of 9
The Apparent Absence of Forward Scattering in the HD 53143 Debris Disk
Christopher C. Stark
1
, Bin Ren
2
,
3
,
4
, Meredith A. MacGregor
5
, Ward S. Howard
5
, Spencer A. Hurt
6
, Alycia J. Weinberger
7
,
Glenn Schneider
8
, and Elodie Choquet
9
1
NASA Goddard Space Flight Center, Exoplanets and Stellar Astrophysics Laboratory, Code 667, Greenbelt, MD 20771, USA;
christopher.c.stark@nasa.gov
2
Université Côte d
Azur, Observatoire de la Côte d
Azur, CNRS, Laboratoire Lagrange, F-06304 Nice, France;
bin.ren@oca.eu
3
Université Grenoble Alpes, CNRS, Institut de Planétologie et d
Astrophysique
(
IPAG
)
, F-38000 Grenoble, France
4
Department of Astronomy, California Institute of Technology, MC 249-17, 1200 East California Boulevard, Pasadena, CA 91125, USA
5
Department of Astrophysical and Planetary Sciences, University of Colorado, 2000 Colorado Avenue, Boulder, CO 80309, USA
6
Department of Earth Sciences, University of Oregon, Eugene, OR 97403, USA
7
Earth & Planets Laboratory, Carnegie Institution for Science, 5241 Broad Branch Road NW, Washington, DC 20015, USA
8
Steward Observatory, The University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA
9
Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France
Received 2022 November 23; revised 2023 February 9; accepted 2023 February 9; published 2023 March 14
Abstract
HD 53143 is a mature Sun-like star and host to a broad disk of dusty debris, including a cold outer ring of
planetesimals near 90 au. Unlike most other inclined debris disks imaged at visible wavelengths, the cold disk
around HD 53143 appears as disconnected
arcs
of material, with no forward-scattering side detected to date. We
present new, deeper Hubble Space Telescope Imaging Spectrograph coronagraphic observations of the HD 53143
debris disk and show that the forward-scattering side of the disk remains undetected. By
fi
tting our KLIP-reduced
observations via forward modeling with an optically thin disk model, we show that
fi
tting the visible wavelength
images with an azimuthally symmetric disk with unconstrained orientation results in an unphysical edge-on
orientation that is at odds with recent ALMA observations, while constraining the orientation to that observed by
ALMA results in nearly isotropically scattering dust. We show that the HD 53143 host star exhibits signi
fi
cant
stellar variations due to spot rotation and revisit age estimates for this system.
Uni
fi
ed Astronomy Thesaurus concepts:
Debris disks
(
363
)
;
Circumstellar disks
(
235
)
;
Stellar activity
(
1580
)
1. Introduction
The outer regions of extrasolar planetary systems are
commonly thought to harbor planetesimals, analogous to the
Kuiper Belt in the solar system. The most massive of these
systems, which are currently acce
ssible with imaging techniques
from visible to millimeter wavelengths, exhibit disks of dusty
debris thought to be continually generated by these planetesimals.
At millimeter wavelengths, obser
vations are sensitive to larger
dust grains that are relatively unaffected by radiative forces and
are thought to track the orbits of
theirlargerparentbodies
(
e.g.,
Hughes et al.
2018
)
. Debris disks often appear as well-de
fi
ned
circumstellar belts
/
rings at millimeter wavelengths, suggesting
parent bodies are relatively con
fi
nedinthesemimajoraxis
(
e.g.,
MacGregor et al.
2019
)
. At visible wavelengths, observations are
sensitive to submicron-sized d
ust grains, which for high-
luminosity stars are likely expelled from the system due to
radiation pressure, but may remai
n bound for stars with similar
luminosity to HD 53143
(
e.g., Arnold et al.
2019
)
.Atnear-
infrared wavelengths, observations probe micron-sized dust
grains, which remain bound but are sent onto eccentric orbits
with large semimajor axes by radiation pressure
(
e.g., Wyatt et al.
1999
)
. The majority, but not all, of
these small marginally bound
grains are collisionally destroye
d prior to being dragged into the
inner system by Poynting
Robertson and corpuscular drag
(
Wyatt
2005
; Kennedy & Piette
2015
; Rigley & Wyatt
2020
)
.
The result is a ring with a well-de
fi
ned inner edge and extended
outer halo at visible wavelengths
(
e.g., Thébault
2014
)
.
Additionally, inclined disks often
exhibit a brightness asymmetry
along the minor axis at visible wavelengths, with the near side of
the disk appearing brighter due to the forward scattering of
starlight by small dust grains
(
Augereau et al.
1999
; Weinberger
et al.
1999
)
.
HD 53143 hosts a peculiar disk that appears to depart from
the typical appearance of debris disks. HD 53143 is a Sun-like
G9V star at 18.3 pc with an estimated age of 1 Gyr
(
Kalas et al.
2006
)
. This mature star hosts an optically thin debris disk with
L
disk
/
L
å
=
0.025%
(
Zuckerman & Song
2004
)
, fairly bright at
infrared wavelengths for a 1 Gyr old system. The debris disk
around HD 53143 extends to the warm inner regions, with the
SED model
fi
ts suggesting dust in the 0.6
16 au region
(
Chen
et al.
2006
,
2014
)
. The outer cold disk was imaged
coronagraphically for the
fi
rst time by Kalas et al.
