of 6
Improving Planet Detection with Disk Modeling: Keck
/
NIRC2 Imaging of the HD 34282
Single-armed Protoplanetary Disk
Juan Quiroz
1
, Nicole L. Wallack
2
, Bin Ren
(
)
1
,
6
, Ruobing Dong
(
)
3
, Jerry W. Xuan
1
, Dimitri Mawet
1
,
4
,
Maxwell A. Millar-Blanchaer
5
, and Garreth Ruane
4
1
Department of Astronomy, California Institute of Technology, MC 249-17, 1200 East California Boulevard, Pasadena, CA 91125, USA;
ren@caltech.edu
2
Division of Geological & Planetary Sciences, California Institute of Technology, MC 170-25, 1200 East California Boulevard, Pasadena, CA 91125, US
A
nwallack@caltech.edu
3
Department of Physics & Astronomy, University of Victoria, Victoria, BC, V8P 1A1, Canada
4
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
5
Department of Physics, University of California, Santa Barbara, CA 93106, USA
Received 2021 October 4; revised 2021 November 23; accepted 2021 November 24; published 2022 January 4
Abstract
Formed in protoplanetary disks around young stars, giant planets can leave observational features such as spirals
and gaps in their natal disks through planet
disk interactions. Although such features can indicate the existence of
giant planets, protoplanetary disk signals can overwhelm the innate luminosity of planets. Therefore, in order to
image planets that are embedded in disks, it is necessary to remove the contamination from the disks to reveal the
planets possibly hiding within their natal environments. We observe and directly model the detected disk in the
Keck
/
NIRC2 vortex coronagraph
L
-band observations of the single-armed protoplanetary disk around HD 34282.
Despite a nondetection of companions for HD 34282, this direct disk modeling improves planet detection
sensitivity by up to a factor of 2 in
fl
ux ratio and
10
M
Jupiter
in mass. This suggests that performing disk modeling
can improve directly imaged planet detection limits in systems with visible scattered light disks, and can help to
better constrain the occurrence rates of self-luminous planets in these systems.
Uni
fi
ed Astronomy Thesaurus concepts:
Protoplanetary disks
(
1300
)
;
Coronagraphic imaging
(
313
)
;
Planetary
system formation
(
1257
)
Supporting material:
data behind
fi
gure
1. Introduction
The most recent generation of high-contrast imaging surveys
that utilize extreme adaptive optics systems have obtained an
occurrence rate of
10% for young self-luminous giant planets
(
i.e., Nielsen et al.
2019
; Vigan et al.
2021
)
. Despite their low
direct occurrence rates using contemporary instruments, giant
planets can gravitationally interact with their surrounding
gaseous protoplanetary disks and leave their mark as observa-
tional signatures in the disk structure
(
e.g., spirals, gaps: Dong
et al.
2015b
,
2015c
; Bae et al.
2018
)
. Therefore, protoplanetary
disks with suspected embedded forming planets not only are
excellent targets for giant planet detection
(
e.g., Haffert et al.
2019
; Wang et al.
2020
)
, but also can help constrain planet
disk interactions
(
e.g., Bae et al.
2019
; Rosotti et al.
2020
)
.
While protoplanetary disks with planet
disk interaction
signatures may be prime targets for observing actively forming
planets, they can also hinder the detection of planets
(
see
Keppler et al.
2018
;Wangetal.
2020
)
. Speci
fi
cally, using the
current prevailing observation and data reduction strategy for
ground-based high-contrast imaging
(
i.e., angular differential
imaging, or ADI; Marois et al.
2006
)
, disk signals can remain in
the reduced images and overwhelm planetary signals, resulting
in lower sensitivity to detecting planets in the regions where disk
signals dominate
(
e.g., Figure 12 of Maire et al.
2017
,Figure6
of de Boer et al.
2021
, Figure 4 of Asensio-Torres et al.
2021
)
.
Moreover, even after processing, disk signals can mimic the
appearances of protoplanets
(
e.g., HD 100546: Quanz et al.
2013
; Currie et al.
2014
; HD 169142: Biller et al.
2014
;
Reggiani et al.
2014
)
, making it challenging to distinguish
planets from disk features. Indeed, it is only after modeling and
removing the disk from the PDS 70 system that Wang et al.
(
2020
)
could recover the disk-embedded protoplanet PDS 70 c.
