Astronomy
&
Astrophysics
A&A 672, A114 (2023)
https://doi.org/10.1051/0004-6361/202245458
© The Authors 2023
Debris disk color with the
Hubble
Space Telescope
⋆
Bin B. Ren (
任
彬
)
1
,
2
,
3
, Isabel Rebollido
4
, Élodie Choquet
5
, Wen-Han Zhou (
周
文
翰
)
1
, Marshall D. Perrin
4
,
Glenn Schneider
6
, Julien Milli
2
, Schuyler G. Wolff
6
, Christine H. Chen
4
, John H. Debes
4
, J. Brendan Hagan
4
,
Dean C. Hines
4
, Maxwell A. Millar-Blanchaer
8
, Laurent Pueyo
4
, Aki Roberge
9
,
Eugene Serabyn
7
, and Rémi Soummer
4
1
Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, 06304 Nice, France
e-mail:
bin.ren@oca.eu
2
Université Grenoble Alpes, CNRS, Institut de Planétologie et d’Astrophysique (IPAG), 38000 Grenoble, France
3
Department of Astronomy, California Institute of Technology, MC 249-17, 1200 East California Boulevard, Pasadena, CA 91125,
USA
4
Space Telescope Science Institute (STScI), 3700 San Martin Drive, Baltimore, MD 21218, USA
5
Aix-Marseille Univ, CNRS, CNES, LAM, Marseille, France
6
Steward Observatory, The University of Arizona, Tucson, AZ 85721, USA
7
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
8
Department of Physics, University of California, Santa Barbara, CA 93106, USA
9
Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
Received 14 November 2022 / Accepted 8 February 2023
ABSTRACT
Context.
Multiwavelength scattered light imaging of debris disks may inform dust properties including typical size and mineral com-
position. Existing studies have investigated a small set of individual systems across a variety of imaging instruments and filters, calling
for uniform comparison studies to systematically investigate dust properties.
Aims.
We obtain the surface brightness of dust particles in debris disks by post-processing coronagraphic imaging observations, and
compare the multiwavelength reflectance of dust. For a sample of resolved debris disks, we perform a systematic analysis on the
reflectance properties of their birth rings.
Methods.
We reduced the visible and near-infrared images of
23
debris disk systems hosted by A through M stars using two coron-
agraphs on board the
Hubble
Space Telescope: the STIS instrument observations centered at
0
.
58
μ
m, and the NICMOS instrument
at
1
.
12
μ
m or
1
.
60
μ
m. For proper recovery of debris disks, we used classical reference differential imaging for STIS, and adopted
non-negative matrix factorization with forward modeling for NICMOS. By dividing disk signals by stellar signals to take into account
intrinsic stellar color effects, we systematically obtained and compared the reflectance of debris birth rings at
≈
90
◦
scattering angle.
Results.
Debris birth rings typically exhibit a blue color at
≈
90
◦
scattering angle. As the stellar luminosity increases, the color tends
to be more neutral. A likely L-shaped color–albedo distribution indicates a clustering of scatterer properties.
Conclusions.
The observed color trend correlates with the expected blow-out size of dust particles. The color–albedo clustering likely
suggests different populations of dust in these systems. More detailed radiative transfer models with realistic dust morphology will
contribute to explaining the observed color and color–albedo distribution of debris systems.
Key words.
stars: imaging – instrumentation: high angular resolution – Kuiper belt: general – techniques: image processing
1. Introduction
Debris disks are extrasolar analogs of the Asteroid Belt and the
Kuiper Belt (e.g., Hughes et al. 2018). They are composed of
second-generation dust, in the sense that their life time is shorter
than the age of their host star (e.g., Wyatt 2008), and they are
produced from and continuously replenished by collisional cas-
cades of larger solid bodies (Dohnanyi 1969). While collisional
cascades produce small dust particles, radiation pressure can
surpass gravity for small dust particles and blow certain dust
particles out of stellar systems (e.g., Strubbe & Chiang 2006;
Krivov et al. 2006). The balance of forces for dust particles
results in a blow-out size that ranges from submicron to several
microns depending on both stellar properties and dust properties
⋆
Data for Figs. 2, 3, and 4 are only available at the CDS
via anonymous ftp to
cdsarc.cds.unistra.fr
(
130.79.128.5
)
or via
https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/
672/A114
(e.g., spectral type, dust composition, dust porosity; Arnold et al.