(
2006
)
using the Advanced Camera for Surveys
(
ACS
)
High
Resolution Camera
(
HRC
)
on the Hubble Space Telescope
(
HST
)
. With a 1
8 occulting spot, the HST ACS images
revealed faint arc-like features along the NW and SE quadrants,
extending from 55 to 110 au. The region interior to 3
′′
was
dominated by point-spread function
(
PSF
)
residuals, and the
arcs were interpreted as the ansae of a disk inclined by
45
°
with a position angle
(
PA
)
=
142
°±
2
°
.
The HD 53143 debris disk was observed again by Schneider
et al.
(
2014
)
using the HST STIS broadband coronagraphs
(
note it is incorrectly referred to as HD 53154 sporadically
throughout the article
)
. Schneider et al.
(
2014
)
used the
WedgeA-0.6 and WedgeA-1.0 masks to image the region of the
disk exterior to its inner working angle of 0
3. The STIS
observations revealed azimuthally symmetric
fl
ux interior to 50
au that appeared more like a face-on inner disk than a disk
aligned with the outer arcs.
The Astrophysical Journal,
945:131
(
9pp
)
, 2023 March 10
https:
//
doi.org
/
10.3847
/
1538-4357
/
acbb64
© 2023. The Author
(
s
)
. Published by the American Astronomical Society.
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
Notably, in both observations, there was no observed
fl
ux
from the disk connecting the arcs of material. The outer arcs at
90 au appear detached from the rest of the disk
(
yet still
comoving with the star
)
. If these arcs are the ansae of a ringlike
disk, we would expect to see even brighter disk
fl
ux along the
minor axis due to the forward scattering that is typical of other
debris disks.
MacGregor et al.
(
2022
)
observed the disk with ALMA
Band 6 at 1.36 mm. These observations revealed the ringlike
structure of the outer disk for the
fi
rst time, showing that the
larger grains, and presumably the parent planetesimals, are
con
fi
ned to a
20 au wide belt with a semimajor axis of
90.1
±
0.5 au, inclined by 56
°
.2
±
0
°
.4 from face on, and with a
PA
=
157
°
.3
±
0
°
.3. With a measured eccentricity of
0.21
±
0.02, the outer belt of material is the most eccentric
debris belt observed to date. Model
fi
ts to the belt suggest the
apocenter roughly aligns with the NW ansa, such that an
observed enhancement in millimeter
fl
ux at this location can be
explained by an apocenter glow effect previously observed in
the eccentric Fomalhaut belt
(
MacGregor et al.
2017
)
. Like the
STIS observations, ALMA also revealed excess
fl
ux near the
star, though the bilobed structure was more suggestive of an
edge-on inner disk than the face-on disk inferred from STIS
observations. Notably, MacGregor et al.
(
2022
)
found the
stellar
fl
ux to vary signi
fi
cantly during the multiepoch ALMA
observations that spanned
12 days, which they attribute to
stellar
fl
ares from this mature Sun-like star.
With these peculiarities in mind, we observed HD 53143
with the HST STIS WedgeA-1.8 coronagraph to peer deeper
into the outer regions of this system in an effort to constrain the
geometry of the arcs to the NW and SE, as well as search for
signs of the forward-scattering side of the ring structure at
visible wavelengths that should connect the ansae. In
Sections
2
and
3
we describe our observations and data
reduction methods. In Sections
4
and
5
we present model
fi
ts to
the disk and discuss our interpretation of this system.
2. Observations
We observed the HD 53143 debris disk via STIS
coronagraphy using the WedgeA-1.8 occulting mask to focus
on the outer arcs at
5
′′
. We chose WedgeA-1.8 to reduce
stellar residuals and improve the signal-to-noise ratio in the
region of the arcs while maintaining adequate roll coverage and
access to a large library of previous PSFs in the event that
principal component analysis
(
PCA
)
was needed for data
reduction. Table
1
summarizes our observations. We observed
HD 53143 for a total of 15 orbits, split into three groups of
fi
ve
orbits to improve schedulability. Each group consisted of a
noninterruptible sequence interleaving the PSF reference star in
the middle to minimize time-dependent artifacts due to changes
in the telescope
s optical assembly temperature. We varied the
orientation of the observations over
18
°
to observe regions
occulted by the wedge at some angles and obtain broader
coverage of the outer arcs. We avoided full roll coverage in
favor of deeper exposure times on the arcs, leaving unobserved
areas where the occulting mask aligned with the disk
s minor
axis. We designed individual exposures such that the stellar
PSF residuals reached 90% of the full-well depth of the STIS
CCD, based on prior observations by Schneider et al.
(
2014
)
.
Because the STIS coronagraph has a broad bandpass
(
0.2
1.2
μ
m
)
and diffracted residual starlight varies with
wavelength, care must be taken when choosing a reference PSF
star. The reference star used by Schneider et al.
(
2014
)
was HD
59780, which has
(
B
V
)
=
0.95. This compares relatively well
with HD 53143
ʼ
s
(
B
V
)
=
0.81 for an expected
Δ
(
B
V
)
=
0.14. At the time of our observations, the circularly
symmetric
fl
ux observed by Schneider et al.
(
2014
)
was suspected
to be chromatic residual starlight due to a color mismatch between
the target and reference star. Th
us, we chose a PSF reference star
with a similar
Δ
(
B
V
)
magnitude, but opposite sign. We
adopted HD 58895 as our PSF reference star, which has
(
B
V
)
=
0.70 for an expected color difference of
Δ
(
B
V
)
=
0.11. In spite of this, as discussed below, the observed
mismatch in PSFs was signi
fi
cantly larger than expected,
requiring us to form a reference PSF from the existing library
of STIS WedgeA-1.8 observations via PCA techniques. We
discuss possible causes for this mismatch in Section
5
.
