A Large Double-ring Disk Around the Taurus M Dwarf J04124068
+
2438157
Feng Long
(
龙
凤
)
1
,
2
,
31
, Bin B. Ren
(
任
彬
)
3
,
4
,
5
, Nicole L. Wallack
6
,
7
, Daniel Harsono
8
, Gregory J. Herczeg
(
沈
雷
歌
)
9
,
Paola Pinilla
10
, Dimitri Mawet
5
,
11
, Michael C. Liu
12
, Sean M. Andrews
2
, Xue-Ning Bai
13
, Sylvie Cabrit
4
,
14
,
Lucas A. Cieza
15
,
16
, Doug Johnstone
17
,
18
, Jarron M. Leisenring
19
, Giuseppe Lodato
20
, Yao Liu
21
, Carlo F. Manara
22
,
Gijs D. Mulders
23
,
24
, Enrico Ragusa
25
, Steph Sallum
26
, Yangfan Shi
9
, Marco Tazzari
27
, Taichi Uyama
28
,
29
,
30
,
Kevin Wagner
19
,
31
, David J. Wilner
2
, and Jerry W. Xuan
5
1
Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA;
fenglong@arizona.edu
2
Center for Astrophysics
|
Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA
3
Université Côte d
’
Azur, Observatoire de la Côte d
’
Azur, CNRS, Laboratoire Lagrange, F-06304 Nice, France
4
Université Grenoble Alpes, CNRS, Institut de Planétologie et d
’
Astrophysique
(
IPAG
)
, F-38000 Grenoble, France
5
Department of Astronomy, California Institute of Technology, MC 249-17, 1200 East California Boulevard, Pasadena, CA 91125, USA
6
Earth and Planets Laboratory, Carnegie Institution for Science, Washington, DC 20015, USA
7
Division of Geological & Planetary Sciences, California Institute of Technology, MC 150-21, 1200 East California Boulevard, Pasadena, CA 91125, US
A
8
Institute of Astronomy, Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
9
Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, People
ʼ
s Republic of China
10
Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
11
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
12
Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
13
Institute for Advanced Study and Department of Astronomy, Tsinghua University, 100084, Beijing, People
ʼ
s Republic of China
14
Sorbonne Université, Observatoire de Paris, Université PSL, CNRS, LERMA, F-75014 Paris, France
15
Instituto de Estudios Astrofísicos, Facultad de Ingeniería y Ciencias, Universidad Diego Portales, Av. Ejercito 441, Santiago, Chile
16
Millennium Nucleus on Young Exoplanets and their Moons
(
YEMS
)
, Chile
17
NRC Herzberg Astronomy and Astrophysics, 5071 West Saanich Rd, Victoria, BC, V9E 2E7, Canada
18
Department of Physics and Astronomy, University of Victoria, Victoria, BC, V8P 5C2, Canada
19
Steward Observatory, University of Arizona, 933 N Cherry Ave, Tucson, AZ 85721, USA
20
Dipartimento di Fisica, Universita Degli Studi di Milano, Via Celoria, 16, I-20133 Milano, Italy
21
Purple Mountain Observatory & Key Laboratory for Radio Astronomy, Chinese Academy of Sciences, Nanjing 210023, People
ʼ
s Republic of China
22
European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748 Garching bei München, Germany
23
Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal las Torres 2640, Peñalolén, Santiago, Chile
24
Millennium Institute for Astrophysics, Chile
25
Univ Lyon, Univ Lyon1, Ens de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574, F-69230 Saint-Genis-Laval, France
26
Department of Physics and Astronomy, University of California, Irvine, 4129 Frederick Reines Hall, Irvine, CA 92697-4575, USA
27
Institute of Astronomy, University of Cambridge, Madingley Road, CB3 0HA Cambridge, UK
28
Infrared Processing and Analysis Center, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, USA
29
NASA Exoplanet Science Institute, Pasadena, CA 91125, USA
30
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
Received 2023 January 30; revised 2023 March 16; accepted 2023 March 20; published 2023 May 24
Abstract
Planet formation imprints signatures on the physical structures of disks. In this paper, we present high-resolution
(
∼
50 mas, 8 au
)
Atacama Large Millimeter
/
submillimeter Array observations of 1.3 mm dust continuum and CO
line emission toward the disk around the M3.5 star 2MASS J04124068
+
2438157. The dust disk consists of only
two narrow rings at radial distances of 0
47 and 0
78
(
∼
70 and 116 au
)
, with Gaussian
σ
widths of 5.6 and 8.5 au,
respectively. The width of the outer ring is smaller than the estimated pressure scale height by
∼
25%, suggesting
dust trapping in a radial pressure bump. The dust disk size, set by the location of the outermost ring, is signi
fi
cantly
larger
(
by 3
σ
)
than other disks with similar millimeter luminosity, which can be explained by an early formation of
local pressure bump to stop radial drift of millimeter dust grains. After considering the disk
’
s physical structure and
accretion properties, we prefer planet
–
disk interaction over dead zone or photoevaporation models to explain the
observed dust disk morphology. We carry out high-contrast imaging at the
¢
L
band using Keck
/
NIRC2 to search
for potential young planets, but do not identify any source above 5
σ
. Within the dust gap between the two rings, we
reach a contrast level of
∼
7 mag, constraining the possible planet below
∼
2
–
4
M
Jup
. Analyses of the gap
/
ring
properties suggest that an approximately Saturn-mass planet at
∼
90 au is likely responsible for the formation of the
outer ring, which can potentially be revealed with JWST.
