Star Forma)on Newsle0er#276 21-25
麻生 有佑

o be relevant
to disks
take withaccountof allthese quantities and related proity can takelayeredaccretion.
studies(e.g.,place fordition,we
discuss
previous
work
in
which
similarcesses simultaneously. In this paper, however, we adopt a
Flock etVISCOUS
al.
INSTABILITY
TRIGGEREDBY
LAYERED
ACCRETION
IN PROTOPLANETARY DISKS
bilities areobserved.
We state
finallyprofile
touch
brieflyonsteadyformagnetic
fields,and assume
that
f non-ideal
the viscous
MHD terms
includedin our
1,2,4
the thatvalueareofnot
Σ playsaYasuhiro
dominantrole in determining
the Takeuchi3
Hasegawa
and Taku
Whilea more remarks
sis. Conclusivearepresented
inSection5.
1 Divisionionizationeﬃciency.
Thisessentiallyleads toObservatory
a situationof Japan, Osawa, Mitaka, Tokyo 181-8588, Japanof Theoretical
Astronomy,
National
Astronomical
eded, this in2it
thatissuﬃcient
to
focus
on
Σ
to
examinetheJet
Propulsion
Laboratory,
California
Instituteof stability
Technology, Pasadena, CA 91109, USA andANALYSIS OF DISKS
ucture2.inSTABILITY
the 3
Department
of
Earth
and
Planetary
Sciences,Tokyo
Instituteof Technology,
Meguro-ku, Tokyo 152-8551, Japanof disks
undergolayeredWe consider
thissuggestthat,Ø 円盤の降着率を説明するために乱流は必要で、その起源としてはMRIが有力。
developa formulation
withthatwhich
the stabilityof accretion.
10, 2015
situation, in order to Draft
shed version
light onNovember
the evolution
planetarybe discussed.
onof disksdisks
is canidealizedØ
層状降着(deadzoneとそれ以外)の考え方と古典的な1D粘性αモデルを比べる。
Viscous Instability & Layered Accretionof Σ for disks with layered accretion and investigate theould be used
ABSTRACT
2.1. Viscous
evolution
resultant
eﬀect
on
disk
stability.
and to mimic
where ingredientsx0 isrelation
the unperturbed
x1 is
the perUnderthea dispersion
canbe quantity andLayeredaccretionisassumption,
oneviscousof the evoinevitableinprotoplanetary
disks
when
disk turbulenceel terms
basic equation
for governing
the
1D
more
turbedone.
Asaresult,equation(2)
canberewritten
givenas(e.g.,
Pringle1981,instabilities
for a derivation),byasmagnetorotational(MRIs). In the accretion, disk surfaces where MRIsn ofØ
gas電離度がΣで決まるとき、WKB線形解析(kr>>1)で円盤が不安定になる条件は以下の通り。
disksisisexcited
written(e.g.,
Pringle
1981)
as
!
"
!
have a" high value. In Section∂ of disk accretion rate
∂ operate∂Σ 3fully
Σ0(Ṁ ), while the disk midplane where MRIs are
1/2 ∂
1/2
r
− generally(r νΣ) ends
= 0,up with
(1) < 0,(νΣ)
+ α0 (2)≡ αprogressνstaunderstanding< 0,(5) MRIs has
c h αysis in∂twhich
sta cs h ≡ on
quenchedr ∂r∂r∂Σ a low value sof Ṁ1. ΣSignificant
1
s is derived.
recently been made by a number of dedicated MHD simulations, which requires improvement of thewhereνviscosity,
is a functionof Σ
alone.
For simplicity,
we
adopt
= αc
the kinematic
cs inis thesound
he νareneededs h isclassical
where
both
αstaend,andweνsta
are functionsof Σ0 . Thus,
treatment
of α
1D
disk
models.
To thisobtaina new expressionof α by utilizingd,n andh = 3,
canis thethe locallypressurescale
height.
We theisothermal
hereafter.
Then,simulations
s /Ωempirical
Sectionunstableofwedisks can of
be stratified
determineddisks
by a with Ohmic
formulathatis assumption
derivedfromrecentcondition
MHD
t approachtheα−prescriptiontothecan expand
Σparameterize
and α that
as AZthisØ famousΣ<Σofのときdeadzoneなし(Σ~Σ)、Σ>Σ
のときdead。
negativecoeﬃcient;diﬀusion.
It is interestingnewformulation
can be zoneありでΣregarded as a generalof thecrit
critdiﬀusion
AZ~Σcritextension
gth
of
disk
turbulence(Shakura&
Sunyaev
1973).
scuss
howaclassical
α.
Armed
with
the
new
α,
we
performalinearstability
analysisofprotoplanetarydisksΣ = Σ0 + Σ1 ,
Ø 古典的なαでは、αがΣで決まるのでdM/dtとΣは比例α(3)(6)
sta < 0.
the results 2.2.
ofthatDispersion
undergo relation
layered accretion, and find that a viscous instability can occur around the outer edge
andiﬀusion.
WeØ
するだけで、かつ円盤は常に安定。
that thewe haveperformed
a linearanalysis
the
of
dead
zones.
Disks
becomein usingclassical
α. We
identify
that withthe diﬀerence
arisesderive a dispersion relation fromequation(1).stable
The# Note
fon
protoplane#
WKB
approximation,
where
Σ
≡
Σ̄
exp(ikr+
ωt)with∂α # Σ is uniquely determined for1a given value of Ṁ in the classicalΣ−dependenceof theṀ ; following
whereaswill serve fromas a fundamental
basis forα0confirmed+ α1 , the(4)above relation. In the followα
≃
α(Σ
=
Σ
)
+
nstability
can
≫Σ1,
and
1 ≡
0
# kr
stability analysis.
approach, the new approach leads
Ṁ
that
is
a
multi-valued
functionof Σ.
Wequantity
confirm our finding∂ΣtoΣ=Σ
ing0 sections, we examine αstathat is themaindescribed inboth
Section1,
thepresence
of
dead
zones
by exploring a parameter space as well as by performing the 1D, viscous evolution of disks. We
ks and the establishment of layered accretion there to regulate whether or not disks become unstable.
finally
discuss other non-ideal MHD eﬀects that are not included in our analysis, but may aﬀect ouretermined by the combination of the strength ofresults.
etic fields thatthread disks and the ionization ef- 3. APPLICATION TO DISKS WITH LAYERED ACCRETION
Keywords:
accretion,accretion
disks – We
instabilities
magnetohydrodynamics(MHD)– turbulence –cy of disks. The magnetic
field strengthis poorly
now apply– theabove unstable condition
to disks
protoplanetaryrained, so that it can generally
be treated disks
as a free that undergo layered accretion. We examine both a clas-

