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# GW Ori: Interactions between a Triple-star System and Its Circumtriple Disk in Action

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GW Ori is a hierarchical triple system with a rare circumtriple disk. We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of 1.3 mm dust continuum and ¹² CO J = 2 − 1 molecular gas emission of the disk. For the first time, we identify three dust rings in the GW Ori disk at ∼46, 188, and 338 au, with estimated dust mass of 74, 168, and 245 Earth masses, respectively. To our knowledge, its outermost ring is the largest dust ring ever found in protoplanetary disks. We use visibility modeling of dust continuum to show that the disk has misaligned parts, and the innermost dust ring is eccentric. The disk misalignment is also suggested by the CO kinematics. We interpret these substructures as evidence of ongoing dynamical interactions between the triple stars and the circumtriple disk.
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GW Ori: Interactions between a Triple-star System and Its Circumtriple Disk in Action
Jiaqing Bi
1
, Nienke van der Marel
1,2
, Ruobing Dong ()
1
, Takayuki Muto
3
, Rebecca G. Martin
4
,
Jeremy L. Smallwood
4
, Jun Hashimoto
5
, Hauyu Baobab Liu
6
, Hideko Nomura
7,8
, Yasuhiro Hasegawa
9
, Michihiro Takami
6
,
Mihoko Konishi
10
, Munetake Momose
11
, Kazuhiro D. Kanagawa
12
, Akimasa Kataoka
7
, Tomohiro Ono
13,14
,
Michael L. Sitko
15,16
, Sanemichi Z. Takahashi
7,17
, Kengo Tomida
14,18
, and Takashi Tsukagoshi
7
1
Department of Physics & Astronomy, University of Victoria, Victoria, BC V8P 5C2, Canada; jiaqing.bi@gmail.com,rbdong@uvic.ca
2
Herzberg Astronomy & Astrophysics Programs, National Research Council of Canada, 5071 West Saanich Road, Victoria, BC V9E 2E7, Canada
3
Division of Liberal Arts, Kogakuin University, 1-24-2 Nishi-Shinjuku, Shinjuku-ku, Tokyo 163-8677, Japan
4
Department of Physics & Astronomy, University of Nevada, Las Vegas, 4505 South Maryland Parkway, Las Vegas, NV 89154, USA
5
Astrobiology Center, National Institutes of Natural Sciences, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
6
Academia Sinica Institute of Astronomy & Astrophysics, No. 1, Section 4, Roosevelt Road, Taipei 10617, Taiwan
7
Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
8
Department of Earth & Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo 152-8551, Japan
9
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
10
Faculty of Science & Technology, Oita University, 700 Dannoharu, Oita 870-1192, Japan
11
College of Science, Ibaraki University, 2-1-1 Bunkyo, Mito, Ibaraki 310-8512, Japan
12
Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
13
Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
14
Department of Earth & Space Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
15
Department of Physics, University of Cincinnati, Cincinnati, OH 45221, USA
16
Space Science Institute, 475 Walnut Street, Suite 205, Boulder, CO 80301, USA
17
Department of Applied Physics, Kogakuin University, 1-24-2 Nishi-Shinjuku, Shinjuku-ku, Tokyo 163-8677, Japan
18
Astronomical Institute, Tohoku University, Sendai, Miyagi 980-8578, Japan
Received 2020 March 28; revised 2020 April 26; accepted 2020 April 29; published 2020 May 21
Abstract
GW Ori is a hierarchical triple system with a rare circumtriple disk. We present Atacama Large Millimeter/
submillimeter Array (ALMA)observations of 1.3 mm dust continuum and
12
CO J=21 molecular gas emission of
the disk. For the rst time, we identify three dust rings in the GW Ori disk at 46, 188, and 338 au, with estimated dust
mass of 74, 168, and 245 Earth masses, respectively. To our knowledge, its outermost ring is the largest dust ring ever
found in protoplanetary disks. We use visibility modeling of dust continuum to show that the disk has misaligned parts,
and the innermost dust ring is eccentric. The disk misalignment is also suggested by the CO kinematics. We interpret
these substructures as evidence of ongoing dynamical interactions between the triple stars and the circumtriple disk.
Unied Astronomy Thesaurus concepts: Protoplanetary disks (1300);Planet formation (1241);Circumstellar
matter (241);Pre-main sequence stars (1290)
Supporting material: data behind gure
1. Introduction
GW Ori is a hierarchical triple system (Berger et al. 2011)at
a distance of 402±10 parsecs (Gaia Collaboration et al.
2018). Two of the stars (GW Ori AB)compose a spectroscopic
binary with a separation of 1au (Mathieu et al. 1991).A
tertiary component (GW Ori C)was detected by near-infrared
interferometry at a projected distance of 8au (Berger et al.
2011). The stellar masses have been constrained to be 2.7,
1.7, and 0.9 M
e
, respectively (Czekala et al. 2017). The system
harbors a rare circumtriple disk, with dust extending to
400 au, and gas extending to 1300 au (Fang et al. 2017).
Spectral energy distribution (SED)modeling indicates a gap in
the disk at 2555 au (Fang et al. 2014).
Here we present high resolution ALMA observations in the
disk around GW Ori at 1.3 mm dust continuum emission and
12
CO J=21 emission, where we nd new substructures of
the disk that indicate ongoing diskstar interactions. We
arrange the paper as follows: In Section 2, we describe the
setups of the ALMA observations and data reduction. In
Section 3, we present the imaged results of dust continuum and
12
CO J=21 observations. In Section 4, we present results
of dust continuum visibility modeling. In Section 5, we discuss
the possible origins of the observed substructures. In Section 6,
we summarize our ndings and raise some open questions.
2. Observation and Data Reduction
The observations were taken on 2017 December 10 (ID:
2017.1.00286.S). The disk was observed in Band 6 (1.3 mm)
by 46 antennas, with baseline lengths ranging from 15 to
3321 m. The total on source integration time was 1.6 hours.
There were two 1.875 GHz-wide basebands centered at 217
and 233 GHz for continuum emission, and three basebands
with 117 MHz bandwidths and 112 kHz resolution, centered at
230.518, 219.541, and 220.380 GHz to cover the
12
CO,
13
CO,
and C
18
OJ=21 lines.
The data were calibrated by the pipeline calibration script
provided by ALMA. We used the Common Astronomy
Software Applications package (CASA; version 5.1.15;
McMullin et al. 2007)to process the data. We adopted CASA
task CLEAN to image the continuum map (Figure 1(a)), with the
UNIFORM weighting scheme and a 0 098 circular restoring
The Astrophysical Journal Letters, 895:L18 (11pp), 2020 May 20 https://doi.org/10.3847/2041-8213/ab8eb4
© 2020. The American Astronomical Society.
Original content from this work may be used under the terms
of the Creative Commons Attribution 3.0 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
Figure 1. All panels are centered on the stellar position provided by GAIA DR2 (ICRS R.A.=5
h
29
m
08 390 and decl.=11°5212 661).(a)The ALMA self-
calibrated dust continuum map performed with a 0 098 circular beam (bottom left corner; rms noise level σ40 μJy beam
1
). A larger view of this panel is provided
in Appendix B.(b)The ALMA
12
CO J=21rst-moment map performed with a 0 122×0 159 beam with a position angle of 32°.3 (bottom left corner). The
inset shows a 1by 0 5 wide (40 by 20 au)zoom, and the dotteddashed line highlights the shape of the twist. The averaged uncertainty in the inset region is
0.2 km s
1
.(c)Simulated ALMA continuum emission map of Model 3, produced in the same way as panel (a).(d)The synthetic rst-moment map of the misaligned
disk model, applying the model parameters listed in Table 2. The color scheme is the same as that in panel (b).(e)The residual map of Model 3. Dashed ellipses mark
the tted location of the three dust rings. The colorbar shows the residual magnitude in units of rms noise level (1σ=40 μJy beam
1
=0.6% of peak surface
density).(f)The synthetic rst-moment map of the coplanar disk model, with an inclination of 37°. 9 and a position angle of 5°throughout the disk. The color scheme
is the same as that in panel (b). The data behind panels (a)and (b)are available in the .tar.gz package in two FITS les.
