SFN #333 (37-44本目)
百瀬宗武(茨城大・理)詳細解説は以下の2本• #40: Modeling disk fragmentation and multiplicity in massive starformation (G. André Oliva and Rolf Kuiper)• #43: Gas trapping of hot dust around main-sequence stars (TimD. Pearce⋆, Alexander V. Krivov and Mark Booth)

x
x1500
run
nr
n✓
n
ndisk
x30
x1500
@t
achieved
inthemidplane
(z
=
0);
and
the
azimuthisuniformly
achieved
ing
of
the
gas,
shear
of
the
disk
and
other
gravito-radiationpres
number
of
cells
that
resolve
thedisk’sphysics(column
5);
cell
The
cloud
dynamics
aremodeled
as
an
ideal
gas
with
the
thus
providingalinkbetweenthetwo
phenomena.
ThesimulaThis
choiceofcoordinatesisexplained
andjustified
in
more
1.50
77.8
10
3
The
variables
involvedinaaredetailed
below.
The
Poisrad11
discretize
x1equations:
34au
32
7.0 ·and
10 energy
6.36359hydrodynamical
processes.
Instead,atime-independent
grid
Accretioninfragmented
disks
isexpected
to
not
be
a
smooth
of pr
size
at
r
=
30
(column
6),
cell
size
at
r
=
1500
au
(column
tions
in
Meyer
et
al.
(2017,
2018,
2019)
show
accretion
bursts;
where
⇢,
P,
E
are
the
density,pressuredensity,rehydrodynamics
6
discretized.
Inthemidplane
the
cells
are
approximately
cubical,
6.36
359
4
son equation of self x2
gravity
is solved
by meansof a di↵usion
detail in Kuiper et al.
(2011),
ina nutshell,a spherical
gridradiuswith two
0.74
37.5
10
67the
21 and
64
5.3
·the
10
3.07computational
167•was
Physics
whose
spatialbut
resolution
scales logarithmicallywiththey performed
extensive accretion
analysis
onofthesome
accretion
process,butcharacterizedbyanepisodic
frag-process, spectively;
isacceleration
sourcevisthevelocity,
a
7).
x
is
also
minimum
cell
size
of
the
doext
30
5
ansatz.
MoredetailsontheimplementationofthePoissonsolver77.8
7This c
1.50
x4
134
41
128
4.2
·
10
guarantees
strictangularmomentumconservation
aroundthewithtwoexample
cell
sizes
given
as
x
in
Table
1.
intensity
andfrequencyofthebursts.
term.
Theseequationsaresolvedwiththehydrodynamics
mod3.0740:
167
10
0.368
18.4
used,
allowing
for
very
high
resolution
in
the
areas
of
most
interments.
The
releaseofgravitational
potential
energycreates
an
main
in
the
disk’s
midplane,andxrepresentsroughlythe1500
Modeling disk fragmentation and multiplicity in massive star
6 (2010a).
detail2.3.
in K
for
the
self-gravity
modulearegiven
in
Kuiper
et
al.
0.74
37.5
x8
268
81
256
3.3
·
10
@⇢
ule
of
the
numerical
grid
code
Pluto
(Mignoneetal.
2007),
withest. Weset
upthe
a seriesof simulations
withincreasing
resolutions,centralmassive
protostar,
andlogarithmic
grid
in
r
allowsincreaseinluminosity,i.e.,anaccretion
burst.
Accretion
burstscell
size= inthe outer region of the disk.7
+
r
·
(⇢v)
0
(1)
guarantee
choiceofandcoordinatesisexplained
andjustified
in
more
1.50
77.8 formation (G.This
The
gas
is
assumedtobecaloricallyperfect,
governed
x16
536
161
512
2.6 that· 10 is,0.368 and18.4
André
Oliva
Rolf
Kuiper)Massive
stars
do
not
typicallyform
inisolation.
Studiesonadditional
modulesforhandling
radiationtransport
selfandexplorethephysicalprocesses
that
occur
in
fragmentationo↵er ancloser
explanation
the luminosity
burststar,
events in regions of @t
to thetoforming
massive
mulation (column 1), num- for a focus on the phenomena
centralThembythecalorical
equation
of
state
P
=
(
1)E
(where=multiplicity
inmore
evolvedsystemsof
massive
stars
show
that
gravity.
int
detailin
Kuiperetal.
(2011),butinanutshell,aspherical(howfragments
andinteract),
thebeenproperties
of in,
thee.g.,frag-grid@massivestarevolve
formation
which
have
reported
Hunter
0.74
37.5
focu
Table
1:
Designationcode
ofmassive
eachEsimulation(column 1),of
num- for agene
whilesavingcomputational
power.
An
explanation
on
how
well
a large portion of them are spectroscopic binaries (see,5/3,
e.g.,theSana
Thegravityoftheformingstar,
theself-gravity
value
for
H
at
low
temperatures,
and
is
the
internal
olumns 2–4); approximate
2
int
I
)
=
⇢a
(2)
(⇢v)
+
r
·
(⇢v
⌦
v
+
P
extthe frequency-dependent opacity; andis theopticaldepth;
(⌫,coordinate
r),
流体の式：
mentset (orbits,
massCarattiandtemperatures),theirfate and(whethertheyal.
(2017),oGarattietal.
(2017)Sugiyamaetal.
while sav
ber
of
cells
for
each
(columns 2–4);
approximate
@t
et
al.
2012;
Kobulnicky
et
al.
2014;
Dunstalletal.
2015).
The
obthe
fluid
and
the
radiation
forcesareincorporated
into
the
code
guarantees
strictangularmomentumconservation
aroundthe【内容】大質量星形成とその周りの円盤進化（分裂，連星形成）をかつenergydensity).
does
thischoiceofgrids
resolvethephenomena
studied
here
is
0.368
18.4
00 au, i.e., the approximate, thestellarradius.
equation
isaau,
integrated
for
R?the
evolvefurtherRecently,
and eventuallycompanion
andthethe possibility
does thisnumberof cells
in theThis
regionr < that
1500
i.e.,
approximate(2019).
Chen ofetbecomeal. (2020)
reportedonthesuggest
observation
servations
fragmenting
accretionstars),
disks
acceleration
sourceterm,
sucha? the+ asg+ eacharad , ray di@E via
ext =Radiationtransport
isincorporatedbythemethoddescribed
presented
in Sect. 9.2,
asofwellascomparison
to thegridchoicesmassive
protostar,
andthelogarithmic
grid
r burstallowsbin in theeachdisk’s
timephysics
step of(column
the hydrodynami((E +ande↵ectsthathasonfragment
statistics.
+ andrrection· numberP)v)= ⇢v· aresolve(3)cell presented
offrequency
cells
that
5);
’s てない高い解像度でシミュレーション。星の進化・ダスト進化を含む
physics (column 5); cell central
ext
diskresolution
substructuresassociatedwithevent,
