractions of adjacent points
)
LR,HR
α
(
1, 2
)
power law for optical depth model
LR,HR
δ
(
0, 1
)
proportionality constant in the optical depth model
LR,HR
T
int
(
300, 2700
)
K
interior temperature of the planet
LR,HR
Chemistry Model Parameters
C
/
O
(
0.3, 1.5
)
C
/
O ratio of the planet atmosphere
LR,HR
[
Fe
/
H
]
(
-1.5, 3
)
log metallicity of planet atmosphere, relative to solar
LR,HR
P
quench
(
-6, 2
)
bars
carbon quench pressure for disequilibrium chemistry model
LR,HR
Gray Cloud Model Parameters
κ
0
log-
(
-6, 10
)
cloud opacity at the cloud base
LR,HR
γ
(
0, 15
)
power law for scaling cloud opacity with pressure
LR,HR
P
0
log-
(
-6, 2
)
bars
log pressure of the cloud base in bars
LR,HR
EddySed Cloud Model Parameters
σ
norm
(
1.0, 3.0
)
width of cloud particle size distribution
LR,HR
f
sed
(
0,15
)
sedimentation ef
fi
ciency
(
for calculating cloud deck parameters
)
LR,HR
K
zz
log-
(
5, 13
)
vertical mixing ef
fi
ciency
(
for calculating cloud deck parameters
)
LR,HR
X
species
log-
(
-4.5,1
)
enhancement factor of given cloud species at the cloud base relative to equilibrium
LR,HR
abundance
(
species included: Fe, MgSiO
3
,Al
2
O
3
.
)
Note.
The parameters for each of our two cloud models are detailed in separate sections. In the third column, we note whether each parameter is used for our hig
h-
resolution
(
HR
)
or low-resolution
(
LR
)
retrievals. All parameters are used in our joint retrievals.
6
The Astronomical Journal,
167:218
(
19pp
)
, 2024 May
Inglis et al.
a scale factor:
⎛
⎝
⎞
⎠
=
()
f
R
d
f
,2
obs
2
emit
where
R
is the object
’
s radius and
d
is the distance to the
system.
We allow for
fl
ux offsets between each of our low-resolution
spectral bands
(
two offsets in total with the
J
band
fi
xed
)
to
account for the fact that they were observed with different
instruments at different observational epochs. As this planet is
located in a young star-forming region, we additionally
fi
t for
an optical extinction coef
fi
cient,
A
V
, and correspondingly
redden our model spectra to compare with our data. Bowler
et al.
(
2014
)
calculated a reddening value for the primary
binary of
-
+
1.7
1.2
0.9
by comparing the optical SNIFS spectrum to
optical templates from Pickles
(
1998
)
. However, the constraints
on this value are asymmetric and wide, and this value was
calcuated assuming a single star, so we opt for a wide uniform
prior on this value for our
fi
ts.
It is possible that the error bars of our data may be
underestimated due to the presence of correlated noise sources.
We therefore add a logarithmic error term,
b
, in quadrature to
the reported measurement errors for each spectral bin, such that
the effective standard deviation of each point,
i
, becomes:
s
=+
()
s
10 .
3
ii
b
22
For retrievals including the high-resolution data, we also
include two additional parameters: the radial-velocity offset,
and the projected rotational velocity,
v
sin
i
.
We adopt wide uniform or log-uniform priors for all
parameters in our models and impose no restrictions other
than excluding combinations of parameters that result in
temperature inversions. A summary table of all the parameters
included in the retrieval and their priors is shown in Table
2
.
4.5. Nested Sampling
We
fi
t the data using nested sampling as implemented in
PyMultiNest, a python wrapper for MultiNest
(
Feroz et al.
2009
)
. We run our retrievals with 1000 live points and perform
multiple runs using the optimal sampling ef
fi
ciency for
PyMultiNest to compute our evidence and posterior separately.