(The data used to create this gure are available.)
2
The Astrophysical Journal Letters, 895:L18 (11pp), 2020 May 20 Bi et al.
beam. We performed phase self-calibration onto the image with
a solution interval of 20 s. This resulted in an rms noise level of
40 μJy beam
1
and an enhanced peak signal-to-noise ratio
(SNR)of 157, compared with 63 μJy beam
1
and 90
before self-calibration, respectively. The integrated ux density
of the disk (195±20 mJy)is consistent with the result from
previous ALMA observations (202±20 mJy; Czekala et al.
2017).
The
12
CO J=21 line data were obtained (after
subtracting the continuum on the self-calibrated data)in the
BRIGGS weighting scheme with robust=0.5, and velocity
resolution 0.5 km s
1
. The resulting line cube has a beam size
of 0 122×0 159 at the position angle 32°. 3. The noise
level is 1.4 mJy beam
1
per channel and the peak signal-to-
noise ratio is 83. Line emission was detected between 7.0 and
20.0 km s
1
with a central velocity of 13.5 km s
1
. The
integrated ux is 60.6 Jy km s
1
intensity-weighted velocity map (a.k.a., the rst-moment map)
was constructed by calculating the intensity-weighted velocity
with a threshold of three times the noise level. The averaged
uncertainty of the twisted pattern in the rst-moment map (i.e.,
the inset in Figure 1(b)) is 0.2 km s
1
, derived from error
propagation theory, assuming the uncertainty of velocity due to
the channel resolution is 0.25 km s
1
. The observations of the
CO isotopologues C
18
O and
13
CO J=21 emission will be
presented in future work.
3. Observational Results
3.1. Dust Continuum Emission
Figure 1(a)shows the continuum map with spatial resolution
of 0 098 (39 au). We identify three dust rings with different
apparent shapes in the disk at 46, 188, and 338 au (hereafter
the inner, middle, and outer ring). The location of the inner ring
coincides with the predicted cavity size from SED modeling
(Fang et al. 2017). The continuum ux densities of the inner,
middle, and outer ring are 42±4, 95±10, and 58±6 mJy,
respectively. To our knowledge, the outer ring is the largest
ever found in protoplanetary disks.
The three rings harbor an enormous amount of solid
material. We estimate the dust (solid)mass M
dust
of the rings
with the equation provided in Hildebrand (1983)
k
=n
nn
MFd
BT ,1
dust
2
dust
() ()
where F
ν
is the continuum surface brightness at a submillimeter
frequency ν,dis the distance from the observer to the source,
B
ν
(T
dust
)is the Planck function at the dust temperature T
dust
,
and κ
ν
is the dust opacity. The dust temperature is estimated
using a tting function provided by Dong et al. (2018b)
=-
TL
L
r
30 38 100 ,2
AU
dust
14 12
⎜⎟
()
where L
å
is the total stellar luminosity, and ris the location of
the ring. The stellar luminosity modied by the distance
provided by GAIA DR2 is 49.3±7.4 L
e
(Calvet et al. 2004;
Gaia Collaboration et al. 2018). We assume a dust grain
opacity of 10 cm
2
g
1
at 1000 GHz with a power-law index of
1(Beckwith et al. 1990). We estimate the dust masses of the
rings to be 74±8, 168±19, and 245±28 M
, respectively,
with the uncertainties incorporating the uncertainties in the
surface brightness of the rings, source distance, stellar
luminosity, and radial location of the rings.
3.2.
12
CO J=21 Emission
Figure 1(b)shows the rst-moment map of
12
CO J=21
emission (with the zeroth-moment map provided in
Appendix A). For regular Keplerian rotating disks, we expect
a well-dened buttery-like pattern in the rst-moment map.
However, we nd a twisted pattern inside 02, which may
result from a misalignment between the inner and outer parts of
the disk (i.e., having different inclinations and orientations;
Rosenfeld et al. 2014), as has been found in the disks around,
e.g., HD 142527 (Casassus et al. 2015; Marino et al. 2015)and
HD 143006 (Benisty et al. 2018; Pérez et al. 2018).
4. Modeling of Dust and Gas Emission
The different apparent shapes of the rings could result from a
few scenarios, such as coplanar rings with different eccentri-
cities, circular rings with different inclinations, or rings with
both different eccentricities and inclinations. Here we present
evidence for disk misalignment and disk eccentricity found in
modeling the dust and gas emission.
4.1. Visibility Modeling of the Dust Continuum Emission
We t the dust continuum map assuming that there are three
dust rings in the disk with Gaussian radial proles of surface
brightness
=s
--
Fr F e ,3
ii0,
rr
i
i
2
22
() ()
()
where F
i
is the surface brightness as a function of the distance to
the center r,withi=1, 2, 3 denoting parameters for the inner,
middle, and outer ring, respectively. F
0,i
is the peak surface
brightness, r
i
is the radius of the ring (i.e., where the ring has the
highest surface brightness),andσ
i
is the standard deviation.
Initially, we assume all three rings are intrinsically circular
when viewed face-on, and their different apparent shapes entirely
originate from different inclinations. For each ring, we assume an
independent set of peak surface brightness, center location, radius,
width, inclination, and position angle as the model parameters.
We call this combination of assumptions Model 1.
After projecting the rings according to their position angles
and inclinations, we calculate the synthetic visibility of the
models using GALARIO (Tazzari et al. 2018), and launch
MCMC parameter surveys to derive posterior distribution of
model parameters using EMCEE (Foreman-Mackey et al. 2013).
In the MCMC parameter surveys, the likelihood function Lis
dened as
=- å´-
+-
=
LmReVReV
ImV ImV
ln 1
2
,4
j
Njjj
jj
1obs, mod, 2
obs, mod, 2
[( )
()] ()
where V
obs
is the visibility data from ALMA observations,
V
mod
is the synthetic model visibility, Nis the total number of
visibility data points in V
obs
, and m
j
is the weight of each
visibility data point in V
obs
. The prior function is set to
guarantee the surface brightness, ring radius, and ring width do
not go below zero, the position angle does not go beyond
(90, 90)degrees, and the inclination does not go beyond
(0, 90)degrees. For each model, there are 144 chains spread in
3
The Astrophysical Journal Letters, 895:L18 (11pp), 2020 May 20 Bi et al.
the hyperspace of parameters. Each chain has 15,000 iterations
including 10,000 burn-in iterations. The results of the
parameter surveys are listed in Table 1.
The tting result of Model 1, listed in Table 1(a), suggests
that the three rings have statistically different centers.
Particularly, the center of the inner ring differs from the
centers of the outer two by 20% of the inner ringʼs radius.
This nonconcentricity indicates nonzero intrinsic eccentricities
in the rings, particularly the inner ring (see Section 5.1).
We explore the nonzero intrinsic eccentricity in the inner
ring with two models. In both models, the outer two rings are
intrinsically circular and concentric. Their center coincides with
one of the two foci of the inner ring. In Model 2, that center is
set free, while in Model 3 it is assumed to coincide with the
stellar position provided by GAIA DR2 (Gaia Collaboration
et al. 2018). In those two models, we introduce two more
parameters for the intrinsic eccentricity and apoapsis angle of
the inner ring. The position angle only indicates the direction to
the ascending node on the axis along which the ring is inclined.
