SFN #371 48-59

担当：土井 聖明 (総研大D2)
56. PRODIGE ‒ Planet-forming disks in Taurus with NOEMA. I. Overview and ﬁrst results for 12CO, 13CO, and C18O
57. Length and Velocity Scales in Protoplanetary Disk Turbulence
58. Small and Large Dust Cavities in Disks around mid-M Stars in Taurus
59. JWST Observations of Young protoStars (JOYS): Linked accretion and ejection in a Class I protobinary system
60. WTP10aaauow: Discovery of a new FU Ori outburst towards the RCW 49 star-forming region in NEOWISE data
61. Curves of growth for transiting exocomets: Application to Fe II lines in the Beta Pictoris system
62. Magnetic ﬁelds in the Southern Coalsack and beyond
63. The interplay between forming planets and photoevaporating discs II: Wind-driven gas redistribution
64. Disk Wind Feedback from High-mass Protostars. III. Synthetic CO Line Emission
65. Dense Core Collisions in Molecular Clouds: Formation of Streamers and Binary Stars
66. Turbulent vortex with moderate dust settling probed by scattering-induced polarization in the IRS 48 system
67. Gas content and evolution of a sample of YSO associations at d 3.5 kpc from the Sun
68. Eﬀects of physical conditions on the stellar initial mass function: The low-metallicity star-forming region Sh 2-209
69. Multi-band reﬂectance and shadowing of RX J1604.3-2130 protoplanetary disk in scattered light

57.

57.

p
wavenumber (k) !
wavenumber (k) !
Length and Velocity ScalesinProtoplanetary
Disk
Turbulence↵H
Length scale (L)Length scale (L)Debanjan Sengupta, Jeﬀrey N. Cuzzi, Orkan M. Umurhan, Wladimir Lyra F In the theory of protoplanetary<latexit sha1_base64="/5SrUXBZCqLvNFA65cdXf5/k2ZA=">AAACCHicbVC7SgNBFJ31GeMramnhYCLEJuwGfJRBG8sI5gHJEmYnN8mQ2ZllZjYhLClt/BUbC0Vs/QQ7/8bJo9DEAxcO59zLvfcEEWfauO63s7K6tr6xmdpKb+/s7u1nDg6rWsaKQoVKLlU9IBo4E1AxzHCoRwpIGHCoBf3biV8bgNJMigczisAPSVewDqPEWKmVORmSAYg4DEDhXL5/3uRSdBXr9gxRSg5zrUzWLbhT4GXizUkWzVFuZb6abUnjEIShnGjd8NzI+AlRhlEO43Qz1hAR2iddaFgqSAjaT6aPjPGZVdq4I5UtYfBU/T2RkFDrURjYzpCYnl70JuJ/XiM2nWs/YSKKDQg6W9SJOTYST1LBbaaAGj6yhFDF7K2Y9ogi1Njs0jYEb/HlZVItFrzLwsV9MVu6mceRQsfoFOWRh65QCd2hMqogih7RM3pFb86T8+K8Ox+z1hVnPnOE/sD5/AFx/pme</latexit><latexit