星形成ゼミ
担当：SFN#341 24-28
2021/06/25
総研大 D2 竹村英晃

SFN#341 24-28
24. Thermal Wave Instability as an Origin of Gap and Ring Structures inProtoplanetary Disks
25. Multicolor Variability of Young Stars in the Lagoon Nebula: Driving
Causes and Intrinsic Timescales
26. Tree-based solvers for adaptive mesh refinement code FLASH - II:radiation transport module TreeRay
27. No impact of core-scale magnetic field, turbulence, or velocity
gradient on sizes of protostellar disks in Orion A

28. TIMES I: a Systematic Observation in Multiple Molecular Lines Toward theOrion A and Ophiuchus Clouds

arXiv:2105.13852v1 [astro-ph.EP] 28 May 2021

3 University Observatory, Faculty of Physics, Ludwig-Maximilians-Universität München, Scheinerstr. 1, 81679 Munich, Germany

•
•

•
•
•
•

4 Exzellenzcluster ORIGINS, Boltzmannstr. 2, D-85748 Garching, Germany

Thermal Wave Instability as an Origin of Gap and Ring Structures(Received April 1, 2021; Revised May 6, 2021; Accepted May 28, 2021)
in Protoplanetary Disks
Submitted to ApJL
Takahiro Ueda, Mario Flock, Tilman Birnstiel
ABSTRACT
Recent millimeter and infrared observations have shown that gap and ring-like structures are common
in both dust thermal emission and scattered-light of protoplanetary disks. We investigate the impactof the so-called Thermal Wave Instability (TWI) on the millimeter and infrared scattered-light imagesof disks. We perform 1+1D simulations of the TWI and confirm that the TWI operates when the disk
is optically thick enough for stellar light, i.e., small-grain-to-gas mass ratio of & 0.0001. The mid-planetemperature varies as the waves propagate and hence gap and ring structures can be seen in bothmillimeter and infrared emission. The millimeter substructures can be observed even if the disk is fully
optically thick since it is induced by the temperature variation, while density-induced substructures
would disappear in the optically thick regime. The fractional separation between TWI-induced ringand gap is r/r ⇠ 0.2–0.4 at ⇠ 10–50 au, which is comparable to those found by ALMA. Due tothe temperature variation, snow lines of volatile species move radially and multiple snow lines areobserved even for a single species. The wave propagation velocity is as fast as ⇠ 0.6 au yr 1 , which
can be potentially detected with a multi-epoch observation with a time separation of a few years.

原始惑星系円盤のミリ波と赤外線の観測において、Thermal
Wave Instability（TWI）が与える影響を、
Keywords: protoplanetary disks — planets and satellites: formation
1+1Dシミュレーションで調べた。
1. INTRODUCTION

tures have been detected even at wavelengths where
the disk is fully
optically
thick (e.g., Carrasco-González
円盤が星の輻射について光学的に厚い場合（small-grain-to-gas
mass
ratio≥0.0001のときなど）、TWI
The recent ALMA observations have revealed that axet al. 2019; Macias et al. 2021).
isymmetric gap and ring structures are common in theがはたらくようになり、ミリ波と赤外線の両方でギャップを見られるようになる。
The recent infrared observations have shown that the
dust continuum emission of protoplanetary disks (Angap and ring-like structures are also common in scatギャップは温度の違いによって見られるので、光学的に厚い場合にも見られる。
drews et al. 2018). The origin of these structures istered light images (Avenhaus et al. 2018; Garufi et al.
still unclear, but several formation mechanisms have⁄𝑟~ 0.2-0.4でALMAの観測結果と整合的。
リングとギャップの間隔は10-50auの位置において、∆𝑟2018).
Although it is unclear if the substructures inbeen proposed such as dust filtering associated with ascattered light are associated with the (sub-)millimeter
planet-induced gap (e.g.,lineが移動し、単一の物質においても複数のsnow
Pinilla et al. 2012; Dipierro
揮発性の物質のsnowlineが生じることになる。
substructures,theprevalenceof substructures in bothet al. 2015), snow lines (Zhang et al. 2015; Okuzumi
dust and gas disk raises the questions how these sub波の伝播速度は~yr-1で、multi-epoch
observationで観測的に確かめられるかもしれない。
et al. 2016; Pinilla 0.6
et al.au2017),
instability induced bystructures are created and howhttp://arxiv.org/abs/2105.13852v1
they are associated with
dust-gas interaction (Takahashi & Inutsuka 2014, 2016)

背景•

原始惑星系円盤に対するALMA観測によって、ギャップやリング構造が見つかっているが (Andrews et al.
2018)、起源はいまだわかっていない。

•

•

•

惑星由来(e.g., Pinilla et al. 2012; Dipierro et al.22015)