The tting results are listed in Tables 1(b)and (c), and the
following calculations are based on the result of Model 3.
Figures 1(c)and (e)show the model image and the residual
map of Model 3, respectively. The residual map is produced by
subtracting model from data in the visibility plane, and then
imaging the results in the same way used for the observations.
We interpret the residuals as additional substructures on top of
the ideal model (e.g., a warp within the ring; Huang et al.
2020).
All three models yield roughly consistent inclinations and
position angles of each ring. However, we cannot determine the
mutual inclinations between them (i.e., the angles between their
angular momentum vectors)from dust emission modeling
alone, due to the unknown direction of orbital motion.
Table 1
The Complete MCMC Result of Dust Continuum Visibility Modeling
(a)Model 1
Inner Ring Middle Ring Outer Ring
R.A Offset [arcsecond]´-
-
-
1
.89 10 2
9.49 10
9.47 10 5
5
-
-
-
2.44 10 3
2.08 10
1.82 10 4
4
-
-
-
4.24 10 3
3.91 10
4.64 10 4
4
decl. Offset [arcsecond]
-
-
-
1.32 10 2
1.01 10
1.09 10 4
4
-
-
-
2.26 10 2
2.06 10
2.22 10 4
4
-
-
-
1.21 10 2
4.67 10
6.57 10 4
4
-
-
1
.15 10 1
1.48 10
1.46 10 4
4
´-
-
-
4
.68 10 1
2.92 10
3.07 10 4
4
´-
-
-
8.40 10 1
1.15 10
1.03 10 3
3
Ring Width [arcsecond]´-
-
-
.97 10 2
6.24 10
3.16 10 4
´-
-
-
1
.74 10 1
7.56 10
6.69 10 4
4
´-
-
-
3
.32 10 1
2.78 10
1.84 10 3
3
Surface Brightness [Jy/pixel]´-
-
-
2
.49 10 4
1.56 10
1.80 10 6
6´-
-
-
3
.96 10 5
1.69 10
8.67 10 7
8´-
-
-
1
.13 10 5
5.52 10
2.77 10 7
8
Inclination [degree]-
+
2
2.24 0.31
0.23 -
+
3
2.62 0.11
0.07 -
+
3
7.93 0.08
0.09
Position Angle [degree]--
+
60.75 0.56
1.0
6
--
+
7.43 0.12
0.19 --
+
3.57 0.12
0.15
(b)Model 2
Inner Ring Middle Ring Outer Ring
R.A Offset [arcsecond]´-
-
-
1
.77 10 2
1.61 10
1.69 10 4
4
decl. Offset [arcsecond]
-
-
-
2.22 10 2
1.99 10
1.95 10 4
4
-
-
1
.17 10 1
1.35 10
1.36 10 4
4
´-
-
-
4
.68 10 1
2.71 10
2.88 10 4
4
´-
-
-
8.40 10 1
9.53 10
9.48 10 4
4
Ring Width [arcsecond]´-
-
-
.97 10 2
3.91 10
3.16 10 4
´-
-
-
1
.74 10 1
6.03 10
6.66 10 4
4
´-
-
-
3
.30 10 1
1.96 10
1.68 10 3
3
Surface Brightness [Jy/pixel]´-
-
-
2
.51 10 4
1.55 10
1.53 10 6
6´-
-
-
3
.96 10 5
1.01 10
8.20 10 7
8´-
-
-
1
.13 10 5
3.37 10
2.65 10 8
8
Inclination [degree]-
+
2
3.15 0.23
0.22 -
+
3
2.64 0.07
0.07 -
+
3
7.91 0.07
0.0
8
Position Angle [degree]--
+
55.67 0.50
0.61 --
+
7.44 0.12
0.1
4
--
+
3.60 0.11
0.13
Apoapsis Angle [degree]-
+
65.04 0.49
0.50 LL
Eccentricity
-
-
0.21 1.43 10
1.75 10 3
3LL
(c)Model 3
Inner Ring Middle Ring Outer Ring
-
-
1
.16 10 1
1.49 10
1.20 10 4
4
´-
-
-
4
.68 10 1
2.98 10
2.72 10 4
4
´-
-
-
8.37 10 1
1.06 10
8.95 10 3
4
Ring Width [arcsecond]´-
-
-
.99 10 2
3.86 10
3.06 10 4
´-
-
-
1
.73 10 1
5.98 10
6.33 10 4
4
´-
-
-
3
.39 10 1
1.85 10
1.90 10 3
3
Surface Brightness [Jy/pixel]´-
-
-
2
.47 10 4
1.42 10
1.64 10 6
6´-
-
-
3
.94 10 5
1.12 10
8.55 10 7
8´-
-
-
1
.13 10 5
3.33 10
2.63 10 8
8
Inclination [degree]-
+
2
0.63 0.29
0.23 -
+
3
2.86 0.07
0.0
6
-
+
3
7.96 0.08
0.09
Position Angle [degree]--
+
60.37 0.65
0.81 --
+
7.26 0.13
0.13 --
+
3.49 0.12
0.13
Apoapsis Angle [degree]-
+
1
21.39 0.25
0.26 LL
Eccentricity
-
-
0.19 6.46 10
8.55 10 4
4
LL
Note.The radius of each ring is the location of the peak in our model in Section 4, and the width is the full width at half maximum (FWHM)of the prole. The center
offsets for Model 1 and Model 2 are relative to the center in Model 3, which is the location of GW Ori provided by GAIA DR2 (ICRS R.A.=5
h
29
m
08 390 and
decl.=11°5212 661). The position angles and apoapsis angles are measured east of north. The inclination is dened in the range from 0°to 90°, with 0°denoting
face-on. The pixel size in the unit of surface brightness is determined internally by GALARIO.
4
The Astrophysical Journal Letters, 895:L18 (11pp), 2020 May 20 Bi et al.
4.2. Kinematics Modeling of the
12
CO J=21 Emission
Following the prescription and parameter values used to t
low resolution CO isotopologue data of GW Ori (Fang et al.
2017), we set up a gas surface density model using a power-law
prole with an exponential tail
S=S
g--- g-
rr
re,5
c
c
rr
c2
() ()
[( ) ]
and the aspect ratio h/rparameterized as
=
y
h
r
h
r
r
r,6
cc
⎜⎟
()
where Σ
c
and (h/r)
c
are corresponding values at the
c
. The disk mass is taken as
0.12 M
e
, corresponding to Σ
c
=3gcm
2
for r
c
=320 au,
with γ=1.0, (h/r)
c
=0.18, and ψ=0.1. The dust surface
density prole is set by assuming a gas-to-dust ratio of 100, and
decreasing the dust surface density by a factor of 1000 inside
the derived gap radii: inside 37 au, from 56 to 153 au, and from
221 to 269 au. The
12
CO channel maps are then computed and
ray-traced by the physical-chemical modeling code DALI
(Bruderer 2013), which simultaneously solves the heating-
cooling balance of the gas and chemistry to determine the gas
temperature, molecular abundances, and molecular excitation
for a given density structure.
Similar to Walsh et al. (2017), we model the misaligned disk
with an inner cavity and three annuli each with its own
inclination and position angle,
19
as listed in Table 2. The
channel map is run through the ALMA simulator using the
settings of the ALMA observations. The resulting rst-moment
map is shown in Figure 1(d). In Figure 1(f)we show the
simulated rst-moment map for another model as a compar-
ison, in which the disk is coplanar with an inclination of 37°.9
and a position angle of 5°.
The models show that the
12
CO J=21rst-moment
map in the ALMA observation cannot be reproduced by a
coplanar disk. Instead, the misaligned disk model described in
Table 2matches the observed rst-moment map better,
indicating the presence of misalignment in the GW Ori disk.