Our
“
best-
fi
t
”
model is taken to be the sample with the highest
likelihood. We compare different models using the Bayes
factor,
B
12
, which gives the evidence for model 1 relative to
model 2. It is calculated as:
=
()
B
Z
Z
,4
12
1
2
where Z is the evidence for each given model as computed by
PyMultiNest. The higher the Bayes factor, the stronger the
evidence supporting one model over another. We evaluate the
Bayes factor for each of our different models relative to our
best-
fi
t model and list the results in Table
3
.
5. Atmospheric Retrievals
5.1. Low-resolution Retrievals
In this section, we describe the results of our retrievals on
our low-resolution spectra. We
fi
t our low-resolution data using
5 different cloud models: a
“
clear
”
model, where there are no
clouds present in the visible portion of the atmosphere, a gray
cloud model, and 3 variations of the EddySed cloud model to
account for the unknown cloud properties. Our variations of the
EddySed cloud model include an iron cloud deck, an enstatite
cloud deck, and a combination of iron and silicate clouds, as
Table 3
Best-
fi
t Values and Con
fi
dence Intervals for key Parameters from ROXs 42B b Retrievals
Cloud Model
C
/
O
[
Fe
/
H
]
Radius
(
R
Jup
)
v
sin
i
(
km s
−
1
)
log
(
g
)(
cgs
)
T
eff
(
K
)
Bayes Factor
(
σ
)
High-Resolution Retrievals
Clear
0.504
±
0.048
−
0.67
±
0.35
N
/
A
10.52
±
0.92
3.49
±
0.57
2720
±
80
1.0
Gray Clouds
0.510
±
0.047
−
0.64
±
0.31
N
/
A
10.57
±
0.83
3.46
±
0.48
2800
±
100
0.18
(
−
2.4
σ
)
EddySed
(
MgSiO
3
+
Fe
)
0.510
±
0.032
−
0.69
±
0.33
N
/
A
10.35
±
0.65
3.40
±
0.45
2750
±
80
2.8
×
10
−
8
(
−
6.2
σ
)
Low-Resolution Retrievals
Clear
0.723
±
0.029
1.37
±
0.13
2.74
±
0.06
N
/
A
3.9
±
0.2
1890
±
35
1.0
Gray clouds
0.705
±
0.031
1.33
±
0.17
2.78
±
0.06
N
/
A
3.70
±
0.21
1886
±
36
0.15
(
−
2.5
σ
)
Gray clouds
+
fi
xed
P
–
T
0.724
±
0.007
1.37
±
0.08
2.72
±
0.05
N
/
A
3.58
±
0.11
1876
±
27
0.37
(
−
2.0
σ
)
Gray clouds
+
fi
xed
P
–
T
,
A
V
0.732
±
0.007
1.11
±
0.08
2.61
±
0.03
N
/
A
3.31
±
0.06
1834
±
11
2.1
×
10
−
9
(
−
6.6
σ
)
EddySed
(
MgSiO
3
)
0.704
±
0.033
1.35
±
0.14
2.77
±
0.06
N
/
A
3.79
±
0.19
1895
±
39
0.37
(
−
2.0
σ
)
EddySed
(
Fe, am
)
0.694
±
0.035
1.33
±
0.18
2.78
±
0.06
N
/
A
3.78
±
0.20
1894
±
34
0.67
(
−
1.6
σ
)
EddySed
(
MgSiO
3
+
Fe, am
)
0.696
±
0.038
1.34
±
0.16
2.77
±
0.06
N
/
A
3.81
±
0.20
1898
±
40
0.034
(
−
3.1
σ
)
EddySed
(
MgSiO
3
+
AlO
2
,am
)
0.702
±
0.032
1.34
±
0.16
2.78
±
0.05
N
/
A
3.74
±
0.18
1893
±
38
0.54
(
−
1.8
σ
)
Joint Retrievals
Clear
0.778
±
0.003
0.37
±
0.03
2.84
±
0.02
5.55
±
0.74
2.76
±
0.08
1843
±
22
1.0
Gray clouds
0.734
±
0.008
0.46
±
0.04
2.83
±
0.01
5.57
±
0.35
2.94
±
0.05
1935
±
12
1808
(
4.3
σ
)
EddySed
(
MgSiO
3
+
Fe
)
0.691
±
0.004
0.67
±
0.02
2.81
±
0.01
10.30
±
0.35 3.47
±
0.017
1905
±
17
44.7
(
3.2
σ
)
Note.