Therefore, in addition to utilizing diverse approaches in both
observation and data reduction methods, it is necessary to
investigate whether disk modeling could also improve our
sensitivity to planets detected via ground-based high-contrast
imaging, which could possibly lead to more detections in blind-
search surveys.
Although spirals and rings are indications of the existence of
planets, they can also possibly result from mechanisms that do
not involve planets
(
e.g., spirals: Dong et al.
2015a
;
Montesinos & Cuello
2018
; Hall et al.
2020
, gaps: Birnstiel
et al.
2015
; van der Marel et al.
2018
)
. Although the formation
of spirals in protoplanetary disks can be caused both with and
without planets, the differing mechanisms may be distinguish-
able via the structure in the disk. For example, gravitational-
instability-triggered spiral arms are likely symmetric and have
even-numbered spirals
(
e.g., Dong et al.
2015a
)
, whereas
planet-induced spirals can be less symmetric. Another reason to
search spiral disks for planet signals is that gap-opening planets
(
e.g., Zhang et al.
2018
; Lodato et al.
2019
)
could be less
massive than spiral-arm-driving planets
(
e.g., Figure 1 of Bae
et al.
2018
)
, and most gap-opening planets are beyond the
detection limits of current instruments. Therefore, in order to
have the best chance of detecting a massive companion, herein
The Astrophysical Journal Letters,
924:L4
(
6pp
)
, 2022 January 1
https:
//
doi.org
/
10.3847
/
2041-8213
/
ac3e62
© 2022. The Author
(
s
)
. Published by the American Astronomical Society.
6
To whom correspondence should be addressed.
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
we focus on planet detection in the single spiral-arm system
HD 34282
(
de Boer et al.
2021
)
, speci
fi
cally focusing on
improving planetary detection limits by modeling the observed
disk structure.
Located at 309
±
2pc
(
Gaia Collaboration et al.
2021
)
,
HD 34282 is an A3V star
(
Merín et al.
2004
)
with a
protoplanetary disk containing a 75 au cavity
7
in 0.87 mm
ALMA continuum emission observations
(
van der Plas et al.
2017
)
. With an overdensity in the southeast region of its
ALMA-detected ring
(
which has an inclination of 59
°
.3
±
0
°
.4
and a position angle of 117
°
.1
±
0
°
.3
)
, van der Plas et al.
(
2017
)
suggested that a
50
M
Jupiter
brown dwarf companion at
0
1
could be responsible for shepherding the dust in the HD 34282
system, favoring this explanation over a nonplanet-driven
photoevaporation mechanism for opening the cavity. In
J
-band
polarized light observations using VLT
/
SPHERE, de Boer
et al.
(
2021
)
identi
fi
ed two rings with a
56
°
inclination and a
119
°
position angle, and a possible tightly wound single-arm
spiral that resembles the pattern driven by a sub-Jupiter- to
Jupiter-mass planet
(
e.g., Dong et al.
2015c
; Dong &
Fung
2017
)
. However, the observations in de Boer et al.
(
2021
)
were not sensitive enough to detect a planet of such
mass. Moreover, the planet-detection map in Figure 6 of de
Boer et al.
(
2021
)
is affected by the signal of the disk, which
causes the sensitivity to drop from
4
M
Jupiter
in exterior
regions of the image to
10
M
Jupiter
in the regions hosting disk
signals.
Herein we present
L
-band imaging of the HD 34282 system
using the Keck
/
NIRC2 vortex coronagraph. Motivated by the
recovery of the PDS 70 c planet via disk modeling in Wang et al.
(
2020
)
, we investigate the effect of disk modeling in planet
detection using HD 34282. Speci
fi
cally, we model the observed
NIRC2 disk as an experiment in a targeted search for planets that
are embedded in disks. We describe the NIRC2 observations in
Section
2
, we present the observed features and investigate the
effects of disk modeling in Section
3
,andwesummarizeour
fi
ndings in Section
4
.
2. Observation and Data Reduction
We observed HD 34282 using Keck
/
NIRC2 in
L
-band
(
central
wavelength: 3.8
μ
m
)
under program C328
(
PI: G. Ruane
)
on UT
2017 February 07 from 04:43 to 07:15. We use the narrow camera
which has a pixel size of 9.942 mas and a 1024
×
1024 pixel
fi
eld
of view
(
i.e., 10
18
×
10
18
)
. With 73 science frames covering a
parallactic angle change of 61
°
.3, where each frame consists of 45
coadds with 1 s exposures, we ha
ve a total integration time of
3285 s on HD 34282. During the observation, the coherence time
was
τ
0
0.87 ms at 0.5
μ
m
(
Xuan et al.