3. Data Reduction
Intravisit pointing stability was b
etter than 0.2 pi
xels end-to-end
rms. A small
(
<
10 mas
)
systematic drift in the observations was
noticed in the
(
+
x
,
y
)
direction in the Science Instrument
Aperture File frame, m
ost likely due to the guidance system.
Neither the jitter nor drift is expected to signi
fi
cantly impact our
results. The astrophysical background varied signi
fi
cantly between
visits, likely due to changes in stray light from Earth, and had to
be subtracted on a visit-by-visit basis.
Figure
1
shows the result of classical PSF subtraction using our
observed PSF reference star HD 58895. The red circle has a radius
of 3
′′
for reference. The stellar residuals are much larger than
anticipated and overwhelm the arcs we seek to observe at 5
′′
,in
spite of a smaller absolute
Δ
(
B
V
)
than prior observations.
Given the poor match of our PSF reference star, we opted to
reduce the data using a PCA analysis via the KLIP algorithm
(
Soummer et al.
2012
)
. We assembled the reference archive
from Ren et al.
(
2017
)
to capture the variation of the PSF for
the STIS broadband
fi
lter. There are 274 individual readout
images in the STIS WedgeA-1.8 location that are thought to
host no circumstellar structure. For each HD 53143 readout, we
selected 30 of the highest-correlated references and performed
KLIP subtraction of the PSF using all of the Karhunen-
Loève
components. We rotated all of the 96 exposures to north
Table 1
Observation Log
Target
UT Obs. Date
Orient
Exposure Time
(
deg
)(
s
)
HD 53143
2021 Oct 11
128
°
.9
2400
HD 53143
2021 Oct 11
130
°
.4
2400
HD 58895
2021 Oct 11
135
°
.3
2340
HD 53143
2021 Oct 11
131
°
.9
2400
HD 53143
2021 Oct 11
133
°
.4
2400
HD 53143
2021 Oct 14
122
°
.9
2400
HD 53143
2021 Oct 14
124
°
.4
2400
HD 58895
2021 Oct 14
127
°
.9
2340
HD 53143
2021 Oct 14
125
°
.9
2400
HD 53143
2021 Oct 14
127
°
.4
2400
HD 53143
2021 Oct 22
116
°
.9
2300
HD 53143
2021 Oct 22
118
°
.4
2300
HD 58895
2021 Oct 22
123
°
.6
2240
HD 53143
2021 Oct 23
119
°
.9
2300
HD 53143
2021 Oct 23
121
°
.4
2300
2
The Astrophysical Journal,
945:131
(
9pp
)
, 2023 March 10
Stark et al.
up and east left, then obtained their median as our reduction
result for the HD 53143 system. Figure
2
shows the
fi
nal
reduced image. The NW and SE arcs of the outer disk are
clearly visible.
We note that we attempted to use the nonnegative matrix
factorization
(
NMF
)
method of Ren et al.
(
2018
)
. The spatial
extent of the HD 53143 disk limits the applicability of this
method and makes it computationally challenging. Further, the
smaller availability of WedgeA-1.8 PSFs, combined with
apparent color variability
(
see Section
5.1.1
)
degraded the
NMF results.
4. Analysis
Despite signi
fi
cantly increased exposure time, there remains
no sign of a ringlike structure connecting the NW and SE arcs
at visible wavelengths. This is notable given that one side of
this ring should be forward scattering and thus signi
fi
cantly
brighter than the arcs.
In an attempt to better understand the observed scattered-
light distribution, we
fi
t models of an optically thin disk to the
observed data set, the
fi
rst time this has been attempted for the
HD 53143 system. We adopted a radial pro
fi
le for the surface
brightness based on the Augereau et al.
(
1999
)
double power-
law pro
fi
le. In the direction perpendicular to the midplane, we
again used the distribution of Augereau et al.
(
1999
)
and set the
parameters
β
=
1 and
γ
=
2, such that our distribution was
equivalent to a Gaussian dispersion of scale height
h
=
H
/
r
,
where
r
is the circumstellar distance measured in the midplane
and
H
is the height above the midplane. We modeled the
scattering phase function
(
SPF
)
of the disk using a linear
combination of two Henyey
Greenstein
(
HG
)
SPFs
with
scattering asymmetry parameters
g
1
and
g
2
, and weighting
factors
f
g
1
and
=-
ff
1
gg
21
(
Henyey & Greenstein
1941
)
.
The KLIP PSF subtraction algorithm is known to over
fi
t
data, which could cause a reduction in surface brightness and a
morphology change
(
e.g., Soummer et al.
2012
)
. To recover the
brightness and morphology of the HD 53143 disk, we adopted
a forward-modeling approach. We subtracted each modeled
disk from the original readouts, performed KLIP reduction
following an identical approach for the reduction of the original
readouts, and inspected the KLIP reduction residuals. To
fi
nd
the best-
fi
t model, we maximized the likelihood function
assuming pixels are independent and follow Gaussian statistics,
using the same procedure as in Ren et al.
(
2021
)
. We performed
the forward-modeling procedure by exploring a broad range of
parameters using the emcee package
(
Foreman-Mackey et al.
2013
)
. We implemented the computation on a computer cluster
using the DebrisDiskFM package
(
Ren et al.
2019
)
to enable
the ef
fi
cient real-time calculation of the model parameters. To
make the multiparameter
fi
tting process numerically tractable,
we binned the STIS images on a 3
×
3 pixel basis.
We adopted uniform priors for all nine parameters of our
Markov Chain Monte Carlo
(
MCMC
)
analysis. We allowed
parameters to vary over the ranges listed in Table
2
. For initial
guesses, we sampled each of the parameters uniformly 18 times
Figure 1.
