D
RAFT VERSION
25
TH
N
OVEMBER
, 2021
Typeset using L
A
T
E
X
twocolumn
style in AASTeX631
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 (
任
彬
)
,
1 ,
∗
Ruobing Dong (
董
若
冰
)
,
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, USA;
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)
Accepted to The Astrophysical Journal Letters
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. There-
fore, 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 protoplan-
etary disk around HD 34282. Despite a non-detection of companions for HD 34282, this direct disk modeling
improves planet detection sensitivity by up to a factor of 2 in flux ratio and
∼
10
M
Jupiter
in mass. This sug-
gests 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.
Unified Astronomy Thesaurus concepts:
Protoplanetary disks (1300); Coronagraphic imaging (313); Planetary
system formation (1257)
1.
Introduction
The most recent generation high-contrast imaging surveys
that utilize extreme adaptive optics systems have obtained an
occurrence rate of
.
10%
for young self-luminous giant plan-
ets (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 surround-
ing gaseous protoplanetary disks and leave their mark as ob-
servational signatures in the disk structure (e.g., spirals, gaps:
Dong et al. 2015b,c; Bae et al. 2018). Therefore, protoplane-
tary 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).
∗
To whom correspondence should be addressed.
While protoplanetary disks with planet-disk interaction
signatures may be prime targets for observing actively form-
ing planets, they can also hinder the detection of planets (cf.
Keppler et al. 2018; Wang et al. 2020). Specifically, using
the current prevailing observation and data reduction strat-
egy for ground-based high-contrast imaging (i.e., angular dif-
ferential 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, Figure 6 of de Boer et al. 2021, Figure 4
of Asensio-Torres et al. 2021). Moreover, even after process-
ing, disk signals can mimic the appearances of protoplan-
ets (e.g., HD 100546: Quanz et al. 2013; Currie et al. 2014;
HD 169142: Reggiani et al. 2014; Biller et al. 2014), making
it challenging to distinguish planets from disk features. In-
deed, it is only after modeling and removing the disk from
arXiv:2111.12708v1 [astro-ph.EP] 24 Nov 2021
HD 34282 Keck/NIRC2 Imaging
Quiroz et al.
the PDS 70 system that Wang et al. (2020) could recover
the disk-embedded protoplanet planet PDS 70c. Therefore,
in addition to utilizing diverse approaches in both observa-
tion and data reduction methods, it is necessary to investi-
gate whether disk modeling could also improve our sensitiv-
ity to planets detected via ground-based high-contrast imag-
ing, 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 forma-
tion of spirals in protoplanetary disks can be caused both with
and without planets, the differing mechanisms may be dis-
trinugishable via the structure in the disk. For example, grav-
itational instability triggered spiral arms are likely symmet-
ric and have even-numbered spirals (e.g., Dong et al. 2015a),
whereas planet-induced spirals can be less symmetric. An-
other 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 plan-
ets are beyond the detection limits of current instruments.
Therefore, in order to have the best chance of detecting a
massive companion, herein we focus on planet detection in
the single spiral arm system HD 34282 (de Boer et al. 2021).
Specifically focusing on improving planetary detection limits
by modeling of the observed disk structure.
Located at
309
±
2
pc (
Gaia
Collaboration et al. 2021),
HD 34282 is an A3V star (Mer
́
ın et al. 2004a) with a proto-
planetary disk containing a 75 au cavity
1
in
0
.
87
mm ALMA
continuum emission observations (van der Plas et al. 2017).
With an overdensity in the south-east region of its ALMA de-
tected ring which has an inclination of
59
.
◦
3
±
0
.
◦
4
and a posi-
tion 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 sys-
tem, favoring this explanation over a non-planet driven pho-
toevaporation mechanism for opening the cavity. In
J
-band
polarized light observations using VLT/SPHERE, de Boer
et al. (2021) identified two rings with a
∼
56
◦
inclination
and a
∼
119
◦
position angle, and a possible tightly-wound
single-arm spiral which 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 the sensitivity to drop from
.
4
M
Jupiter
in
1
Size scaled to match
Gaia
Collaboration et al. (2021) distance.