The rightmost column lists the Bayes factor
(
B
)
for each retrieval relative to the clear model
(
B
=
1
)
. The uncertainties for each parameter quoted are determined
using the 68% con
fi
dence interval from our posteriors assuming a Gaussian distribution. For our cloudy models,
“
am
”
stands for amorphous cloud particles
+
Mie
scattering. Our reported Bayes factor is calculated relative to the clear model and then converted to a minimum sigma value using the method described
in Benneke &
Seager
(
2013
)
7
The Astronomical Journal,
167:218
(
19pp
)
, 2024 May
Inglis et al.
well as a combination of enstatite and corundum clouds. In
Figure
2
we show the best-
fi
t spectra and residuals for our clear
model, the best
fi
tting model. The corresponding best-
fi
t P-T
pro
fi
le is shown in Figure
3
(
left
)
. In Figure
4
we show the
posteriors for a few select parameters from each retrieval,
including log
(
g
)
,
T
eff
,C
/
O ratio and
[
Fe
/
H
]
. The best-
fi
t values
and 1-sigma uncertainties for key parameters are reported in
Table
3
.
We
fi
nd that our clear model is preferred at 2.4
σ
over our
gray cloud model, and 6.2
σ
from our EddySed cloud model.
We
fi
nd a supersolar metallicity of 1.37
±
0.13. We also
fi
nd a
supersolar C
/
O ratio of 0.798
±
0.019. Our retrieved C
/
O
ratio,
[
Fe
/
H
]
, and
P
–
T
pro
fi
le are consistent between our clear,
gray, and EddySed cloud models
(
Figure
4
)
. When cloud
parameters are included in our
fi
ts, we
fi
nd either clouds too
deep in the atmosphere to affect the spectrum, or completely
unconstrained values, which indicates that clouds are not
necessary to reproduce our data or there is insuf
fi
cient
information to constrain cloud properties.
Even with constraints on the anchor points of our spline
P
–
T
pro
fi
le, our
fi
ts strongly prefer an isothermal temperature
structure at pressures lower than 1 bar. These kinds of steep,
isothermal
P
–
T
pro
fi
les have been seen in other studies
(
e.g.,
Burningham et al.
2017
)
and are thought to be an attempt to
Figure 2.
Retrieved best-
fi
t model
(
green
)
compared to our low-resolution
JHK
-band spectrum from Bowler et al.
(
2014
; top panel
)
and error-weighted residuals
(
lower panel
)
. Our full low-resolution retrievals are compared to the best-
fi
t model
(
yellow
)
from our retrievals, where our
P
–
T
pro
fi
le is
fi
xed to a Sonora Bobcat
P
–
T
pro
fi
le from
(
Marley et al.
2021b
)
. The horizontal black line indicates the wavelength coverage of our Keck
/
NIRSPEC high-resolution
K
-band data for comparison.
Figure 3.
Retrieved pressure
–
temperature
(
P
–
T
)
pro
fi
les for our best-
fi
t models
(
bold in Table
3
)
for our low-resolution data
(
left
)
, high-resolution data
(
center
)
, and
both combined
(
right
)
. Randomly sampled
P
–
T
curves are plotted in green. Condensation curves for important cloud species in young hot objects, Fe, Al
2
O
3
, TiO
2
,f
and MgSiO
3
are shown for comparison
(
dotted lines
)
. We overplot a Sonora Bobcat model
(
Marley et al.