2019). Observationally, depending on the blow-out size and other
dust properties in disks, there could be noticeable differences
(e.g., scattering phase function: Muñoz et al. 2021).
In the birth ring of a debris disk, dust particles under col-
lisional cascade have an expected number distribution
n
(
a
)
∝
a
−
3
.
5
, where
a
is the particle size (e.g., Pan & Schlichting 2012).
Assuming that the cross section of each particle is proportional
to
a
2
, a collisional cascade can make the smaller particles domi-
nate more surface area of a debris disk. In reality, stellar radiation
pressure can drive smaller particles to higher eccentricity or even
unbound orbits, resulting in blow-out sizes above which dust
particles are bound. Nevertheless, the balance between radia-
tion and gravity predicts that dust particles can be unbound only
within a certain size range (e.g., Thebault & Kral 2019), and that
there is no stellar radiation–driven blow-out size for certain later-
type stars (e.g., M stars: Arnold et al. 2019). Other mechanisms,
including stellar winds in M stars (e.g., AU Mic: Augereau &
Beust 2006, TWA 7: Olofsson et al. 2020), can also remove dust
A114, page 1 of 17
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A&A 672, A114 (2023)
particles from stellar environments, complicating the size distri-
bution of dust in debris systems. The joint effect of these mech-
anisms could lead to observational complexity for debris disks.
Studies on the spectral energy distribution (SED) of debris
disks show that the ratio of dust temperature to blackbody tem-
perature at the disk radius decreases with increasing stellar
luminosity (e.g., Pawellek et al. 2014). Although this trend can
be explained by the hypothesis that typical dust size increases
with stellar luminosity (Pawellek et al. 2014; Pawellek & Krivov
2015), the blackbody location of disks can be offset from their
resolved locations by a factor of
∼
4
(e.g., scattered light imaging:
Esposito et al. 2020) since debris dust particles are inefficient
emitters at longer wavelengths. This offset makes SED modeling
a degenerate problem between dust property and disk location.
With resolved disk images in scattered light, we can break these
known degeneracies for the smallest dust in debris systems.
Using a variety of coronagraphic imaging instruments from
the ground (e.g., NaCo: Lagrange et al. 2003; Lenzen et al. 2003,
GPI: Macintosh et al. 2008, SPHERE: Beuzit et al. 2008) and
from space (e.g., ACS: Ford et al. 1998, NICMOS: Ramberg
1993, STIS: Woodgate et al. 1998), multiwavelength scattered
light imaging studies revealed dust properties for debris disks
individually, such as 49 Ceti (Choquet et al. 2017; Pawellek et al.
2019), AU Mic (Fitzgerald et al. 2007), Beta Pic (Golimowski
et al. 2006), HD 15115 (Kalas et al. 2007), HD 32297 (Kalas
2005; Duchêne et al. 2020), HD 35841 (Esposito et al. 2018),
HD 107146 (Ertel et al. 2011), HD 191089 (Ren et al. 2019),
HD 192758 (Choquet et al. 2018), HR 4796A (Debes et al. 2008;
Milli et al. 2015; Rodigas et al. 2015; Chen et al. 2020; Arriaga
et al. 2020), and TWA 7 (Ren et al. 2021). These multiwave-
length studies, when further augmented with the advantage of
uniform imaging exploration from identical instruments (e.g.,
GPI debris disk survey: Esposito et al. 2020), would minimize
the offsets from different instruments to enable uniform sys-
tematic studies of dust properties, and would thus bring forth
essential information on the ensemble properties of debris disks
in scattered light.
With debris disks resolved in scattered light, existing studies
have investigated their ensemble properties, especially on scat-
tering phase functions (SPFs), which depict the scattered light
intensity dependence on scattering angles. Hughes et al. (2018)
suggested that the SPFs of debris disks could follow a uniform
trend; however, more recent observations with high-precision
measurements showed diverse SPFs in different systems (e.g.,
Ren et al. 2019; Engler et al. 2022) or even potential SPF change
at different wavelengths (e.g., Ren et al. 2020). In addition,
SPF measurements could be impacted by instrumentation effects
including convolution, by data reduction artifacts such as overfit-
ting and self-subtraction in high-contrast total intensity imaging,
and by vertical thickness effects (e.g., Milli et al. 2017; Olofsson
et al. 2020); these complications make it necessary to study
debris disks from another complementary perspective, namely
multiband imaging (e.g., Chen et al. 2020; Arriaga et al. 2020),
to depict their collective properties.