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 sys-
tem using the Keck/NIRC2 vortex coronagraph. Motivated
by the recovery of the PDS 70c planet via disk modeling in
Wang et al. (2020), we investigate the affect of disk mod-
eling in planet detection using HD 34282. Specifically, we
model the observed NIRC2 disk as an experiment in a tar-
geted search of planets that are embedded in disks. We de-
scribe the NIRC2 observations in Section 2, we present the
observed features and investigate the effects of disk modeling
in Section 3, and we summarize our findings 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 field 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 have 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 in Xuan et al. (2018), the
WRF seeing
2
was between
1
.
′′
32
and
1
.
′′
45
, 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 observations by performing flat-fielding, 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 descrip-
tion of both our pipeline that utilizes the
VIP
package and a
thorough characterization of the Keck/NIRC2 vortex coron-
agraph.
To reveal the extent of the disk while maximizing com-
putational efficiency, we crop each preprocessed image to
a
201
×
201
pixel field while discarding the last 4 expo-
sures due to poor image quality. In the following analy-
sis, we focus on an annular region that is between 20 pix-
els and 100 pixels from the star. To extract the HD 34282
system from the raw observations, we first capture the
speckle features using the principal-component-analysis-
based Karhunen–Lo
`
eve 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 first 6 KLIP components to remove speckles while
preserving the morphology of the disk. We rotate each of
2
http://mkwc.ifa.hawaii.edu/current/seeing/index.cgi
2
HD 34282 Keck/NIRC2 Imaging
Quiroz et al.
0.
′′
75
0.
′′
5
0.
′′
25
0
0.
′′
25
0.
′′
5
0.
′′
75
Decl.
N
E
0.
′′
25
77 au
ring
blob
+
B1
R2
R1
+
B1
R2
R1
+
0.
′′
75
0.
′′
5
0.
′′
25
0
0.
′′
25
0.
′′
5
0.
′′
75
R.A.
0.
′′
75
0.
′′
5
0.
′′
25
0
0.
′′
25
0.
′′
5
0.
′′
75
Decl.
+
0.
′′
75
0.
′′
5
0.
′′
25
0
0.
′′
25
0.
′′
5
0.
′′
75
R.A.
0.
′′
75
0.
′′
5
0.
′′
25
0
0.
′′
25
0.
′′
5
0.
′′
75
Decl.
+
0.
′′
75
0.
′′
5
0.
′′
25
0
0.
′′
25
0.
′′
5
0.
′′
75
R.A.
+
20
30
60
100
200
400
Surface Brightness (counts pixel
1
)
Figure 1.
Keck/NIRC2 imaging and modeling of the HD 34282 system in
L
′
-band. (a) Reduction result of the original exposures. (b) SPHERE
Q
φ
image, following Figure 2 of de Boer et al. (2021) annotations. (c) SPHERE contours overlaid on the NIRC2 image: we confirm the
existence of the B1 spiral. (d) Best-fit disk model for the NIRC2 ring. (e) Best-fit 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-fit 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 data have different display limits from the
NIRC2 data.
(The data used to create this figure are available in the “anc” folder on arXiv.)
the reduced 69 images to north-up and east-left, then calcu-
late their mean to obtain the final image for the HD 34282
system, shown in Figure 1a.
We also acquire the de Boer et al. (2021)
J
-band observa-
tions of HD 34282 in polarized light from UT 2015 Decem-
ber 19 using SPHERE/IRDIS (e.g., de Boer et al. 2020) un-
der European Southern Observatory (ESO) program 096.C-
0248(A) (PI: J.-L.Beuzit) from the ESO Science Archive Fa-
cility. 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 1b and 1c, we show the SPHERE
Q
φ
map, and over-
lay the SPHERE contours (the contour levels are selected to
match features in both datasets) on our NIRC2 data.
3.
Analysis
3.1. Disk features
The ADI image of HD 34282 in NIRC2
L
′
-band is com-
prised of a ring and a blob in the north-west direction (shown
in Figure 1a). The ring extends to
≈
0
.
′′
5
, and its south-east
half is brighter than the north-west half by
≈
40%
. The north-
west blob is located outside the inner working angle of
0
.
′′
2
at a position angle of
−
60
◦
east of north.
The north-west NIRC2 blob is not a planetary signal.