parameter in MHD simulations. The ionization sical approach that has widely been adopted in the literency is regulated by the value of Σ, grain physics ature and a more realistic approach that can be derived
1. INTRODUCTION
wellnumericalstudied simulations.
eﬀects (e.g.,We
Jinwill
1996; Sano & Miyamasks, and disk ionizing sources
such as UV and X- from the results ofthe
recent1999;
Fleming
&
Stone
2003;
Lesur
from thecentralstars
andcosmic
rays.
It
is
ideal
show below
The origin of disk turbulence is still poorly known(e.g., that the latter approach of layered accretion & Longaretti 2007;
ke accountof allthese
relatedpro- itscan
Okuzumi& Hiroseend up with disksthat canbecome2011).
unstable.It is widely accepted that
Armitage2011,
forquantities
a recent andreview),
while
existences simultaneously. In this paper, however, we adopt a
Ohmic
diﬀusiontends
to damp MRIs by smoothing flucis clearlyto accountfor assume
the observed
y stateprofilerequired
for magnetic
fields, andthat disk accretuations
in modelsmagnetic fields. The situation becomes more
3.1. Disk(e.g.,
Hartmannal. 1998; Williams& Cieza
aluetionof Σrateplays
a dominantrole etin determining
thecomplicatedwhen ambipolar
diﬀusion
As discussed
in and Hall term are2011).
the most
ideas Weis modelcur- disks with layered accretion.
ation
eﬃciency.One
This ofessentiallyleadspromising
to a situationconsidered.
Formostinstance,
numerical simulations
Section and2, we assume
that Σ is the
crucialrecent
quantitythemagnetorotationalt isrently
suﬃcient
to focuson Σ to examine instability
the stability (MRI)
show
that
sustainabilityofMRIs
to regulate the excitation of layered accretion. Under thewith ambipolar diﬀu-

VISCOUS INSTABILITY TRIGGERED BY LAYERED ACCRETION IN PROTOPLANETARY DISKS
Yasuhiro Hasegawa1,2,4 and Taku Takeuchi3の続き

Viscous Instability & Layered Accretion

1 Division of Theoretical Astronomy, National Astronomical Observatory of Japan,
evolution
Σ can Tokyo
somewhatalter ⟨BJapanZ ⟩. Then, theOsawa, ofMitaka,
181-8588,
2 Jet Propulsion Laboratory, California Institute of Technology, Pasadena,change incan be expressed as a funcZ ⟩ (∆ ⟨B
Z ⟩) andCA⟨B91109,
USA
2
3 Department of Earth and Planetary Sciences, Tokyo Institute of Technology,tionof Σ. ForTokyo
simplicity,
we assume
Meguro-ku,
152-8551,
Japanthat ∆ ⟨B ⟩ ∝Draft version November 10, 2015pΣp−1 ∆Σ (i.e., ⟨BZ ⟩2 =Z

ABSTRACT
Layered accretion is one of the inevitable ingredients in protoplanetary disks when disk turbulenceis excited by magnetorotational instabilities (MRIs). In the accretion, disk surfaces where MRIs
fully operate have a high value of disk accretion rate (Ṁ ), while the disk midplane where MRIs are
generally quenched ends up with a low value of Ṁ . Significant progress on understanding MRIs has
recently been made by a number of dedicated MHD simulations, which requires improvement of theclassical treatment of α in 1D disk models. To this end, we obtain a new expression of α by utilizing
an empirical formula that is derived from recent MHD simulations of stratified disks with Ohmic
diﬀusion. It is interesting that this new formulation can be regarded as a general extension of theclassical α. Armed with the new α, we perform a linear stability analysis of protoplanetary disksthat undergo layered accretion, and find that a viscous instability can occur around the outer edgeof dead zones. Disks become stable in using the classical α. We identify that the diﬀerence arises
from Σ−dependence of Ṁ ; whereas Σ is uniquely determined for a given value of Ṁ in the classicalapproach, the new approach leads to Ṁ that is a multi-valued function of Σ. We confirm our finding
both by exploring a parameter space as well as by performing the 1D, viscous evolution of disks. We
finally discuss other non-ideal MHD eﬀects that are not included in our analysis, but may aﬀect our
results.
Keywords: accretion, accretion disks – instabilities – magnetohydrodynamics (MHD) – turbulence –protoplanetary disks
1. INTRODUCTION

The origin of disk turbulence is still poorly known (e.g.,
Armitage 2011, for a recent review), while its existence
is clearly required to account for the observed disk accretion rate (e.g., Hartmann et al. 1998; Williams & Cieza2011).
One of the most promising ideas is currently the magnetorotational instability (MRI) andthe resultant MHD turbulence (Balbus & Hawley 1991;
Hawley & Balbus 1991). The fundamental process of
MRIs is angular momentum transport that is triggeredby magnetic tensions acting on charged particles in differentially rotating disks. Based on the intensive studies that have been done over the past, more than two
decades (e.g., Balbus & Hawley 1998; Turner et al. 2014,
for reviews), a number of paramount evidence has beenobtained that the MRI is a robust instability and canprobably operate in protoplanetary disks. In fact, linear stability analyses and numerical simulations under
the ideal MHD limit confirm the feasibility of MRIs in