2018
)
,theWRFseeing
8
was between 1
32 and 1
45, and the airmass was 1.19
±
0.05.
We preprocess the data using the
VIP
(
Gomez Gonzalez et al.
2017
)
package that is customized for NIRC2 vortex observa-
tions by performing
fl
at-
fi
elding, background removal, and
image centering. By comparing the central pixels between the
output point-spread function
(
PSF
)
and an ideal model, the
Strehl ratio was between 0.63 and 0.66 for this observation. See
Xuan et al.
(
2018
)
for a description of both the pipeline that
utilizes the
VIP
package and a thorough characterization of the
Keck
/
NIRC2 vortex coronagraph.
To reveal the extent of the disk while maximizing computa-
tional ef
fi
ciency, we crop each preprocessed image to a 201
×
201
pixel
fi
eld while discarding the last 4 exposures due to poor image
quality. In the following analysis
, we focus on an annular region
that is between 20 pixels and 100 pixels from the star. To extract
the HD 34282 system from the raw observations, we
fi
rst capture
the speckle features using the principal-component-analysis-based
Karhunen
Loève image projection
(
KLIP; Soummer et al.
2012
)
method implemented in the
DebrisDiskFM
package
(
Ren et al.
2019
)
. To balance speckle removal and ADI self-subtraction, with
the former requiring more and the latter requiring fewer KLIP
components in data reduction, we use the
fi
rst 6 KLIP
components to remove speckles while preserving the morphology
of the disk. We rotate each of the reduced 69 images to north
up
and east
left,thencalculatetheirmeantoobtainthe
fi
nal image
for the HD 34282 system, shown in Figure
1
(
a
)
.
We also acquire the de Boer et al.
(
2021
)
J
-band
observations of HD 34282 in polarized light from UT 2015
December 19 using SPHERE
/
IRDIS
(
e.g., de Boer et al.
2020
)
under European Southern Observatory
(
ESO
)
program 096.C-
0248
(
A
)(
PI: J.-L. Beuzit
)
from the ESO Science Archive
Facility. To reveal the extent of the disk, we use
IRDAP
which
performs polarimetric differential imaging
(
PDI
)
from van
Holstein et al.
(
2020
)
to reduce the IRDIS observations. In
Figures
1
(
b
)
and
(
c
)
, we show the SPHERE
f
map and
overlay the SPHERE contours
(
the contour levels are selected
to match features in both data sets
)
on our NIRC2 data.
3. Analysis
3.1. Disk Features
The ADI image of HD 34282 in the NIRC2
L
-band is
composed of a ring and a blob in the northwest direction
(
shown in Figure
1
(
a
))
. The ring extends to
0
5, and its
southeast half is brighter than the northwest half by
40%. The
northwest blob is located outside the inner working angle of
0
2 at a position angle of
60
°
east of north.
The northwest NIRC2 blob is not
a planetary signal. Compared
with the SPHERE PDI data in Figure
1
(
c
)
, it is the inner ring
component
R2
identi
fi
ed in de Boer et al.
(
2021
)
.However,we
do not recover the southeast side of R2 in our NIRC2
observations; this could be explained by self-subtraction effects
with ADI using KLIP. Either reference-star differential imaging
(
e.g., Ruane et al.
2019
)
, or advanced ADI speckle-removal
methods
(
e.g., Ren et al.
2020
;Flasseuretal.
2021
;Pairetetal.
2021
)
are needed to recover the whole extent of R2.
The NIRC2 ring, which has an apparent brightness asymmetry,
is in fact composed of multiple features identi
fi
ed in the SPHERE
data in de Boer et al.
(
2021
)
.Speci
fi
cally, the southeast half of the
NIRC2 ring is a superposition of the SPHERE arm and outer ring,
or the
B1
and
R1
features in de Boer et al.
(
2021
)
,
respectively. As evident in the SPHERE data, the southeast half of
R1 is fainter than B1, causing B1 to dominate the signal in our
NIRC2 data.
3.2. Disk Forward Modeling
Observing an apparent ring-like structure in our
L
-band data
in Figure
1
(
a
)
, we use the Millar-Blanchaer et al.
(
2015
)
code
9
to model the system with a ring. To take into account the
observed apparent brightness asymmetry of HD 34282 evident
7
Size scaled to match Gaia Collaboration et al.