2021a
,
2021b
)
corresponding to the photometrically derived
temperature and log
(
g
)
. The gray gradient corresponds to the value of the wavelength-integrated
fl
ux contribution function.
8
The Astronomical Journal,
167:218
(
19pp
)
, 2024 May
Inglis et al.
compensate for the effect of cloud opacity using the
fl
exibility
of the
P
–
T
pro
fi
le. While it has been suggested by Tremblin
et al.
(
2017
)
that the atmospheres of these planets could in fact
be isothermal and the observed reddening attributed to clouds
could be explained by
fi
ngering convection, we
fi
nd that this is
unlikely in the case of ROXs 42B b. Given that these objects
are internally heated, it is very unlikely that their atmospheres
would be isothermal; indeed, radiative equilibrium grid models
predict a much steeper temperature pro
fi
le for ROXs 42B b
(
e.g., the ATMO and Sonora Bobcat model grids; Phillips et al.
2020
; Marley et al.
2021a
,
2021b
)
. The changing colors of
brown dwarfs as a function of the effective temperature, as well
as the high frequency of rotational variability near the L-T
transition, all provide strong evidence that clouds should be
ubiquitous in the atmospheres of objects like ROXs 42B b
(
Bailer-Jones & Mundt
1999
; Gelino et al.
2002
; Marley et al.
2010
; Apai et al.
2013
; Radigan et al.
2014
; Vos et al.
2019
)
.
We also consider
fi
ts where we
fi
x the
P
–
T
pro
fi
le to a self-
consistent Sonora model
(
Marley et al.
2021a
,
2021b
)
with log
(
g
)
=
3.5 and an effective temperature of 2100 K, matching the
spectroscopically and photometrically derived parameters for
ROXs 42B b
(
Currie et al.
2014a
,
2014b
)
. With this
fi
xed
P
–
T
pro
fi
le, we
fi
nd that we are no longer able to adequately
fi
t our
low-resolution data using a cloud-free model, as there are no
combinations of parameters that can reproduce the data. With
the
P
–
T
pro
fi
le
fi
xed, we
fi
nd a smaller radius and
T
eff
than in
our free
P
–
T
retrieval case, indicating that it is trading off with
the radius in an attempt to conserve total luminosity. We
Figure 4.
Corner plot comparing the posterior probability distributions of key parameters from retrievals on our low-resolution spectrum for our three consi
dered
cloud models, a clear sky, a simple gray cloud deck, and EddySed condensate clouds composed of Fe and MgSiO
3
.
9
The Astronomical Journal,
167:218
(
19pp
)
, 2024 May
Inglis et al.
additionally
fi
nd a higher reddening coef
fi
cient, indicating the
need for extra absorption to match our observed spectrum.
When we include gray clouds in our
fi
xed
P
–
T
pro
fi
le
retrievals, we are able to match our low-resolution spectrum
nearly as well as the retrievals with the free
P
–
T
pro
fi
le, with
the free
P
–
T
pro
fi
le model preferred only slightly at 2
σ
.We
fi
nd that the cloud base becomes constrained in the retrievals,
but the optical depth of the clouds trades off with the reddening
coef
fi
cient. We therefore try an additional
fi
t where we
fi
x the
reddening value to the value calculated by Bowler et al.
(
2014
)
for the primary binary. In Figure
5
we compare the posteriors
for our
fi
xed
P
–
T
pro
fi
le retrievals to our free
P
–
T
pro
fi
le
retrieval using the gray cloud model. We
fi
nd that with the
reddening and
P
–
T
pro
fi
le
fi
xed, cloud opacity becomes
important to match our observed spectrum, and the metallicity,
log
(
g
)
, and planetary radius values all decrease substantially,
while the C
/
O ratio increases only slightly. We conclude that
there is a degeneracy between our retrieved chemistry and
atmospheric temperature structure. It is most strongly observed
to affect our retrieved metallicity. We
fi
nd that our retrieved
metallicity increases or decreases as the slope of our
P
–
T
pro
fi
le changes from more isothermal to less. This makes it
evident that the model is using the effects of the
P
–
T
pro
fi
le to
account for the effects of cloud on absorption depth, as a more
Figure 5.