Uni
fi
ed Astronomy Thesaurus concepts:
Protoplanetary disks
(
1300
)
;
Planetary-disk interactions
(
2204
)
;
Coronagraphic imaging
(
313
)
;
Planetary system formation
(
1257
)
Supporting material:
data behind
fi
gure
1. Introduction
Our observational understanding of planet formation in
circumstellar disks has greatly advanced in the past decade,
largely due to the advent of the Atacama Large Millimeter
/
submillimeter Array
(
ALMA
)
. On one hand, near-complete
The Astrophysical Journal,
949:27
(
14pp
)
, 2023 May 20
https:
//
doi.org
/
10.3847
/
1538-4357
/
acc843
© 2023. The Author
(
s
)
. Published by the American Astronomical Society.
31
NASA Hubble Fellowship Program Sagan Fellow.
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
ALMA disk surveys in a number of star-forming regions with
moderate spatial resolution have revealed important trends
among the global stellar and disk properties, for example,
suggesting higher mass stars host more massive disks thus with
larger potential to form giant planets
(
e.g., Ansdell et al.
2016
;
Pascucci et al.
2016
; Ruíz-Rodríguez et al.
2018
; Cazzoletti
et al.
2019
, see also pre-ALMA results in Andrews et al.
2013
)
.
On the other hand, high-resolution imaging toward a targeted
group of disks has shown that large and massive disks are often
associated with substructures, mostly seen as gaps and rings
(
e.g., Partnership et al.
2015
; Andrews et al.
2018a
; Long et al.
2018
; Cieza et al.
2021
)
, but also as arcs and spiral arms
(
van
der Marel et al.
2013
; Huang et al.
2018b
; Dong et al.
2018
)
.
Given the ubiquitous nature of planetary systems in the Galaxy
(
e.g., Winn & Fabrycky
2015
)
, the frequent appearance of disk
substructures suggests that they might be relevant to the
process of planet formation, though establishing the direct
connection between a disk feature and a planet is so far
challenging, considering the complex physics involved in disk
and planet evolution
(
e.g., Nayakshin
2020
)
.
These substructures provide an immediate observational
solution to the long-standing problem in dust evolution and
planet formation
—
the so-called radial drift barrier
(
Wei-
denschilling
1977
; Nakagawa et al.
1986
)
. In the default
assumption of a smooth gas disk, millimeter-sized particles
tend to move toward the
(
global
)
pressure maximum
(
the inner
disk region
)
due to aerodynamic drag and quickly deplete the
outer disk, in contradiction to early observations of large
millimeter disks. Those recently identi
fi
ed dust rings
/
gaps, as
regions of material accumulation
/
depletion, suggest the
presence of local pressure maxima that stop the inward
migration of particles and sustain them locally
(
Pinilla et al.
2012b
)
. For this reason, these are also favorable places of
planet formation through planetesimal and
/
or pebble accretion
(
e.g., Cummins et al.
2022
; Jiang & Ormel
2022
)
.
Pressure bumps can result from planet
–
disk interactions,
where the planet motion carves the disk material and builds
some over-dense regions outside its orbit
(
e.g., Rice et al.
2006
;
Dodson-Robinson & Salyk
2011
; Pinilla et al.
2012a
; Zhu et al.
2012
; Paardekooper et al.
2022
)
. Many other mechanisms,
including a variety of
(
magneto-
)
hydrodynamic instabilities,
have also been proposed to produce pressure modulations and
then trap particles
(
see references in Andrews
2020
; Bae et al.