thatclosebinariesmayformanbyaccretion
disk infragmentation
and
later
in⇢(r, tin Kuiper(2010b),but
advancedto6),a cell
two-temperature
ap-au (column of previou@t et al.
size
at
r
=
30
au
(column
size
at
r
=
1500
cal
simulation.
ward
migrationof thecompanions(Meyer The
et al. simula2018).
of previous
studies.
thus providing
a linkbetweenthetwo phenomena.
zeat(column
r = 15001),
au (column
for
a
focus
on
the
phenomena
closertotheforming
massive
star,
onGridnumproach, which wewillsummarizein the rest
ofsizethisofsection.
We
GM
?
7).
x
is
also
the
minimumcellthecomputational
do-dust30
Thefrequency-dependent
opacity(⌫)
isthesum ofrethe
base自己重力RHDコードを用い，分裂片に対しsubgridやsinkを使The
outcomeofoursimulation
wasalreadyused
in
Ahmadi
=
e
a
tions
in
Meyer
et
al.
(2017,
2018,
2019)
show
accretion
bursts;
where
⇢,
P,
E
are
the
density,pressure
andenergydensity,?
re of the computational do- while saving computational power.
2 theoftreat the star asanemitterradiation;
thedustdust
andgasrepresents
present
inroughly
mainindisk’s
midplane,andopacities,
x1500
the
ropacities.
An
explanation
on
how
well
In
this
study,
we
present
thehighest-resolution
self-gravityand
gas
For
the
we
use
the
tabulateds 2–4);
approximate
et al.they(2019)
forproducingsynthetic
observations
with
ALMA
performed an extensive analysis on the accretion process,istheacceleration
sourcespectively;visthevelocity,
anda2.3. We
Initiacextthetodisk.
2 addition
the
cloud
absorbit,andre-emitit,inthethermalradicell
size
in
the
outer
regionofrepresentsroughlythe
わず可能な限り流体計算で構造を高解像度に分解。円盤の進化とそこか, wherer sg =(1993),
4⇡G⇢ including 79 frequency bins,
radiation-hydrodynamical
simulations up toquandate on disk frag- avalues
1500
sg = rbysgLaor& Draine
and
NOEMA.
Inthat
paper,
many
observationally-relevant
intensity
andfrequencyofthebursts.
term.
Theseequationsaresolvedwiththe Thishydrodynamics
mod加速度：
does
thischoiceofgrids
resolvethephenomena
studied
here
is
2.3.
Initialandboundary
conditions
i.e.,
the
approximate
ation
due
purelytohydrodynamic
compression.
treatment
mentationaroundaforming
massive(proto)star.
We
continue
The clouinitia
DrE
r
·
F
k.
and
we
calculatethe
local
evaporation
temperature
of
the
dust
tities were computed, including 1.37 mm continuum images,
?
R
ule
of
the
numerical
grid
code
Pluto
(Mignoneetal.
2007),
wither radiation
R
Thefo
らできる分裂片の進化，分裂片周りにできるsecondarydisksとその分裂
allowsus to adivide
the
total
flux
F
into
two
contrirad =the approachtaken by Meyer
et al.
(2018),
in whichno sink
general
tot
in
Sect.
9.2,
as
well
as
comparison
to
the
grid
choicesgrainsbyusing
theformulaofIsella&Natta(2005).
The
gas
sics
(column 5); cell presented⇢c forc r), theintegrated
intensity
anddointensity-weighted
velocity maps
is modules
theopticaldepth;
(⌫,frequency-dependent
opacity; andMassivestars
notformpeakin thatisolation.
Studiesisbutions:on
additional
handling
radiationtransportulati
particles
are typicallyset on purpose,sofragmentation
described
The initial density profile
issphericallysymmetric,
and
has
the
the flux
from
the
star,
F
,
and
the
flux
from
2thermal
1 and self?
g
.
We
also
requireopacityissettoaconstant
value
of
0.01
cm
of CH
11
plots,
andself-gravity
ToomreQ thethat
R? , the stellar radius. This equation is integrated for each ray di3 CN(124 in
4 ), position–velocity
multiplicity
more
evolved assystemsof massive
stars show
gravity.
previous
studies.
self-consistently
theinterplay
of
of
gas,
coolsion=まで高解像度トレース。分裂片を捉える際に高解像度計算の重要性を示
1500 au (column ofgeneral(re-)emission
from
dust
and
gas, F. bin
form
the
flux
of
the
formingstar
atthestellarradius
R
,
for
which
we
rectionandfrequency
in
each
time
step
of
the
hydrodynamimaps,
takingintoaccount
severalinclinations.
We
refer
the
?
of thearegas,
shear of the binaries
disk and (see,other e.g.,gravito-radiationa large portioningof them
spectroscopic
Sana StellarThegravity
ofisthesolved
forming
massivestar,
theself-gravity
ofncy-dependent
opacity;and⇢(r, t = 0)T
irradiation
by
means
of
the
time状態方程式：P=(γ-1)
E
,
where
γ=5/3
The
variables
involvedinaaredetailed
below.
The
Poiscalsimulation.
use
tabulated
evolutionary
tracksforaccretinghigh-mass
stars,radhe すため，異なるグリッドモデルでも比較。
computational doreader
tothatreference
for
an
ample
discussionontheobservhydrodynamical
processes.
Instead,time-independent
grid fluid
et al. 2012; Kobulnicky
et al. 2014;
Dunstallet al.a 2015).
The obthe
andthetransport
radiation
forcesis areincorporated
into
the
code
independent
radiation
equation
(with
the
valid
assumps integrated for each ray dison
equationofself
gravitysolved
by
means
of
a
di↵usionThefrequency-dependent
opacity
(⌫)
is
the
sum
of
the
dust
calculated by Hosokawa & Omukai (2009).
!
abilityoftheresultspresented
here.
whose
spatialresolution
scaleslogarithmicallywithradiuswasservations of fragmenting accretion disks suggest the possibility⇢
via thetheansatz.
acceleration
source
term,
such
that
aext
=we
aPoisson+time
athe+tabulated
arad ,
the?use
sgsolverMoredetailsontheimplementation
of
the
tion
that
photontravel
time
is
small
compared
to
the
and
gas
opacities.
For
the
dust
opacities,represents
step of theroughlyhydrodynamiFor
theremainingthermal(re-)emission
contribution,
F isused,mayallowing
forby
very
high
resolution in theareasof mostinter(Hatlowtemperature想定)
We choos2
2.3.
Initialandboundary
conditions
that
close
binariesform
disk
fragmentation
and
later
inand
for