Corner plot comparing the posterior probability distributions of key parameters from our
fi
xed and free
P
–
T
pro
fi
le retrievals on our low-resolution spectrum
using a gray cloud model and
(
a
)
an unrestricted spline pressure
–
temperature
(
P
–
T
)
pro
fi
le,
(
b
)
a
P
–
T
pro
fi
le
fi
xed to a Sonora
P
–
T
pro
fi
le
(
Marley
et al.
2021a
,
2021b
)
, and
(
c
)
a
P
–
T
pro
fi
le
fi
xed to a Sonora model
P
–
T
pro
fi
le and the reddening coef
fi
cient
fi
xed to the best-
fi
t stellar value from Bowler et al.
(
2014
)
.
10
The Astronomical Journal,
167:218
(
19pp
)
, 2024 May
Inglis et al.
isothermal atmosphere makes it harder to have deep absorption
features. The metallicity, as a result, is driven up to account for
the observed absorption features.
To con
fi
rm this, we perform similar tests restricting our
metallicity to values lower than 0.5. In this case, the
P
–
T
structure is less isothermal. We observe the worst
fi
t to occur in
the
H
-band peak, suggesting that this is driving this degeneracy
(
Figure
2
)
. As this feature is also a strong indicator of surface
gravity strength, we therefore conclude that we cannot trust our
retrieved gravity value either. We additionally observe a
degeneracy between our optical extinction coef
fi
cient,
A
V
, and
the cloud properties. For our free
P
–
T
pro
fi
le retrievals,
A
V
=
2.43
±
0.41, and for our
fi
xed
P
–
T
pro
fi
le retrievals, it
increases slightly to 2.67
±
0.25. We
fi
nd that the retrievals
prefer to increase the
A
V
value rather than add clouds, likely
because this involves toggling only a single parameter versus a
combination of parameters, as the net effect of silicate clouds is
to redden the observed spectrum.
In all versions of the
fi
t, we consistently struggle to
fi
t the
J
-band data with our models, particularly at the blue edge. This
may be related to the extended wings of the Na and K lines. We
compare retrievals using three different wing treatments
described in Section
4.1
but are still unable to replicate the
observed
J
-band shape. TiO also has absorption features
around 1.2 microns; however, we
fi
nd that even when we
include TiO with free abundance, it does not improve the
quality of our
fi
t.
Based on the observed degeneracies between various
parameters in our low-resolution retrievals, we conclude that
our retrieved abundances and other properties are likely
unreliable.
5.2. High-resolution Retrievals
In this section, we present the results of our retrievals on the
high-resolution data and compare them with the results from
our retrievals using the low-resolution data. We run the same
suite of cloud models as we did on our low-resolution data and
additionally
fi
t for a projected rotational velocity
(
v
sin
i
)
and a
radial-velocity offset. The best-
fi
t values and uncertainties for
key parameters, including the C
/
O ratio,
[
Fe
/
H
]
,
v
sin
i
, log
(
g
)
,
and
T
eff
, are listed in Table
3
.
For our high-resolution data, we also
fi
nd no difference in
the quality of the
fi
t between models with and without clouds.
We compare the posteriors for the clear, gray cloud, and
EddySed cloud models in Figure
6
and
fi
nd that they all
overlap. As a result, the Bayes factor prefers the simpler cloud-
free model. As our inferred parameters are not sensitive to our
choice of cloud model, we use the parameters from the cloud-
free model moving forward. We retrieve a moderately
substellar metallicity of
[
Fe
/
H
]
=
−
0.67
±
0.35, rather than
the superstellar metallicity preferred in our low-resolution
retrievals. We
fi
nd a C
/
O ratio of 0.505
±
0.05, which is
consistent with the solar C
/
O ratio of 0.59
±
0.13
(
Asplund
et al.