U•

Snow line (Zhang et al. 2015; Okuzumi et al. 2016; Pinilla et al. 2017)•

ダストとガスの相互作用による不安定性 (Takahashi & Inutsuka 2014, 2016)•

円盤表面に小さなバンプができると、中心星側は照らさ

ceives more stellar light and the shadowed outer side
the bump receives insufficient flux. At the illuminate•
磁気流体力学的効果 (Flock et al. 2015; Ruge et al. 2016; Krapp et al. 2018; Riols et al. 2020)
side, the disk surface pu↵s up further as the mid-plan
Ø ほとんどのメカニズムにおいて、密度の変化からsubstructureを作るが、光学的に厚い波長でもtemperature increases, resulting in further decrease
substructureが観測されている(e.g., Carrasco-Gonz
́alez et2019;
MaciasSince
et al. the2021)。
the temperature
at al.
thebackside.
heating e
ficiency depends on(Avenhaus
the grazing
angle,
which
is etdefine赤外線の散乱光でもリングやギャップのような構造が観測されている
et al.
2018;
Garuﬁ
as the angle between the incident stellar light and th
al. 2018)。
disk surface, the bump responsible of increase the gra
リング/ギャップ構造を作れるメカニズムが Thermal Wave Instability (TWI; DʼAlessio et al. 1999;
ing angle moves inward and the next bump is generate
Dullemond 2000; Watanabe & Lin 2008; Siebenmorgen& Heymann
2012;
Ueda1).
et al.
just behind theformer one(FigureIn 2019)。
this letter, w
れて、反対側は影になる。
•

照らされた側は、mid-planeの温度が上がるにつれてさらに膨らみ、反対側は温度がさらに下がる。

•

加熱効率は中心星からの放射と円盤表面のなす角に依存し、バンプは内側に移動し、バンプの後ろに新しいバンプが生まれる。

Illuminated frontside

Shadowed outer side

puff upshrink downric disk. The mid-plane temperature Tm of a passively
heated disk
is calculated with the energy equation
軸対象の円盤についての1+1Dシミュレーション(Watanabe & Lin 2008)

シミュレーション•

エネルギー方程式+ 1 kB ⌃g @Tm= 2(Fs2(1) µmH @t

Fm + Fe ),(1)•

𝑅∗ = 2.08𝑅⊙ 、 𝑀∗ =where
1𝑀⊙ 、=𝑇∗1.4= 4000
K 、 𝐿∗ = 1𝐿
𝑇$ = 10 K⊙ 、 k𝑇# ：表面のダストの温度、
is the adiabatic
index,
is the Boltz-•

mann constant, µ = 2.34 is the molecular weight of disk
中心星からの放射のﬂux：
gas, mH is the atomic mass unit, ⌃g is the gas surface
ダストからの放射のﬂux：
density. The three fluxes, Fs , Fm and Fe , represent theincident stellar flux, released energy emitted from dust
外部からの放射のﬂux：

•
•

B

•

加熱されたダスト粒子のﬁlling factor•

ダストの密度分布•

円盤が垂直方向に静水圧平衡にあると仮定•→dynamical timescale Ω&'% よりも 𝑡() が短いときに成り立つ（≤ 50 au）。

•

光学的厚み

•

ガスの面密度•ダストの面密度：小さなダストのダストガス比（0.01 ー 0.0001）

結果（温度、円盤の厚み）

4

0. 25 au yr-1@10 au

Ueda et al.

0. 24 au yr-1@10 au𝑡̃ = 𝑡⁄𝑡(),1 ,𝑡(),1 = 41.2 yr

0. 14 au yr-1@10 au

6.4𝑡!",$ ≈ 264 yr
2.4𝑡!",$ ≈ 99 yr

3.2𝑡!",$ ≈ 132 yr

Figure 2. Time evolution of the mid-plane temperature (top) and the height of disk surface (bottom) for the model with
• 𝑓=.-*,00.01の場合、𝑡̃ = 10auにある波が𝑡̃ = 11.2version
で10ofauに達している。→速度~0.
625 evolution
au yr-1 of
fd2g,s0.01=(left),
0.001 (center)
andで400.0001(right). An animatedthis figure provides the whole time
the TWI from t̃ = 0 to 19.8.