(
2021
)
distance.
8
http:
//
mkwc.ifa.hawaii.edu
/
current
/
seeing
/
index.cgi
9
https:
//
github.com
/
maxwellmb
/
anadisk_model
2
The Astrophysical Journal Letters,
924:L4
(
6pp
)
, 2022 January 1
Quiroz et al.
in both the SPHERE data presented in de Boer et al.
(
2021
)
and
our NIRC2 data, we use the function in the updated code which
can offset the ring from the assumed central star location
(
presented in Millar-Blanchaer et al.
2016
)
. We aim to
reproduce the observed ring using geometric models to
investigate the effect of disk modeling on planet detection;
therefore, we assume the disk is optically thin for simplicity.
Thus, we do not focus on retrieving physical parameters for the
observed HD 34282 ring or on the physical meaning of the
ring-center offset from the star
(
e.g., Table 1 of de Boer et al.
2021
)
. We acknowledge that such a disk model is not
physically motivated, especially after the polarized light
observations in de Boer et al.
(
2021
)
; therefore, we only focus
on the visible structure seen in the NIRC2
L
data and not on its
physical origins.
We use the Ren et al.
(
2021
)
modi
fi
cation of the Millar-
Blanchaer et al.
(
2015
)
code, which describes the ring with a
double power law
(
Augereau et al.
1999
)
along the midplane
and a Gaussian dispersion along the vertical axis:
r
μ+ -
aa
--
-
⎜⎟⎜⎟
rz
r
r
r
r
z
hr
,exp,1
c
2
c
2
2
in
out
1
2
()()
where
r
c
is the critical radius,
α
in
and
α
out
are the asymptotic
power-law indices interior and exterior to
r
c
, and
h
is the scale
height. We use the
DebrisDiskFM
framework by Ren et al.
(
2019
)
to explore disk parameters using
emcee
(
Foreman-
Mackey et al.
2013
)
. Speci
fi
cally, we perform forward
modeling to minimize the residuals in our reduction. We
fi
rst
generate a ring model using the Millar-Blanchaer et al.
(
2015
)
code assuming given ring parameters
(
i.e., inclination, position
angle, brightness, ring-center offsets along the apparent major
and minor axes, critical radius, and power-law indices
)
and
forward-scattering coef
fi
cient of the dust particles
(
i.e., Henyey
& Greenstein
1941
)
. We then simulate the NIRC2 instrument
response on the disk model by rotating the model according to
the parallactic angles for each of the 69 exposures, convolving
with the PSF, and multiplying the result by the transmission
map of the NIRC2 vortex coronagraph.
To obtain the best-
fi
t disk model for the observed disk structure,
we note that disk signals are over
fi
t by speckle features using KLIP
(
Pueyo
2016
)
; we thus perform forward modeling using negative
injection of the disk signals to minimize the residuals. Speci
fi
cally,
we remove the instrument
s response to the disk models from the
original exposures and perform KLIP ADI reduction using 6
Figure 1.
Keck
/
NIRC2 imaging and modeling of the HD 34282 system in the
L
-band.
(
a
)
Reduction result of the original exposures.
(
b
)
SPHERE
f
image,
following annotations in Figure 2 of de Boer et al.
(
2021
)
.
(
c
)
SPHERE contours overlaid on the NIRC2 image: we con
fi
rm the existence of the B1 spiral.
(
d
)
Best-
fi
t
disk model for the NIRC2 ring.
(
e
)
Best-
fi
t disk model with instrumentation effects taken into account
(
i.e., convolution, transmission
)
for a representative one of the
69 exposures: the actual convolution is performed for all of the exposures.
(
f
)
Reduction residuals after removing the best-
fi
t instrumental disk model from the original
exposures. Note: the images are shown in log scale, the dashed central region with a 20 pixel radius is masked out in our data analysis; and the SPHERE dat
a have
different display limits than the NIRC2 data.
(
The data used to create this
fi
gure are available.
)
3
The Astrophysical Journal Letters,
924:L4
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)
, 2022 January 1
Quiroz et al.
components
(
i.e., identical KLIP parameters to the original data
reduction in Section
2
)
. The best-
fi
t model is the one that minimizes
the chi-squared residuals. We list in the
Appendix
the best-
fi
t
parameters, with their uncertainti
es derived assuming the pixels are
mutually independent. By focusi
ng on the ring regions, we obtain
the best-
fi
tdiskmodelshowninFigure
1
(
d
)
, and the corresponding
residual map presented in Figure
1
(
f
)
.