On board the
Hubble
Space Telescope (HST), the Space
Telescope Imaging Spectrograph (STIS: Woodgate et al. 1998)
and Near Infrared Camera and Multi-Object Spectrometer
(NICMOS: Thompson 1992) instruments can offer unparalleled
stability and sensitivity in the coronagraphic imaging of circum-
stellar disks from visible light to near-infrared wavelengths. In
comparison with protoplanetary disks that are relatively bright
and easily observed from ground-based extreme-adaptive-
optics-equipped systems in polarized light (e.g., Avenhaus et al.
2018; Laws et al. 2020), HST coronagraphs can offer both stable
stellar point spread function (PSF) and optimal sensitivity for
faint target imaging. These advanced instruments provide the
most effective method for imaging faint debris disks in total
intensity (e.g., STIS: Krist et al. 2010, 2012; Schneider et al.
2018). In addition, HST operates in vacuum, which makes it
more straightforward to calibrate detector readouts to physical
units (e.g., Viana et al. 2009) than ground-based observations
(e.g., Milli et al. 2015); it is also sensitive to the faintest materials
such as debris halos that are elusive from the ground (e.g., halos:
Schneider et al. 2018; Ren et al. 2019).
With the high stability, high sensitivity, and high spatial
resolution offered by HST, resolved scattered light imaging of
debris disks can directly probe the spatial and surface bright-
ness distributions for the smallest dust particles within (e.g.,
Schneider et al. 2014, 2018). When imaged at multiple wave-
lengths, the color information of the scatterers can inform dust
properties (e.g., composition, porosity: Debes et al. 2008). In
addition, resolved imaging of debris disks enabled by the appli-
cation of advanced statistical methods, especially when applied
to archival observations and recovering the hidden debris disks
(e.g., Soummer et al. 2014; Choquet et al. 2014), can allow the
study of dust properties to an unprecedented degree (e.g., albedo:
Choquet et al. 2018). Combining the advantages of multiwave-
length images offered by HST and disk recovery from advanced
methods, here we perform a uniform recovery and study of
resolved debris disks to investigate their ensemble properties.
We describe the observation and the data reduction procedures
to recover resolved disk images in Sect. 2, analyze the data in
Sect. 3, discuss our findings in Sect. 4, and conclude this study
in Sect. 5.
2. Observation and data reduction
We summarized a total of 23 systems observed in corona-
graphic imaging mode using both STIS (filter: 50CORON;
λ
c
=
0
.
58
μ
m, pixel scale:
50
.
72
mas pixel
−
1
, Riley et al. 2018) and
NICMOS Camera 2 (NIC2; filter:
F
110
W
or
F
160
W
;
λ
c
=
1
.
12
μ
m or
1
.
60
μ
m, pixel scale:
75
.
65
mas pixel
−
1
, Viana
et al. 2009). In Fig. 1, we display the transmission curves of
the three filters (obtained from Rodrigo et al. 2012; Rodrigo
& Solano 2020). The debris systems are 49 Ceti, AU Mic,
Beta Pic, HD 377, HD 15115, HD 15745, HD 30447, HD 32297,
HD 35650, HD 35841, HD 61005, HD 104860, HD 110058,
HD 131835, HD 141569A, HD 141943, HD 181327, HD 191089,
HD 192758, HD 202917, HR 4796A, TWA 7, and TWA 25. We
summarize the properties
1
of the targets in Table 1, and the
exposure information in Table A.1.
2.1. Space telescope imaging spectrograph
Using STIS, we observed four systems (HD 30447, HD 35841,
HD 141943, and HD 191089) under HST GO-13381
2
(PI:
M. Perrin) and nine systems (49 Ceti, HD 377, HD 35650,
HD 104860, HD 110058, HD 131835, HD 192758, TWA 7, and
TWA 25) under HST GO-15218
3
(PI: É. Choquet). From the
MAST archive,
4
we retrieved six systems (AU Mic, HD 15115,
HD 15745, HD 32297, HD 61005, and HD 181327) from HST
1
Unless otherwise specified, the error bars calculated in this paper are
1
σ
.
2
https://www.stsci.edu/cgi-bin/get-proposal-info?id=
13381&observatory=HST
3
https://www.stsci.edu/cgi-bin/get-proposal-info?id=
15218&observatory=HST
4
https://archive.stsci.edu
A114, page 2 of 17
Ren, B. B., et al.:
A&A proofs
, manuscript no. aa45458-22
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Wavelength ( m)
0
5
10
15
20
25
Transmission (%)
STIS-50CORON
NIC2-F110W
NIC2-F160W
Fig. 1.