sha1_base64="/5SrUXBZCqLvNFA65cdXf5/k2ZA=">AAACCHicbVC7SgNBFJ31GeMramnhYCLEJuwGfJRBG8sI5gHJEmYnN8mQ2ZllZjYhLClt/BUbC0Vs/QQ7/8bJo9DEAxcO59zLvfcEEWfauO63s7K6tr6xmdpKb+/s7u1nDg6rWsaKQoVKLlU9IBo4E1AxzHCoRwpIGHCoBf3biV8bgNJMigczisAPSVewDqPEWKmVORmSAYg4DEDhXL5/3uRSdBXr9gxRSg5zrUzWLbhT4GXizUkWzVFuZb6abUnjEIShnGjd8NzI+AlRhlEO43Qz1hAR2iddaFgqSAjaT6aPjPGZVdq4I5UtYfBU/T2RkFDrURjYzpCYnl70JuJ/XiM2nWs/YSKKDQg6W9SJOTYST1LBbaaAGj6yhFDF7K2Y9ogi1Njs0jYEb/HlZVItFrzLwsV9MVu6mceRQsfoFOWRh65QCd2hMqogih7RM3pFb86T8+K8Ox+z1hVnPnOE/sD5/AFx/pme</latexit><latexit sha1_base64="fsJThMRs9DGwLVyYBBq0B/u2uRY=">AAAB9XicbVBNS8NAEJ34WetX1aOXYBE8lUT8Oha99FjBfkATy2S7aZduNnF3o5TQ/+HFgyJe/S/e/Ddu2xy09cHA470ZZuYFCWdKO863tbS8srq2Xtgobm5t7+yW9vabKk4loQ0S81i2A1SUM0EbmmlO24mkGAWctoLhzcRvPVKpWCzu9CihfoR9wUJGUBvp3lMPUmce8mSA41q3VHYqzhT2InFzUoYc9W7py+vFJI2o0ISjUh3XSbSfodSMcDoueqmiCZIh9mnHUIERVX42vXpsHxulZ4exNCW0PVV/T2QYKTWKAtMZoR6oeW8i/ud1Uh1e+RkTSaqpILNFYcptHduTCOwek5RoPjIEiWTmVpsMUCLRJqiiCcGdf3mRNE8r7kXl/PasXL3O4yjAIRzBCbhwCVWoQR0aQEDCM7zCm/VkvVjv1sesdcnKZw7gD6zPH/3nktg=</latexit><latexit sha1_base64="FJnaYt8+ox7yKWq3LN8acnaLqQY=">AAACDHicbVC7SgNBFJ31GeMramkzmAixCbuCj1K0sUgRwTwgCTI7uZsMzs4sM3eVEPIBNv6KjYUitn6AnX/j5FGo8cDA4ZxzuXNPmEhh0fe/vLn5hcWl5cxKdnVtfWMzt7Vdszo1HKpcS20aIbMghYIqCpTQSAywOJRQD28vRn79DowVWl1jP4F2zLpKRIIzdNJNLl9oSa26EiJkxuj7Ai2D6mKPWs4k0EKxfFBwKb/kj0FnSTAleTJF5Sb32eponsagkEtmbTPwE2wPmEHBJQyzrdRCwvgt60LTUcVisO3B+Jgh3XdKh0bauKeQjtWfEwMWW9uPQ5eMGfbsX28k/uc1U4xO2wOhkhRB8cmiKJUUNR01QzvCAEfZd4RxI9xfKe8xwzi6/rKuhODvybOkdlgKjktHV4f5s/NpHRmyS/ZIkQTkhJyRS1IhVcLJA3kiL+TVe/SevTfvfRKd86YzO+QXvI9vaSCZ6g==</latexit><latexit sha1_base64="FJnaYt8+ox7yKWq3LN8acnaLqQY=">AAACDHicbVC7SgNBFJ31GeMramkzmAixCbuCj1K0sUgRwTwgCTI7uZsMzs4sM3eVEPIBNv6KjYUitn6AnX/j5FGo8cDA4ZxzuXNPmEhh0fe/vLn5hcWl5cxKdnVtfWMzt7Vdszo1HKpcS20aIbMghYIqCpTQSAywOJRQD28vRn79DowVWl1jP4F2zLpKRIIzdNJNLl9oSa26EiJkxuj7Ai2D6mKPWs4k0EKxfFBwKb/kj0FnSTAleTJF5Sb32eponsagkEtmbTPwE2wPmEHBJQyzrdRCwvgt60LTUcVisO3B+Jgh3XdKh0bauKeQjtWfEwMWW9uPQ5eMGfbsX28k/uc1U4xO2wOhkhRB8cmiKJUUNR01QzvCAEfZd4RxI9xfKe8xwzi6/rKuhODvybOkdlgKjktHV4f5s/NpHRmyS/ZIkQTkhJyRS1IhVcLJA3kiL+TVe/SevTfvfRKd86YzO+QXvI9vaSCZ6g==</latexit>

disk turbulence, a Figure
widely 1.
adoptedansatz,or assumption,is thattheturnoverof ofthelargestturbulent
eddy,
A cartoon
showing
turbulent kinetic
energyspectraE(k) frequency
as a function
spatialwavenumber
k for
two di↵erent
cases: ⌦L frequency= ⌦K and ⌦⌦K terms. Note ofthatwhen⌦L exceeds⌦K the largest
energy containing ↵lengthscale of thatthe turbulence⌦L , is the local Keplerian⌦LK>. Inthestandard
dimensionless
Shakura-Sunyaev
parameter
shiftstowards right.