the well studied eﬀects (e.g., Jin 1996; Sano & Miyama
1999; Fleming & Stone 2003; Lesur & Longaretti 2007;
Okuzumi & Hirose 2011). It is widely accepted that
Ohmic diﬀusion tends to damp MRIs by smoothing fluctuations in magnetic fields. The situation becomes more
complicated when ambipolar diﬀusion and Hall term areconsidered. For instance, recent numerical simulations
show that sustainability of MRIs with ambipolar diﬀusion is determined both by the net vertical magnetic fluxand by the vertical structure of disks (e.g., Bai & Stone
2011, 2013; Simon et al. 2013). It is important that theseresults are roughly consistent with classical linear analyses which simply suggest that the impact of ambipolar
diﬀusion is weak and minor (e.g., Blaes & Balbus 1994;
Wardle 1999; Desch 2004). Hall term provides a fundamentally diﬀerent eﬀect on MRIs, since it can principally
alter the configuration of magnetic fields, rather than diffusing them. The importance of Hall term is still unclear
and currently a matter of debate (e.g., Sano & Stone
2002a,b; Wardle & Salmeron 2012; Kunz & Lesur 2013).

5

CHONDRULE FORMATION VIA IMPACT JETTING TRIGGERED BY PLANETARY ACCRETION
Yasuhiro Hasegawa1,3 , Shigeru Wakita2 , Yuji Matsumoto2 , Shoichi Oshino2
1 Division of Theoretical Astronomy, National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588, Japan and2 Center for Computational Astrophysics, National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588, Japan

Draft version November 12, 2015

ABSTRACTChondrules are one of the most primitive elements that can serve as a fundamental clue as to the originof our Solar system. We investigate a formation scenario of chondrules that involves planetesimalcollisions and the resultant impact jetting. Planetesimal collisions are the main agent to regulate
planetary accretion that corresponds to the formation of terrestrial planets and cores of gas giants.
The key component of this scenario is that ejected materials can melt when the impact velocity
between colliding planetesimals exceeds about 2.5 km s−1 . The previous simulations show that theprocess is eﬃcient enough to reproduce the primordial abundance of chondrules. We examine this
scenario carefully by performing semi-analytical calculations that are developed based on the resultsof direct N -body simulations. As found by the previous work, we confirm that planetesimal collisions
that occur during planetary accretion can play an important role in forming chondrules. This arises
because protoplanet-planetesimal collisions can achieve the impact velocity of about 2.5 km s−1 orhigher, as protoplanets approach the isolation mass (Mp,iso ). Assuming that the ejected mass is afraction (Fch ) of colliding planetesimals’ mass, we show that the resultant abundance of chondrules
is formulated well by Fch Mp,iso , as long as the formation of protoplanets is completed within a given
disk lifetime. We perform a parameter study and examine how the abundance of chondrules and theirformation timing change. We find that the impact jetting scenario generally works reasonably well fora certain range of parameters, while more dedicated work would be needed to include other physicalprocesses that are neglected in this work and to examine their eﬀects on chondrule formation.
Keywords: meteorites, meteors, meteoroids – minor planets, asteroids: general – planets and satellites:
formation – planets and satellites: terrestrial planets – protoplanetary disks
1. INTRODUCTION

Chondrules are one of the most primitive materials
that probably contain profound information of how ourSolar system formed (e.g., Davis et al. 2014, for a mostrecent review). As they are named, chondrules are themost abundant ingredient in chondrites (up to 80 % involume). Chondrules have a number of the interestingCHONDRULE FORMATION VIA IMPACT JETTING TRIGGERED BY PLANETARY ACCRETION
Yasuhiro Hasegawa1,3 , Shigeru Wakita2 , Yuji Matsumoto2 , Shoichi Oshino2の続き

1 Division of Theoretical Astronomy, National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588, Japan and2 Center for Computational Astrophysics, National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588, Japan

Draft version November 12, 2015

ABSTRACTChondrules are one of the most primitive elements that can serve as a fundamental clue as to the originof our Solar system. We investigate a formation scenario of chondrules that involves planetesimalcollisions and the resultant impact jetting. Planetesimal collisions are the main agent to regulate
planetary accretion that corresponds to the formation of terrestrial planets and cores of gas giants.
The key component of this scenario is that ejected materials can melt when the impact velocity
between colliding planetesimals exceeds about 2.5 km s−1 . The previous simulations show that theprocess is eﬃcient enough to reproduce the primordial abundance of chondrules. We examine this
scenario carefully by performing semi-analytical calculations that are developed based on the results
Chondrule
Formation and As
Planetary
Accretionof direct N -bodysimulations.
foundby the previous work,9 we confirm that planetesimal collisions
that occur during planetary accretion can play an important role in forming chondrules. This arises
because protoplanet-planetesimal collisions can achieve the impact velocity of about 2.5 km s−1 orhigher, as protoplanets approach the isolation mass (Mp,iso ). Assuming that the ejected mass is afraction (Fch ) of colliding planetesimals’ mass, we show that the resultant abundance of chondrules
is formulated well by Fch Mp,iso , as long as the formation of protoplanets is completed within a given
disk lifetime. We perform a parameter study and examine how the abundance of chondrules and theirformation timing change. We find that the impact jetting scenario generally works reasonably well fora certain range of parameters, while more dedicated work would be needed to include other physicalprocesses that are neglected in this work and to examine their eﬀects on chondrule formation.
Keywords:
meteorites,
meteoroids–onminorplanets,
Figure 4.
The value of τand
τ
as a function of a.meteors,
While the standard
case (f = 1) is shown
the left panel,
the massive asteroids: general – planets and satellites:case (f = 3) is on the right one. For comparison purpose, the results of the time-dependent calculations are denoted by thesquares. Following planetary accretionthatbecomesslowerasaincreases,
both
τ
and
τ
becomeanincreasing
functionformation – planets and satellites: terrestrialof a.planets – protoplanetary disks
The value of τ
approaches at τ = 10 years at a = 2 AU for the standard case (the left panel), and at a = 3 AU for the massive
int

end

d

d

end

7

int

end

case (the right panel). Since τd = 107 years may be an upper limit of disk lifetimes, chondrule formation via impact jetting canoccur within these orbital radii (see the hatched region).