the
self-gravity
modulearegiven
in
Kuiperetal.
(2010a).
⇢(r, t = 0) = ⇢0
step
of
the
simulation,andonlyconsidering
absorption),which
valuesby
Laor&
Draine(1993),
including79
frequencybins,
est. We set up a series of simulations with increasing resolutions,assumed to be frequency-independent. First, we take the zeroth ⌦(R
5 30【用いたモデル】
This
is organized
as follows.
Sections
2 and 4cloud, ⇢0
r0
The
gas
is
assumedtobecaloricallyperfect,
thatis,governed
wardpaper
migrationofthecompanions(Meyeretal.
2018).
andwecalculatethe
local
evaporation
temperature
of
the
dust
yieldsand explore
the thephysicalprocessesandthat theoccur
in fragmentation
momentof theequation
radiationtransport
equationGM
The valuepresent the methodology
of bothsimulations,
post?
by
the
calorical
of
state
P
=
(
1)E
(where=y (⌫) •is the
sum
of
the
dust
grainsbyusing
theformulaofIsella&Natta(2005).
Thegas
int
輻射場：中心星からの放射はHosokawa&
Ohmukai(2009)流用era? =(how fragments
evolveand interact),
the propertiesof the fragInitial condition & Boundary
conditions
ulations aThe
initialdensity
profileissphericallysymmetric,
and
has
the
2
2
1 the internal
processingofthegenerated
data.
Sections
3
and
5–7
present
5/3,
the
value
for
H
at
low
temperatures,
and
E
is
r
g
.
We
also
requireopacityissettoaconstant
value
of
0.01
cm
2
int
In
this
study,
we
present
thehighest-resolution
self-gravitywhe
ments (orbits, mass and temperatures), their fate (whether they
ities, we use the tabulated We choose = 3/2,
sion
in Se
Z
2
our
results
andadiscussionofdisk
fragmentation,
thefragments
energydensity).
and
from
the
total
mass
and
radius
of
the
◆
✓
the
flux
of
the
formingstar
atthestellarradius
R
,
for
which
we
r
2
⇢
?
generalform
r radsg , wherer sg = 4⇡G⇢
evolve further simulations
and eventuallyup
becomecompanion
radiation-hydrodynamical
to dateon diskstars),frag-and atheTheinsg = @E
R?
The⌧(⌫,r)
cluding79
frequency
bins,
Radiationtransport
isincorporatedbythemethoddescribed
themselves
andcompanion
formation.
Section8
containsacon(4⇡B
cE
)
(5)
r
·
F
=
⇢
初期設定：200M⦿,
r=0.1pcのガス球
123
use
tabulated
evolutionary
tracksforaccretinghigh-mass
stars,
F? (⌫, r) = F? (⌫, R? )e(⌫, r)⇢dr
P , whererad ⌧(r, ⌫)rad=pendent opacity; ande↵ectsresolution
hasronfragment
statistics.
cloud,⇢
isdetermined
to
be
⇡
4.79
·
10
g
cm
at
=
1
au.
mentationarounda thatforming
massive(proto)star.
We continue
is se
0
0
@t
DrE
r
·
F
? etral.by
Rbut &
in Kuiper(2010b),advanced
to(2009).
a two-temperatureapcalculated
Hosokawa
OmukaiR?
on temperature of the dust
vergence study of our results, and Sect. 9, a literature review ander weRwill summarize in the rest of this section. We
the approachtaken
by Meyer
et al. (2018),
in which no sink arad = proach,
⇡ 9.
rated
for
each
ray
diThe
value
of
was
chosenbasedontheresultsofprevious
simwhich⇢Fortheremainingthermal(re-)emission
contribution,
F
is
⇢c
c
(4)
comparison
our results
withprevious
studies.
4! ⇢particlesofare
Thepurpose,outcomeof oursimulation
was alreadyused in Ahmadi
a & Natta (2005). The gas
=
aT
is
the
black-bodyenergydensity,
where
B
rad
set
on
so
that
fragmentationisdescribed⌦(R,desc
t=0
treat
the
star
as
an
emitterofradiation;
the
dust
and
gas
present
in c is theassumedtobefrequency-independent.
First,
wetakethezerothβp=-3/2
ulationsandobservationsofmassive
dense
cores
(see
the
discusetal.
(2019)
forproducingsynthetic
observations
with
ALMA
2
1
r
ofcm
theghydrodynamispeed
ofabsorb
light
inradiation
vacuumandisequation
the Planckmean opacity.
. We also require ⇢(r, t = 0) = ⇢01
self-consistentlyasthe interplayof self-gravityof 流体自身の再放射を解く
the gas, cool- quan- the
cloud
it,
and
re-emitit, inP addition
to the thermal
radi- This rame
momentofthetransport3
Articlenumber,
page
2
of
22
and
NOEMA.
Inthat
paper,
many
observationally-relevant
ρ0 = 4.79E-12 g/cm
sion
in
Sect.
9.3).
密度分布
0
equation
is solved
by means ofcompression.
the flux-limiteddi↵usion (FLD) keep
ation
due purely
to hydrodynamic
This treatment
ing
of
the
gas,
shear
of
the
disk
and
other
gravito-radiationlar radius R? , for which wetitieswere
computed,
including
1.37
mm
continuum
images,r0 velocity
Thevariables
involved
in consists
arad
are ondetailed
The
PoiswhereR@ 1auallowsus to divide
the totalradiation
flux
Ftotbelow.
intotwo
contriapproximation,
which
setting
F
=
DrE
,
that
is,
rad
dent
The
initialangular
is
given
by
the
profilehydrodynamical
processes.
Instead,atime-independent
grid
integrated intensity and intensity-weighted peak velocity maps
stars,@EradofThe ratioson
equationgravityisstar,solvedby)canmeansofa di↵usionsaccretingthe sumhigh-massof the dust
butions:
the self
flux
from
the
F?cE
, and
thebe
fluxtreatedfrom
thermalassuming
that
radiationtransportasadi↵usion
chos
(4⇡B
(5)
r
·
F
=
⇢
whose spatial ofresolution
scaleslogarithmicallywithradiuswas
CH3 CN(1211),
position–velocity
plots,
andToomreQPradrad
0次の輻射輸送式
4
4
is
set
to
@t details(re-)emission
from
dust
and constantgas, F. is Dof=thec/⇢
ansatz.
Moreontheimplementation
Poissonsolver2009).
problem.
Thedi↵usion
,
where
is
the
R
man
maps,
takingaccount inseveralinclinations.
refer theallowing
for= veryhighinto
resolution
the areasof most We
interwe use the tabulated We choose = 3/2,
βp
-3/4
! ⌦used,⇡9.84·1Stellarirradiationissolved
by
means
of
the
timefortheself-gravity
modulearegiven
in
Kuiperetal.
(2010a).
and
from
the
total
mass
and
radius
of
the
4
flux
limiter,
and