Reduction of our STIS observations using classical PSF subtraction,
shown with a circle of radius 3
′′
for reference. The inner 2
′′
(
as well as a
background object to the SE
)
has been masked off due to residuals from the
poor match of our PSF reference star. The NW and SE arcs at 5
′′
are detected,
but their extent and geometry are dif
fi
cult to discern among PSF subtraction
artifacts.
Figure 2.
Reduction of our STIS observations using the KLIP method, clearly
revealing the NW and SE arcs. Image units are mJy arcsec
2
.
Table 2
Disk Model Parameter Ranges for MCMC Analysis
Parameter
Range Allowed Initial Guess Range
Position angle
(
PA
)
90
°<
PA
<
180
°
130
°<
PA
<
170
°
Inclination
(
i
)
45
°<
i
<
90
°
70
°<
i
<
85
°
Cross-over radius
(
R
c
)
50
<
R
c
<
280 au 70
<
R
c
<
140 au
Inner power law
(
α
in
)
0
<
α
in
<
10
2
<
α
in
<
9
Outer power law
(
α
out
)
10
<
α
out
<
0
3
<
α
out
<
1
Scale height
(
h
)
0
<
h
<
0.5
0.04
<
h
<
0.2
Forward-scattering parameter
(
g
1
)
0
<
g
1
<
1
0.2
<
g
1
<
0.8
Back-scattering parameter
(
g
2
)
1
<
g
2
<
0
0.8
<
g
2
<
0
Scattering weight
(
f
g
1
)
<<
f
01
g
1
<<
f
0.7
1
g
1
3
The Astrophysical Journal,
945:131
(
9pp
)
, 2023 March 10
Stark et al.
over a smaller range, also provided in Table
2
. We adopted 18
walkers, 16,000 MCMC steps, and 8000
burn-in steps, after
which the likelihood values were not systematically increasing.
The left panel of Figure
3
shows our best-
fi
t model when all
parameters are freely explored. The best-
fi
t model has a
PA
=
146
°
.3
±
0
°
.1, which agrees with prior visible-wavelength
estimates
(
Kalas et al.
2006
; Schneider et al.
2014
)
but
disagrees with the ALMA observations
(
PA
=
157
°
.3
±
0
°
.3
)
.
The surface brightness of our model measured at 5
′′
separation
along the PA
(
i.e., at the location of the arcs
)
is
3
μ
Jy
arcsec
2
, in agreement with the contrast per resolution element
reported in Figure 10 of Schneider et al.
(
2014
)
, for which a
resolution element was de
fi
ned as a 0
1 wide photometric
aperture. Most notably, our best-
fi
t model has an inclination of
i
=
88
°
.3 from face on, which disagrees substantially with the
ALMA observations
(
i
=
56
°
.2
±
0
°
.4; MacGregor et al.
2022
)
.
The scale height of our best-
fi
t model is
h
=
0.35, which is
extremely large and incompatible with the ALMA constraint
(
h
=
0.04
±
0.02; MacGregor et al.
2022
)
. Figure
4
shows the
posterior distributions of our model
fi
ts.
The middle panel of Figure
3
shows the residuals of our data
set after subtracting the best-
fi
t model. The right panel shows
those same residuals with our best-
fi
t model, rotated by
Δ
PA
=
90
°
, injected prior to our KLIP data reduction. This
panel clearly shows our disk model to the NE and SW, where
we would expect to see the minor axis of the disk. We can
therefore conclude that the KLIP reduction method is not
oversubtracting the disk along the minor axis and cannot
explain the observed absence of a forward-scattering side of
the disk.
Given the very large discrepancy in inclination with the
ALMA data, we
fi
nd our best-
fi
t model shown in Figure
3
to be
unreliable. Qualitatively, our
fi
tting routine is attempting to
reproduce the seemingly
detached
arcs of material to the NW
and SE via an edge-on disk orientation. This circumvents the
issue regarding an absence of forward scattering along the
minor axis of a semi-inclined disk. The azimuthal extent of the
arcs causes the
fi
tting routine to adopt a large scale height. This
behavior of our
fi
tting routine again points to a lack of forward-
scattering material along the minor axis of the ALMA ring.
In an attempt to produce a more physically plausible model,
we restricted our disk model to the same orientation as
measured by the ALMA observations. Speci
fi
cally, we set the
PA
=
157
°
.3 and inclination
i
=
56
°
.2, and let all other
parameters vary freely according to Table
2
. We adopted 14
walkers, 14 k MCMC steps, and 7k burn-in steps for our
MCMC analysis.
The left panel of Figure
5
shows the best-
fi
t disk model. The
right panel shows the residuals after disk subtraction, revealing
correlated residuals in excess of those of our best-
fi
t model
shown in Figure
3
. Figure
6
shows the posterior distribution for
our best-
fi
t parameters when constrained to the ALMA-
measured orientation. The best-
fi
t HG scattering asymmetry
parameters are
g
1
0.1 and
g
2
0.0, indicating relatively
isotropically scattering dust grains. The scale height
=
-
+
h
0.07
0.00
0.01
and radius of the peak density
=
-
+
R
86.5
C
1.0
0.
9
au of our model are both in near agreement with the symmetric
model
fi
t by MacGregor et al.
(
2022
)
to ALMA data. The inner
power law
a
=
-
+
0.00
in
0.00
0.01
suggests material extends interior to
the outer arcs, similar to the excess
fl
ux imaged by Schneider
et al.