2022
)
. Though, in most cases, the origin of disk substructures
is still debated, they are likely fundamental to the planet-
formation process. Thus, characterizing disk substructures in
different star and disk environments is crucial in building a
complete view of planet formation.
Currently, most high-resolution observations are designed to
target disks around early-type stars
(
M3 or earlier
)
and
/
or
bright disks
(
that also mostly surround solar-mass stars, see
references above
)
. Though gaps and rings have been reported
in the disks of a few bright M dwarfs
(
Hashimoto et al.
2021
;
Kurtovic et al.
2021
; Pinilla
2022
)
, our generic knowledge
about dust substructure properties in disks around these late-
type stars is still missing. In addition, we expect that the dust
radial drift problem is even more severe for disks around lower
mass stars, as the drift velocity is faster when surrounding
lower mass stars
(
μ
*
*
vLM
drift
14
, which is mostly
controlled by stellar mass in the low-mass regime, Pinilla
et al.
2013
)
. To understand how M-dwarf disks overcome the
radial drift barrier and how substructure properties vary across
stellar mass, we have conducted a high-resolution ALMA
survey toward a number of M-dwarf disks in the Taurus star-
forming region
(
Y. Shi et al. 2023, in preparation
)
.
This paper reports on the interesting object 2MASS
J04124068
+
2438157 in our M-dwarf disk sample, which
hosts a very extended dust disk composed of two dust rings.
We arrange the paper as follows. Section
2
provides a detailed
summary of the source properties. Section
3
describes the
ALMA and Keck observations, as well as their corresponding
data reduction. Section
4
presents our characterization of the
disk morphology, and Section
5
discusses this target in the
context of other disks and the origin of the dust rings. A
summary is then given in Section
6
.
2. Source Properties
The object 2MASS J04124068
+
2438157
(
hereafter
2M041240
)
was
fi
rst identi
fi
ed as a member of Taurus in a
search for objects with mid-IR excess emission in the WISE
survey
(
Rebull et al.
2011
, as Class II disks
)
. Membership is
con
fi
rmed with Gaia DR2 proper motions
(
Galli et al.
2019
)
.
The Gaia EDR3 parallax leads to a distance of 148.7
±
0.5 pc
(
Gaia Collaboration
2022
)
.
We adopt the spectral type of M3.5
32
and the extinction
A
J
=
0.37 from the compilation of Taurus members by Esplin
& Luhman
(
2019
)
. The spectral type corresponds to an
effective temperature of
∼
3300 K
(
Herczeg & Hillen-
brand
2014
)
, consistent with temperatures measured from
LAMOST spectra
(
Luo et al.
2022
)
. The luminosity of
2M041240 is 0.153
L
e
, measured from the 2MASS
J
-band
magnitude of 11.151, the bolometric correction from Pecaut &
Mamajek
(
2013
)
, and zero-point
fl
ux of 3.013
×
10
35
erg s
−
1
.
The temperature and luminosity lead to a radius of 1.20
R
e
and
correspond to a mass of 0.25
M
e
and an age of 1.6 Myr using
the Baraffe et al.
(
2015
)
and spotless Somers et al.
(
2020
)
models. When relying on Feiden
(
2016
)
magnetic models of
pre-main sequence evolution and the Somers et al.
(
2020
)
models for a young star with 50% spot coverage, we obtain a
mass of 0.38
M
e
and an age of 4.4 Myr, and 0.42
M
e
and
4.7 Myr, respectively. The
∼
0.4
M
e
estimate is adopted here,
given the consistency of those evolutionary tracks with the
dynamical measurement of stellar mass for two M4 members of
Taurus
(
Pegues et al.
2021
)
. The sizes of dust disks around
most stars are well within 100 au, which also gradually
decrease with stellar mass
(
Hendler et al.
2020
)
, thus the
fi
nding of an
∼
120 au disk
(
see results in Section
4.1
)
around
this mid-M star is rather surprising and studied in detail here.
The object 2M041240 is actively accreting, as indicated
from the H
α
equivalent widths of 42 and 46
Å
measured by
LAMOST on two different nights
(
Luo et al.
2022
)
. The He
I
λ
6678 equivalent width is 0.64
Å
in a Keck
/
HIRES high-
resolution optical spectrum obtained on UT 2019 November 29
(
PI: L. Hillenbrand
)
. This equivalent width translates to a
fl
ux
of
∼
1.3
×
10
−
15
erg cm
−
2
s
−
1
, calculated based on the
continuum
fl
ux obtained by
fl
ux-calibrating a low-resolution
optical spectrum obtained from UH88
/
SNIFS
(
see description
in Guo et al.