2021
)
.We
fi
nd a radial-velocity value
rv
=
1.44
±
0.42 km s
−
1
. We additionally constrain the projected spin rate
v
sin
i
to be 10.52
±
0.92 km s
−
1
, which is in good agreement
with the value of
-
+
9
.5
2.3
2.1
km s
−
1
found by Bryan et al.
(
2018
)
for these same data using a radiative equilibrium model and
calculating the autocorrelation function. It is important to note
that we utilized the instrumental broadening value reported by
Bryan et al.
(
2018
)
in our
fi
ts rather than re-deriving our own
estimate of this parameter; this means that our result is not a
fully independent con
fi
rmation of the measurement reported in
this study.
Unlike the low-resolution data, the
P
–
T
pro
fi
le in the cloud-
free retrieval does not appear to be compensating for the effects
of clouds by adopting an isothermal stratosphere. In Figure
3
we show that the shape of our derived
P
–
T
pro
fi
le for cloud-
free retrieval agrees with predictions from the cloudless Sonora
Bobcat forward model grid for an object of the same effective
temperature and log
(
g
)(
Marley et al.
2021a
,
2021b
)
, though it
is possible that the presence of clouds would alter this pro
fi
le.
For models with clouds included, we
fi
nd that the cloud
parameters are unconstrained. This indicates that our high-
resolution data are not biased in the same way as the low-
resolution retrievals by the presence of clouds, and are instead
relatively unaffected by the presence of clouds.
In order to investigate why our high-resolution retrievals do
not appear to be biased by the presence of clouds the same way
our low-resolution retrievals are, we examine where the
fl
ux
originates in our atmosphere relative to the expected positions
of cloud layers. In Figure
7
we plot the
fl
ux contribution
functions for our best-
fi
t models for our high-resolution and
low-resolution retrievals. In the low-resolution retrievals, we
see that the
fl
ux primarily originals at pressures greater than
10
−
1
bars, with some smearing out to lower pressures in the
strong water features. For our high-resolution data, a
substantial portion of the
fl
ux is emitted higher in the
atmosphere, in the cores of individual lines. In Figure
3
,we
show the contribution compared to our
P
–
T
pro
fi
les and
condensation curves. We see that the intersection between the
P
–
T
pro
fi
les and condensation curves occurs deeper than where
the
fl
ux contribution peaks in our high-resolution data. Based
on this, it seems that the high-resolution data are less sensitive
to clouds because the cores of the absorption lines probe higher
in the atmosphere, above the clouds. In other words, the
wavelength-averaged contribution function for our high-
resolution data lies above the predicted cloud base for all three
cloud species considered here
(
see Figure
3
)
. While the
continuum is probably still affected by clouds, we lose
continuum information in our data analysis. Larger wavelength
coverage out to other bands, or
fl
ux-calibrated high-resolution
data should improve the sensitivity of high-resolution data to
cloud properties.
5.3. Joint Retrievals
In addition to
fi
tting both our high-resolution and low-
resolution data sets for ROXs 42B b individually, we
fi
t both
together in a joint retrieval. As with the individual retrievals,
we consider all three types of cloud model, and
fi
t for all the
parameters shown in Table
2
. We show a subset of our
retrieved values for these retrievals in Table
3
, and the full
posteriors are shown in Figure
8
.
In this joint
fi
t, we
fi
nd a lower metallicity and better
constrained cloud properties for both our gray clouds and
EddySed models, which were unconstrained in the
fi
ts using
only the low-resolution data. We additionally
fi
nd that our
retrieved parameters depend strongly on the cloud model used.
Like in other retrievals, we observe a trade-off between
retrieved radius and
T
eff
, which is expected as those parameters
together determine the total luminosity of the planet. For our
cloud-free case, we
fi
nd a multimodal posterior, and that it is
disfavored over either of our cloudy models.
11
The Astronomical Journal,
167:218
(
19pp
)
, 2024 May
Inglis et al.