Due to the existence of the ring brightness asymmetry in the
NIRC2 data and the two-ringed architecture in the SPHERE data,
we have performed additional model
fi
tting not shown in
Figure
1
. We have attempted to
fi
t the two halves
(
i.e., northwest
and southeast
)
of the NIRC2 ring with two half-rings, both
centered on the star. The preferred two half-ring models drift
toward nearly edge-on, incons
istent with observations of this
system, which suggests they are likely offset from the star. We
have also tried to
fi
t the northwest blob in the NIRC2 data with a
smaller ring, as motivated by the existence of R2 in the SPHERE
observations. We cannot
fi
nd a model that
fi
ts this structure since
such a ring requires a counterpart in the southeast
(
e.g.,
Figure
1
(
c
))
, which is missing in the NIRC2 observations. We
thus adopt an offset ring to describe the NIRC2 data to minimize
the number of free parameters in our model.
3.3. L
-band Magnitude of HD 34282
The WISE
W
1 band covers a portion of the Keck
/
NIRC2
L
-
band wavelengths, we thus use the former to obtain the
L
magnitude for HD 34282. We
fi
rst generate a high-resolution
stellar spectrum by interpolating within the PHOENIX stellar
model grid from Husser et al.
(
2013
)
to match the stellar
parameters from Merín et al.
(
2004
)
. In order to match the
model spectrum to the observed WISE
W
1 value of
7.072
±
0.016
(
CatWISE2020; Marocco et al.
2021
)
, we scale
the resulting model
fl
ux when integrated across the
W
1
bandpass
(
Rodrigo et al.
2012
; Rodrigo & Solano
2020
)
.We
then take the resulting scaled spectrum, account for the
transmission through the atmosphere, and integrate across the
Keck
/
NIRC2
L
fi
lter pro
fi
le
(
Rodrigo et al.
2012
; Rodrigo &
Solano
2020
)
to obtain an
L
magnitude of
-
+
7
.729
0.017
0.01
5
.
3.4. Detection Limits
We obtain the detection sensitivity to planets by injecting
point sources into the observations and calculating their signal-
to-noise
(
S
/
N
)
values after KLIP ADI reduction. To investigate
the effect of disk modeling on point-source detection, we
calculate the contrast before and after removing the best-
fi
t
model in Figure
1
(
d
)
from the observations. We calculate 1D
contrast curves with radial distance from the host star using
VIP
which utilizes fake companion injection and recovery
when determining the contrast achieved at different radial
distances. We compare the contrast achieved in the image
where we remove the best-
fi
tting disk to that in which we do
not in Figure
2
. Comparing the two contrast curves, we
fi
nd a
marked improvement in the contrast achieved at the radial
separations where the disk is visible. We also test the effect of
utilizing a high-pass
fi
lter
(
HPF
)
to remove the disk structure,
which in essence is treating the disk as noise. We
fi
nd that an
improvement is seen for both the original data and the data in
which we use an HPF.
10
While using an HPF allows us to achieve better contrast than
not using an HPF, the data with the HPF does degrade the
quality of the extended disk structure seen in this system;
therefore, we focus on the data without the HPF in order to
highlight the effect that disk modeling has. For the data without
the HPF, we then utilize our 1D contrast curves and the
AMES
Cond models
(
Baraffe et al.
2003
)
to determine what
mass planets we are sensitive to with our improved contrast
limits after removing the disk. The AMES
Cond evolutionary
models predict how luminous an object will be given a mass
and age. We use our
L
stellar magnitude, our contrast limits,
and the published age for this system
(
6.4
-
+
2.6
1.
9
Myr; van der Plas
et al.
2017
)
to determine expected mass limits in the disk plane
based on disk parameters in van der Plas et al.
(
2017
)
.We
interpolate within the AMES
Cond model grid and determine
the mass corresponding to our contrast with radial separation in
Figure
3
.
We can reach a typical sensitivity of
10
M
Jupiter
assuming
the AMES
Cond models. However, our sensitivity is sub-
optimal in the region where the disk signal resides at
200 au,
as has been observed in Figure 6 of de Boer et al.
(
2021
)
.
Figure 2.