Comparing with the SPHERE PDI data in Figure 1c, it is
the inner ring component “R2” identified in de Boer et al.
(2021). Nevertheless, we do not recover the south-east side
of R2 in our NIRC2 observations; this could be explained by
self-subtraction effects with ADI using KLIP. In order to re-
cover the whole extent of R2, either reference star differential
imaging (e.g., Ruane et al. 2019), or advanced ADI speckle
removal methods (e.g., Ren et al. 2020; Pairet et al. 2021;
Flasseur et al. 2021), are needed.
The NIRC2 ring, which has an apparent brightness asym-
metry, is in fact composed of multiple features identified in
3
HD 34282 Keck/NIRC2 Imaging
Quiroz et al.
the SPHERE data in de Boer et al. (2021). Specifically, the
south-east half of the NIRC2 ring is a superposition of the
SPHERE arm and outer ring, or the “B1” and “R1” fea-
tures in de Boer et al. (2021), respectively. As evident in
the SPHERE data, the south-east 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 1a, we use the Millar-Blanchaer et al. (2015)
code
3
to model the system with a ring. To take into account
the observed apparent brightness asymmetry of HD 34282
evident in both the SPHERE data presented in de Boer et al.
(2021) and our NIRC2 data, we use the function in the up-
dated 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 geometrical models
to investigate the affect 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, nor 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 ob-
servations 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) modification of the Millar-
Blanchaer et al. (2015) code, which describes the ring with a
double power law (Augereau et al. 1999) along the mid-plane
and a Gaussian dispersion along the vertical axis:
ρ
(
r,z
)
∝
[
(
r
r
c
)
−
2
α
in
+
(
r
r
c
)
−
2
α
out
]
−
1
2
exp
[
−
(
z
hr
)
2
]
,
(1)
where
r
c
is the critical radius,
α
in
and
α
out
are the asymp-
totic 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). Specifically, we perform for-
ward modeling to minimize the residuals in our reduction.
We first generate a ring model using the Millar-Blanchaer
et al. (2015) code assuming given ring parameters (i.e., in-
clination, position angle, brightness, ring center offsets along
the apparent major and minor axes, critical radius, power-law
indices) and forward scattering coefficient of the dust parti-
cles (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
3
https://github.com/maxwellmb/anadisk
model
result by the transmission map of the NIRC2 vortex corona-
graph.
To obtain the best-fit disk model for the observed disk
structure, we note that disk signals are overfit by speckle
features using KLIP (Pueyo 2016), we thus perform for-
ward modeling using negative injection of the disk signals to
minimize the residuals. Specifically, we remove the instru-
ment’s response to the disk models from the original expo-
sures, and perform KLIP ADI reduction using
6
components
(i.e., identical KLIP parameters in original data reduction in
Section 2). The best-fit model is the one that minimizes the
chi-squared residuals. We list in Appendix A the best-fit pa-
rameters, with their uncertainties derived assuming the pixels
are mutually independent. By focusing on the ring regions,
we obtain the best-fit disk model in Figure 1d, and the corre-
sponding residual map is presented in Figure 1f.
Due to the existence of the ring brightness asymmetry in
NIRC2 and the two-ringed architecture in SPHERE, we have
performed additional model fitting not shown in Figure 1.
We have attempted to fit the two halves (i.e., north-west and
south-east) of the NIRC2 ring with two half-rings both cen-
tering at the star. The two half-rings drift towards nearly
edge-on, inconsistent with observations of this system, which
suggests they are likely offset from the star. We have also
tried to fit the north-west blob in NIRC2 with a smaller ring,
as motivated by the existence of R2 in the SPHERE observa-
tions. We cannot find a model that fits for this structure, since
such a ring requires a counterpart in the south-east (e.g., Fig-
ure 1c) that 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 fraction of the Keck/NIRC2
L
′
-band wavelengths, we thus use the former to obtain the
L
′
magnitude for HD 34282.
We first generate a high-
resolution stellar spectrum using a PHOENIX stellar model
from Husser et al. (2013), and interpolate within the grid to
match the stellar parameters from Mer
́
ın et al. (2004b). In
order to match the model spectrum with the observed
WISE
W
1
value of
7
.
072
±
0
.
016
(CatWISE2020; Marocco et al.