2018
)
with Gaia DR3 spectrophotometry. This
fl
ux should be robust to continuum variability, since the Gaia
32
The stellar parameters adopted for this paper were based on measurements
from the literature. In Y. Shi et al.
(
2023, in preparation
)
, we are reevaluating
the stellar properties with a new spectral analysis and measure a spectral type of
M4.3, which, if adopted here, would decrease the 50% spotted mass to
0.30
M
e
. The main results from this paper are unchanged.
2
The Astrophysical Journal,
949:27
(
14pp
)
, 2023 May 20
Long et al.
R
P
-band
fl
ux varies by
∼
0.04 mag
(
ignoring one outlier, Gaia
Collaboration
2022
)
. After correcting for extinction and
distance, the line luminosity is 2.4
×
10
−
6
L
e
, which
corresponds to an accretion luminosity of 0.012
L
e
(
from the
correlations of Alcalá et al.
2017
)
and a mass accretion rate of
∼
1.4
×
10
−
9
M
e
yr
−
1
. This accretion rate is likely variable, as
the H
α
equivalent width in the epoch of Keck observation is
30
Å
, lower than those measured in the two epochs with
LAMOST. The
[
O
I
]
λ
6300 line has an equivalent width of
1.34
Å
and a FWHM of 32 km s
−
1
, indicating the presence of a
disk wind
(
e.g., Banzatti et al.
2019
)
.
3. Observations
3.1. ALMA Observations
The object 2M041240 was observed with ALMA Band 6
receivers on UT 2021 August 27, during the Return to
Operations phase after the Covid19 shutdown, as part of
program 2019.1.00566.S
(
PI: G. Herczeg
)
. The observations
were performed with 39 antennas spanning baselines from
92 m to 10.8 km, with a total on-source time of 16.8 minutes.
The receivers were con
fi
gured into four spectral windows
(
SPWs
)
, including two continuum SPWs centered at 217 and
234.4 GHz, each with a bandwidth of 1.875 GHz. The two
remaining SPWs targeted
12
CO,
13
CO, and C
18
O
J
=
2
−
1
lines at a channel spacing of 0.244 MHz
(
∼
0.3 km s
−
1
)
.
The raw visibilities were
fi
rst pipeline calibrated using the
speci
fi
ed CASA version 6.1.1
(
CASA Team et al.
2022
)
to
fl
ag
problematic data segments, correct for bandpass responses, set
absolute
fl
ux scales, and solve for complex gain variations. We
inspected the calibrated visibilities and identi
fi
ed some residual
features of atmospheric absorption correction around channel
500 in the 234.4 GHz SPW. The corresponding channel range
of 400
–
600 was then
fl
agged. Finally, one round of phase-only
self-calibration
(
solint =
‘‘
inf
’’
)
was performed. As the
improvement of continuum image quality is subtle
(
∼
10% in
peak S
/
N
)
, self-calibration solutions were not applied to the
line SPWs.
Continuum images at a mean frequency of 225.6 GHz
(
1.3 mm
)
were generated with the
tclean
task. To better
visualize the faint disk millimeter emission, we produced two
images with synthesized beam sizes of 0
06
×
0
05
(
PA
=
17
°
)(
robust = 0.5
)
and 0
12
×
0
12
(
PA
=
26
°
)
(
robust = 2
)
, where uv taper is applied for a more circular
beam.
33
The 1
σ
noise levels computed from nearby emission-
free regions in the images are
∼
32 and 35
μ
Jy beam
−
1
,
respectively. The three CO lines were imaged at a velocity
resolution of 0.4 km s
−
1
with a coarser beam size of 0
2,
reaching a 1
σ
noise level of
∼
5
–
6 mJy beam
−
1
in individual
channels.
3.2. Keck
/
NIRC2 High-contrast Imaging Observations
We used the Keck
/
NIRC2 vortex coronagraph
(
Mawet
et al.
2017
; Serabyn et al.
2017
)
to suppress central starlight
and observed the surroundings of 2M041240 in the
¢
L
band
(
∼
3.78
μ
m
)
on UT 2021 October 27 under the Keck program
H290
(
PI: M. Liu
)
. The Gaia DR3
R
P
-band magnitude of 13.27
for 2M041240
(
Gaia Collaboration
2022
)
is too faint for
existing Shack-Hartmann wave-front sensors that perform
adaptive optics corrections in visible wavelengths to ef
fi
ciently
conduct high-contrast imaging for companions. In comparison,
its
H
-band magnitude of 10.38
±
0.02
(
Cutri et al.