(
2014
)
.
We note that for these
fi
ts, we ignored eccentricity and
assumed the disk was centered on the star. We attempted to
include eccentricity, to
fi
rst order, by simply offsetting the
model from the star. All MCMC-retrieved centers were shifted
to unrealistic values inconsistent with ALMA observations, and
we consider these models unreliable.
5. Discussion
5.1. The Star
5.1.1. PSF Mismatch and Variability
In spite of a smaller absolute
Δ
(
B
V
)
than previous
observations, our reference star, HD 58895, provided a poor
match to the HD 53143 PSF. Upon closer inspection, the PSF
mismatch was determined to be worst during the last two
epochs during which we observed HD 53143. We observed no
variability in the reference star PSF, indicating that the
variability in the PSF
fi
tting was likely due to HD 53143.
In an effort to better understand the nature of the HD 53143
star, we analyzed its TESS light curves. HD 53143 is located
near the TESS continuous viewing zone, providing an extended
temporal baseline. We downloaded calibrated, 2 minute
cadence TESS light curves of HD 53143, spanning 24 sectors
between Sector 1 and Sector 39, from the Mikulski Archive for
Figure 3.
Left: best-
fi
t model to the observations. The
fi
tting routine avoids placing
fl
ux along the minor axis of the ALMA observed ring by favoring an edge-on
orientation. Middle: KLIP-reduced data set with the best-
fi
t model subtracted. Right: the model-subtracted residuals with the best-
fi
t model injected at a
Δ
PA
=
90
°
,
showing that
fl
ux to the NE and SW due to forward scattering would have been detectable if it were present.
4
The Astrophysical Journal,
945:131
(
9pp
)
, 2023 March 10
Stark et al.
Space Telescopes
(
MAST
)
.
10
We chose to download Simple
Aperture Photometry
(
SAP
)
light curves rather than Pre-search
Data Conditioning
(
PDC
)
light curves to avoid removing the
rotational variability. The light curves showed signs of
signi
fi
cant spot evolution, with changes to the amplitude and
phase of rotational variability occurring between Cycle 1 and
Cycle 3. The
fi
nal four months of TESS observations were
obtained from March to June of 2021, prior to our GO 16202
STIS observations in October of 2021. These observations
exhibit a sinusoidal rotation signal, indicative of the presence
of a stable spot group. We measured the variability period
during Cycle 3 to be 9.6
±
0.1 days using a Lomb
Scargle
periodogram as shown in Figure
7
.
We used a bootstrap approach to extrapolate the sinusoidal
variability of the TESS data from 2021 March to June to our
STIS observation window in 2021 October. We assumed the
dominant spot persisted over the 4 months after the end of the
TESS window, which is supported by the presence of
consistent patterns of rotational variability that last similar
amounts of time in the rest of the multiyear TESS light curve.
For each of the 1000 trials, we randomly dropped 10% of the
light curve during the 2021 March
June observations and
fi
ta
sine with a period sampled from the 1
σ
range of a normal
distribution centered at 9.6 days and a width of 0.1 days. We
computed the average and standard deviation of the predicted
Figure 4.
Posterior distribution for our best-
fi
t disk model.
10
https:
//
mast.stsci.edu
. The speci
fi
c observations analyzed can be accessed
via doi:
10.17909
/
t9-nmc8-f686
.
5
The Astrophysical Journal,
945:131
(
9pp
)
, 2023 March 10
Stark et al.
fl
ux values across all trials at each time during the GO 16202
window. We estimate the
fl
ux of HD 53143 to be signi
fi
cantly
lower during the last two epochs of GO 16202 STIS
observations, as shown in Figure
8
. This qualitatively agrees
with the behavior of our STIS PSF reference
fi
ts
our
reference star HD 58895, which is bluer than HD 53143,
should provide a worse
fi
t when HD 53143 appears redder due
to enhanced star spots, which correspond to the minima of the
light curve shown in Figure
8
. We conclude that HD 53143
may exhibit star spots at a level that signi
fi
cantly impacts STIS
coronagraphic PSF subtraction.
This behavior was not noticed during the two epochs of STIS
observations obtained during 2011 as part of the GO 12228
program
(
Schneider et al.
2014
)
. While spot evolution time-
scales prohibit us from extrapolating the TESS data obtained 7
yr after the GO 12228 observations
(
Giles et al.
2017
)
, the
precision of the TESS rotation period is suf
fi
cient to constrain
the relative phase during the 2011 observations. We performed
100,000 Monte Carlo trials in which the stellar rotation period
is drawn from the same period distribution as in our previous
model. For each period, we folded the two GO 12228 times in
phase and compared the magnitude of the phase difference. We
found a mean and standard deviation in the phase of
0.25
±
0.1, where the phase is normalized from 0 to 1. We
may therefore say that the GO 12228 observations were not
taken at opposite rotational phases and likely occurred at
similarly high
or low
fl
ux values, consistent with the lack of
any observed changes to the quality of the reference PSF
during the GO 12228 observations.
5.1.2. Age
Given the signi
fi
cant observed stellar variability and massive
debris disk of this reportedly Sun-like star, we revisited the age
estimates for HD 53143. We can attempt to estimate the age of
the star from membership in a young association, gyrochronol-
ogy, and chromospheric emission. Although membership in IC
2391 has been claimed, Banyan
Σ
(
Gagné et al.
2018
)
fi
nds a
0% probability of membership with IC 2391 or any other
young stellar association using Gaia DR2 parallaxes and proper
motions.
The publicly available HARPS radial velocity database
HARPS-RVBANK
11
(
Trifonov et al.