5. Discussions
Several disks have been observed to have nonzero
eccentricity and/or misalignment (e.g., MWC 758, Dong
et al. 2018a; HD 142527, Casassus et al. 2015; Marino et al.
2015; and HD 143006, Benisty et al. 2018; Pérez et al. 2018).
Unlike most of them, in which the origin is uncertain, the GW
Ori system provides a strong and direct link between
substructures and stardisk gravitational interactions. There-
fore, it offers a unique laboratory to probe three-dimensional
stardisk interactions. In this section, we discuss the possible
origins of the observed substructures due to stardisk
interactions.
5.1. Disk Eccentricity
The AB binary and the C component can be dynamically
viewed as an ABC binary. The eccentricity of the circumbin-
ary disk may increase through resonant interactions with the
binary (Papaloizou et al. 2001). In the case of no binary-disk
misalignment, the binaryʼs perturbing gravitational potential on
the midplane of the disk is given by Lubow (1991). The
coupling of this perturbing potential with the imposed
eccentricity of the disk excites density waves at the 1:3 outer
tum removal in the inner parts of the disk. As no energy is
removed along with the angular momentum in this process, the
disk orbit cannot remain circular (Papaloizou et al. 2001).In
the case of GW Ori, the inner dust ring is the most susceptible
to this effect, which could explain why its center in Model 1 is
more deviated from those of the other two rings.
5.2. Binary-disk Misalignment
Our dust and gas observations alone cannot break the
degeneracy in the mutual inclination between different parts in
the disk due to the unknown on-sky projected orbital direction
of the disk. Previous studies indicate that the on-sky projected
gas motion is likely to be clockwise (Czekala et al. 2017), same
as the orbital motion of GW Ori C given by astrometric
observations (Berger et al. 2011). Given the inclination and
longitude of ascending node of the AB-C binary orbit being
150±7 and 282±9 degrees (Czekala et al. 2017), we assume
that the entire disk has the same clockwise on-sky projected
orbital direction. Following Fekel (1981),wend out that the
binary-disk misalignments at 46 au (the inner ring),100 au
(a gap), 188 au (the middle ring), and 338 au (outer ring)are
11±6, 28,
20
35±5, and 40±5 degrees, respectively. A
schematic diagram of our disk model is displayed in Figure 2.
Therefore, the inner ring and the AB-C binary plane are close
to being coplanar, and there is a monotonic trend of binary-disk
misalignment from 10°at 50 au to 40°at 340 au,
consistent with the expected outcome of the disk misalignment
(see Section 5.3).
Several mechanisms could produce an initial binary-disk
misalignment, such as turbulence in the star-forming gas clouds
(Bate 2012), binary formation in the gas cloud whose physical
Table 2
The Parameters Used in the Gas Kinematics Modeling
Inner Ring Outer Ring Longitude of the Inclination
Ascending Node
(au)(au)(degree)(degree)
0 32 No Emission
32 48 60 22.3
48 153 10 17.3
153 1000 5 37.9
Note.The annuli are concentric with the center located at the stellar position
provided by GAIA DR2 (ICRS R.A.=5
h
29
m
08 390 and decl.=11°52
12 661). The longitude of the ascending node is measured east of north, and
the inclination is dened in the range from 0°to 90°with 0°meaning face-on.
The disk model is composed of an empty inner cavity and three annuli, inside
out. The inner annulus (from 32 to 48 au)is for the inner dust ring. The outer
annulus (from 153 to 1000 au)is for the middle and outer dust rings. The
middle annulus (from 48 to 153 au)is for the gap in between.
19
DALI is unable to vary inclination as a function of radius. The nal channel
map is constructed by concatenating three channel maps, each for one
component, ray-traced at its inclination and position angle and cut out at the
specied radius range listed in Table 2.
20
The manual tting of the gas model cannot provide any uncertainties for the
gap between the inner and middle rings.
5
The Astrophysical Journal Letters, 895:L18 (11pp), 2020 May 20 Bi et al.
axes are misaligned to the rotation axis (Bonnell &
Bastien 1992), and accretion of cloud materials with mis-
aligned angular momentum with respect to the binary after the
binary formation (Bate 2018).
5.3. Misalignment within the Disk
A test particle orbiting a binary on a misaligned orbit
undergoes nodal precession due to gravitational perturbations
from the binary (Nixon et al. 2011; Facchini et al. 2018). For a
protoplanetary disk in the bending-wave regime (i.e., where the
aspect ratio is higher than the α-prescription of viscosity;
Shakura & Sunyaev 1973), disk parts at different radii shall
undergo global precession like a rigid body with possibly a
small warp (Smallwood et al. 2019). Therefore, the timescale of
radial communication of disk materials (i.e., for pressure-
induced bending waves propagating at half of the sound speed)
and the timescale of global precession determine whether the
disk can develop a misalignment inside.
Assuming an inner radius at 32 au (34 times the AB-C
binary semimajor axis; Czekala et al. 2017; Kraus et al. 2020)
and an outer radius at 1300 au (size of the gas disk; Fang et al.
2017), the global precession timescale of the entire disk is
0.83 Myr, and the radial communication timescale is
0.06 Myr (see Appendix D.1 and D.2 for detailed calcula-
tions). The radial communication is able to prevent the disk
from breaking or developing a signicant warp, and we would
not expect the observed large deviations in the inclination and
position angle between the inner and middle ring. Therefore,
we propose that the gap between the inner and middle ring is
deep enough to break the disk into two parts (hereafter the
inner and outer disk), undergoing nodal precession indepen-
dently, due to another mechanism.
Due to the viscous dissipation, the precessing disk is torqued
toward either polar alignment (i.e., the binary-disk misalign-
ment becomes 90°; Martin & Lubow 2017; Zanazzi &
Lai 2018), or coplanar alignment/counteralignment. The
minimum critical initial binary-disk misalignment for which a
disk moves toward polar alignment is 63°in the limit of zero
disk mass. Since a higher disk mass will lead to a larger critical
angle (Martin & Lubow 2019), the GW Ori disk is most likely
moving toward coplanar alignment. As we propose that the
disk breaks into two parts undergoing global precession
independently, they are also aligning to the binary indepen-
dently on different timescales.
Assuming the radial communication is blocked at 60 au, we
estimate the alignment timescales to be 1 Myr for the inner
disk and above 100 Myr for the outer disk (see Appendix D.3).
This is consistent with the observed signicantly smaller
inclination of the inner ring with respect to the binary than
those of the outer rings. The latter are likely inherited from
birth and have not evolved much given the system age.
If the radial communication is also blocked at the gap
between the middle and outer rings (e.g., 250 au), the nodal
precession timescales for the middle and outer rings would be
0.6 Myr and 120 Myr, respectively, and the two rings are
likely to develop signicantly different position angles. Thus
we propose that the gap between the middle and outer rings
does not cut off the radial communication, and the two rings
Figure 2. Schematic diagram showing the proposed geometry of the system. Orbital planes of the AB-C binary (red), the inner dust ring (orange), the gap between the
inner and middle dust rings (white dots), the middle dust ring (green), and the outer dust ring (blue)are marked inside out. The left panel is a sky-projected view, and
in the right panel the binary is edge-on. The size of the disk components are not to-scale. The orientation axes are shown at the bottom left corner of each panel, with
the x-axis being antiparallel to the R.A. direction, the y-axis being parallel to the decl. direction, and the z-axis pointing at the observer.
6
The Astrophysical Journal Letters, 895:L18 (11pp), 2020 May 20 Bi et al.
precess roughly as a rigid body with only a small warp
between them.