•

速度は中心にいくにつれ遅くなり、≤0.3 auで消える（速度はダストガス比に依存）。

disk thinner and hence cooler, the TWI can grow only
plane temperature at 5 and 50 au for the models with
fd2g,s= 0.01, 0.001 and 0.0001. At 5 au, the mid-planeat more inner region for smaller fd2g,s . At 50 au, we• 温度の変動のタイムスケールもダストガス比に依存。
temperature varies from ⇠ 30 K to ⇠ 80–90 K for all
clearly see that the amplitude of the temperature varimodels. The time separation of each peak is larger foration decreases with fd2g,s and almost vanishes whensmaller fd2g,s . This is because smaller fd2g,s makes the
fd2g,s = 0.0001. This trend indicates that the TWI can結果（輻射輸送）
𝑓!"#,% = 0.01•

RADMC-3Dでモデル画像→地球から140 pcの距離にあるとして0.03”のビームでスムージング•

ダストは次の分布をもつとする•

小さなダスト：最大半径は10 μm、ダストガス比は
𝑓.-*,0•

大きなダスト：最大半径は1 mm、ダストガス比は
80.01 − 𝑓.-*,0Ueda et al.

Figure 4. Synthesized images of the thermal wave instability observed at= 1.65 µm (left), 870 µm and 3.1 mm for the mode•3。
with fd2g,s = 0.01. The images are convolved
with a beam size of 0.00 03 which is denoted with a filled white circle at bottom lef
ミリ波のリングとギャップの強度比は~3、赤外線では~10•ギャップとリングの間隔は、0.2-0.4r•

can potentially detect the radial motion of the
wave. The substructures induced by the othermechanisms would move more slowly. For exam温度の差によってリング/ギャップが生じるので、円盤が光学的
ple, substructures associated with planet-induced
gap would migrate with a velocity slower than theに厚くても観測できる。
type I migration (e.g., Kanagawa et al. 2018).

in each panel. The simulated intensity atstellar flux attenuation.
gap•= 1.65 µm is multiplied by a square of the radial distance to compensate for the

で観測結果とほぼ同じ。

3. The gap and ring structure should appear both
密度差起源のリング/ギャップは光学的に厚い円盤では見えなくなる。

in millimeter dust continuum and infrared scattered light. The intensity variation is more pronounced for the scattered light. The other mech-

substructures between the TWI-induced ring andgap, which makes the apparent separation smaller
4.3. Caveats

Here we summarize our assumptions and discuss thepotential e↵ect on the TWI. First, we assumed that thedisk is in hydrostatic equilibrium in vertical direction
This assumption would be broken in outer region (> 50
au). The hydrodynamical motion of the disk gas might
potentially suppress the TWI at outer region, although結果（snow line）

𝑓!"#,% = 0.01 TWI• snow lineの位置が時間変化する。
•

•

•

10

Figure 5. Radial locations of the snow lines of volatile
species at t̃ = 0 and 11 for fd2g,s = 0.01.

We investigated the impact of the lineが存在し、Thermal Wave
ひとつの分子についても複数のsnow
stability (TWI) on the millimeter and infrared emissi
リングやギャップを作りうる。
of disks using the 1+1D simulations of disk temperatu
evolution.
confirm that the TWI operates when t• snow We
lineの位置を調べるときには、円盤のdisk is optically thick enough for stellar light, i.e., t
温度を正確に求める必要がある。
dust-to-gas mass ratio of small grains is & 0.0001. T
温度の変化のタイムスケールは、radial
driftのタ
mid-plane temperature varies as the waves
propagaand hence gap and ring structures can be seen in bo
イムスケールよりも短いので、ダストの焼結由来
millimeter and infrared emission even if the dust aのギャップ/リング形成は同時は起きない。
gas surface density have no substructures. Since t
substructures are induced by the temperature variatio
ただし、昇華と再凝縮によってダストサイズに変the millimeter substructures can be seen even if the d化が起きる可能性があり、substructureの形成に
is completely optically thick, while the density-inducsubstructures would disappear for optically thick dis
つながりうる。
Ueda et al.
The fractional separation
between the TWI-induced ri
and gap is typically ⇠ 0.2–0.4 at ⇠ 10–50 au, althou
additional substructures might form within them, e
by snow lines. Due to the temperature variation, snlines of volatile species move radially and multiple snlines are observed even for a single species, which wou
a↵ect the disk chemistry. The wave propagation veloc
is as fast as ⇠ 0.6 au yr 1 , which can be potentially dtected with a multi-epoch observation with a time searation of a few years. The TWI might be stabiliz
by the radial energy di↵usion and/or hydrodynami
motion of the disk gas, which are not fully taken inaccount in this work. The two-dimensional radiati

arXiv:2106.00148v1 [astro-ph.GA] 31 May 2021

Hsi-Wei Yen,1 Bo Zhao,2, 3 Patrick M. Koch,1 and Aashish Gupta4, 1•

Academia Sinica
of Astronomy and Astrophysics,
11F of Astro-Math
Bldg, 1, Sec.
4, Roosevelt Rd, Taipei 10617,
No impactofInstitutecore-scale
magnetic
ﬁeld,
turbulence,orTaiwanvelocity
Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, L8S 4M1, Canada
gradientMax-Planck-Institut
on sizesof protostellar
disks
in Orion A
für extraterrestrische
Physik (MPE), Garching,
Germany, 85748
1