As this is thegoverning
scale settingtheturbulent
dynamics,
transport
anddi↵usion
properties
get altered.
quantifies turbulent
viscosityor
diﬀusivity,
thisassumption
leads
tocharacteristic
lengthandvelocity
scalesgiven
pp
respectively by ↵H
andwith↵c,which
H and c are the local gas scalelargest
heighteddy
andassoundHowever,
thisvelocity ofstarting
theinusual
formulation⌦L ⇠ Vspeed.
VL is theL /L, whereLengthand
Velocity
scalesin(energy
turbulentassumption is not applicable in cases whenturbulence
is forced
numericallyor largest
drivenbysomenatural nebula.
processes
suchthecontaining)eddy and L
is the corre2
0
(D,
⌫)
⇠
LV
⇠
↵
˜
cH
⇠
↵
˜
H
⌦K ,general (1)sponding
lengthscale.
We
define⌦/⌦⌘R, whereas Vertical Shear Instability. Here we Lexplore the morecase where
⌦
⌦
and
show
that
under
these
L
K
K
p 0 L
p
0 number Ro (Cushman0twice
0 c, whereRisthe
traditional
Rossbyconditions, the characteristic
lengthandvelocity
scalesarerespectively
↵/R
H
and
↵R
R
⌘
⌦
isK
When
⌦
>
L /⌦
K⌦
When
⌦
=
⌦
L
p
K speed and wewhere c is theLlocal sound0 have used H ⌘Roisin 2011).
twice the Rossby number. It follows that ↵ = ↵t/R , where ↵tc is the root-mean-square
average of the turbulentc/⌦K , where H is the local gas scale height. In this case,With(L)this,(2) nowreads as in shearing
scale
velocities. Properly allowing for this eﬀect naturally explains the Largest
reduced particle
scaleEq.
heights
producedLarc and H are considered as the characteristic velocity andLargestlength scale
box simulations oflength
particles
inforcedturbulence,
and
may
help
with
interpreting
recentedge-ondisk
observations;
if
⌦
=
⌦
L
K
2
scales of the system. Now, if the ansatz ⌦L = ⌦K 0
(D, ⌫) ⇠ LVL ⇠ L ⌦L ⇠ R0 L2 ⌦K(4)(L, ⌦ are) also presented.
more general implications
for observations
For R > 1 the eﬀective particle Stokes numbers are
is valid, thenEq. (1) can beK
re-written
asSets ↵
increased, which has implications
forparticle
collision
dynamics
andgrowth,
as
well
as
for
planetesimalformation.