is
the
Rosselandmean
opacity.
Thechangemission contribution, F isreadertothat
reference
for
an
ample
discussionontheobservpola⇢
Rest. We set
up
a series of simulations
with increasing resolutions,aTis theequation
black-bodyenergydensity,c is the described
whereradiation
Brad = Rlimited-1
この式をFlux
diﬀusion
近似で解く
independenttransport
(with
the
valid
assumpΩ=9.84E-11s0
g 79
frequency
Theofgas
is assumed
tovacuum
bethe
caloricallythatis, opacity.
governedabilityof the processes
results12presented
here.
internal
energyofsystemisperfect,⌦(R, t = 0) = ⌦0
3 in fragmentation
speed
of
light
in
and

is
the
Planckmean
This rameter sI
角速度分布
nt.
First,
we take thebins,
zeroth cloud,andexplorethephysical
that
occur
P
tion
that
the
photontravel
time
is
small
compared
to
the
time
⇢
is
determined
to
be
⇡
4.79
·
10
g
cm
at
r
=
1
au.
@ 10auR0 (how fragments00
by the caloricalequationof meansstate Pof =(flux-limited
1)Eint di↵usion(where (FLD)=
equationissolvedbythekeepsclouthemperature
of
the
dust
evolveandinteract),theproperties
ofthefragstep of the simulation, and only considering absorption), whichuationThis paper is organized as follows. Sections 2 and
4
5/3, the valuefor H2 at which
low temperatures,and E
the internal
approximation,
consists on setting
Fint= is DrE, that is,