1. INTRODUCTION

Chondrules are one of the most primitive materials
hat probably contain profound information of how ourolar system formed (e.g., Davis et al. 2014, for a mostcent review). As they are named, chondrules are theost abundant ingredient in chondrites (up to 80 % inolume). Chondrules have a number of the interestingroperties; they are millimeter-sized particles, formed asolten droplets of silicate that has the melting temperture of around 1800 K. These properties provide inaluable constraints on their formation mechanisms. In

1996, 2001), solar nebula lighting (e.g., Morfill et al.
1993; Desch & Cuzzi 2000), and nebular shocks excitedby planetesimals in eccentric orbits (e.g., Wood 1963;
Iida et al. 2001; Morris & Desch 2010). While diﬀerent
models focus on diﬀerent physical mechanisms, the main
motivation of these models is to re-construct the thermal history of chondrules; the progenitor of chondrules
is melted first and then the resultant liquid of silicate
cools down rapidly to form spherical droplets. It is currently recognized that none of them can fully reproduce
a wealth of chondrules’ properties.

Xiv:1512.02064v1 [astro-ph.EP] 7 Dec 2015

A New Mechanism for Chondrule Formation:
Radiative Heating by Hot Planetesimals
William Herbst

Astronomy Department, Wesleyan University, Middletown, CT 06459
Ø コンドルールの形質には1750-2100
Kのピーク温度、数分の加熱と100-1000 K/hrの冷却が必要。
wherbst@wesleyan.edu
Ø 星雲モデル・・・ガス円盤内で重力不安定による圧力衝撃波で太陽に近づいて~3 AUに戻って隕石になる。熱の歴史が実験室の結果と合う。
andØ しかし、Na2Oができる高密度(ρs=10–5-10–3 gm cm–3)は円盤の幅<10 kmに相当。
Ø また、コンドルールはCalsium-Alminium-rich
Inclusionsより1 Myr後にできて2-3 Myr作ら
James P. Greenwood
れ続けるという年齢の問題もある。
Earth & Environmental Sciences Department, Wesleyan University, Middletown, CT 06459
Ø 惑星モデル・・・微惑星衝突でできる。ß衝突はいつでも起こるが、形成時間には制限がある。複数回の加熱に合わない。
jgreenwood@wesleyan.edu
Ø 石基(matrix)とコンドルールには炭素質コンドライトが同じように含まれるが、Si/Mg, Fe/
Mgの比が異なる。à石基とコンドルールは同じ太陽系起源となり、問題が難しくなった。
; accepted
ReceivedØ 新しい生成過程を提唱する。
Ø dust clumpからできるが、加熱される頃にはガスはなく(つまり圧力衝撃波は起きない)、
熱源は微惑星表面のマグマからの輻射。熱的な歴史が簡単になる。

– 19 –

arXiv:1511.02955v1 [astro-ph.GA] 10 Nov 2015

Sgr B2(N): A bipolar outflow and rotating hot core revealed by
ALMA
Aya E. Higuchi1 , Tetsuo Hasegawa2 , Kazuya Saigo3 , Patricio Sanhueza2 , James O.
4~~~~~~~~
Chibuezeaya.higuchi.sci@vc.ibaraki.ac.jp
Ø 大質量星形成は埋もれていて、かつ短時間で領域も遠いので謎。
Ø Sgr B2は銀河中心に近く、最も明るい大質量星形成領域。d~8 kpc。
ABSTRACTØ Sgr B2(N)はHII領域Kに付随(Kは水メーザーに対応するK1からK6に分解)。
– 26 –
Ø K2のNW-SE速度勾配は分子流なのか、東西方向の円盤なのか議論が分かれている。
We present the results of SiO (2− 1) and SO2 (124,8 − 133,11 ) line observa– 28 –tions of Sgr B2(N) made with the Atacama Large Millimeter/submillimeter Array (ALMA) at an angular resolution of ∼2′′ . Our analysis of the SiO and SO2
Ø ALMA Cycle 0 (Belloche+2014),
θ~2”, ΔV~1.6 km/s, σ~3-7 mJy/b, SO2 (107.8 GHz), SiO
line emission reveals a bipolar molecular outflow in an east-west direction whose(v=0,1,2のJ=2-1driving
at 86
GHz)
sourceis located at K2. In addition, SO2 line core shows a north-south– 24 –
velocity gradient most probably indicating
a hot core of molecular gas rotating
SO2の速度勾配の方向が高速(プロファイルのウイ
around K2. Fractional abundances of
SO2 and SiO (X(SO2 ) and X(SiO), respecング)では東西、低速(プロファイルのline
core)では
tively) in the outflowing molecular gas are derived from comparisons with the
南北。高速成分は分子流(P.A.=120°)。
C18 O emission. Assuming an excitation
temperature of 100 ± 50 K, we calculate+2.6−8
X(SO2 ) = 2.3
and X(SiO) = 1.2+0.1 −0.1 ×10−9 . The outflow from
−0.4 ×10
Sgr B2(N) K2 is characterized as a young (5×103 yr) and massive (∼2000 M⊙ ),but moderately collimated (∼60◦ ) outflow. We also report a possible detection of
the SiO (v = 2, J = 2 − 1) maser emission from the position of K2. If confirmed,
it would make Sgr B2(N) the 4th star forming region associated with SiO masers.
Subject headings: ISM: kinematics and dynamics — ISM: molecules — ISM:
individual (Sgr B2) — ISM: outflows — stars: massive — stars: formation1

College of Science, Ibaraki University, 2-1-1 Bunkyo, Mito, 310-8512, Japan

Fig. 3.— (a): The first moment map of SO2 emission made using all velocityFig.
ranges5.— (33(a) SO2 integrated intensity map (gray-scale image and black contours) and the2
109 km s−1 ). (b): The first moment map of SO2 emission made using velocity
ranges intensityofintegrated
map of the SiO outflows (blue and red contours) of Sgr B2(N). The
Fig. 1.— Integrated spectra around the (a) SO2 and (b) SiO emission lines in Sgr B2(N).
The spectra were integrated over a region of 20′′ ×20′′ region, centered on the continuum−1
blue color
represents blueshifted gas, while the red color represents the redshifted gas. The
59-65
km
s
.
(c):
A
zoom
into
the
SO
peak
positionofFigure
3(b).
The
red
crossesmark2−1source K2. V LSR of 63 km s is the systemic velocity of Sgr B2(N).