Sets ↵, StK & coupling
As before, setting this result equal to Eq. (1) in terms<latexit sha1_base64="6tNwRYxhD3bCVzeRtDUlY0xmwVI=">AAACCXicbZDLSgMxFIYzXmu9VV26CbaCqzJT8LKSohtBwQr2Am0ZMumZNjTJDElGKKVbN76KGxeKuPUN3Pk2pu0stPWHwMd/zkly/iDmTBvX/XYWFpeWV1Yza9n1jc2t7dzObk1HiaJQpRGPVCMgGjiTUDXMcGjECogIONSD/uW4Xn8ApVkk780ghrYgXclCRomxlp/DLQrSgMrWeyBxoXUroEv8m/MUrgt+Lu8W3YnwPHgp5FGqip/7anUimgh7LeVE66bnxqY9JMowymGUbSUaYkL7pAtNi5II0O3hZJMRPrROB4eRskcaPHF/TwyJ0HogAtspiOnp2drY/K/WTEx41h4yGScGJJ0+FCYcmwiPY8EdpoAaPrBAqGL2r5j2iCLUZqOzNgRvduV5qJWK3knx+K6UL1+kcWTQPjpAR8hDp6iMrlAFVRFFj+gZvaI358l5cd6dj2nrgpPO7KE/cj5/AIDdmPE=</latexit><latexit sha1_base64="SxCKw10fDI3l8ethFfoB0i6/1Vg=">AAACCXicbZDLSgMxFIYzXmu9VV26CbaCqzJT8LIRim4EBSvYC7RlyKRn2tAkMyQZoZRu3fgqblwo4tY3cOfbmLaz0NYfAh//OSfJ+YOYM21c99tZWFxaXlnNrGXXNza3tnM7uzUdJYpClUY8Uo2AaOBMQtUww6ERKyAi4FAP+pfjev0BlGaRvDeDGNqCdCULGSXGWn4OtyhIAypb74HEhdatgC7xb85TuC74ubxbdCfC8+ClkEepKn7uq9WJaCLstZQTrZueG5v2kCjDKIdRtpVoiAntky40LUoiQLeHk01G+NA6HRxGyh5p8MT9PTEkQuuBCGynIKanZ2tj879aMzHhWXvIZJwYkHT6UJhwbCI8jgV3mAJq+MACoYrZv2LaI4pQm43O2hC82ZXnoVYqeifF47tSvnyRxpFB++gAHSEPnaIyukIVVEUUPaJn9IrenCfnxXl3PqatC046s4f+yPn8AX9QmPA=</latexit><latexit sha1_base64="flIA3FSwl7jTUNj71sAAEyXG0QM=">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</latexit><latexit sha1_base64="L9srNg7LzSG9eZ+z94+Ypnpb9Ko=">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</latexit>(D, ⌫) ⇠ LVL ⇠ L2 ⌦L ⇠ L2 ⌦K .

Energy (E)Energy (E)<latexit sha1_base64="ev3j7+os989GcfhfsLREYnYjqn8=">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</latexit>(2)of ↵, we get<latexit sha1_base64="3+FSwQbikjF32bp1ledjFL+eg0A=">AAAB83icbVDLSgNBEOyNrxhfUY9eBhMhXsJuwMcxKAGPEYwJJEuYnXSSIbOzy8yssIT8hhcPinj1Z7z5N04eB00saCiquunuCmLBtXHdbyeztr6xuZXdzu3s7u0f5A+PHnWUKIYNFolItQKqUXCJDcONwFaskIaBwGYwup36zSdUmkfywaQx+iEdSN7njBordWoS1SAlxVLtvNjNF9yyOwNZJd6CFGCBejf/1elFLAlRGiao1m3PjY0/pspwJnCS6yQaY8pGdIBtSyUNUfvj2c0TcmaVHulHypY0ZKb+nhjTUOs0DGxnSM1QL3tT8T+vnZj+tT/mMk4MSjZf1E8EMRGZBkB6XCEzIrWEMsXtrYQNqaLM2JhyNgRv+eVV8lgpe5fli/tKoXqziCMLJ3AKJfDgCqpwB3VoAIMYnuEV3pzEeXHenY95a8ZZzBzDHzifPwmekGI=</latexit><latexit sha1_base64="3+FSwQbikjF32bp1ledjFL+eg0A=">AAAB83icbVDLSgNBEOyNrxhfUY9eBhMhXsJuwMcxKAGPEYwJJEuYnXSSIbOzy8yssIT8hhcPinj1Z7z5N04eB00saCiquunuCmLBtXHdbyeztr6xuZXdzu3s7u0f5A+PHnWUKIYNFolItQKqUXCJDcONwFaskIaBwGYwup36zSdUmkfywaQx+iEdSN7njBordWoS1SAlxVLtvNjNF9yyOwNZJd6CFGCBejf/1elFLAlRGiao1m3PjY0/pspwJnCS6yQaY8pGdIBtSyUNUfvj2c0TcmaVHulHypY0ZKb+nhjTUOs0DGxnSM1QL3tT8T+vnZj+tT/mMk4MSjZf1E8EMRGZBkB6XCEzIrWEMsXtrYQNqaLM2JhyNgRv+eVV8lgpe5fli/tKoXqziCMLJ3AKJfDgCqpwB3VoAIMYnuEV3pzEeXHenY95a8ZZzBzDHzifPwmekGI=</latexit>r
Scales not relevant↵
円盤乱流をより一般化した場合の、ダスト分布や成長への影響を議論
Dustequations
Cavities
in2 Disks
mid-M
Stars in TaurusL =2 around2r (5)H.