2021), we scale the resulting model flux 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 in-
tegrate across the Keck/NIRC2
L
′
filter profile (Rodrigo et al.
2012; Rodrigo & Solano 2020) to obtain an
L
′
magnitude of
7
.
729
+0
.
015
−
0
.
017
.
3.4. Detection limits
We obtain the detection sensitivity to planets by inject-
ing point sources into the observations and calculating their
4
HD 34282 Keck/NIRC2 Imaging
Quiroz et al.
0.
′′
2
0.
′′
3
0.
′′
4
0.
′′
5
0.
′′
6
0.
′′
7
0.
′′
8
Separation (
r
)
10
4
10
3
10
2
5 contrast
Original
Disk-removed
1.0
1.2
1.4
1.6
1.8
2.0
2.2
Improvement Factor
Disk Modeling Improvement
0.
′′
2
0.
′′
3
0.
′′
4
0.
′′
5
0.
′′
6
0.
′′
7
0.
′′
8
Separation (
r
)
10
4
10
3
10
2
5 contrast
Original (HPF)
Disk-removed (HPF)
1.0
1.2
1.4
1.6
1.8
2.0
2.2
Improvement Factor
Disk Modeling Improvement
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 black solid for the data with the
best-fit disk model removed. By dividing the two contrast curves,
see blue dash-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 filtered data in panel (b).
signal-to-noise (S/N) values after KLIP ADI reduction. To
investigate the affect of disk modeling on point source detec-
tion, we calculate the contrast before and after removing the
best-fit model in Figure 1d from the observations. We cal-
culate 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-fitting disk to that in which
we do not in Figure 2. Comparing the two contrast curves,
we find a marked improvement in the contrast achieved at the
radial separations where the disk is visible. We also test the
affect of utilizing a high-pass filter (HPF) to remove the disk
structure, which in essence is treating the disk like noise. We
find that an improvement is seen for both the original data
and the data in which we use a HPF
4
.
While using a HPF allows us to achieve better contrast than
not using a HPF, the data with the HPF does degrade the qual-
ity of the extended disk structure seen this system, therefore,
we focus on the data without the HPF in order to highlight
the affect 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 lim-
its 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
+1
.
9
−
2
.
6
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 de-
termine the mass corresponding to our contrast with radial
separation in Figure 3.
We can reach a typical sensitivity of
∼
10
M
Jupiter
mass
assuming the AMES-Cond models. However, our sensitiv-
ity 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). Utilizing disk modeling, we are able to reach a
sensitivity of
∼
15
M
Jupiter
at
∼
200
au, a factor of
∼
2
bet-
ter in comparison with 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 plan-
ets, ultimately 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 non-physical simplified 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 plan-
ets. In fact, the importance of modeling observed disks is
demonstrated in Wang et al. (2020), where the luminosity of
PDS 70c was only evident after disk modeling. In addition
to the established two steps of planet imaging (instrumenta-
tion and observation design, and post-processing for speckle
noise removal), our study here suggests that a third step is
necessary in cases where we detect disks in scattered light
– performing disk modeling to disentangle non-planetary as-
trophysical 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
4
We smooth each raw exposure with a Gaussian that is 2 times the full-width
at half-maximum of the PSF, and remove it from the raw exposure.
5
HD 34282 Keck/NIRC2 Imaging
Quiroz et al.
150
200
250
300
350
400
450
500
Stellocentric Separation (au)
10
1
10
2
Companion mass limit (
M
Jupiter
)
Original
Disk-removed
Figure 3.
Mass limits using the AMES-Cond models for our ob-
servations with the disk present (in red) and after removing the disk
(in black) as a function of separation in au (after accounting for
inclination-based projection affects). The width of the shaded re-
gions account for uncertainties in the distance, age, and magnitude
of the host star. We are sensitive to planets
∼
10
M
Jupiter
smaller af-
ter removing the best fitting 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 oc-
cultation; future analysis at shorter separations should take the oc-
cultation probability into account.
modeling process as in Wang et al. (2020) for PDS 70c. In
our study of NIRC2 imaging of HD 34282, one additional
caveat is that possible planets can be fit 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 expect to be not detectable even
after us removing the disk signal following the Wang et al.