5.4. Hydrodynamic Simulations
The analytical results suggest that the radial communication
is able to prevent the binary from breaking the disk (e.g., Nixon
et al. 2013). As a result, we propose a break at 60 au that is
due to other mechanisms in order to explain the observed
structures. We carry out a demonstrative smoothed particle
hydrodynamic (SPH)simulation with the PHANTOM code
(Lodato & Price 2010; Price & Federrath 2010; Price et al.
2018)to test the nonbreaking hypothesis in the nonlinear
regime. The results are shown in Figure 3.
We model the triple-star system as the outer binary in order
to speed up the simulation. The simulation consists of 10
6
equal
mass Lagrangian SPH particles initially distributed from
r
in
=40 au to r
out
=400 au. The initial truncation radius of
the disk does not affect the simulation signicantly, since the
material moves inwards quickly due to the short local viscous
timescale. A smaller initial outer truncation radius r
out
than
what is observed is chosen in order to better resolve the disk.
The binary begins at apastron with e
b
=0.22 and a
b
=9.2 au
(Czekala et al. 2017). The accretion radius of each binary
component is 4 au. Particles within this radius are accreted, and
their mass and angular momentum are added to the star. We
ignore the effect of self-gravity since it has no effect on the
nodal precession rate of at circumbinary disks.
The initial surface density prole is taken by
S=S -
rrr,7
00
32
() ( ) ()
where Σ
0
is the density normalization at r
0
=40 au, corresp-
onding to a total disk mass of 0.1 M
e
. We take a locally
isothermal disk with a constant aspect ratio h/r=0.05, where
his the scale height. The Shakura & Sunyaev (1973)α
parameter varies in the range 0.0080.013 over the disk. The
SPH articial viscosity α
AV
=0.31 mimics a disk with
aa
»áñH
h10 8
AV ()
(Lodato & Price 2010), where
á
ñHis the mean smoothing
length on particles in a cylindrical ring at a given radius and we
take β
AV
=2. The disk is resolved with average smoothing
length per scale height of 0.32.
The evolution of surface density, binary-disk misalignment,
and longitude of the ascending node at different radii suggest
that the disk does not show any sign of breaking in 3000
binaryʼs orbital periods (0.04 Myr), which is sufciently long
to tell if the disk would break or not since the radial
communication timescale in the simulation is 0.01 Myr.
Instead, the disk presents a global warp. The warp is not taken
into account in the analytic estimates. The small outer
timescale than that predicted by the analytic model, comparable
to the radial communication timescale. The simulations
suggests that unless the disk is very cool (i.e., low aspect
ratio)and in the viscous regime, some other mechanism, e.g., a
companion, is needed to break the disk at the gap between the
inner and middle rings. This mechanism may also be
responsible for producing the observed misalignment in
the disk.
A disk with a lower aspect ratio or a higher αvalue, such
that it falls into the viscous regime (h/r<α), may break due to
the binaryʼs torque (Nixon et al. 2013). However, observations
have suggested lower αvalues than our adaption here (e.g.,
α10
3
, Flaherty et al. 2017). A lower viscosity leads to a
larger binary truncation radius (Artymowicz & Lubow 1994),
and a longer global precession timescale (Equation (D4)).
Therefore we expect even less warping (and no break)in the
GW Ori disk than in our simulation.
Figure 3. Result of the SPH simulation. Upper panel:radial prole of the
surface density of the disk. Mand aare the total mass and separation of the
AB-C binary in code units, respectively. Middle panel:radial prole of the
binary-disk misalignment. Lower panel:radial prole of the longitude of the
ascending node of the disk, measured from the binaryʼs orbital plane.
7
The Astrophysical Journal Letters, 895:L18 (11pp), 2020 May 20 Bi et al.
6. Conclusions
We present the ALMA 1.3 mm dust continuum observation
and
12
CO J=21 emission of the circumtriple disk around
GW Ori. Our main conclusions are the following:
1. For the rst time, we identify three dust rings in the GW
Ori disk at 46, 188, and 338 au, with their estimated
dust mass being 74, 168, and 245 M
, respectively. The
three dust rings have enough solids to make many cores
of giant planets (10 M
; Pollack et al. 1996).
2. We built three models under various assumptions to t
the dust continuum observations using MCMC tting.
Our results (Table 1)suggest that the inner ring has an
eccentricity of 0.2, and the three rings have statistically
different on-sky projected inclinations. The inner, middle,
and outer rings are likely misaligned by 11, 35, and
40 degrees to the orbital plane of the GW Ori AB-C
binary system, respectively.
3. A twisted pattern is identied in the rst-moment map,
suggesting the presence of a warp in the disk, consistent
with what we have found in the dust continuum emission.
4. Using analytical analysis and hydrodynamic simulations,
we nd that the torque from the GW Ori triple stars alone
cannot explain the observed large misalignment between
the inner and middle dust rings. The disk would not break
due to the torque, and a continuous disk is unlikely to
show the observed large misalignment. Therefore, this
hints at some other mechanism that breaks the disk and
prevents radial communication of bending waves
between the inner and middle rings.
There are still open questions associated with the system. For
example, are there any companions in the disk? Dust rings and
gaps have been shown to be common in protoplanetary disks
(Andrews et al. 2018; Huang et al. 2018; Long et al. 2018; van
der Marel et al. 2019), and one of the most exciting hypotheses
is that they are produced by embedded companions ranging
from stellar-mass all the way to super-Earths (Artymowicz &
Lubow 1994; Dong et al. 2015; Zhang et al. 2018).
Specically, a companion may be opening the gap between
the inner and middle rings and breaking the disk there.
Companions at hundreds of astronomical units from their host
stars have been found before (e.g., HD 106906 b; Bailey et al.
2014). But how they form, i.e., forming in situ or at closer
distances, or followed by scattering or migration to the outer
regions, is unclear. If GW Oriʼs dust rings are in the process of
forming companions, there will be circumtriple companions,
which have not been found before (excluding quadruple
systems; Busetti et al. 2018). The system will offer direct
clues on the formation of distant companions.
We thank Sean Andrews, Myriam Benisty, John Carpenter,
Ian Czekala, Sheng-Yuan Liu, Feng Long, Diego Muñoz,
Rebecca Nealon, Henry Ngo, Laura Pérez, John Zanazzi, and
Zhaohuan Zhu for discussions. We also thank the anonymous
referee for constructive suggestions that largely improved the
quality of the paper. J.B. thanks Belaid Moa for help on the
numerical implementation. This paper makes use of the
ALMA is a partnership of ESO (representing its member
states), NSF (USA)and NINS (Japan), together with NRC
(Canada), MOST and ASIAA (Taiwan), and KASI (Republic
of Korea), in cooperation with the Republic of Chile. The Joint
ALMA Observatory is operated by ESO, auI/NRAO, and
NAOJ. The National Radio Astronomy Observatory is a
facility of the National Science Foundation operated under
cooperative agreement by Associated Universities, Inc. Num-
erical calculations are performed on the clusters provided by
ComputeCanada. This work is in part supported by JSPS
KAKENHI grant Nos. 19K03932, 18H05441, and 17H01103
and NAOJ ALMA Scientic Research grant No. 2016-02A.
Financial support is provided by the Natural Sciences and
Engineering Research Council of Canada through a Discovery
Grant awarded to R.D. N.v.d.M. acknowledges support from
the Banting Postdoctoral Fellowships program, administered
by the Government of Canada. R.G.M. acknowledges support
from NASA through grant NNX17AB96G. H.B.L. is sup-
ported by the Ministry of Science and Technology (MoST)of
Taiwan (grant Nos. 108-2112-M-001-002-MY3). Y.H. is
supported by the Jet Propulsion Laboratory, California Institute
of Technology, under a contract with the National Aeronautics
and Space Administration. K.T is supported by JSPS
KAKENHI 16H05998 and 18H05440, and NAOJ ALMA
Scientic Research Grant 2017-05A.