The
value
of
was
chosenbasedontheresultsofprevious
simraddent situaof thyields⇢ments(orbits,mass
andtemperatures),
their
fate
(whether
they
@E
int
present the methodology of both the simulations, and the postatta (2005). The gas
assuming
that
radiationcEtransport
canbe treated as a di↵usion (6)energydensity).
chosen
in
=
⇢
(4⇡B
)
r
·
F
as
w
内部エネルギー変化
P
rad
rad
?
evolvefurtherandeventually
becomecompanion
stars),
and
the
where
R
is
the
cylindricalradius,andwechoose=3/4.
ulationsandobservationsofmassive
dense
cores
(see
the
discusprocessingofthegenerated
data.
Sections
3
and
5–7
present⌦
2
1 ※重力エネルギーと回転エネルギーが半径によらず5%，現実のコアを真似
problem.
The di↵usion
constant isbyDthe= methodc/⇢R , whereis the man et al@t
Radiationtransport
is incorporated
described
g . We also requireThee↵ectsthat
resolution
hasonfragment
statistics.
Z
our results and apotential
discussion ofenergy
disk fragmentation, the fragments✓RR is◆2the Rosseland mean opacity.
r The change
flux
limiter,
and
The
ratio
of
kinetic
energytogravitational
polar
velo
in
Kuiperetal.
(2010b),buttoa
two-temperature
ap? advanced
sion
in
Sect.
9.3).
⌧(⌫,r)
disk
=
c
⇢T
.
We
solve
equations(5)
where,
for
the
ideal
gas,
E
themselves and companion formation. Section 8 contains a con- Fこの式を(5)と合わせて解く（twov⌧(r, ⌫) == F? (⌫,
R? ) of theesystem
, int
where
(⌫, r)⇢dr
初期温度を10K,g/d=100(ダストのκ(ν)計算に使う）
ofr)internalenergyis rest? (⌫,ius R? , for whichwe(5) is set
In sumproach,
which
we
will
summarize
in
the
of
this
section.
We
toto 5%,
which fixes The
the outcome
normalization
parameter
⌦
r
0
R
tion
vergence
study
of
our
results,
and
Sect.
9,
a
literature
reviewandand (6) for the unknowns Erad and T by using the so called twoof
oursimulation
wasalreadyused
in
Ahmadicloud,
soThe
initialangularvelocity
is
given
by
the
profiletreat thetemperaturestar as an emitterofradiation;
the
dust
and
gas
present
in(4)comparisonof our resultsprocesswith previous⇡ 9.84 · 10 11 s 1 at R0 = 10 au. The
normalizationis studies.
ting high-mass stars,
condlinearization approach, described in Commerçon