2020
)
has 26 measure-
ments of HD 53143, which show clear variability with an
amplitude of
37 m s
1
. The periodogram calculated on that
site produces the strongest period at 9.6 days. This agrees with
the stellar rotation period measured from TESS data, indicating
that the RV signal is due to spots. We apply gyrochronology to
estimate the age of the star using the calibration in Mamajek &
Hillenbrand
(
2008
)
and the
B
V
color of the star. The star is
spectral type G9-K0 with a
B
V
=
0.77
0.81 depending on
the source
(
e.g., Tycho-2; Høg et al.
2000
and Koen et al.
2010
)
, which yields an age of 540 Myr
(
460
600 Myr
)
.We
also applied the stardate code that combines isochrone and
gyrochronology
(
Angus et al.
2019
)
using the stellar para-
meters from Gaia DR3
(
T
eff
=
5332, log
g
=
4.45
)
and got an
age of
-
+
1.29
0.68
1.01
Gyr.
Another constraint on the stellar age comes from stellar
activity. The predicted Ca chromospheric activity index R
(
HK
)
at an age of 540 Myr in Mamajek & Hillenbrand
(
2008
)
is about
4.4. The measured R
(
HK
)
for this star is
4.52
±
0.05
(
Herrero et al.
2012
; Boro Saikia et al.
2018
)
,
which would make it a bit older. Stanford-Moore et al.
(
2020
)
use the star
s
B
V
color and R
(
HK
)
index to
fi
nd an age
between 245 Myr and 9.24 Gyr, with a median posterior value
of 1.31 Gyr.
Altogether, the best constraint we can place is that the HD
53143 star is between 500 Myr and 2.4 Gyr in age.
5.1.3. Inclination
The derived stellar inclination is sensitive to the assumed
stellar radius and to the assumed uncertainties. Taking stellar
Figure 5.
Left: best-
fi
t model to the observations while restricting the PA and inclination of the disk to the ALMA-measured values. Right: KLIP-reduced data set with
the best-
fi
t model subtracted showing signi
fi
cantly correlated residuals.
11
https:
//
www2.mpia-hd.mpg.de
/
homes
/
trifonov
/
HARPS_RVBank.html
.
Note the HD 53143 star is referred to as GJ 260.
6
The Astrophysical Journal,
945:131
(
9pp
)
, 2023 March 10
Stark et al.
radius
R
å
=
0.90
±
0.02
R
(
Gaia Collaboration et al.
2016
,
2022
)
, the observed 9.6
±
0.1 day rotational period,
and
v
sin
i
=
4.0
±
0.7
(
Saar & Osten
1997
; Nordström et al.
2004
)
,we
fi
nd a stellar inclination of 54
°±
8
°
. This agrees well
with the inclination of the disk seen by ALMA. Using
somewhat different values, Hurt & MacGregor
(
2022
)
found
a stellar inclination of 67
°±
18
°
, which is still consistent with
the ALMA disk given the larger uncertainties.
5.1.4. Binarity
We
fi
nd no evidence of a stellar companion that would affect
the dynamics of the observed disk around HD 53143. A query
for common proper-motion companions reveals a low-mass
0.1
M
star with similar proper motion at 28 kilo-au
(
Kervella et al.
2019
)
. The Gaia EDR3 shows no evidence of a
proper motion anomaly with residuals
<
4ms
1
(
Gaia
Collaboration et al.
2022
)
, and no additional radial velocity
signals were noticed in the HARPS data set.
5.2. Outer Disk
The multiwavelength data available for the HD 53143 disk
seems to suggest two possible scenarios for the outer disk at
90 au. The
fi
rst is that the small dust grains observed with
HST STIS are smoothly distributed over a disk with the same
orientation as their larger counterparts observed with ALMA.
This azimuthally symmetric disk would require the small dust
Figure 6.
Posterior distribution for our disk model constrained to the orientation measured by ALMA.
7
The Astrophysical Journal,
945:131
(
9pp
)
, 2023 March 10
Stark et al.
grains to be roughly isotropically scattering over the range of
observable scattering angles, unlike most other observed debris
disks. This may suggest that we are observing grains much
smaller than the wavelength. Our
fi
ts indicate that in this
scenario, dust extends into the inner regions of the system.
Truly isotropically scattering dust is not the only explana-
tion. The SPF
must only appear isotropic over the range of
observable scattering angles. This could actually be explained
by larger dust that is extremely forward scattering but with a
phase function that is relatively
fl
at over the observed angles.
Such a phase function would likely be even more forward
scattering than that observed by Hedman & Stark
(
2015
)
and
would imply a minimum grain size signi
fi
cantly larger than the
wavelength.
An alternative explanation for the apparent absence of
forward scattering could simply be that there is less dust along
the minor axes, or equivalently, density enhancements at the
ansae, which we do not explicitly model here. Density
enhancements seen at visible wavelengths could result from
an unseen companion trapping inward-migrating small dust
grains into exterior mean motion resonances. We consider this
unlikely, as the drag time is much longer than the collision time
for micron-sized grains at these circumstellar distances
(
Stark
& Kuchner
2009
)
. However, density enhancements could also
result from the increased production of small grains at the
ansae. Increased production of small grains could be due to
planetesimals trapped in the exterior mean motion resonances
of a planet
(
Wyatt
2006
)
. Alternatively, given that ALMA
observations constrain the apastron of the HD 53143 outer
debris ring to be near the NW ansa
(
MacGregor et al.