Transmission of the STIS-50CORON, NIC2-
F
110
W
, and NIC2-
F
160
W
coronagraphic filters used to image debris disks in this study.
GO-12228 (PI: G. Schneider; Schneider et al. 2014) and two sys-
tems (HD 202917 and HR 4796A) from HST GO-13786 (PI:
G. Schneider; Schneider et al. 2016, 2018). For Beta Pic, we
retrieved its observations from three programs: SM2/ERO-7125
(PI: S. Heap; Heap et al. 2000), HST GO-12551 (PI: D. Apai;
Apai et al. 2015), and HST GO-12923 (PI: A. Gaspar; Schneider
et al. 2017). For HD 141569A, from three programs: HST GO-
8624 (PI: A. Weinberger), HST GO-8674 (PI: A.-M. Lagrange;
Mouillet et al. 2001), and HST GO-13786 (PI: G. Schneider;
Konishi et al. 2016).
For each target, we reduced the observation data with multi-
roll combined PSF template subtraction (MRDI:
Schneider
et al. 2014) using its corresponding PSF reference images des-
ignated in each HST program. We note that although HD 377
was previously observed in HST GO-12291 (PI: J. Krist), it was
not recovered since the major axis of the disk coincides with
either the STIS occulter or the diffraction spikes. In addition, we
observed negligible differences between median-combined and
mean-combined images, and thus we used the mean-combined
MRDI images for a proper propagation of errors. We present the
reduced images in Fig. 2.
2.2. NICMOS
We assembled the NICMOS observations for the targets and
their corresponding PSF references from the Archival Legacy
Investigations of Circumstellar Environments (ALICE) project
5
(PI: R. Soummer; Choquet et al. 2014; Hagan et al. 2018). We
reduced the data with the non-negative matrix factorization
method (NMF; Ren et al. 2018) using
30%
of the most correlated
references with
50
sequentially constructed NMF components.
To recover the true surface brightness of these disks, we adopted
a forward modeling approach assuming simple geometric
models for debris architecture (Augereau et al. 1999) and ana-
lytical SPFs (e.g., Henyey & Greenstein 1941). Due to the high
computational cost of NMF component calculation (Ren et al.
2018), we saved the components computed in data reduction for
subsequent forward modeling. We present the reduced images
in Figs. 3 and 4 for filters
F
110
W
and
F
160
W
, respectively.
As opposed to the classical PSF subtraction method used for
the STIS observations where there are dedicated stable reference
star images, the NMF algorithm used for NICMOS, which was
5
https://archive.stsci.edu/prepds/alice/
shown to be able to better extract faint signals with higher quality
than previous methods (e.g., Ren et al. 2018, 2021), still intro-
duces certain levels of overfit of disk signals. This is due to the
diversity in stellar types, instrument observing conditions, and
image stability in archival NICMOS observations, which makes
the reference images not able to fully capture target PSFs for all
observations in the near-infrared. To recover the surface bright-
ness of a NICMOS disk, we did not adopt the scaling factor in
Ren et al. (2018) that requires stable PSFs. Instead, we estimated
the throughput of the algorithm by performing forward modeling
to capture the PSF variation in the NICMOS archive. Specif-
ically, we adopted the Millar-Blanchaer et al. (2015) code to
create a disk model whose dust particles follow analytical SPFs
in Henyey & Greenstein (1941), and modified them in our study.
To depict the spatial geometry of a debris disk, we used
the Ren et al. (2021) modification of the Millar-Blanchaer et al.
(2015) code: a combined power law in the disk mid-plane, and
a vertical Gaussian dispersion (see Augereau et al. 1999). In
cylindrical coordinates the disk follows
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
>
0
and
α
out
<
0
are the asymp-
totic power law indices when
r
≪
r
c
and
r
≫
r
c
, respectively.
Although the scale height parameter is
h
=
0
.
04
from a theoret-
ical study by Thébault (2009), we note that edge-on disks may
deviate from this value, and thus retrieve it in our disk model-
ing procedure. To account for the inner and outer clearing radii
beyond which there are no dust particles,
r
in
and
r
out
, we only
evaluate Eq. (1) when
r
in
<
r
<
r
out
, and it equals 0 otherwise.
To depict the SPF of the scatterers in a debris disk, we adopted
a two-component Henyey–Greenstein function (e.g., Chen et al.