58. Small and Large
Combining
1
and
gives
L
=
↵
˜
H
or
L
=
0
for
true
turbulenceRp↵
Yangfan Shi, Feng ↵Long,
GregoryJ.
Herczeg,
DanielHarsono,
Yao
Liu,
Paola
Pinilla,EnricoRagusa,Doug
˜ H. Substituting L back in LVL = ↵˜ cH reveals
L=H・乱流は円盤ガス進化、ダスト分布、ダスト成長に大きな影響
0
Using Eq. Lucas(5), theA.velocity
the largest eddyRcan
L for
Johnstone, Xue-Ning Bai, pIlaria Pascucci,p Carlo F. Manara, Gijs D. Mulders,Cieza VF
High-angularbewritten
as
V
=
↵
˜
c.
(3)
resolution
imagingbyALMA
has
revealedthenear-universality
anddiversityofsubstructuresin protoplanetary disks.
L=↵H
L・α円盤モデルでは、、の乱流を仮定することが多い<latexit sha1_base64="T+ctDtaaxSIPXFKBtOwXy33c1ts=">AAACGnicbVC7TgMxEPTxDMcrQEljESFRRXdIPMoIGsogCETKRZHP2QMLn32y15GiKN9Bw6/QUIAQHaLhb3BCCiBMNZrZ1e5MWkhhMYo+g5nZufmFxdJSuLyyurZe3ti8stoZDg2upTbNlFmQQkEDBUpoFgZYnkq4Tu9OR/51D4wVWl1iv4B2zm6UyARn6KVOOU44KAQTXnAmwVKlkRqQ0GMKkyTMtKFoHFB0JnUSFIdOuRJVozHoNIknpEImqHfK70lXc5f7O1wya1txVGB7wAwKLmEYJs5Cwfgdu4GWp4rlYNuDcbQh3fVKl47eyLRCOlZ/bgxYbm0/T/1kzvDW/vVG4n9ey2F23B4IVTj0qb4PZU5S1HTUE+0KAxxl3xPGjfC/Un7LDOO+LBv6EuK/kafJ1X41PqwenO9XaieTOkpkm+yQPRKTI1IjZ6ROGoSTe/JInslL8BA8Ba/B2/foTDDZ2SK/EHx8AVNuoRM=</latexit><latexit sha1_base64="rWXAwkHxyT4NfajPjE3GZlGvp7M=">AAACBHicbVC7SgNBFJ2Nrxhfq5ZpBoNoFXbFVyMEbVJYRDEPyC7h7mQ2GTL7cGZWCMsWNv6KjYUitn6EnX/j5FFo4oELh3Pu5d57vJgzqSzr28gtLC4tr+RXC2vrG5tb5vZOQ0aJILROIh6JlgeSchbSumKK01YsKAQep01vcDXymw9USBaFd2oYUzeAXsh8RkBpqWMWry8ceS9U6vgCSOoAj/uQpbcHWVbtmCWrbI2B54k9JSU0Ra1jfjndiCQBDRXhIGXbtmLlpiAUI5xmBSeRNAYygB5taxpCQKWbjp/I8L5WutiPhK5Q4bH6eyKFQMph4OnOAFRfznoj8T+vnSj/3E1ZGCeKhmSyyE84VhEeJYK7TFCi+FATIILpWzHpg05D6dwKOgR79uV50jgq26flk5vjUuVyGkceFdEeOkQ2OkMVVEU1VEcEPaJn9IrejCfjxXg3PiatOWM6s4v+wPj8ATAjmHU=</latexit><latexit sha1_base64="twlwMLu1frT9tBkzHv06coxPx3Q=">AAAB+XicbVDLSsNAFL2pr1pfUZduBovgqiTiayMU3XThooJ9QBPKZDpph04mcWZSKKF/4saFIm79E3f+jdM2C209cOFwzr3ce0+QcKa043xbhZXVtfWN4mZpa3tnd8/eP2iqOJWENkjMY9kOsKKcCdrQTHPaTiTFUcBpKxjeTf3WiErFYvGoxwn1I9wXLGQEayN1bfv+xlNPUmce5skAT2pdu+xUnBnQMnFzUoYc9a795fVikkZUaMKxUh3XSbSfYakZ4XRS8lJFE0yGuE87hgocUeVns8sn6MQoPRTG0pTQaKb+nshwpNQ4CkxnhPVALXpT8T+vk+rw2s+YSFJNBZkvClOOdIymMaAek5RoPjYEE8nMrYgMsMREm7BKJgR38eVl0jyruJeVi4fzcvU2j6MIR3AMp+DCFVShBnVoAIERPMMrvFmZ9WK9Wx/z1oKVzxzCH1ifP5dFk6Y=</latexit>r
However, disks around M-type pre-main-sequence stars are still poorly sampled,