2022
)
, the
increased production of small grains could be due to increased
collision rates of the eccentric parent bodies at periastron and
apastron. In both of these scenarios, we would expect density
enhancements in the ALMA data set. There is some evidence
for a density enhancement along the NW ansa in the ALMA
observations, which has been attributed to an
apocenter glow
effect expected for eccentric planetesimal belts
(
Pan et al.
2016
)
.
The simulations of Lee & Chiang
(
2016
)
suggest that small
dust grains originating from an eccentric belt should create an
asymmetric halo beyond the belt, with an extension in the
direction of apastron. The degree of this asymmetry depends on
where dust grains are launched from in the belt; preferential
production of dust grains at the parent bodies
periastron
produces a larger halo asymmetry, while preferential produc-
tion at apastron mutes the asymmetry. We examined radial cuts
through our STIS observations along the disk
s PA. Our
analysis showed no signi
fi
cant
fl
ux asymmetry between the
NW and SE sides of the disk beyond 5
′′
, potentially favoring
the apastron production scenario.
5.3. Inner Disks
Chen et al.
(
2014
)
modeled the HD 53143 IR SED using
WISE and Spitzer MIPS photometry, as well as IRS spectra,
and reported
fl
ux in excess of the stellar photosphere
corresponding to dust in the 0.6
16 au region. Schneider
et al.
(
2014
)
directly imaged excess
fl
ux extending farther out,
from
5.5 to 55 au. The imaged
fl
ux was azimuthally
symmetric in nature, suggesting a possible disk with a face-
on orientation. MacGregor et al.
(
2022
)
con
fi
rmed the presence
of warm dust with the detection of a signi
fi
cant excess in
ALMA Band 6 and estimated the circumstellar distance to be
25 au with a width of
5 au. However, the ALMA data have
a bilobed appearance, which is more consistent with an edge-on
inner disk.
Unlike other observed debris rings that feature sharp inner
edges
(
e.g., Kalas et al.
2005
; Schneider et al.
2014
; Perrin
et al.
2015
; Millar-Blanchaer et al.
2016
)
, our ALMA-
constrained model
fi
t to the outer disk has a very shallow
inner radial power law of
α
in
=
0.0. Notably, this is even less
steep than the outer halo component
(
α
out
=
2.3
)
. This
suggests that dust from the outer disk may be migrating into the
inner regions of the system, possibly contributing to the
observed warm dust. Assuming that the optical depth of the HD
53143 disk can be approximated as
τ
L
IR
/
L
å
, this seems
unlikely for a disk with optical depth
τ
10
4
based on the
simulations of Stark & Kuchner
(
2009
)
. Alternatively, our
shallow inner radial power law may also be due to an extended
halo from a dynamically separate inner disk.
6. Conclusions
The HD 53143 debris disk has a peculiar appearance that
may suggest a dynamically active system. This disk lacks any
clear sign of a forward-scattering side, as expected near the
minor axis of the disk, connecting two
arcs
of cold material
at
90 au. Symmetric disk model
fi
ts to our HST STIS data set
avoid placing disk
fl
ux in the region where the minor axis is
expected to be, resulting in unphysical edge-on models. Models
with constrained geometries provide poorer
fi
ts and require
either near-isotropically scattering small dust or very forward-
Figure 7.
Lomb
Scargle periodogram of the Cycle 3 TESS data showing the
9.6
±
0.1 day rotation period of HD 53143. This period is typical of K0 dwarfs
of 1 Gyr in age.
Figure 8.
Predicted rotational variability during the 2021 October HST STIS
observations. The HST observations taken near peak stellar brightness and
minimum brightness correspond with over- and undersubtractions in the HST
data. The rotational variability is shown in red and is extrapolated from the
rotation period and TESS light curve using bootstrap
fi
ts to the stable
sinusoidal modulation in the light curve from 2021 March to June.
8
The Astrophysical Journal,
945:131
(
9pp
)
, 2023 March 10
Stark et al.
scattering
(
i.e., large
)
dust grains whose phase function appears
relatively
fl
at over all observable scattering angles. Alterna-
tively, the apparent absence of forward scattering could be
explained by a lack of dust along the minor axes, with the ansae
of the HD 53143 disk being regions of enhanced grain
production due to the in
fl
uence of an unseen planet.
Observations suggest the presence of multiple inner disks, the
geometry of which is not well understood. The apparent
dichotomy between the dynamical distributions of small and
large grains in this system suggests that the HD 53143 disk
may provide insights into the dynamics of dust in the outer
regions of planetary systems.
The authors acknowledge Pierre Kervella for assistance in
assessing the binarity of HD 53143. This research is based on
observations made with the NASA
/
ESA Hubble Space
Telescope obtained from the Space Telescope Science Institute,
which is operated by the Association of Universities for
Research in Astronomy, Inc., under NASA contract NAS
526555. These observations are associated with program
16202. 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. This work has made use
of data from the European Space Agency
(
ESA
)
mission Gaia
(
https:
//
www.cosmos.esa.int
/
gaia
)
, processed by the Gaia
Data Processing and Analysis Consortium
(
DPAC,
https:
//
www.cosmos.esa.int
/
web
/
gaia
/
dpac
/
consortium
)
. Funding
for the DPAC has been provided by national institutions, in
particular the institutions participating in the Gaia Multilateral
Agreement.