2020) since the original analytical phase function in Henyey &
Greenstein (1941) is monotonous; however, that monotonicity
is not always observed in actual debris disk observations (e.g.,
Stark et al. 2014; Chen et al. 2020).
For each target, we first generated a model disk image, then
convolved it with the corresponding NICMOS point source PSF
created by
TinyTim
(Krist et al. 2011)
6
using the effective tem-
perature of the star from Table 1. We subtracted the convolved
disk from the observations to perform again the NMF reduction
using the originally calculated NMF components to reduce com-
putational cost. For the debris disks in this study, we did not see
major differences on re-computing the NMF components; this is
likely due to the fact that the PSF wings are sufficiently brighter
than debris disks in the data analyzed here, thus the latter do
not contribute significantly to the selection of best-matching
reference images. In comparison, when circumstellar disks are
brighter than PSF wings, we do indeed expect improvement
of data reduction quality with NMF component re-computation
(e.g., HD 100453 with VLT/SPHERE: Xie et al., in prep.).
We distributed the calculation and forward modeling pro-
cess using
DebrisDiskFM
(Ren et al. 2019) on a computer
cluster, and explored the parameter space with
emcee
(Foreman-
Mackey et al. 2013). The best-fit models minimize the residuals
by maximizing the log-likelihood,
ln
L
(
Θ
|
X
obs
)
=
−
1
2
N
X
i
=
1
X
obs
,
i
−
X
model
,
i
σ
obs
,
i
!
2
−
N
X
i
=
1
ln
σ
obs
,
i
−
N
2
ln(2
π
)
,
(2)
6
http://tinytim.stsci.edu
A114, page 3 of 17
A&A 672, A114 (2023)
Table 1.
Property of debris disk hosts observed by HST/STIS and HST/NICMOS.
ID
Target
SpType
V
Distance
T
e
ff
M
star
L
star
log
g
a
BO
Reference
(mag)
(pc)
(K)
(
M
⊙
)
(
L
⊙
)
(cm s
−
2
)
(
μ
m)
SpType
V
-mag
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
a
49 Ceti
A1V
5.61
57
.
23
+
0
.
18
−
0
.
18
9000
+
170
−
400
2
.
2
+
0
.
3
−
0
.
3
15
.
7
+
0
.
7
−
0
.
7
4
.
32
+
0
.
07
−
0
.
07
2
.
5
+
0
.
4
−
0
.
4
1
13
b
AU Mic
M1V
8.63
9
.
714
+
0
.
002
−
0
.
002
3992
+
150
−
166
0
.
710
+
0
.
014
−
0
.
014
0
.
073
+
0
.
004
−
0
.
004
4
.
6
+
0
.
06
−
0
.
06
0
.
036
+
0
.
002
−
0
.
002
2
14
c
Beta Pic
A6V
3.86
19
.
63
+
0
.
06
−
0
.
06
7100
+
300
−
300
1
.
9
+
0
.
2
−
0
.
2
(
a
)
8
.
97
+
0
.
07
−
0
.
07
(
a
)
4
.
4
+
0
.
3
−
0
.
3
(
a
)
1
.
65
+
0
.
17
−
0
.
17
3
15
d
HD 377
G2V
7.59
38
.
40
+
0
.
04
−
0
.
04
5871
+
30
−
40
1
.
07
+
0
.
13
−
0
.
13
1
.
16
+
0
.
03
−
0
.
03
4
.
44
+
0
.
08
−
0
.
08
0
.
38
+
0
.
05
−
0
.
05
4
15
e
HD 15115
F4IV
6.80
48
.
77
+
0
.
07
−
0
.
07
6811
+
150
−
150
1
.
4
+
0
.
2
−
0
.
2
3
.
73
+
0
.
15
−
0
.
15
4
.
31
+
0
.
08
−
0
.
08
0
.
90
+
0
.
15
−
0
.
15
5
16
f
HD 15745
F0
7.49
71
.
73
+
0
.
12
−
0
.
12
6840
+
130
−
140
1
.
5
+
0
.
3
−
0
.
3
4
.
21
+
0
.
17
−
0
.
17
4
.
27
+
0
.
09
−
0
.
09
1
.
0
+
0
.
18
−
0
.
18
6
16
g
HD 30447
F3V
7.86
80
.
31
+
0
.
14
−
0
.
14
6709
+
130
−
150
1
.
5
+
0
.
3
−
0
.