despitetheprevalenceof M-dwarfspParticle
dynamics
↵
2 2
0
0 ↵c,
Often
invoked
in
the
form
↵
˜
=
V
/c
,
this
resultis・この関係が成り立たない場合、特に、乱流スケールがより小さい場合の惑星形成への影響を調べた
V
=
L⌦
=
R
H⌦
=
R
(6)
L
L
L six disks
Kin the galaxy. Here we present high-resolution ( 50 mas, 8 au) ALMA Band 6 observationsofaroundmid-M
0governed byRwidelyusedtocalculateparticle
relative
velocities
instars in Taurus. We detect dust continuum emission in all six disks, 12CO in fivethis
disks,
and 13CO line in two disks.
scale
・乱流サイズスケールがより小さい場合には、同じαの値でも、growth models
Ormel& Cuzzial. The ratio
which ofis about
equivalent
the expression
Eq. (3). Thus,
The size ratios between
gas and(e.g.
dust
disks
range2007;
fromBirnstiel
1.6 to et
5.1.
5 forto 2M0436
and 2M0450
2010, 2016; Estrada et al. 2016; Sengupta et al. 2019). p while L and V change form, their product does not,・ダスト層がより薄く沈澱する
L smooth.
indicates eﬃcient dust
radial drift. (k)Four !
disks show rings and cavities and two disks are
The cavity sizes
wavenumber(k)!
wavenumber
The estimate ↵˜ is also used as a measure of turbulent
↵H
and
we
recover Detailed visibility modelingoccupy a wide range:
60
au
for
2M0412,
and
10
au
for
2M0434,
2M0436and
2M0508.
Length scale (L)Lengthscaleturbulence(L)・ダストの相対速度が上がり、サイズはより小さい状態でfragmentationする
intensity
in forced
models, i.e., based on rootindicates that small cavities of 1.7 and 5.7 au may hide in the two smooth disks 2M0450 and CIDA 12. We performmean square (rms) velocities (Gole et al. 2020, see sec(D, ⌫) ⇠ LVL = ↵cH.
(7)
radiative transfer fittingoftheinfraredSEDs
toconstrainthecavitysizes,
findingthat
micron-sized
dust
grainsmaytion 3.2 for more discussion).
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Figure 1. A cartoon showing turbulent kinetic energy spectra E(k) as a function of spatial wavenumberL = ↵H
asbulencewithparticlesresultingthat satisfy
simultaneously thecomes less influential,
potentiallyinParticle dynamics
nebulaparametersand ⌦L . Without
and time ofcriticaloverthe largest
eddiesdeviating↵fromgovernedactuallybythis scalen.
It is this knowingcase we investigate
this paper. turbulent frequency
mpwhat the inappropriate⌦Ls. contribution,
we numericallyassess Stokes
the propp St ⌘ ts ⌦ may bewavenumber (k) !
is,therelevant
particlenumberwavenumber(k)!