(2020) approach. Despite this, we note that a variation of the
Wang et al. (2020) approach – specifically, masking out dif-
ferent regions while disk modeling for an exhaustive search
of unknown planets – could still be necessary for other sys-
tems.
We also caution that physically motivated disk models sat-
isfying dynamical constraints are preferred in order to char-
acterize the scattered light signals while modeling. Our sim-
ple assumptions in the models presented herein show a first
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 refine the models.
We thank the anonymous referee for their comments that
improved this Letter. This research is partially supported
by NASA ROSES XRP, award 80NSSC19K0294.
We
thank Jean-Baptiste Ruffio, Jason Wang, Christian Ginski,
and Myriam Benisty for discussions on calculating contrast
curves. R.D. acknowledges financial 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 scientific
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 financial support of the W. M. Keck Foun-
dation. The authors wish to recognize and acknowledge the
very significant cultural role and reverence that the summit
of Maunakea has always had within the indigenous Hawai-
ian community. We are most fortunate to have the opportu-
nity 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
Resnick Sustainability Institute at the California Institute of
Technology. Based on observations collected at the Euro-
pean Organisation for Astronomical Research in the South-
ern Hemisphere under ESO programme 096.C-0248(A). This
publication makes use of data products from the
Wide-field
Infrared Survey Explorer
, which is a joint project of the
University of California, Los Angeles, and the Jet Propul-
sion Laboratory/California Institute of Technology, funded
by the National Aeronautics and Space Administration. This
research has made use of the SVO Filter Profile Service
(http://svo2.cab.inta-csic.es/theory/fps/) supported from the
Spanish MINECO through grant AYA2017-84089.
Facility:
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 A.
Disk Modeling Parameters
We list the best-fit 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 analyti-
cally 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.
6
HD 34282 Keck/NIRC2 Imaging
Quiroz et al.
References
Asensio-Torres, R., Henning, T., Cantalloube, F., et al. 2021, A&A, 652,
A101
Augereau, J. C., Lagrange, A. M., Mouillet, D., et al. 1999, A&A, 348, 557
Bae, J., Pinilla, P., & Birnstiel, T. 2018, ApJL, 864, L26
Bae, J., Zhu, Z., Baruteau, C., et al. 2019, ApJL, 884, L41
Baraffe, I., Chabrier, G., Barman, T. S., et al. 2003, A&A, 402, 701
Biller, B. A., Males, J., Rodigas, T., et al. 2014, ApJL, 792, L22
Birnstiel, T., Andrews, S. M., Pinilla, P., & Kama, M. 2015, ApJL, 813, L14
Currie, T., Muto, T., Kudo, T., et al. 2014, ApJL, 796, L30
de Boer, J., Langlois, M., van Holstein, R. G., et al. 2020, A&A, 633, A63
de Boer, J., Ginski, C., Chauvin, G., et al. 2021, A&A, 649, A25
Dong, R., & Fung, J. 2017, ApJ, 835, 146
Dong, R., Hall, C., Rice, K., & Chiang, E. 2015a, ApJL, 812, L32
Dong, R., Zhu, Z., Rafikov, R. R., & Stone, J. M. 2015b, ApJL, 809, L5
Dong, R., Zhu, Z., & Whitney, B. 2015c, ApJ, 809, 93
Flasseur, O., Th
́
e, S., Denis, L., et al. 2021, A&A, 651, A62
Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP,
125, 306
Gaia
Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649,
A1
Gomez Gonzalez, C. A., Wertz, O., Absil, O., et al. 2017, AJ, 154, 7