2003
)
situates within the operation range of the pyramid wave-front
sensor that performs wave-front sensing in
H
-band
(
∼
1.63
μ
m;
Bond et al.
2020
)
at the Keck II telescope. The single
integration time is 0.5 s and each exposure frame comprises 60
integrations. During the observation, we obtained 105 frames
that cover a parallactic angle change of 97
°
.5 to perform angular
differential imaging
(
ADI
)
. The total on-target integration time
is 3150 s.
The raw exposures of 2M041240 from Keck
/
NIRC2 require
pre- and post-processing to reveal the surroundings that have
been overwhelmed by starlight. We followed Xuan et al.
(
2018
)
, which customized the
VIP
package
(
Gomez Gonzalez
et al.
2017
)
, to perform pre-processing of the data, including
fl
at-
fi
elding, bad-pixel removal, background removal, and
image centering. We then performed ADI post-processing
using the principal-component-analysis-based Karhunen
–
Loève image projection algorithm
(
KLIP; Amara &
Quanz
2012
; Soummer et al.
2012
)
to remove the central
starlight and speckles. In the processing of high-contrast
imaging data, ADI and KLIP can introduce reduction artefacts
including self-subtraction and over-subtraction, respectively.
These artefacts can vary with different reduction parameters,
including the number of KLIP components, the rotation angle,
etc. To address these artefacts and explore the best limits for
our NIRC2 observations, we followed the procedures outlined
in Wallack et al.
(
2023
)
and varied these reduction parameters
to obtain the deepest contrast limits. Speci
fi
cally, we generated
5
σ
contrast curves using
VIP
(
Gomez Gonzalez et al.
2017
)
for
different combinations of inner and outer image mask sizes and
number of principal components, accounting for the effects of
small sample statistics
(
Mawet et al.
2014
)
. We then compared
our achieved contrast across all of the combinations of mask
sizes and principal components, and determined the best
contrast for an angular separation from the star. We performed
the contrast calculation with a 1 pixel step
(
9.971 mas
34
)
to
generate an optimal contrast curve for the entire image.
4. Results
4.1. A Disk with Two Dust Rings
The 1.3 mm continuum image of the 2M041240 disk at a
resolution of 0
06 is shown in the upper left panel of Figure
1
.
As the peak emission is only detected at
∼
6
σ
level, a radial
intensity pro
fi
le is created by averaging the emission along the
azimuthal direction to boost the signi
fi
cance of faint emission
features
(
displayed in Figure
1
alongside the image
)
. The image
deprojection adopts an inclination angle of 16
°
.0 and position
angle of 122
°
.7
(
derived from visibility modeling below
)
. All of
the emission is concentrated in two narrow dust rings, peaking
at 0
47 and 0
78
(
70 and 116 au, hereafter B70 and B116
)
,
with the inner ring narrower and fainter than the outer one.
Both rings are optically thin, with
τ
∼
0.03
–
0.04, assuming a
dust temperature of 15
–
20 K
(
e.g., Andrews et al.
2013
)
,in
contrast to many dust rings that appear to have optical depths of
∼
0.6 but are probably optically thick with scattering
(
Huang
et al.
2018a
)
. The wide gap separating the two rings is nearly
empty, and the average emission does not exceed three
33
The Gaussian uv tapers are 0
04
×
0
0
(
PA
=
−
50
°
)
and 0
08
×
0
04
(
PA
=
−
65
°
)
for images with 60 and 120 mas resolution, respectively.
34
https:
//
github.com
/
jluastro
/
nirc2_distortion
/
wiki
3
The Astrophysical Journal,
949:27
(
14pp
)
, 2023 May 20
Long et al.
times the local noise level, where the noise level is estimated as
the 1
σ
scatter along the whole azimuth divided by the square
root of beam numbers across the region and shown as the
shaded region in Figure
1
.
A better visualization of the morphology of dust emission is
provided by the image with a coarser resolution of 0
12
(
lower
left panel of Figure
1
)
. Some dusty
fi
laments
(
at
∼
3
σ
level
)
seem to emerge and connect the inner and outer rings, while the
low surface brightness of the ring emission suggests that these
features are likely due to imaging artifacts
(
but see a claimed
dusty
fi
lament across the gap in HD 135344B, Casassus et al.