2

3

4

Graduate Institute of Astronomy, National Central University, 300 Zhongda Road, Zhongli, Taoyuan 32001, Taiwan

Hsi-Wei Yen, Bo Zhao, Patrick M. Koch, Aashish Gupta

ABSTRACT
We compared the sizes and fluxes of a sample of protostellar disks in Orion A measured with the ALMA
0.87 mm continuum data from the VANDAM survey with the physical properties of their ambient environmentson the core scale of 0.6 pc estimated with the GBT GAS NH3 and JCMT SCUPOL polarimetric data. We did
not find any significant dependence of the disk radii and continuum fluxes on a single parameter on the corescale, such as the non-thermal line width, magnetic field orientation and strength, or magnitude and orientationof the velocity gradient. Among these parameters, we only found a positive correlation between the magnitudeof the velocity gradient and the non-thermal line width. Thus, the observed velocity gradients are more likely
related to turbulent motion but not large-scale rotation. Our results of no clear dependence of the disk radii onthese parameters are more consistent with the expectation from non-ideal MHD simulations of disk formationin collapsing cores, where the disk size is self-regulated by magnetic braking and diffusion, compared to othersimulations which only include turbulence and/or a magnetic field misaligned with the rotational axis. Therefore, our results could hint that the non-ideal MHD effects play a more important role in the disk formation.
Nevertheless, we cannot exclude the influences on the observed disk size distribution by dynamical interaction
in a stellar cluster or amounts of angular momentum on the core scale, which cannot be probed with the current
data.

原始星周りの円盤の形成メカニズムを調べるために、円盤のパラメータ（サイズ、線幅、磁場）の相関関
Keywords: Star formation (1569), Interstellar magnetic fields (845), Star forming regions (1565), Protostars係を調べた。

(1302), Circumstellar disks (235)•

protostellar sources but not inACUPOLのデータを使用。
the others (Li et al. 2014a;
1. INTRODUCTION
ターゲットはOrion
A分子雲で、ALMA（VANDAM survey）、GBT、JCMT•

速度勾配と非熱的な線幅のみで正の相関が見られ、他では相関関係は得られなかった。
The growth of a protostellar disk is related to the trans-••

Tsukamoto et al. 2020; Zhao et al. 2020a).
Protostellar disks around young protostars are potential sites of planet formation (Manara et al. 2018;
fer of mass and angular momentum from its parental dense
Sheehan & Eisner 2018; Segura-Cox et al. 2020). Large
非理想MHD効果が円盤形成に重要な役割を担っていると考えられる。
core to the vicinity of its central protostar via collapsing masamples of protostellar disks have been observed in therterial. In hydrodynamics, where the angular momentum of
現状のデータでは、円盤のサイズ分布に対する星団内の力学相互作用やコアスケールの角運動量の影響に
mal dust continuum emission (e.g., Segura-Cox et al. 2018;
collapsing material in dense cores is more or less conserved,
Cieza et al. 2019; Maury et al. 2019; Tobin et al. 2020).
ついて調べることはできない。
the size of a protostellar disk is proportional to the rotation
Keplerian rotation of several protostellar disks around
http://arxiv.org/abs/2106.00148v1

背景•Class 0/I天体の周りのケプラー回転する円盤の観測例はあるが、そのサイズは1桁以上異なる。

•

このサイズの違いは円盤の時間進化や円盤のサイズの成長を抑制するプロセスによるかもしれないが、詳しくはよくわかっていない。

•

円盤の成長と母体となる分子雲コアから原始星近傍へ質量や角運動量を運ぶプロセスとは関係がある。

•

角運動量が保存する流体力学的には、円盤のサイズはコアの角速度や円盤の質量に比例するはず。

•

母体の分子雲コアの回転軸と磁場の向きが揃っている場合において理想MHD的にはmagnetic brakingによって円盤の成長が抑制される。
•

向きが揃っていない場合にはmagnetic brakingの効率が下がり、大きな円盤形成される。

•

磁場の拡散が起こる非理想MHDの効果によっても、大きな円盤を形成することができる。

•（観測的には）どのメカニズムが円盤の形成と成長に大切なのかはわかっていない。

•

原始星周りの円盤のサイズ、ガスの運動、磁場の関係を調べることで、円盤の形成と成長のメカニズムに関する手がかりが得られると思われる。
•

→本研究

データ
ALMA 0.87 mm

6
(a)