3
3
.
73
+
0
.
14
−
0
.
14
4
.
31
+
0
.
09
−
0
.
09
0
.
89
+
0
.
16
−
0
.
16
7
16
h
HD 32297
A6V
8.14
129
.
7
+
0
.
5
−
0
.
5
7980
+
170
−
80
1
.
9
+
0
.
3
−
0
.
3
8
.
5
+
0
.
4
−
0
.
4
4
.
36
+
0
.
08
−
0
.
08
1
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12
17
Notes.
Column (1): Letter identifiers of the targets in this paper. Column (2): Target name. Column (3): Spectral type from the literature
(Col. 11). Column (4):
V
-band magnitude from the literature studies in Col. (12). Column (5): Distance computed from
Gaia
DR3 parallaxes
(Gaia Collaboration 2022). Column (6): Effective temperature from
Gaia
DR2 (Gaia Collaboration 2018). Values in Col. (7) for star mass, Col. (8)
for stellar luminosity, and Col. (9) for stellar surface gravity are from the
Transiting Exoplanet Survey Satellite
input catalog (Stassun et al. 2018).
Column (10): Expected dust blow-out size for nonporous amorphous olivine using Eq. (5). While M stars do not have sufficient radiation pressure
to blow out small dust (e.g., Arnold et al. 2019), we report the corresponding blow-out sizes for color–size correlation analysis in Sect. 4.2.
(
a
)
For
Beta Pic, the uncertainties of
M
star
,
L
star
, and
log
g
are scaled from David & Hillenbrand (2015), Anders et al. (2019), and Gaia Collaboration (2018),
respectively. If the upper and lower uncertainties are different, the bigger one is adopted.
References.
: In Cols. (11) and (12), the references are for spectral type and
V
-mag, respectively: (1) Houk & Smith-Moore (1988); (2) Keenan &
McNeil (1989); (3) Gray et al. (2006); (4) Torres et al. (2006); (5) Harlan (1974); (6) Cannon & Pickering (1993); (7) Houk (1982); (8) Rodigas
et al. (2014); (9) Kahraman Aliçavus
,
et al. (2016); (10) Houk (1978); (11) Gray et al. (2017); (12) Herczeg & Hillenbrand (2014); (13) Høg et al.
(2000); (14) Kiraga (2012); (15) Ducati (2002); (16) Wenger et al. (2000); (17) Zacharias et al. (2012).
where
N
is the number of pixels,
σ
is the uncertainty, and
we assume that the pixels
i
follow independent normal dis-
tributions, with
X
obs
and
X
model
denoting the observation and
model datasets, respectively. To quantify the uncertainty, we first
obtained the algorithmic throughput of the best-fit model by
comparing the model with the NMF reduction, then performed
uncertainty measurement on the original individual NMF reduc-
tions with throughput correction.
2.3. Data for joint analysis
Given that the observed debris disks are of different inclina-
tions, and that scatterers in debris disk systems redistribute
incident light to different directions with varying intensity via
SPFs (e.g., Stark et al. 2014; Milli et al. 2017), we measured the
light with a scattering angle of
≈
90
◦
to minimize such effects
to enable a uniform comparison of different systems. We used
the regions annotated in Appendix A.2 for measurements on
the signal and background for both instruments. Specifically for
NICMOS, by comparing our reduction of the original dataset
with the best-fit convolved disk model, we can quantify the algo-
rithmic throughput from the NMF post-processing procedure by
dividing the NMF-reduced data with the best-fit model. We per-
formed photometry on originally reduced data, subtracted flat
halo backgrounds, and corrected the throughput measured from
forward modeling. By doing so rather than performing measure-
ments on the best-fit models, we expect to better capture the
minor variations in observed disk signals.
We obtained the regions for birth ring photometry and halo
background measurements as follows. Using the HD 181327 sys-
tem as an example, we first identified the debris birth ring in
Fig. A.1(q) using the ring parameters (e.g., semimajor axis, posi-
tion angle, inclination) from Stark et al. (2014), then calculated
for each pixel its scattering angle and associated angle uncer-
tainty assuming an infinitely thin disk following Ren et al. (2019,
Appendix A therein). To identify the pixels that host birth ring
signals, if a pixel’s
1
σ
range of scattering angles overlaps with
the
[80
◦
,
100
◦
]
interval, we categorize it as a birth ring pixel
with a scattering angle of
≈
90
◦
. To reduce certain contributions
A114, page 4 of 17