Haffert, S. Y., Bohn, A. J., de Boer, J., et al. 2019, NatAs, 3, 749
Hall, C., Dong, R., Teague, R., et al. 2020, ApJ, 904, 148
Henyey, L. G., & Greenstein, J. L. 1941, ApJ, 93, 70
Husser, T. O., Wende-von Berg, S., Dreizler, S., et al. 2013, A&A, 553, A6
Keppler, M., Benisty, M., M
̈
uller, A., et al. 2018, A&A, 617, A44
Lodato, G., Dipierro, G., Ragusa, E., et al. 2019, MNRAS, 486, 453
Maire, A. L., Stolker, T., Messina, S., et al. 2017, A&A, 601, A134
Marocco, F., Eisenhardt, P. R. M., Fowler, J. W., et al. 2021, ApJS, 253, 8
Marois, C., Lafreni
`
ere, D., Doyon, R., et al. 2006, ApJ, 641, 556
Mer
́
ın, B., Montesinos, B., Eiroa, C., et al. 2004a, A&A, 419, 301
—. 2004b, A&A, 419, 301
Millar-Blanchaer, M. A., Graham, J. R., Pueyo, L., et al. 2015, ApJ, 811, 18
Millar-Blanchaer, M. A., Wang, J. J., Kalas, P., et al. 2016, AJ, 152, 128
Montesinos, M., & Cuello, N. 2018, MNRAS, 475, L35
Nielsen, E. L., De Rosa, R. J., Macintosh, B., et al. 2019, AJ, 158, 13
Pairet, B., Cantalloube, F., & Jacques, L. 2021, MNRAS, 503, 3724
Pueyo, L. 2016, ApJ, 824, 117
Quanz, S. P., Amara, A., Meyer, M. R., et al. 2013, ApJL, 766, L1
Reggiani, M., Quanz, S. P., Meyer, M. R., et al. 2014, ApJL, 792, L23
Ren, B., Pueyo, L., Chen, C., et al. 2020, ApJ, 892, 74
Ren, B., Choquet,
́
E., Perrin, M. D., et al. 2019, ApJ, 882, 64
—. 2021, ApJ, 914, 95
Rodrigo, C., & Solano, E. 2020, 182
Rodrigo, C., Solano, E., & Bayo, A. 2012, SVO Filter Profile Service
Version 1.0, IVOA Working Draft 15 October 2012, IVOA Working
Draft 15 October 2012
Rosotti, G. P., Benisty, M., Juh
́
asz, A., et al. 2020, MNRAS, 491, 1335
Ruane, G., Ngo, H., Mawet, D., et al. 2019, AJ, 157, 118
Soummer, R., Pueyo, L., & Larkin, J. 2012, ApJL, 755, L28
van der Marel, N., Williams, J. P., & Bruderer, S. 2018, ApJL, 867, L14
van der Plas, G., M
́
enard, F., Canovas, H., et al. 2017, A&A, 607, A55
van Holstein, R. G., Girard, J. H., de Boer, J., et al. 2020, A&A, 633, A64
Vigan, A., Fontanive, C., Meyer, M., et al. 2021, A&A, 651, A72
Villenave, M., Benisty, M., Dent, W. R. F., et al. 2019, A&A, 624, A7
Wang, J. J., Ginzburg, S., Ren, B., et al. 2020, AJ, 159, 263
Wolff, S. G., Perrin, M. D., Stapelfeldt, K., et al. 2017, ApJ, 851, 56
Xuan, W. J., Mawet, D., Ngo, H., et al. 2018, AJ, 156, 156
Zhang, S., Zhu, Z., Huang, J., et al. 2018, ApJL, 869, L47
7
HD 34282 Keck/NIRC2 Imaging
Quiroz et al.
Table 1
. Posterior values for the HD 34282 ring parameters in Keck/NIRC2
L
′
-band
Parameter
Maximum
50
th
±
34
th
Unit
Parameter Meaning
Likelihood
Percentiles
(1)
(2)
(3)
(4)
(5)
g
0
.
38
0
.
40
+0
.
05
−
0
.
03
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
.
4
−
1
.
5
degree
Position angle of the apparent major axis of the ring, measured east of north.
r
c
140
135
+9
−
9
au
Critical radius of the dust distribution for the ring model, see Equation (1).
α
in
2
.
1
6
+8
−
3
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).
∆
X
1
2
.
7
2
+11
−
14
au
Ring center offset along the disk major axis, positive is towards southeast (Millar-Blanchaer et al. 2016).
∆
X
2
8
.
5
7
+5
−
5
au
Ring center offset along the disk minor axis, positive is towards disk backside (Millar-Blanchaer et al. 2016).
Notes.
Column 1: disk parameters of interest. Column 2: best-fit parameters used to generate the best-fit disk model. Column 3:
50
th
±
34
th
percentiles assuming independent pixels. Column 4: parameter units. Column 5: meaning of parameters.
8