Appendix A
ALMA
12
CO J=21 Zeroth-moment Map
Figure A1 shows the ALMA zeroth-moment map of
12
CO
J=21 emission. The spiral-like structure at 075 to the
northwest is likely due to cloud contamination, as reported by
previous studies (Czekala et al. 2017; Fang et al. 2017).
Figure A1. ALMA zeroth-moment map of
12
CO J=21 emission.
8
The Astrophysical Journal Letters, 895:L18 (11pp), 2020 May 20 Bi et al.
Appendix B
A Larger View of Figure 1(a)
Figure B1 shows a larger view of Figure 1(a).
Figure B1. Larger view of Figure 1(a).
9
The Astrophysical Journal Letters, 895:L18 (11pp), 2020 May 20 Bi et al.
Appendix C
The UV-plot and Posterior Distribution of Dust Modeling
Figure C1 shows the uv-plot and posterior distribution of
Model 3.
Appendix D
Equations for the Timescale Analysis
For a disk around a binary system of separation a
b
communication timescale t
c
can be estimated by Lubow &
Martin (2018)
»W
thr
r
a
8
5,D1
c
bout
out
b
32
() ()
where r
out
is the outer radius within which the disk is in good
out
is the aspect ratio at r
out
,
calculated based on the estimated temperature in the disk
(Equation (2)). The radial communication timescale of the
entire disk (i.e., r
out
=1300 au)is estimated to be 0.06 Myr.
D.2. Nodal Precession Timescale
If there is no radial communication in the disk, each part of the
disk shall undergo differential precession with its local precession
angular frequency ω
n,local
given by Smallwood et al. (2019)
w=Wka
r,D2
n,local b72
b
⎜⎟
()
where
=+- +
kee
MM
MM
3
413 4 D3
b
2
b
412
12
2
() ()
is a constant depending on the eccentricity of binaryʼsorbite
b
,
and the primary and secondary mass of the binary M
1
and M
2
.
However, for a protoplanetary disk in the bending-wave regime,
where radial communication is active and prompt, the disk parts
Figure C1. Quality of MCMC parameter search for Model 3. The uv-visibility panel shows the uv-plot of both the ALMA observation and its best-t model, with the
upper panel for the real part of visibility and the lower panel for the imaginary part. The surrounding panels show the histograms of chains in the MCMC tting. The
best-t value is taken from the ftieth percentile of the distribution (vertical red line), and the negative and positive uncertainties are taken from sixteenth and eighty-
fourth percentile, respectively. The seven columns are for the peak surface brightness, apoapsis angle (inner ring only), eccentricity (inner ring only), inclination,
position angle, radius, and width, from left to right. The three rows (top-down)are for the inner, middle, and outer rings. The units of parameters in the histograms are
the same as those in Table 1(c).
10
The Astrophysical Journal Letters, 895:L18 (11pp), 2020 May 20 Bi et al.
at different radii shall undergo global precession with the angular
frequency ω
n,global
given by Smallwood et al. (2019)
w=Wka
r,D4
n,global b72
b
⎜⎟
()
and
ò
ò
=SW
SW
a
r
rar r
rr
d
d
D5
r
r
r
r
b72 3b72
3
in
out
in
out
⎜⎟
()
()
is the angular momentum weighted averaging term, in which Ω
(r)is the angular frequency at a given radius r,Σ(r)is the disk
surface density with a radial dependence of r
3/2
, and r
in
and
r
out
are inner and outer radii of the disk. Assuming r
in
=32 au
and r
out
=1300 au, we take t
n,global
=2π/ω
n,global
and esti-
mate the global precession timescale of the entire GW Ori disk
to be 0.83 Myr.
D.3. Alignment Timescale
The alignment timescale t
a
is given by Lubow & Martin
(2018)and Bate et al. (2000)
aw
=W
thr ,D6
a
2b
n
2
() ()
where α=0.01, h/ris dened in Equation (6), and the angular
frequency of global precession (Equation (D4)) is used for ω
n
.
ORCID iDs
Jiaqing Bi https://orcid.org/0000-0002-0605-4961
Nienke van der Marel https://orcid.org/0000-0003-
2458-9756
Ruobing Dong ()https://orcid.org/0000-0001-
9290-7846
Rebecca G. Martin https://orcid.org/0000-0003-2401-7168
Jun Hashimoto https://orcid.org/0000-0002-3053-3575
Hideko Nomura https://orcid.org/0000-0002-7058-7682
Michihiro Takami https://orcid.org/0000-0001-9248-7546
Mihoko Konishi https://orcid.org/0000-0003-0114-0542
Munetake Momose https://orcid.org/0000-0002-3001-0897
Kazuhiro D. Kanagawa https://orcid.org/0000-0001-
7235-2417
Akimasa Kataoka https://orcid.org/0000-0003-4562-4119
Tomohiro Ono https://orcid.org/0000-0001-8524-6939
Michael L. Sitko https://orcid.org/0000-0003-1799-1755
Sanemichi Z. Takahashi https://orcid.org/0000-0003-
3038-364X
Kengo Tomida https://orcid.org/0000-0001-8105-8113
Takashi Tsukagoshi https://orcid.org/0000-0002-6034-2892
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The Astrophysical Journal Letters, 895:L18 (11pp), 2020 May 20 Bi et al.
... Nixon et al. 2013). Broken and misaligned disc rings have recently been observed in the protoplanetary disc around GW Ori (Bi et al. 2020;Kraus et al. 2020). The cause of the break in this case may be a result of the inner binary torque, or the presence of gap-forming planets. ...
Preprint
Pleione is a Be star that is in a 218 day orbit with a low-mass binary companion. Recent numerical simulations have shown that a Be star disc can be subject to breaking when material is actively being fed into the inner parts of the disc. After breaking, the disc is composed of two rings: an inner ring that is anchored to the stellar equator and an outer ring that is free to nodally precess. A double ring disc may explain some of the observed variability in Pleione. We model the nodal precession of the outer disc ring that is driven by the companion on an observed timescale of $80.5\,\rm yr$. We find that the outer ring of a broken disc in a binary with an eccentricity of $e_{\rm b}= 0.6$ can precess on the observed timescale and have an outer radius that is in rough agreement with the observed disc size. An unbroken disc model cannot fit both the observed precession rate and disc size. Suppression of Kozai-Lidov driven disc eccentricity is more likely for a high binary eccentricity if the disc extends to the tidal truncation radius.
... GG Tau A, another pre-main sequence binary, has a circumbinary disc that is inclined by about 37° ( Keppler et al. 2020). The pre-main sequence circumtriple disc around the hierarchical triple star system, GW Ori, is misaligned by about 38° (Bi et al. 2020;Kraus et al. 2020;Smallwood et al. 2021a). The young binary IRS 43 has a circumbinary disc with an observed misalignment of about 60° (Brinch et al. 2016). ...
Preprint
We present hydrodynamical simulations to model the accretion flow from a polar circumbinary disc onto a high eccentricity ($e=0.78$) binary star system with near unity mass ratio ($q=0.83$), as a model for binary HD 98800 BaBb. We compare the polar circumbinary disc accretion flow with the previously studied coplanar case. In the coplanar case, the circumbinary disc becomes eccentric and the accretion alternates from being dominant onto one binary member to the other. For the polar disc case involving a highly eccentric binary, we find that the circumbinary disc retains its initially low eccentricity and that the primary star accretion rate is always about the same as the secondary star accretion rate. Recent observations of the binary HD 98800 BaBb, which has a polar circumbinary disc, have been used to determine the value of the $\rm H\alpha$ flux from the brighter component. From this value, we infer that the accretion rate is much lower than for typical T Tauri stars. The eccentric orbit of the outer companion HD 98800 A increases the accretion rate onto HD 98800 B by $\sim 20$ per cent after each periastron passage. Our hydrodynamical simulations are unable to explain such a low accretion rate unless the disc viscosity parameter is very small, $\alpha < 10^{-5}$. Additional observations of this system would be useful to check on this low accretion rate.