National Astronomical Observatory of Japan 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan
グレー: SO , コントア: SiO
2black contours range
from 10
to 1-190%ofthe peak emission, in steps of 10%. The blue color
Departmenttheof position
Physical
University,
Gakuenof K2Science,(Gaume etGraduate
al. 1995). School of Science, Osaka Prefecture
点:
水メーザー
represents blueshifted gas (VLSR = 29 to 50 km s−1 ), while the red color represents thecho, Naka-ku, Sakai, Osaka 599-8531, Japanredshifted gas (VLSR = 91 to 111 km s−1 ). The contours for integrated intensity maps, with

3

Sgr B2(N): A bipolar outflow and rotating hot core revealed by
ALMA

の続き

ØAya
南北の速度勾配は回転で、速度勾配88
AUから42 Mo/sin2i。より高E. Higuchi1 , Tetsuo Hasegawa2 , Kazuya Saigo3 , Patricio km/s/pcとr=5800
Sanhueza2 , James O.
4
温高密度を見るSO2 (99.4
GHz)でも剛体的なのでr~6000
AUのリングだろう(ケプラー円
Chibueze
盤より外のcircumcluster
troids)。
aya.higuchi.sci@vc.ibaraki.ac.jp
Ø 分子流の物理量を出すために、同時に観測されたC18O
ABSTRACT(XC18O=1×10–7)と合わせて、T
ex=50, 100, 150 KでLTEを仮定。
Ø XSO2=2.3×10–8, XSiO=1.2×10–9。ß他のhigh-mass hot coreと合う。

We present the results of SiO (2 − 1) and SO2 (124,8 − 133,11 ) line observations of Sgr B2(N)made with the Atacama Large Millimeter/submillimeter Ar– 30 –ray (ALMA) at an angular resolution of ∼2′′ . Our analysis of the SiO and SO2line emission reveals a bipolar XからdM/dv∝|ΔV|^(–1)を得た。
molecular outflow in an east-west direction whose– 22 –
小質量星分子流では~–4で若いほど浅い。
driving source is located at K2.
In addition, SO2 line core shows a north-south
velocity gradient most probably
indicating
a hot core of molecular
gas rotating
Table 3. Physical parameters of the outflow
Srg
B2(N)もtdyn~5000yrと若い。
◦
around K2. Fractional abundances of SO2 and SiO (X(SO2 ) andrespec- diagrams along the outflow in SOParameter
Fig. X(SiO),
6.— Position-velocity
2 and SiO emission, P.A.=120
他の大質量星形成領域に比べると分子流◦(panel a and withc), andthe
perpendicular to the outflow in SO2 emission, P.A.=30 (panel btively) in the outflowing molecular gas are derived from comparisonsDistance from K2 to SiO peak position : l [pc]and d). (a) contour levels [5, 10, 30, 60, 90, 120,
150, 180, 210, 240, 270, and0.08300] ×18
Blue lobe
C O emission. Assuming an excitation
temperature of 100 ± 50 K, we calculate −1の質量は同じだが、小さく若い。また少し細Red[5,
lobe10, 30, 60, 90, 120, and 150]
0.06 × σ
1σ
(1
σ
=
3
mJy
beam
).
(b)
contourlevelsDistance from K2 to SiO outer contour : l [pc]X(SO2 ) = 2.3+2.6 −0.4 ×10−8 and X(SiO) = 1.2+0.1 −0.1 ×10−9 .(1Thefrom−1
σ = 5outflow
mJy beam) (c) contour levels [5, 10,Blue
15,lobe20, 25, 30, 35, and 40] × σ0.3(1 σ =い(~60°)。 3−1
Red lobe
0.2
10 mJy (∼2000
beam ). M(d)SO
SO2 (124,8 –133,11) (contours), contours
Sgr B2(N) K2 is characterized as a young (5×10 yr) and massive⊙ ), 2 (294,26 –285,23 ) (color) andmass (M )−1levels [5, 10, 30, 60, 90, 120, and 150] × σ (1 σOutflow
=
5
mJy
beam
).
Other
molecular
lines◦
Blue lobe
5.7×10
but moderately collimated (∼60 ) outflow. We also report a possible detection of(e.g., C2 H5 OH, n-C3 H7 CN) are also displayed. Red lobe
1.4×10the SiO (v = 2, J = 2 − 1) maser
emissionfrom the position of K2. If confirmed,
Total
2.0×10SiO
v=2は線幅が細く、K2の位置で点源、Momentum (M km s )thit would make Sgr B2(N) the 4 star forming region associated44
with SiO masers.
Blue lobe
7.4×10
a

b

1

2

⊙

c

2

d

3

3

ΔV=9 km/s, Lν=2.8×10 /sà4番目の星形
成領域SiOメーザーか？v=2,
J=1-0は初めて。
Subject headings: ISM: kinematics
and dynamics — ISM: molecules —ISM:
individual (Sgr B2) — ISM: outflows — stars: massive — stars: formation1

College of Science, Ibaraki University, 2-1-1 Bunkyo, Mito, 310-8512, Japan

Fig. 7.— Masses, momenta, and energies of the outflow per unit velocity width as a functionof velocity
2 from the systemic velocity (|∆V |=VLSR -VSYS) for the blueshifted and redshifted
outflow lobes. The dashed line marks the defined separation between line core (low velocity)
and wing (high velocity) emission.