ody energy density, c is the?

et al. (2019) for producing synthetic observations with ALMA

temperature linearization approach)@Eint it, and re-emit it, in addition to the thermal radithe cloudabsorbet al.
(2011).

situation,

tial cOverview of the temporal evolution
G. André Oliva and Rolf Kuiper: Modeling disk fragmentation and multiplicity in massive star formation• Geometry

initial setup

r＝30au - 20625au (=0.1pc), log的なメッシュ，

disk formation epochfragmentation epoch

quiescent epoch

rotation profile
density profile

30au以内はsink, 中心に大質量星ができる設定

fragment

sink cellmassive protostar

surviving fragment(s)gravity
disk

midplane density

Θ：cosで等間隔，赤道面で高解像度

spiral arm

Φ：等間隔

円盤Spiral
+ 分裂片

n✓
11
21
41
81
161

n
32
64
128
256
512

ndisk
7.0 · 103
5.3 · 104
4.2 · 105
3.3 · 106
2.6 · 107

x30
6.36
3.07
1.50
0.74
0.368

x1500
359
167
77.8
37.5
18.4

Table 1: Designation code of each simulation (column 1), number of cells for each coordinate (columns 2–4); approximate
number of cells in the region r < 1500 au, i.e., the approximate
number of cells that resolve the disk’s physics (column 5); cellsize at r = 30 au (column 6), cell size at r = 1500 au (column
7). x30 is also the minimum cell size of the computational domain in the disk’s midplane, and x1500 represents roughly thecell size in the outer region of the disk.
is the optical depth; (⌫, r), the frequency-dependent opacity; andfor each ray diR※観測可能性の論文は別に出版済み（ALMA,? , the stellar radius. This equation is integrated
NOEMA）
rection and frequency bin in each time step of the hydrodynamiAhmadi et al. 2019cal simulation.
The frequency-dependent opacity (⌫) is the sum of the dust

achieved in the midplane (z = 0); and the azimuth is uniformly
discretized. In the midplane the cells are approximately cubical,
with two example cell sizes given as x in Table 1.
This choice of coordinates is explained and justified in moredetail in Kuiper et al. (2011), but in a nutshell, a spherical grid
guarantees strict angular momentum conservation around thecentral massive protostar, and the logarithmic grid in r allows
for a focus on the phenomena closer to the forming massive star,
while saving computational power. An explanation on how well
does this choice of grids resolve the phenomena studied here ispresented in Sect. 9.2, as well as comparison to the grid choicesof previous studies.

※secondcollapseはtemperature

nr
34
67
134
268
536

扱えないが
高温領域ありToomre parameter

run
x1
x2
x4
x8
x16

vertical density※5つの異なる高解像度計算，x8,
x16をメインに議論
G. André Oliva and Rolf Kuiper: Modeling disk fragmentation and multiplicity in massive star formation（他は主に解像度依存性を議論するための比較計算）

Fig. 1: Time evolution of the system (run x8). In the elaboration of the plots, snapshots of the simulation were taken specifically at
3.0, 8.0 and 17.5 kyr, for each respective column. The rightmost column shows double the size of the other two (the dotted squarecorresponds to the area shown in the snapshotslocatedthe left).no.
Forfrag-main-arxiv
the rightmost column, notice the existence of a surviving
A&A
proofs:tomanuscript
fragment at r ⇠ (900, 1200) au for the midplane views.

2.3. Initial and boundary conditions

The initial density profile is spherically symmetric, and has thegeneral form⇢(r, t = 0) = ⇢0

r
r0

!⇢

Article number, page 5 of 22

中心星の進化
間欠的な降着有

(a)

(b)

(c)

Fig. 2: (a) Mass, (b) luminosity and (c) accretion rate of the central massive protostar, as formed in run x16. The dotted line in panel(b) that corresponds to the stellar luminosity, is calculated using the evolutionary tracks of Hosokawa & Omukai (2009).