2021
)
. Likewise, the clumpiness of the dust rings could be
attributed to the low sensitivity of the observations and
imperfect uv sampling. To better demonstrate any azimuthal
emission variations, we created intensity pro
fi
les along the
azimuthal direction by averaging emission within a radial
annulus of 0
44
–
0
52 and 0
72
–
0
82 for B70 and B116,
respectively. Around the azimuthal angle of 300
°
(
see the
azimuthal angle conversion in Figure
1
)
, both rings exhibit a
drop of dust emission by a factor of two compared with the
averaged ring emission. It is unclear if the faintness of this
azimuth in both rings shares a common origin
(
e.g., inner disk
shadowing, though the inner disk of 2M041240 lacks large
grains that can emit predominantly at millimeter wavelength
)
,
as such a de
fi
cit of dust emission is also seen around 140
°
but
only in the B70 ring. Small-scale azimuthal asymmetries in
dust rings have been predicted in hydrodynamic simulations
from a number of instabilities
(
e.g., Huang et al.
2020b
;Bi&
Fung
2022
; Lehmann & Lin
2022
)
. Observational evidence of
such instabilities would, however, require deep integration for
high-signi
fi
cance detection of asymmetries in dust rings.
To quantify the dust emission morphology and disk geometry,
we performed model
fi
tting in the visibility domain. We adopted
an axisymmetric model with two Gau
ssian rings, representing the
two peaks in the radial pro
fi
le, which can be expressed as
⎡
⎣
⎢
⎤
⎦
⎥
⎡
⎣
⎢
⎤
⎦
⎥
ss
=-
-
+-
-
()
()
( )
()
Ir A
rR
A
rR
exp
2
exp
2
,1
1
1
2
1
2
2
2
2
2
2
where
A
i
,
R
i
, and
σ
i
are the amplitude, peak location, and width
for individual rings, respectively. Four additional disk
geometry parameters
(
inclination
i
, position angle PA, and
offsets from the phase center
Δ
R.A.
and
Δ
decl.
)
were also
included in the
fi
tting. The model visibilities are then calculated
Figure 1.
Top left: Continuum emission image of the 2M041240 disk at 1.3 mm with a beam size of 0
06
×
0
05. The synthesized beam shape is shown in the
bottom-left corner of the panel. White contours are at levels of 3,5
σ
. Top right: Azimuthally averaged radial intensity pro
fi
le based on image to the left
(
after
deprojection
)
. The Gaussian pro
fi
le in the bottom-right corner shows the FWHM of the synthesized beam. Bottom left: Continuum emission image at 1.3 mm with a
beam size of 0
12. White contours are at levels of 3,5,7
σ
. The azimuthal angle conversion is shown in the bottom right corner. Bottom right: Azimuthal intensity
pro
fi
les at the two dust-ring locations using the image to the left. The horizontal shaded regions mark the 1
σ
scatter of dust emission within the ring, centered at the
averaged ring intensity.
4
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949:27
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)
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Long et al.
through Hankel transformation
(
Pearson
1999
)
and sampled at
the same observed spatial frequencies. The comparison of
model and data visibilities uses a Gaussian likelihood
c
μ-
(
)
exp
2
2
, where
c
=
å
-
∣( )
( )∣
Vuv V uv w
,,
kk
kk k
2
obs
mod
2
,
with
w
k
as the observed visibility weights. We assumed
uniform priors for the
fi
tted parameters and explored the
parameter space with 50 walkers and 5000 steps using a
Markov Chain Monte Carlo
(
MCMC
)
method
(
emcee
,
Foreman-Mackey et al.
2013
)
. As the number of steps largely
exceeds the autocorrelation time, which is on the order of 100
steps, the MCMC chains are believed to have reached a
stationary state.
35
The
fi
nal adopted parameters are summarized
in Table
1
, as the median values of the posterior distributions
(
computed from the last 1000 steps of the chains
)
, with
uncertainties estimated from the 16th and 84th percentiles.
Figure
2
compares the best-
fi
t model to the data. Our adopted
model reproduces the real part of the deprojected and azimuthally
averaged data visibilities reaso
nably well. The imaginary part
should be clustered around zero for axisymmetric emission; the
non-zero
fl
uxes in the short baselines
suggest the presence of
some non-axisymmetric struct
ures on large scales, which our
observations may not capture very well
(
the maximum recover-
able scale based on the
fi
fth percentile of the baseline lengths is
only 0
6
)
. The model and residual images, created with the same
tclean
parameters as the data image, are also shown in
Figure
2
. No residual emission exceeds 5
σ
. Interestingly, there is
some 4
σ
residual emission within the dust gap
(
between B70 and
B116
)
, as part of the aforementioned dust
fi
lament. As there is
other residual emission at similar detection signi
fi
cance, con
fi
rm-
ing that the emission within the gap is real would require deeper
observations. Similar to the da
ta image, the model image also
exhibits negative
fl
uxes in the inner cavity
(
see bottom right panel
in Figure
2
)
, suggesting that this feature is likely related to the
sparse sampling in the uv space among the short baseline range.