National Astronomical Observatory of Japan 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan3

Department of Physical Science, Graduate School of Science, Osaka Prefecture University, 1-1 Gakuen-

⊙

−1

3

Red lobe
Total
Kinetic energy (erg)Blue lobe
Red lobe
Total
Typical outflow velocitye : Voutflow ( km s−1 )Blue lobe
Red lobe
Total
Dynamical timef : tdyn (yr)Blue lobe
Red lobe
Average

2.2×104
3.0×104

1.1×1048
4.4×1048
5.5×104813
16
15
5.6×103
3.7×103
4.7×103

by looking at the detailed structure of

Xiao Hu (·S)1 , Zhaohuan Zhu (1g)2 , Jonathan C. Tan1,3 , Sourav Chatterjee1,4
Draft version November 10, 2015

5. GAP OPENING

5.1. Gap Structure & Opening Mass f

The gap opening process in IOPF is

ABSTRACTnation of pebble accretionof the first p
Ø ケプラー衛生が見つけた4000の系外惑星の3割強がSystems
with Tightly-packed
Inner
its mass. It may also be important, in
The Kepler mission has discovered more than 4000 exoplanet candidates. Manythem
arein indeadofzone
retreat,setting the locati
Planets(1-10M
でP~100日が3個以上)。
E
systems with tightly
packed inner planets (STIPs). Inside-Out Planet Formation (IOPF)(Chatterjee
maximumthat leads to new pebble r
second planet
formation.
& Tan 2014) has been proposed as a scenario to explain these systems. It involves thensequential
in situ(1)外でできて内に移動するシナリオßresonanceにあるものが少ないのでダメ。
We now investigate the disk structu
planet formation at the local pressure maximum of a retreating dead zone inner boundary(DZIB).
by introducing
planets of various mass
(2)その場でできるシナリオß惑星ができるとpebbleが入れないのでダメ。
tion aof rplanet.
= 0.1 AU,The
i.e., at the transitio
Pebbles accumulate at this pressure trap, which builds up a pebble ring, and then
4
with
a
fixed
↵
profile.
planet is expected
to grow in massuntil it opens a gap, whichhelps to both truncateof pebble
accretionFigure 3 showsØ Inside-Out
Planet Forma)on:
MRI-ac)veとdeadzoneの境で惑星ができ、境が外へ移る。
mass surface density, midplane presand also induce DZIB retreat that sets the location of formation of the next planet.
Thisafter
simpletemperature1000 orbits of evo
Ø 惑星が移動しないか、ギャップを開ける質量(Vulcan惑星との比較)、ギャップが境(Deadduction of planetsof masses Mp = 0.1
scenario may be modified if the planet undergoes significant migration from its formation
location.
of 0.1 MG . We note that the gas
planet-disk
interactions play a crucial role in the IOPF scenario. Here we steps
present
numerical
ZoneThus
Inner
Boundary)をずらす方法、を調べる。
quickly, within ⇠ 100 orbits, to a profi
simulations that first assess the degree of migration for planets of various masses thatare state
forming
the final
at 1000atorbits.
As planetmass increases,
the radi
the DZIB of an active accretion disk, where the e↵ective viscosity is undergoing a rapid
increasein
gradual deepening of the gap in bo
the radially inward direction. We find that torques exerted on the planet by the face
diskdensity
tendand
topressure
trap profiles. The
the planet at a location very close to the initial pressure maximum where it formed.
We
then
study
dips due to reduced viscous heating
cal depths.
this particular set-up,
opening by theseplanets to assess at what mass a significant gap iscreated. Finally
weForpresent
2D gapFARGO-ADSG(エネルギー方程式を含む)、0.002x0.002
AUグ
zone width of 0.03 AU, it is only ona simple model for DZIB retreat due to penetration of X-rays from the star to the
disk
midplane.
are &
0.5M
G that there is significan
リッド、粘性αは一様か>0.1
AUで0.01の2層。
azimuthally
averaged pressure ma
Overall, these simulations help AUで0.001、<0.07
to quantify both the massscale of first, “Vulcan,”theplanetformationtheplanet’s
orbitalradius. Table 1
and the orbital separation to thelocationformation.
Figure of
2. second
Transitionplanet
zone migration
torque,, profiles
for inner boundary
Planet-disk
interaction
at thedeadzonetion of the pressure maximum from
0.1 MG (top), 0.5 MG (middle) and 1.0 MG (bottom) planets
Subject headings: protoplanetary disks,interactions,planetssatellites:
formation
bital radius
at 0.1 AU, rPmax , but nheld planet-disk
at fixed radius. Medium
resolution (MR)and high andresolution
MR
HR

0.20
0.15

Torque ( 0 ).02791v2 [astro-ph.EP] 8 Nov 2015

sition zone is a key requirement of IO

lows a planet to continue to grow by
INSIDE-OUT PLANET FORMATION. III.
from low to relatively high masses. N
PLANET-DISK INTERACTION AT THE DEAD ZONE INNER BOUNDARY
how pebble accretion may be disrupte

0.10
0.05
0.00
0.05
0.10
0.15

r (AU)

惑星移動) α一様でMp=0.1, 0.5, (HR)
1.0runs
MareGに対してr=0.085
tothe0.115
shown, with the torque induced bydisk on theplanet’s Hill radius, R = (M /(3mplanetbeing
theaverage
from
orbit
400
to
500
after
introduction
Given
this
disk
structure,theviscouscriterion
for
the
[r
,
1.25r
] and⌘ [0.84r, rmax],r/R. As
M incr
min
min
max
of
the
planet.
A
positive
torqueleads
tooutwardmigration;a
AUでトルクΓを計算。àΓ=0となるr~0.1
AUにとどまる。
0.5 M ,
grows by a factor onegative torque to inward migration. The HR results show deH

r,Pmax1. INTRODUCTION
gap opening planet
mass is :