(d) Temperature (midplane)(e) Radial mass flow (sph. sh

4: (a-e) Radial profiles of several quantities for the background disk. T
The fragmenting accretion diskFig.
quantity has been time-averaged in that interval, excluding the endpoint. The

A&A proofs: manuscript no. frag-main-arxiv(f) Accretion rate into the central massive protostar as a function of time.

102

Q

101

Qdisk
Qmean
Qmin

(1996) (sefirst fragm
New s
in Fig. 13aand mass
frequently
interaction

100(a) Keplerianity (midplane)(b) Density (midplane)(c) Surface density
run x8(d) Temperature (midplane)(e) Radial mass flow (sph. shell)(f) Accretion rate

Fig. 4: (a-e) Radial profiles of several quantities for the background disk. The intervals in profiles (a), (d) and (e) mean that thequantity has been time-averaged in that interval, excluding the endpoint. The filled diamond indicates the value at the disk radius.
(f) Accretion rate into the central massive protostar as a function of time.
(1996) (see also, e.g., Kratter et al. 2008; Kuiper et al. 2011). The
Keplerian 領域が外に広がる，境界領域=遠心力バリアで密度上昇，
first fragments form at the outermost parts of the spiral arms.
New spiral arms are created by convergent flows, as shown
それより外はinfall領域，円盤分裂のため，柱密度や動径マスフローの間欠的上昇が有り
in Fig. 13a; the flows left and below the fragment are convergent
and mass accumulates as spiral arms. These type of flows are
frequently created by turbulent motions arising after fragmentinteractions.

6. Fragm

6.1. Fragm

Fragments
fragmenta
10-1
they fragm
reported i
2
3
10
10
planetaryr [au]
fragment f
spiral arm
Fig. 5: Comparison of the Toomre parameter values computed ral arms. T
for the background disk (Qdisk ), the mean value (Qmean ) and the the primar
minimum values corresponding to the e↵ects of the fragments fragments
and spiral arms (corresponding to Qmin ). These curves were calThe fi
culated with run x16, and they are time-averaged for the frag- lustrated imentation epoch.
geneities adevelops a
starts, form
process isunstable and develops small inhomogeneities that become two 14 of pane
円盤はグローバルには安定だがローカルに不安定
primordial spiral arms at opposite sides of the disk, that is, they geneities tarise from the m = 2 mode described in Laughlin & Rozyczka panel A4,
Article number, page 8 of 22

Fragmentsの進化色々(2) fragmentの誕生と消滅，
この例だと60個できて22個(1) fragmentの形成：渦状腕の形成→分裂 (Takahashi+ 2016)

が200yr以上生き残る
G. André Oliva and Rolf Kuiper: Modeling disk fragmentation and multiplicity in massive star formation

within spiral arm
spiral arm collisionrotationA

new fragment
inhomogeneity

Fig. 7: (a) Number of fragments with a minimum lifetime of
200 yr present in the simulation as a function of time. (b) Radial
position at formation time for each fragment, color-coded withthe fragment lifetime.

する（上がx8, 下がx16）

6.5. Fragment dynamics: orbits

The rest of Sect. 6 will be devot
ments move in space, their interacand their substructures. First, an o
A&A proofs: manuscript no. frag-main-arxiv
sented. In Fig. 10, the orbits of lo
have been plotted. During the simu
8 fragments complete more than obits of the fragments are highly inwith spiral arms and other fragme
run x8etc.; more details below). They als
some orbits of run x16, that show arespect to the midplane during ce
riod is ⇠ 1 kyr. The orbits of the frwith an average eccentricity of ⇠minimum and maximum radial pos
ments undergo di↵erent types of inin the eccentricity of their orbits, indue to spiral arm action and gravi
fragments.
The orbits of long-lived fragme10b), develop in the middle disk,
Fig. 8: Mass of the fragments with life span longer than 200 yr. that survive at the end of the sim
more massive than short-li
G. André Oliva andRolf Kuiper:fragmentation
andcalculations
multiplicity instar also
formation
A fixedradius Modelingof 50 au disk
is assumed
for theofmassive
this areththeirmasses⇠ 1.5 M ), and anplot.
G. André Oliva and Rolf Kuiper: Modelingdiskarefragmentation
vides more stability against interac

6.4. Hydrostatic corescreasenew fragment
spiral arm AB(a)spiral arm B

1

適当な範囲で積分して質量と(b)

the sink cell. The erratic behavior of fragment 94, in the other
hand, is mostly numeric: it moves outwards in the simulation
domain, where there is less resolution; and by e↵ect of numerical di↵usion, increases in radius, making our assumed radius of
50 au insufficient in the calculation. The mass of fragment 94,
assuming a bigger radius of ⇠ 100 au, is ⇠ 6.5 M at t = 13 kyr.

fragment creation mechanisms

gravity(3) fragmentの質量進化

calculated the enclosed mass in th(run x16) over its evolution. Durin
the fragment (Fig. 14a), the massuntil a value of a few 10 2 M wa
results of Bhandare et al. (2018). T
is shown also in Figs. 13b and 14b
disk (the figures correspond to thethe density field, respectively). As
yellow circle in Fig. 13b indicate
size of the first core), and the yelloindicates the assumed size of a fragof its (total) mass.