The clumpiness in the rings is probably attributed to both the
sparse uv coverage
(
see the model image
)
and noise.
The inner ring B70 has a Gaussian width
(
σ
)
of 38 mas
(
FWHM of 90 mas
)
,
∼
40% narrower than B116. The
integrated
fl
ux for each ring is also listed in Table
1
; the inner
ring is a factor of about four fainter
(
in total
fl
ux
)
. Assuming a
dust temperature of 20 K
36
and the DSHARP opacity of
κ
1.3 mm
=
1.9 cm
2
g
−
1
for a maximum grain size of 1 mm
37
(
Birnstiel et al.
2018
)
, we calculate the dust masses of 2.5
±
0.2
and 9.6
±
0.2
M
⊕
for B70 and B116, respectively. The
continuum disk size estimated from the model intensity pro
fi
le
is 0
85
±
0
003
(
126.4
±
4.5 au
)
when adopting the effective
disk size de
fi
nition at 90% fractional luminosity
(
Tripathi et al.
2017
,or0
80
±
0
002 at 68%, slightly beyond the peak of the
outer ring
)
.
4.2. Dust Versus Gas Distributions
Three CO isotopologue lines were included in our observa-
tions. Emission from
12
CO and
13
CO
J
=
2
−
1 lines is clearly
seen in channel maps within a narrow velocity range of
5
–
8kms
−
1
(
Figure
A2
)
, mostly tracing the Keplerian disk
rotation, though the central channels
(
around the systemic
velocity of
∼
7kms
−
1
)
are cloud contaminated. The integrated
line
fl
uxes are 1.01
±
0.12 and 0.55
±
0.11 Jy km s
−
1
for
12
CO
and
13
CO lines, respectively, estimated within a circular
aperture in radius of 2
0 over the velocity range of
5
–
8kms
−
1
. The uncertainty is measured as the standard
deviation of line
fl
uxes from 50 randomly distributed apertures
with the same extraction area and velocity range outside the
disk emission region. For the C
18
O line, we obtain a line
fl
ux
upper limit
(
3
σ
)
of 0.2 Jy km s
−
1
.
Figure
3
compares the radial pro
fi
les of CO gas and
millimeter dust emission. The line radial pro
fi
les were extracted
from the peak intensity maps
(
eighth moment
)
adopting the
same disk geometry parameters as the continuum emission for
image deprojection.
38
Within the dust cavity, line emission is
clearly detected, but both CO lines exhibit a drop in emission
toward the inner region. The identi
fi
ed peak emission locations
are 0
24 and 0
36 for the
12
CO and
13
CO lines, respectively,
though the gas cavity sizes may be affected by foreground
cloud absorption. CO emission is con
fi
ned to within 2
0 from
the disk center, resulting in a low CO-to-millimeter disk size
ratio
(
about 2, see Long et al.
(
2022a
)
for this size ratio in a
collection of disks
)
. As the maximum recoverable scale in this
observation is only 0
6
(
based on the
fi
fth percentile of the
baseline lengths
)
, faint line emission on larger scales might be
fi
ltered out.
5. Discussion
5.1. Context with other Disks
Previous disk population studies have revealed a general
trend that more massive stars host brighter disks, though
associated with signi
fi
cant scatter
(
e.g., Andrews et al.
2013
;
Ansdell et al.
2016
; Pascucci et al.
2016
)
. The top panel of
Figure
4
compares 2M041240 with other Taurus members in
the
M
*
−
L
mm
plane, where millimeter
fl
uxes for other Taurus
disks are taken from Andrews et al.
(
2013
)
and updated with
Table 1
Dust Disk Model Results
Ring Number
Flux
Ring Location
Ring Width
(
σ
)
incl.
PA
Δ
R.A.
Δ
decl.