・乱流の円盤への役割↵H
externallyforcedturbulence
underconditions
Length scale defined(L)
h inincorrectly– here, ts is the aerodynamic stop-Length scale (L)・円盤ガス粘性として働く→
ガス円盤の時間進化を引き起こす
ating,
shearednebula
flow,
under
the
general
ping
time
of
the
particles.
This
appears
to
be
the
case
beFigure
1.⌦A .cartoon
showingofturbulent
kinetic
energyspectra E(k) as a function of spatial wavenumber k for two di↵erentn ⌦L ・ダストの相対速度を駆動
The
utility
the
work
is
to
alK
→ length
成長・破壊を引き起こす
lociof→particle
behavior
in nebula
ases: ⌦L = ⌦inand ⌦Lprior> ⌦K simulations. Note that when
⌦L ダスト衝突を引き起こす
exceeds⌦K the largest
energy containing
scale of the turbulence
K manyinitialconditions
inforcedsimulationsofturhifts towards turbulenceright. As this foris thegoverningsettingproperties
the turbulentare
dynamics,
997)
which
thescaleparticledefinedtransport and di↵usion properties get altered.
with particles that satisfy simultaneously thebyan⌦-basedStokesnumber(Birnstiel
et
al.
2010;
uzzi
K
tarting
with
the
usual
formulation
largest
eddy
as
⌦
⇠
V
/L,
where
V
is
the
velocityofL
LL
nebulaparameters
↵
and
⌦
.
Without
actuallyL・これまでの仮定：α円盤モデル(Shakura & Sunyaev 1973)
largestcontaining) eddy and L is the corregwhatof the appropriate
Estrada etturbulent
al. 2016;frequency
Sengupta⌦Let al. 2019;theGoleet (energy
al.
2
0
(D,
⌫)
⇠
LV
⇠
↵
˜
cH
⇠
↵
˜
H
⌦
,
(1)
L
K
sponding
lengthscale.
We
define⌦/⌦⌘R, where・（D：拡散、ν：粘性、c：等温音速、H：ガススケールハイト)LK
delevant
to- particle2020),
which
we St
defineStKbe= ts ⌦K , and in which
Stokesnumber⌘ ts ⌦asmay0R
is twice
the traditional Rossby number Ro (Cushmanthe
possibility
of
⌦
>
⌦
was
not
considered.
In
this
992)
tly defined– localhere,soundts is theaerodynamic
L we have
K stop（ΩL：largest
eddy、Ωk：ケプラー角速度)
wherec・乱流の最大渦は、
is the
speed
and
used
H⌘
Roisin 2011).
paper
we
will
introduce
utilize
injection scale eddye⌦ofthe particles.
This
appearstobe and
the
case
K
c/⌦
H
is
the
local
gas
scale
height.
In
this
case,
K , where
With this, Eq. (2) now reads as
・これよりもタイムスケールの大きいeddyはケプラー回転で壊れる
prior
particle
behaviorhereafterin nebula
Stokesofnumber
definedcselfand Hsimulations
are consideredas the characteristic
velocityby
andStL = ts ⌦L .
2
0 2
・この仮定のもとで、ダストの空間分布や相対速度が計算されてきた
ce for scales
whichdefinedength
ofthe
theparticle
system. properties
Now, if the areansatz⌦L = ⌦K
pro(D, ⌫) ⇠ LVL ⇠ L ⌦L ⇠ R L ⌦K
(4)-basedthen
StokesnumbersKbut
valid,
Eq. (1)can be(Birnstiel
re-writtenetasal. 2010;
As before, setting this result equal to Eq. (1) in terms
et
al.
2016;
Sengupta
et
al.
2019;
Gole
et
al.
2. GENERALIZING
idea・近年の乱流の計算
2
2 THE COMPONENTS OF ↵(D, ⌫)as
⇠ St
LVL ⇠
Lt ⌦
⌦L ,⇠andL ⌦in
K . which (2)of ↵, we getwhich we define
=
K
s K
r
nifi↵
The current
ansatz⌦=⌦LK
ibility ・of ⌦L > ⌦Kの場合がある
was2.1.
not considered.
In
this
2
2
L=
H.