Pmax

H

p

p

⇤

G
r,Pmaxsupply of pebbles
radial(outer)
drift
may
be truncatedifthe byinner
radiusof the disk
' 5. Figure 3 shows this also corresp
planet formation,
perhaps isinitiated
thefrompebblestreamsurfaceby
densitymaximum
retreating
rameterincreased
zero
to ao
Since launch in 2009, Kepler has revealed
more than40⌫milar amount.2005) , occurs ining
instability(Youdin&Goodman4000(e.g.,
edge of dampingzone
to theedge
of
We havecomparedgap opening(4) disk (Lambrechts
gap exoplanet
openingcandidates
mass M
G =Mullally
G 2 et al.. 2015). A
the outer& withJohansen
2014;
LevisonetresuMp = 0.1,
0.5, 1.0M
large percentage (& 30%) of these candidatesr ⌦ are in sysG at MR aneachorbit,
the damping
MRとHRは分解能
al. 2015;
Bitsch etWithinal. 2015).
In findsitu
formationmodelsWe
verysimilar radial
profiles otems with tightly-packed inner planets (STIPs). These
agreement
invaluesat
betterthanconstant:theactualdamping
is 10%
thalsopotential
face
thechallengeof alreproducing the observed massが2倍違う。
our havedisk3model,
obtain:the planet’s
gravitationalof 0.6h(Müller et
areImplementing
systems that usuallyor more we
detectedplanetsof the gap region.
2012).
versus orbital radius
distributions
once
ofview
gasofoning
functiontimes
ae↵ects
coefficient,
whp
Figure4 shows
the 2Dtheof radii ⇠ 1 10 R ✓and withthan
100torque,days , is scaled2
4 2
2◆1/5periods less
The
as
=
(M
/m
)
⌃
r
⌦
h
,
0
pmigration⇤g
pduring the
⇣
⌘
disk
mass
surfacedensity(compared
protoplanet
oligarchic
growthphase
4/5
one,inlinearlywith time.t(Fang & Margot 2012).
scenarios
3 There are2/5two µmainwherer 4/5
is the orbital
radius of the planetfromand ⌃g zerois the toplanet)
1/5arethe r- plane. The strength
accounted
for(Ogiharaetal.
2015).
40 Gsuch close-in planets:⇡
average gas in
mass
density at this orbital
radius.
thatM
canproduce(1) formation
G =along with deepening
gap, are evidentFor
ourstandard“medium
SBsurfaceThe
Inside-Out
Formation(IOPF)
scenarioresolut
pro128k (e.g.,
The gridsize
in our standardMR
run is morePlanet
than twice
Vulcan・・・水星の近日点移動を説明するために提唱された水星より内側の惑星。
the outer disk followed by inward migration
Kley&
5.2. by
DZIB300
Retreatwith an Evolv
isisG .aevenly
dividedsectorsaz
the Hill radius of a planetwithWe
therep = 0.1M
posed
byMCT14
new
type
of
in
situ
formationmodel.
Figure 2.
Transition zone migration torque, , profiles for0.

creasing from positive to negative values in the transition region(where ↵ starts decreasing as r increases just interior of 0.1 AU). We expect the planet will migrate inwards from positions where⇤the total torque is negative and migrate outwards where the total
torque is positive. It will stop at zero torque. Thus these torqueare indicative of there being a stable “planet trap”in thisK profiles
location, where = 0.

0.010

r (AU)

r,Pmax =rPmax /RH

0.61

0.48

0.42

a The separation between new pressure maximum and planet orbita
INSIDE-OUT PLANET FORMATION. III.
fixedの続き↵ profile with a transition width of rDZIB = 0.03 AU. Note, l
PLANET-DISK INTERACTION AT THE DEAD ZONE INNER BOUNDARY maximum pressure.

Xiao Hu (·S)1 , Zhaohuan Zhu (1g)2 , Jonathan C. Tan1,3 , Sourav Chatterjee1,4600

Ø gap opening) 2層αでr=0.1 AUに惑星(Mp=0.1-1.0 MG)を置
き、1000周期。
ABSTRACT
Kepler
hasMdiscovered
more than 4000 exoplanet candidates. Many of them are inØ mission
MP>0.5Gで圧力最大の半径がヒル半径より有意に外。
500(g/cm2 )Draft version November 10, 2015

400
300
200
100

0

r (AU)