5
σ
detection limit of point sources as a function of radial separation
for our observations. The red dashed line is the contrast curve for the original
data, and the black solid line is the contrast curve for the data with the best-
fi
t
disk model removed. By dividing the two contrast curves
(
see blue dashed
dotted line
)
, we obtain a better overall detection limit. For the disk region,
when removing the disk, we are more sensitive by a factor of
2 over the
original data in panel
(
a
)
, and
1.6 for the high-pass
fi
ltered data in panel
(
b
)
.
10
We smooth each raw exposure with a Gaussian that is two times the full
width at half maximum of the PSF, and remove it from the raw exposure.
4
The Astrophysical Journal Letters,
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)
, 2022 January 1
Quiroz et al.
Utilizing disk modeling, we are able to reach a sensitivity of
15
M
Jupiter
at
200 au, a factor of
2 better in comparison to
the original reduction. As a result, we are able to achieve better
sensitivity by performing disk modeling, allowing us to be
more sensitive to smaller planets, possibly allowing for better
constraints on the occurrence rate of less massive planets.
4. Summary
We model the
L
observation of the single-armed spiral disk
HD 34282 using an offset geometric disk model. We show that
even using a nonphysical simpli
fi
ed model allows for better
achieved sensitivity over not modeling the disk. Therefore, we
recommend modeling the disks in scattered light systems to
increase the sensitivity to less massive planets. In fact, the
importance of modeling observed disks is demonstrated in
Wang et al.
(
2020
)
, where the luminosity of PDS 70 c was only
evident after disk modeling. In addition to the established two
steps of planet imaging
(
instrumentation and observation
design, and postprocessing for speckle noise removal
)
, our
study herein suggests that a third step is necessary in cases
where we detect disks in scattered light
performing disk
modeling to disentangle nonplanetary astrophysical signals to
reveal possibly obscured planets.
We caution that for the purpose of targeted planet searches,
one should mask out expected planet regions during the disk-
modeling process as in Wang et al.
(
2020
)
for PDS 70 c. In our
study of NIRC2 imaging of HD 34282, one additional caveat is
that possible planets can be
fi
t out by the offset ring model.
Nevertheless, the simulations in Dong & Fung
(
2017
)
suggest
that planets inducing a single spiral arm can be 0.1
1
M
Jupiter
.
Such a planet is expected to be undetectable even after the
removal of the disk signal following the Wang et al.
(
2020
)
approach. Despite this, we note that a variation of the Wang
et al.
(
2020
)
approach
speci
fi
cally, masking out different
regions while disk modeling for an exhaustive search of
unknown planets
could still be necessary for other systems.
We also caution that physically motivated disk models
satisfying dynamical constraints are preferred in order to
characterize the scattered light signals while modeling. Our
simple assumptions in the models presented herein show a
fi
rst
attempt at subtracting disk signals in order to improve planet-
detection capabilities. Future studies, including those along the
lines of, e.g., Wolff et al.
(
2017
)
and Villenave et al.
(
2019
)
,to
characterize the dust properties in the HD 34282 disk, are
needed to re
fi
ne the models.
We thank the anonymous referee for comments that
improved this Letter. This research is partially supported by
NASA ROSES XRP award 80NSSC19K0294. We thank Jean-
Baptiste Ruf
fi
o, Jason Wang, Christian Ginski, and Myriam
Benisty for discussions on calculating contrast curves. R.
D. acknowledges
fi
nancial support provided by the Natural
Sciences and Engineering Research Council of Canada through
a Discovery Grant as well as the Alfred P. Sloan Foundation
through a Sloan Research Fellowship. Some of the data
presented herein were obtained at the W. M. Keck Observatory,
which is operated as a scienti
fi
c partnership among the
California Institute of Technology, the University of California,
and the National Aeronautics and Space Administration. The
Observatory was made possible by the generous
fi
nancial
support of the W. M. Keck Foundation. The authors wish to
recognize and acknowledge the very signi
fi
cant cultural role
and reverence that the summit of Maunakea has always had
within the indigenous Hawaiian community. We are most
fortunate to have the opportunity to conduct observations from
this mountain. Part of the computations presented here were
conducted in the Resnick High Performance Computing
Center, a facility supported by the Resnick Sustainability
Institute at the California Institute of Technology. Based on
observations collected at the European Organisation for
Astronomical Research in the Southern Hemisphere under
ESO program 096.C-0248
(
A
)
. This publication makes use of
data products from the Wide-
fi
eld Infrared Survey Explorer,
which is a joint project of the University of California, Los
Angeles, and the Jet Propulsion Laboratory
/
California Institute
of Technology, funded by the National Aeronautics and Space
Administration. This research has made use of the SVO Filter
Pro
fi
le Service
(
http:
//
svo2.cab.inta-csic.es
/
theory
/
fps
/
)
sup-
ported from the Spanish MINECO through grant AYA2017-
84089.