(
mJy
)(
′′
)(
′′
)(
°
)(
°
)(
′′
)(
′′
)
#
1
(
B70
)
3.3
±
0.3
0.472
±
0.004
0.038
±
0.006
16.0
±
1.1
122.6
±
4.3
0.003
±
0.002
−
0.001
±
0.002
#
2
(
B116
)
12.7
±
0.3
0.782
±
0.002
0.058
±
0.003
Note.
In the
fi
tting, we assumed the same inclination, position angle, and phase center offsets for both rings. The disk total
fl
ux should be the sum of the two rings. A
recent SMA observation suggests a total
fl
ux of 20
±
2 mJy
(
Liu, Terada et al., private comm.
)
35
We note that other approaches, for example, the rank-normalized split-R
diagnostic
(
Vehtari et al.
2021
)
, have been suggested to check the MCMC
convergence.
36
Here we adopt the widely used dust temperature of 20 K, but disks around
lower mass stars could be cooler. Dust mass will be higher by
∼
50% if
assuming 15 K.
37
This is a reasonable assumption based on the dust fragmentation barrier
(
see
Equation
(
8
)
in Pinilla et al.
2020
)
. A large source of uncertainty in dust opacity
also relies on the unknown properties of grain composition.
38
Radial pro
fi
les derived from moment 0 maps show similar variations.
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The Astrophysical Journal,
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Long et al.
new ALMA measurements
39
when available
(
Ward-Duong
et al.
2018
; Akeson et al.
2019
; Long et al.
2019
)
. We also
recalculate the stellar masses using the spot models
(
with 50%
spot coverage
)
of Somers et al.
(
2020
)
to be consistent with our
adoption of 0.4
M
e
for 2M041240. The disk around 2M041240
falls within the top 10% of millimeter brightness in the group
of mid-M-dwarf disks in Taurus
(
disks around stars of
0.3
–
0.5
M
e
)
, a factor of
fi
ve brighter than the median
L
mm
(
∼
3 mJy
)
in this group. However, when compared to other
disks with known dust substructures in Taurus
(
Long et al.
2018
; Kurtovic et al.
2021
)
and other young clusters
(
Huang
et al.
2018a
; Cieza et al.
2021
)
, the disk around 2M041240 lies
in the very faint end
(
Figure
4
)
. In particular, we note that the
three disks around very low-mass stars
(
M5
)
with substructures
in Kurtovic et al.
(
2021
)
have
L
mm
comparable to 2M041240.
As these early high-resolution disk surveys have often selected
bright disks, the detection of dust rings in 2M041240 suggests
that substructures might also be prevalent in faint disks around
low-mass stars, emphasizing the potentially ubiquitous nature
of disk substructures.
40
Systematic high-resolution millimeter
imaging surveys of faint disks are needed to determine if
substructure is common.
Disks with large inner cavities are typically brighter and
have a much shallower
M
*
−
L
mm
relation
(
equivalent to
M
*
−
M
d
used in Pinilla et al.
2018
)
than that from the full disk
populations. With an inner cavity of
∼
70 au, the 2M041240
disk deviates signi
fi
cantly
(
fainter by
∼
0.5 dex
)
from the
relation reported in Pinilla et al.
(
2018
)
for inner cavity disks.
Dust rings are widely interpreted as pressure bumps that trap
particles locally and eliminate the loss of particles from radial
drift. In an attempt to understand the observed stellar mass and
disk brightness correlations, Pinilla et al.
(
2020
)
found that the
correlations established from the full disk sample in a number
Figure 2.
Top left: The deprojected and binned visibilities as a function of baseline length for the data and the axisymmetric model. Top right: The model radial
intensity pro
fi
le. Bottom: Comparisons of the data, model, and residual in the image plane, constructed with the same
tclean
parameters. The two ring locations are
marked out in the residual map, with black contours at 3 and 4
σ
. The comparison of data and mode radial pro
fi
les is shown in the rightmost panel to demonstrate the
match in the central depression in the image with the observed uv coverage.
Figure 3.
Azimuthally averaged radial intensity pro
fi
les for CO lines from the
deprojected peak intensity maps. The shaded regions mark the 1
σ
scatter at
each radial bin divided by the square root of the number of beams across the
bin. The continuum emission pro
fi
le extracted from an image with the same
beam size as the line data is shown for comparison. The color ticks at the top of
the
fi
gure denote the peak emission location for each tracer.
39
If new measurements are only available at 0.89 mm, we scaled them to
1.3 mm using a spectral index of 2.2
(
Andrews
2020
)
.
40
Substructures have also been found in disks around brown dwarfs
(
e.g.,
ISO-Oph 2B, González-Ruilova et al.
2020
)
.
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