ORCID iDs
Meredith A. MacGregor
https:
/
/
orcid.org
/
0000-0001-
7891-8143
Ward S. Howard
https:
/
/
orcid.org
/
0000-0002-0583-0949
Spencer A. Hurt
https:
/
/
orcid.org
/
0000-0002-6903-9080
Alycia J. Weinberger
https:
/
/
orcid.org
/
0000-0001-
6654-7859
Glenn Schneider
https:
/
/
orcid.org
/
0000-0002-4511-5966
References
Angus, R., Morton, T. D., Foreman-Mackey, D., et al. 2019,
AJ
,
158, 173
Arnold, J. A., Weinberger, A. J., Videen, G., & Zubko, E. S. 2019,
AJ
,
157, 157
Augereau, J. C., Lagrange, A. M., Mouillet, D., Papaloizou, J. C. B., &
Grorod, P. A. 1999,
A&A
,
348, 557
Boro Saikia, S., Marvin, C. J., Jeffers, S. V., et al. 2018,
A&A
,
616, A108
Chen, C. H., Mittal, T., Kuchner, M., et al. 2014, yCat, J
/
ApJS
/
211
/
25
Chen, C. H., Sargent, B. A., Bohac, C., et al. 2006,
ApJS
,
166, 351
Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013,
PASP
,
125, 306
Gagné, J., Mamajek, E. E., Malo, L., et al. 2018,
ApJ
,
856, 23
Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016,
A&A
,
595, A1
Giles, H. A. C., Collier Cameron, A., & Haywood, R. D. 2017,
MNRAS
,
472, 1618
Hedman, M. M., & Stark, C. C. 2015,
ApJ
,
811, 67
Henyey, L. G., & Greenstein, J. L. 1941,
ApJ
,
93, 70
Herrero, E., Ribas, I., Jordi, C., Guinan, E. F., & Engle, S. G. 2012,
A&A
,
537, A147
Høg, E., Fabricius, C., Makarov, V. V., et al. 2000, A&A,
355, L27
Hughes, A. M., Duchêne, G., & Matthews, B. C. 2018,
ARA&A
,
56, 541
Hurt, S. A., & MacGregor, M. A. 2022, ApJ, submitted
Kalas, P., Graham, J. R., & Clampin, M. 2005,
Natur
,
435, 1067
Kalas, P., Graham, J. R., Clampin, M. C., & Fitzgerald, M. P. 2006,
ApJL
,
637, L57
Kennedy, G. M., & Piette, A. 2015,
MNRAS
,
449, 2304
Kervella, P., Arenou, F., Mignard, F., & Thévenin, F. 2019,
A&A
,
623, A72
Koen, C., Kilkenny, D., van Wyk, F., & Marang, F. 2010,
MNRAS
,
403, 1949
Lee, E. J., & Chiang, E. 2016,
ApJ
,
827, 125
MacGregor, M. A., Hurt, S. A., Stark, C. C., et al. 2022,
ApJL
,
933, L1
MacGregor, M. A., Matrà, L., Kalas, P., et al. 2017,
ApJ
,
842, 8
MacGregor, M. A., Weinberger, A. J., Nesvold, E. R., et al. 2019,
ApJL
,
877, L32
Mamajek, E. E., & Hillenbrand, L. A. 2008,
ApJ
,
687, 1264
Millar-Blanchaer, M. A., Wang, J. J., Kalas, P., et al. 2016,
AJ
,
152, 128
Nordström, B., Mayor, M., Andersen, J., et al. 2004,
A&A
,
418, 989
Pan, M., Nesvold, E. R., & Kuchner, M. J. 2016,
ApJ
,
832, 81
Perrin, M. D., Duchene, G., Millar-Blanchaer, M., et al. 2015,
ApJ
,
799, 182
Ren, B., Choquet, É., Perrin, M. D., et al. 2019,
ApJ
,
882, 64
Ren, B., Choquet, É., Perrin, M. D., et al. 2021,
ApJ
,
914, 95
Ren, B., Pueyo, L., Perrin, M. D., Debes, J. H., & Choquet, É. 2017,
Proc.
SPIE
,
10400, 1040021
Ren, B., Pueyo, L., Zhu, G. B., Debes, J., & Duchêne, G. 2018,
ApJ
,
852, 104
Rigley, J. K., & Wyatt, M. C. 2020,
MNRAS
,
497, 1143
Saar, S. H., & Osten, R. A. 1997,
MNRAS
,
284, 803
Schneider, G., Grady, C. A., Hines, D. C., et al. 2014,
AJ
,
148, 59
Soummer, R., Pueyo, L., & Larkin, J. 2012,
ApJL
,
755, L28
Stanford-Moore, S. A., Nielsen, E. L., De Rosa, R. J., Macintosh, B., &
Czekala, I. 2020,
ApJ
,
898, 27
Stark, C. C., & Kuchner, M. J. 2009,
ApJ
,
707, 543
Thébault, P. 2014, in IAU Symp. 299,
Exploring the Formation and Evolution
of Planetary Systems, ed. M. Booth, B. C. Matthews, & J. R. Graham
(
Cambridge: Cambridge Univ. Press
)
,
358
Trifonov, T., Tal-Or, L., Zechmeister, M., et al. 2020,
A&A
,
636, A74
Vallenari, A., Brown, A. G. A., et al. 2022, arXiv:
2208.00211
Weinberger, A. J., Becklin, E. E., Schneider, G., et al. 1999,
ApJL
,
525, L53
Wyatt, M. C. 2005,
A&A
,
433, 1007
Wyatt, M. C. 2006,
ApJ
,
639, 1153
Wyatt, M. C., Dermott, S. F., Telesco, C. M., et al. 1999,
ApJ
,
527, 918
Zuckerman, B., & Song, I. 2004,
ApJ
,
603, 738
9
The Astrophysical Journal,
945:131
(
9pp
)
, 2023 March 10
Stark et al.