0.1MG
0.2MG
0.3MG
0.4MG
0.5MG

P/kB (K cm 3 )2.0e+18

0.6MG
0.7MG
0.8MG
0.9MG
1.0MG

s with tightly packed inner planets (STIPs). Inside-Out Planet Formation (IOPF) (Chatterjee2014) has been proposed as a scenario to explain these systems. It involves sequential in situ
formationat the local pressure
maximum of a retreating
dead zone inner boundary (DZIB).
Ø DZIBの移動)
2層αでX線が(r,h)=(0,11Ro)から来るとし、0.1
s accumulate at this pressure trap, which builds up a pebble ring,and then a planet. The–2, φPlanet-disk
interaction
at the dead zone inner boundary
AUから積分して柱密度がφ
Σ
(Σ
=100
gcm
is expected
to grow in mass until it opens a gap,
which
helps
to
both
truncate
pebble accretion
X X XX=5)になる
so induce半径を測る
DZIB retreat (Σthatsets the locationof formation of the next planet. This simple
keVでτ=1-10)。
Table 1
XはE=10-30
o may be modified if the planet
undergoes significant migration fromRetreat
its formation
location.
of the local pressureduring ofgap
opening
Figure 3.maximum
Radial structure
diskmass surface density (top),
midplane pressure (middle) and midplane temperature (bottom)
àα一様よりも~5倍広がり、rplanet-disk
interactions play a crucial role iniに依存。
the IOPF scenario. Here we present numericalduring gap opening for planets of mass Mp = 0.1 MG to 1.0 MG in/MG
0.1 are0.2
0.3of 0.1 0.4
0.6
0.7
0.8 radius
0.9of 0.11.0
steps
MG held0.5
fixed atthe transitionzone
AU.
tions that first assess the degree of migration for planets ofMpvarious
masses that
forming
at
Profilesarer-shownfor
mediumresolution
runs after
1000 orbits. ⌃Figure
4.
2D
view
of
the
mass
surfacedensity
perturbation,
=
r
/R
0.61
0.48
0.42
0.38
4.75
4.47
5.09
4.86
4.68
5.27
Pmax
Ha rapid increase
IB of an active accretion disk, where the e↵ective viscosityr,Pmax
is undergoing
Gap openingin
manifests itself via a decrease in ⌃, P and T in the⌃0 is the surface
in and,the absenceplanet).
of density
the planet
once Mpof&a 0.5M
, a significant rea The separation between new pressure maximum and planet
orbitalradius,scaledtoplanet’s
Hill Gradius.
resu
dially inward direction. We find that torques
exerted on the planet by the disk tendvicinity
totrap
treat of the local surface
densityand pressure
maxima These
outwards
fixed ↵ profile with a transition width of rDZIB = 0.03 AU.byNote,locationofpressuremaximumismeasured at theseveral Hill radii.
net at a location very close to the initial pressure
maximum where it formed. We then study
maximum pressure.
70
0.22
ening by these planets to assess at what mass a significant gap is created. Finally we
present
dead zone innerHigherlevels ofalong
ionization
thereboundary.
is negligible
material
this60
le model for DZIB retreat due to penetration of X-rays from the star to the disk 0.20
midplane.
may also arise due to shock heating in spiral arms thatcations
interiortotheplanet,i.e.,
at r
are induced by the planet. We note that these spiral, these simulations help to quantify both the mass scale of first, “Vulcan,” planet formation
weconsider
to
be
a
good
approximatioarms, propagating outwards into the dead zone, will50 bye orbital separation to the location of second planet formation.
clearingof theof innerdiske↵ective
and als
themselves cous
also provide
a sourceenhanced
0.18
viscosity.
The
lower
densities
of
the
gap
regionmay
also rverticalscaleheight
is
small
in
this
40
headings: protoplanetary disks, planet-disk interactions, planets and satellites: formation
allow for increased penetration of X-rays that raise the
1.5e+18
1.0e+18

5.0e+171800

r (AU)

1600

T (K)

1400
1200
1000

800
600

1. INTRODUCTION

in 2009, Kepler has revealed more thancandidates (e.g., Mullally et al. 2015). Ae (& 30%) of these candidates are in systly-packed inner planets (STIPs). Theset usually have 3 or more detected planets
0 R and with periods less than 100 days
ot 2012). There are two main scenarios
ce such close-in planets: (1) formation in
ollowed by inward migration (e.g., Kley &ossou et al. 2013, 2014); (2) formation in

0.16

0.08

0.10

0.12
r (AU)

0.14

0.16

0.18

0.20

r,Pmaxr (AU)

0.06

path integral starts from r = 0.1 AU aionization level and activate the MRI. Such e↵ects could
30 withrDZIB . toNote,
this transition
path starts
cause the viscosity
make thatits radial
further
low
angle
to
the
midplane
of
'
24
, wh
out
in
the
disk,
which
would
lower
the
densityinthegap
0.14 be truncated if
supply of pebbles by radial drift may
20
region and vicinity
as the evendiskmore.
evolves and rDZIB increases
planet formation, perhaps initiated by theThepebblestreamfull treatmentof these processes
complex
In addition,
we needis atovery
specify
theproblem,,beyond
the
scope
of
the
present
paper.
Here10 we
ing instability (Youdin & Goodman 0.12
2005)
occursin
Case
A transition
Case zone
B
Case CX-ray penetr↵
inthepresent a simple, heuristic model for DZIB retreat based
expect itfrom
be protostellar
broader thanthetran
the outer disk (Lambrechts & Johansen
Levisonetto theon2014;
X-ray penetration
coronato0 the
0.10
1000
2000
3000
4000
5000
6000
7000
thermalionizationofalkalimetals.
disk midplane.models
The X-rays are assumed to propagate F
al. 2015; Bitsch et al. 2015). In situ formationof Orbitsfrom a heightof 0.05Number
AU at
r = 0 (i.e., shape
11R , whichassumethefunctionalof theis r
also face the challenge of reproducing theobserved
mass
expected
to↵beis⇠the
3–4 samestellar asradiithatfor aadopted
solar massinpre§3.
5. Radius of DZIB (i.e., the outer transition radius of ↵The
thicknessof thetransitionzone
versus orbital radius distributions Figure
oncemaine↵ectsof star).
gas
onprofile)assetsequenceby X-raypenetrationin risingevolving↵ disks.
Mediumwhere↵starts
from
the
DZIB
from
the MRI-active
regionwith
to deadzonelines;
is assumed
to be va
resolution(MR)
results areshowndashedhigh resoluprotoplanet migration during the oligarchic
growth
phase
by
the
mass
surfacedensityalong
thecharacterizeda massthattion (HR)results withbysolidlines.
The
three surface
cases of density
inner tranX⌃
X , i.e.,scalesthe (Case
X-ray
mass
surfacedensitysition radiiof with0.07 AU
red
0.1
AU
(Case
B,
blue
equal
toA,penetration
note
that
the w
are accounted for (Ogihara et al. 2015).
X ⌃lines),
X . WeFigure 3. Radial structure of disk mass surface density(top),
lines) andAU (CaseC,⌃
green
lines)
shown.
In each case,due0.11
to absorption,X.
sitionfinal
regionmayarebe
somewhatlarge
Inside-Out
PlanetFormation(IOPF)
scenario
protheestimatedconverged,
retreat radius
is shown
withGa =horimidplaneThepressure(middle) andmidplanetemperature(bottom)Starting
from
the
FARGO
simulation
with
0.5
penetration
depth
of
the
X-rays(i.e.,
zontaldot-dashed
line
(see
text).
duringgap
openingforplanets
of
mass
M
=
0.1
M
to
1.0
M
in
p
G situ afterG
300 orbits model.
(i.e., when a wide, but relatively shallow,
posed by CT14 is a new typeof information
0.5MG MR ri =0.07 AU
0.5MG HR ri =0.07 AU

0.5MG MR ri =0.1 AU
0.5MG HR ri =0.1 AU

0.5MG MR ri =0.11 AU
0.5MG HR ri =0.11 AU