(5)
Combining
equations
1
and
2
gives
L
=
↵
˜
H
or
L
=
0
ssed
R
p
e will introduce
andutilize
injection
scale
eddy
We
first
revisittheoriginal
ansatzwhichisgenerally↵˜H.
Substituting
L
back
in
LV
=
↵
˜
cH
revealsL・VSIのような乱流の計算結果
byaumber defined
hereafterts ⌦Using theEq. tur(5), the velocity VL for the largest eddy can
L =inL.
assumed
to by
bepSt
true
literature
in cases where98),
be written as
・この場合はダスト成長等の描像は？
V
=
↵
˜
c.
(3)
L
bulence parameter is calculated from numerical simulasimrp・その場合の数値計算を↵ 0
tions.
We
shall
call
this
˜
,
the
turbulence
intensity
when
2 2↵
0 ↵c,
Often invoked inTHE
the form↵
˜ = VL /c , OF
this ↵result is
ENERALIZINGCOMPONENTS
VL = L⌦L =
R
H⌦
=
R
(6)
K
0
R
= ⌦K . particle relative velocities inwidely used ⌦toLcalculate

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手法
・乱流を外的に注入した場合の数値計算を行う
・stratiﬁedなシアリングボックス計算
・設定した波数 k で、設定したエネルギーの乱流を注入
・ダスト粒子も入れる

結果
・エネルギーを注入した
渦の大きさが最大渦になる(今回の設定だとΩL＞ΩKになる)・速度は注入したエネルギーによる

結果

結果

2
02 2
V12 = R Vg (St1K

2

w
議論
(
We
underscore
that
particlelayer
thicknesses
aresenrly, in the most important range (2) above, Eq.
sitive
to
↵,
not
↵
˜
(section
4
andfigure4).
Itisinterestt
Ormel
&
Cuzzi
(2007)
showsthecollision
veloc⌘・ダスト成長への影響
h can be written with the new scaling included
ing to note that, while uncertainties remain significantp
ダストの相対速度は(especially in St), the estimated ↵ from the analysess2
0 2
V12 = R Vg ⇤St1K (26) になるので、Rʼの分(26)
of particle scale heights seem to be consistently smallerw
he term ⇤相対速度が大きく、より小さいダストでも衝突破壊が起きる
is only weakly dependent on StL forcompared to the ones obtained from the turbulent linep(Ormel & Cuzzi 2007). Thus, Eq. (26), along
broadening, and this is just what would be expectedB. (6), shows that the collision velocity is inby ・観測的なαの制限
a factor of R01/2 for a given ↵, and thus
2from the di↵erence between values of particle height de0
reach・gas
the bouncing
orfragmentation
barriers
rived from˜ を制約
and ↵ if R > 1.
dline broadening：速度擾乱を測定→ ↵cal sizes which are smaller by a related factor.
Itispossibletocombinetheindependentanddistinctt・ダスト/ガス分布：拡散を測定
0 → αを制約
heavy particle limit, a higher StL with R > 1dobservational constraints discussed above (on h/H fromcollision velocities, allowing for bigger particles.
difiedexpression
from
Ormel
&
Cuzzi
(2007,
Eq.
particlelayer
thicknesses
and
V
from
spectral
line
im
rms
発表者注
A&A proofs: manuscr
ld read as:
observations) with other observed constraints on particle
g
✓
◆
・今回は
VSI に着目してよりサイズの小さい乱流が起きている場合の分布を考えたが、
size
and
gas
disk
surfacemass
density(eg.,
Carrasco1
1
2
2
V12= VgVSIは大局的な流れも作るのでダストをより巻き上げる可能性もある+(27)
1 + R0 St1K
1 + R0 St2K
in
González et al. 2019; Macı́as et al. 2021; Doi & Kataoka
0(Dullemond et al. 2022)2023) to actually constrain the critical value of R andB
5.4. Planetesimal Formationthus
thenatureoftheunderlying
processes
causing
disk
2esults have implications for the process of planw
turbulence in the first place. We sketch the logic byformation, an outstanding problem in planet
St2K )(25)2023).