... The stars carved a central cavity, where we observe streamers and filaments of gas. Another multiple system that shows cavities and nested discs separated by low density regions is the GW Orionis triple stellar system (Kraus et al. 2020;Bi et al. 2020). Other similar examples are the binary BHB 2007 (Alves et al. 2019), in which a complex structure of filaments supply gas from the circum-binary disc to the circum-stellar discs and L1448 IRS3B (Reynolds et al. 2021), that is really young multiple stellar system in formation. ...
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Young multiple systems accrete most of their final mass in the first few Myr of their lifetime, during the protostellar and protoplanetary phases. Previous studies showed that in binary systems the majority of the accreted mass falls onto the lighter star, thus evolving to mass equalisation. However, young stellar systems often comprise more than two stars, which are expected to be in hierarchical configurations. Despite its astrophysical relevance, differential accretion in hierarchical systems remains to be understood. In this work, we investigate whether the accretion trends expected in binaries are valid for higher order multiples. We performed a set of 3D Smoothed Particle Hydrodynamics simulations of binaries and of hierarchical triples (HTs) embedded in an accretion disc, with the code Phantom. We identify for the first time accretion trends in HTs and their deviations compared to binaries. These deviations, due to the interaction of the small binary with the infalling material from the circum-triple disc, can be described with a semi-analytical prescription. Generally, the smaller binary of a HT accretes more mass than a single star of the same mass as the smaller binary. We found that in a HT, if the small binary is heavier than the third body, the standard differential accretion scenario (whereby the secondary accretes more of the mass) is hampered. Reciprocally, if the small binary is lighter than the third body, the standard differential accretion scenario is enhanced. The peculiar differential accretion mechanism we find in HTs is expected to affect their mass ratio distribution.
... GW Ori is a triple star system that includes a misaligned circumtriple disc. With ALMA observations, three dust rings which have different mutual inclinations (> 10 • ) to the stars have been identified (Bi et al. 2020;Kraus et al. 2020). An initially misaligned disc that is not at a stationary inclination around an eccentric orbit binary undergoes tilt oscillations, even if it is evolving towards coplanarity (Smallwood et al. 2019), and may evolve towards a more misaligned (polar) configuration with respect to the binary, such as in HD98800 (Kennedy et al. 2019). ...
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We investigate the orbital dynamics of circumbinary planetary systems with two planets around a circular or eccentric orbit binary. The orbits of the two planet are initially circular and coplanar to each other, but misaligned with respect to the binary orbital plane. The binary-planet and planet-planet interactions result in complex planet tilt oscillations. We use analytic models and numerical simulations to explore the effects of various values of the planet semi-major axes, binary eccentricity, and initial inclination. Around a circular orbit binary, secular tilt oscillations are driven by planet-planet interactions and are periodic. In that case, planets undergo mutual libration if close together and circulation if far apart with an abrupt transition at a critical separation. Around an eccentric orbit binary, secular tilt oscillations are driven by both planet-planet interactions and binary-planet interactions. These oscillations generally display more than one frequency and are generally not periodic. The transition from mutual planet libration to circulation is not sharp and there is a range of separations for which the planets are on orbits that are sometimes mutually librating and sometimes circulating. In addition, at certain separations, there are resonances for which tilt oscillations are complicated but periodic. For planets that are highly misaligned with respect to an eccentric orbit binary, there are stationary (non-oscillating) tilt configurations that are generalisations of polar configurations for the single planet case. Tilt oscillations of highly inclined planets occur for initial tilts that depart from the stationary configuration.
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Pleione is a Be star that is in a 218 day orbit with a low-mass binary companion. Recent numerical simulations have shown that a Be star disc can be subject to breaking when material is actively being fed into the inner parts of the disc. After breaking, the disc is composed of two rings: an inner ring that is anchored to the stellar equator and an outer ring that is free to nodally precess. A double ring disc may explain some of the observed variability in Pleione. We model the nodal precession of the outer disc ring that is driven by the companion on an observed timescale of $80.5\, \rm yr$. We find that the outer ring of a broken disc in a binary with an eccentricity of eb = 0.6 can precess on the observed timescale and have an outer radius that is in rough agreement with the observed disc size. An unbroken disc model cannot fit both the observed precession rate and disc size. Suppression of Kozai-Lidov driven disc eccentricity is more likely for a high binary eccentricity if the disc extends to the tidal truncation radius.
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Young multiple systems accrete most of their final mass in the first few Myr of their lifetime, during the protostellar and protoplanetary phases. Previous studies showed that in binary systems the majority of the accreted mass falls on to the lighter star, thus evolving to mass equalisation. However, young stellar systems often comprise more than two stars, which are expected to be in hierarchical configurations. Despite its astrophysical relevance, differential accretion in hierarchical systems remains to be understood. In this work, we investigate whether the accretion trends expected in binaries are valid for higher order multiples. We performed a set of 3D Smoothed Particle Hydrodynamics simulations of binaries and of hierarchical triples (HTs) embedded in an accretion disc, with the code Phantom. We identify for the first time accretion trends in HTs and their deviations compared to binaries. These deviations, due to the interaction of the small binary with the infalling material from the circum-triple disc, can be described with a semi-analytical prescription. Generally, the smaller binary of a HT accretes more mass than a single star of the same mass as the smaller binary. We found that in a HT, if the small binary is heavier than the third body, the standard differential accretion scenario (whereby the secondary accretes more of the mass) is hampered. Reciprocally, if the small binary is lighter than the third body, the standard differential accretion scenario is enhanced. The peculiar differential accretion mechanism we find in HTs is expected to affect their mass ratio distribution.
Article
We present hydrodynamical simulations to model the accretion flow from a polar circumbinary disc on to a high eccentricity (e = 0.78) binary star system with near unity mass ratio (q = 0.83), as a model for binary HD 98800 BaBb. We compare the polar circumbinary disc accretion flow with the previously studied coplanar case. In the coplanar case, the circumbinary disc becomes eccentric and the accretion alternates from being dominant on to one binary member to the other. For the polar disc case involving a highly eccentric binary, we find that the circumbinary disc retains its initially low eccentricity and that the primary star accretion rate is always about the same as the secondary star accretion rate. Recent observations of the binary HD 98800 BaBb, which has a polar circumbinary disc, have been used to determine the value of the $\rm H\alpha$ flux from the brighter component. From this value, we infer that the accretion rate is much lower than for typical T Tauri stars. The eccentric orbit of the outer companion HD 98800 A increases the accretion rate on to HD 98800 B by ∼20 per cent after each periastron passage. Our hydrodynamical simulations are unable to explain such a low accretion rate unless the disc viscosity parameter is very small, α < 10−5. Additional observations of this system would be useful to check on this low accretion rate.