(b)

Figure 2. Comparisons between the disk radii measured with the ALMA 0.87 mm continuum data and (a) the projected separations and (b) thebolometric temperatures of the protostars. If the disks are not resolved with the synthesized beam of 0.!! 11 (43 au), the upper limits of their radii
are plotted as triangles. Red dots are the Class 0 protostars, and blue dots are Class I and flat-spectrum protostars. For a given protostar, theseparation is defined as its distance to the protostar nearest to it. Single protostars are also plotted here with the separations calculated with thesame definition, and they are labelled with open circles. In (a), a dashed line presents the expected truncation radius as a function of separation
in a binary system with equal masses and a non-eccentric binary orbit, and a vertical dotted line denotes a separation of 800 au. In (b), a verticaldashed line denotes a bolometric temperature of 70 K, which is adopted to separate Class 0 and more evolved protostars.

This difference within a factor of two has also been foundin the synthetic observations of the numerical simulationsof a Keplerian disk formed in a magnetized collapsing core
(Aso & Machida 2020). Therefore, we expect that othermechanisms, such as initial angular momentum distributions, magnetic field, and/or turbulence in parental dense
cores (e.g., Terebey et al. 1984; Basu 1998; Li et al. 2014a;
Hennebelle et al. 2016; Wurster & Lewis 2020), are more
important in determining the disk radius distribution in our
sample.

4.2. Dependence on turbulence and magnetic field
Figure 3a compares the disk radii with the non-thermalline widths, which are expected to trace the levels of the turbulence on the core scale. There is no correlation between
the turbulence and the disk radii, neither in the entire subsample or only for the young protostars with T bol < 70 K

Pearson correlation3 coefficients between the disk radii andthese parameters of the turbulence and the magnetic fields.
The absolute values of the correlation coefficients are mostly
less than 0.1 and at most 0.17. We also computed the Spearman’s rank correlation4, which is more sensitive to a nonlinear correlation. No significant correlations were foundamong these parameters, and the confidence levels of having correlations are all lower than 50%, no matter we consider the entire subsample or only the young protostars withT bol < 70 K in the subsample.
We also compared the disk radii with the misalignments
between the rotational axes of the disks and the magnetic
field orientations on the core scale projected on the plane of
the sky. The rotational axes of our sample disks are definedas the axes perpendicular to the disk major axes measured
with the ALMA observations, and the misalignments of 0◦
and 90◦ mean the magnetic fields are parallel and perpendicular to the rotational axes, respectively. The disk radii in our
entire subsample do not show any dependence on the mis-

データ
GBT NH3

3

JCMT 850 μm

結果①

(a)

(b)

(c)

(d)

(e)

(f) Class 0 protostars

・Class 0
・Class I▼unresolved◉singleいずれも相関なし

in 3D space

結果②
9

議論
•

•

•
•

•
•

理想MHD
• 乱流と磁場ー回転軸間のmisalignmentによってmagnetic brakingの効率が落ち、円盤が大きくなる（シミュレーション結果より）。
• 観測結果と異なる。
非理想MHD• 乱流と磁場ー回転軸間のmisalignmentの円盤の成長へさほど影響せず、 magnetic
braking / diffusionによってサイズが決まる（シミュレーション結果より） 。
• パラメータ間の相関がないことと無矛盾。
• 円盤のサイズは、宇宙線の電離率やダストサイズなどから決まる磁気拡散係数に依存する可能性がある。
Class 0天体20個に対する観測では、磁場と円盤が揃っていない場合、エンベロープが大きな角運動量を持つ傾向にあることを示している。
本研究では、より小さなスケールにおいて、そのような傾向は見られていない。
• 原始星近傍の100 auスケールではmagnetic braking / diffusionが効率的になる。

コアスケールにおいて速度勾配と非熱的な線幅の間に相関が見られたので、速度勾配はlarge-scale motionではなく乱流によって生じていると考えられる。
Class 0天体に対する800-900 auの分解能の観測において、比角運動量 𝑗 のradial profile
は、𝑗 ∝ 𝑟%.'となる（剛体回転は𝑗 ∝ 𝑟 ( 、乱流は𝑗 ∝ 𝑟%.) 、Pineda et al. 2019）。
• 速度勾配や角運動量を正確に見積もるにはより高い分解能が必要。