Facilities:
Keck II
(
NIRC2
)
, VLT:Melipal
(
SPHERE
)
.
Software:
DebrisDiskFM
(
Ren et al.
2019
)
,
emcee
(
Foreman-Mackey et al.
2013
)
,
IRDAP
(
van Holstein et al.
2020
)
,
VIP
(
Gomez Gonzalez et al.
2017
)
.
Appendix
Disk-modeling Parameters
We list the best-
fi
t parameters and their meanings in our disk
models in Table
1
. We have not adopted a physically motivated
model to describe the observed ring, but analytically modeled
the observed distribution of light assuming the disk is optically
thin. Due to the unphysical nature of our disk model, we do not
further discuss the physical implications of these parameters.
Figure 3.
Mass limits using the AMES
Cond models for our observations with
the disk present
(
in red
)
and after removing the disk
(
in black
)
as a function of
separation in au
(
after accounting for the effects of an inclination-based
projection
)
. The width of the shaded regions account for uncertainties in the
distance, age, and magnitude of the host star. We are sensitive to planets
10
M
Jupiter
smaller after removing the best-
fi
tting disk model in the region
where the disk is present. Note: the minimum stellocentric separation presented
here is outside the coronagraph to avoid possible coronagraphic occultation;
future analysis at shorter separations should take the occultation probability
into account.
5
The Astrophysical Journal Letters,
924:L4
(
6pp
)
, 2022 January 1
Quiroz et al.
ORCID iDs
Juan Quiroz
https:
/
/
orcid.org
/
0000-0001-8037-3779
Nicole L. Wallack
https:
/
/
orcid.org
/
0000-0003-0354-0187
Bin Ren
(
)
https:
/
/
orcid.org
/
0000-0003-1698-9696
Ruobing Dong
(
)
https:
/
/
orcid.org
/
0000-0001-9290-7846
Jerry W. Xuan
https:
/
/
orcid.org
/
0000-0002-6618-1137
Dimitri Mawet
https:
/
/
orcid.org
/
0000-0002-8895-4735
Maxwell A. Millar-Blanchaer
https:
/
/
orcid.org
/
0000-0001-
6205-9233
Garreth Ruane
https:
/
/
orcid.org
/
0000-0003-4769-1665
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Table 1
Posterior Values for the HD 34282 Ring Parameters in the Keck
/
NIRC2
L
-Band
Parameter Maximum 50th
±
34th Unit Parameter Meaning
Likelihood Percentiles
(
1
)(
2
)(
3
)(
4
)(
5
)
g
0.38
-
+
0.40
0.03
0.05
Forward-scattering parameter in the Henyey & Greenstein
(
1941
)
phase function.
θ
inc
72.3
-
-
+
73
2
2
degree Inclination of the ring, measured from face-on.
θ
PA
74.1
-
-
+
73.8
1.5
1.
4
degree Position angle of the apparent major axis of the ring, measured east of north.
r
c
140
-
+
1
35
9
9
au
Critical radius of the dust distribution for the ring model; see Equation
(
1
)
.
α
in
2.1
-
+
6
3
8
Asymptotic power-law index of dust distribution for
r
=
r
c
; see Equation
(
1
)
.
α
out
23.1
-
-
+
19
8
8
Asymptotic power-law index of dust distribution for
r
?
r
c
; see Equation
(
1
)
.
Δ
X
1
2.7
-
+
2
14
11
au
Ring-center offset along the disk major axis; positive is toward the southeast
(
Millar-Blanchaer et al.
2016
)
.
Δ
X
2
8.5
-
+
7
5
5
au
Ring-center offset along the disk minor axis; positive is toward disk backside
(
Millar-Blanchaer et al.
2016
)
.
Note.
Column 1: disk parameters of interest. Column 2: best-
fi
t parameters used to generate the best-
fi
t disk model. Column 3: 50th
±
34th percentiles assuming
independent pixels. Column 4: parameter units. Column 5: meaning of parameters.
6
The Astrophysical Journal Letters,
924:L4
(
6pp
)
, 2022 January 1
Quiroz et al.