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Aims. We studied the accretion disk of the archetypal eruptive young star FU Orionis with the use of mid-infrared interferometry, which enabled us to resolve the innermost regions of the disk down to a spatial resolution of 3 milliarcseconds (mas) in the L band, that is, within 1 au of the protostar. Methods. We used the interferometric instrument MATISSE/VLTI to obtain observations of FU Ori’s disk in the L , M , and N bands with multiple baseline configurations. We also obtained contemporaneous photometry in the optical (UBVRIr ′ i ′ ; SAAO and Konkoly Observatory) and near-infrared (JHK s ; NOT). Our results were compared with radiative transfer simulations modeled by RADMC -3 D . Results. The disk of FU Orionis is marginally resolved with MATISSE, suggesting that the region emitting in the thermal infrared is rather compact. An upper limit of ~1.3 ± 0.1 mas (in L ) can be given for the diameter of the disk region probed in the L band, corresponding to 0.5 au at the adopted Gaia EDR3 distance. This represents the hot, gaseous region of the accretion disk. The N -band data indicate that the dusty passive disk is silicate-rich. Only the innermost region of said dusty disk is found to emit strongly in the N band, and it is resolved at an angular size of ~5 mas, which translates to a diameter of about 2 au. The observations therefore place stringent constraints for the outer radius of the inner accretion disk. Dust radiative transfer simulations with RADMC -3 D provide adequate fits to the spectral energy distribution from the optical to the submillimeter and to the interferometric observables when opting for an accretion rate M ~ 2 × 10 ⁻⁵ M ⊙ yr ⁻¹ and assuming M * = 0.6 M ⊙ , Most importantly, the hot inner accretion disk’s outer radius can be fixed at 0.3 au. The outer radius of the dusty disk is placed at 100 au, based on constraints from scattered-light images in the literature. The dust mass contained in the disk is 2.4 × 10 ⁻⁴ M ⊙ , and for a typical gas-to-dust ratio of 100, the total mass in the disk is approximately 0.02 M ⊙ . We did not find any evidence for a nearby companion in the current interferometric data, and we tentatively explored the case of disk misalignment. For the latter, our modeling results suggest that the disk orientation is similar to that found in previous imaging studies by ALMA. Should there be an asymmetry in the very compact, inner accretion disk, this might be resolved at even smaller spatial scales (≤1 mas).
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The nonlinear behaviour of low-viscosity warped discs is poorly understood. We verified a nonlinear bending-wave theory, in which fluid columns undergo affine transformations, with direct 3D hydrodynamical simulations. We employed a second-order Godunov-type scheme, Meshless Finite Mass (MFM), and also the Smoothed Particle Hydrodynamics (SPH) method, with up to 128M particles. For moderate nonlinearity, MFM maintains well the steady nonlinear warp predicted by the affine model for a tilted inviscid disc around a central object with a quadrupole moment. However, numerical dissipation in SPH is so severe that even a low-amplitude nonlinear warp degrades at a resolution where MFM performs well. A low-amplitude arbitrary warp tends to evolve towards a nonlinear steady state. However, no such state exists in our thin disc with an angular semi-thickness H/R = 0.02 when the outer tilt angle is beyond about 14○. The warp breaks tenuously and reconnects in adiabatic simulations, or breaks into distinct annuli in isothermal simulations. The breaking radius lies close to the location with the most extreme nonlinear deformation. Parametric instability is captured only in our highest-resolution simulation, leading to ring structures that may serve as incubators for planets around binaries.
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We investigate the orbital dynamics of circumbinary planetary systems with two planets around a circular or eccentric orbit binary. The orbits of the two planet are initially circular and coplanar to each other, but misaligned with respect to the binary orbital plane. The binary-planet and planet-planet interactions result in complex planet tilt oscillations. We use analytic models and numerical simulations to explore the effects of various values of the planet semi-major axes, binary eccentricity, and initial inclination. Around a circular orbit binary, secular tilt oscillations are driven by planet-planet interactions and are periodic. In that case, planets undergo mutual libration if close together and circulation if far apart with an abrupt transition at a critical separation. Around an eccentric orbit binary, secular tilt oscillations are driven by both planet-planet interactions and binary-planet interactions. These oscillations generally display more than one frequency and are generally not periodic. The transition from mutual planet libration to circulation is not sharp and there is a range of separations for which the planets are on orbits that are sometimes mutually librating and sometimes circulating. In addition, at certain separations, there are resonances for which tilt oscillations are complicated but periodic. For planets that are highly misaligned with respect to an eccentric orbit binary, there are stationary (non-oscillating) tilt configurations that are generalisations of polar configurations for the single planet case. Tilt oscillations of highly inclined planets occur for initial tilts that depart from the stationary configuration.
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Context. Numerous theoretical studies of the stellar dynamics of triple systems have been carried out, but fewer purely empirical studies that have addressed planetary orbits within these systems. Most of these empirical studies have been for coplanar orbits and with a limited number of orbital parameters. Aims. Our objective is to provide a more generalized empirical mapping of the regions of planetary stability in triples by considering both prograde and retrograde motion of planets and the outer star; investigating highly inclined orbits of the outer star; extending the parameters used to all relevant orbital elements of the triple’s stars and expanding these elements and mass ratios to wider ranges that will accommodate recent and possibly future observational discoveries. Methods. Using N -body simulations, we integrated numerically the various four-body configurations over the parameter space, using a symplectic integrator designed specifically for the integration of hierarchical multiple stellar systems. The triples were then reduced to binaries and the integrations repeated to highlight the differences between these two types of system. Results. This established the regions of secular stability and resulted in 24 semi-empirical models describing the stability bounds for planets in each type of triple orbital configuration. The results were then compared with the observational extremes discovered to date to identify regions that may contain undiscovered planets.
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We analyse the evolution of a mildly inclined circumbinary disc that orbits an eccentric orbit binary by means of smoothed particle hydrodynamics (SPH) simulations and linear theory. We show that the alignment process of an initially misaligned circumbinary disc around an eccentric orbit binary is significantly different than around a circular orbit binary and involves tilt oscillations. The more eccentric the binary, the larger the tilt oscillations and the longer it takes to damp these oscillations. A circumbinary disc that is only mildly inclined may increase its inclination by a factor of a few before it moves towards alignment. The results of the SPH simulations agree well with those of linear theory. We investigate the properties of the circumbinary disc/ring around KH 15D. We determine disc properties based on the observational constraints imposed by the changing binary brightness. We find that the inclination is currently at a local minimum and will increase substantially before settling to coplanarity. In addition, the nodal precession is currently near its most rapid rate. The recent observations that show a reappearance of star B impose constraints on the thickness of the layer of obscuring material. Our results suggest that disc solids have undergone substantial inward drift and settling towards to disc mid-plane. For disc masses ∼0.001 M⊙, our model indicates that the level of disc turbulence is low (α ≪ 0.001). Another possibility is that the disc/ring contains little gas.
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An initially sufficiently misaligned low-mass protoplanetary disc around an eccentric binary undergoes damped nodal oscillations of tilt angle and longitude of ascending node. Dissipation causes evolution towards a stationary state of polar alignment in which the disc lies perpendicular to the binary orbital plane with angular momentum aligned to the eccentricity vector of the binary. We use hydrodynamic simulations and analytical methods to investigate how the mass of the disc affects this process. The simulations suggest that a disc with non-zero mass settles into a stationary state in the frame of the binary, the generalized polar state, at somewhat lower levels of misalignment with respect to the binary orbital plane, in agreement with the analytical model. Provided that discs settle into this generalized polar state, the observational determination of the misalignment angle and binary properties can be used to determine the mass of a circumbinary disc. We apply this constraint to the circumbinary disc in HD 98800. We obtain analytical criteria for polar alignment of a circumbinary ring with mass that approximately agree with the simulation results. Very broad misaligned discs undergo breaking, but the inner regions at least may still evolve to a polar state. The long-term evolution of the disc depends on the evolution of the binary eccentricity that we find tends to decrease. Although the range of parameters required for polar alignment decreases somewhat with increasing disc mass, such alignment appears possible for a broad set of initial conditions expected in protostellar circumbinary discs.
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