2

3

4

Fig. 6: Fragment creation mechanisms. The color scale for the midplane density maps is the same as the one shown in Fig. 1.
crease; in the case of fragment 59, the crease was formed in aspiral arm of the secondary disk around fragment 40.
The second process, spiral arm collision, is illustrated in panels B1 and B2. When two spiral arms or regions of high density
collide, they create perturbations that make the region Toomreunstable and therefore, a collapse is triggered. The example inpanel B3 is from run x8, and shows the formation of fragment
32, which is generated by this mechanism. Panel B4 provides anadditional example from run x16, where two spiral arms, connecting fragments 32 and 68 to the inner disk, have collided andgave rise to fragment 71.
Early during the fragmentation epoch, both processes occur
predominantly in the primary disk. However, towards the endof the fragmentation epoch, and as fragments gain more mass,
the fragmentation inside substructures becomes dominant: spiralarm breakdown and spiral arm collisions become more frequentin the secondary disks and yield fragmentation. This behavior
was observed especially in runs x4 and x16. This hierarchicalfragmentation is in principle analogous with the observations

9 kyr, although we do not consider it as of great interest, since it
is not observed in the other runs (see Fig. 20).
Lifetimes of the fragments (color code) and the radial location when they are formed (vertical axis) are shown in Fig. 7b,
as a function of time (horizontal axis). We see that the longest
lived fragments are formed in the outer disk, and that the innerdisk forms fewer fragments over time. This trend is tied to thefact that fragmentation is occurring in the spiral arms of the primary disk. The figure was generated with the data from run x8.
In run x16, as the spiral arms of the secondary disks fragment,
new long-lived fragments start to form again in the inner disk.

※ 2つの機構：spiral内での収縮＆

spiral arm同士の衝突

密度の高まりを同定したら，少し後の時間の位置をケ
6.3. Mass
プラー回転から予想，その通りの場所に見つかったら

The masses of the fragments are presented in Figs. 8 and 9 (corresponding to runs x8 and x16, respectively), obtained using themethod described in Sect. 4. The masses of the fragments are ofa few solar masses, and increase over time. Peaks and sudden increases are observed, and correspond to fragment mergers, thatare described in Sect. 6.6. Some decreases and oscillatory behav-

fragment候補として同定し，後は目視とかで確認(b)Fig. 7: (a) Number of fragments with a minimum lifetime of
200 yr present in the simulation as a function of time. (b) Radial
position at formation time for each fragment, color-coded withthe fragment lifetime.

As we discuss in Sect. 7, fragments collapse and form hydroArticle number,
10 of 22 that the masses presented instatic cores. We remind
thepagereader
this section are calculated by assuming a fixed fragment radiusof 50 au for run x8, and 40 au for run x16, which means thatthe enclosed region includes the hydrostatic core as well as thesecondary disk. This is important when comparing to modelsof core collapse, such as the ones described in Bhandare et al.
(2018): for an initial core mass of a few solar masses, they findhydrostatic first Larson cores of radii of ⇠ 3 au, and masses ofthe order of a few 10 2 M .
Fig. 9: Masses of the fragments with life span longer than 200 yr, for run x16. A fixed radius of 40 au is assumed for the calculationsof this plot.
In run x16, cell sizes of . 1 au are reached at radial positionsof r . 100 au, allowing us to barely resolve the hydrostatic corecrease and small oscillations are observed after the collision.
region of質量が減るのは，fragment周囲のfragments located there witha few
gridoccur
cells,
enoughCollisions
typically
not headon, but with a certain impact parameter, which increases the spin angular momentum of
for an order of magnitude check with thea corecollapse
We of the fragment,
merged fragment.
In themodel.
frame of reference
the increased
centrifugal
force favors the12development of seccalculated
the enclosed massdiskの一部が外に流さin the inner⇡ 3arms,
au whichof fragment
secondary
ondaryspiralcan transport
mass
outwards,
is exFig. 9: Masses of the fragments
with
life
span
longerthan
200
yr,
forinasrun
x16.
plained
in
Sect.
6.7.
Duringthefragmentation
epoch
run
x8,
(run x16) over of
itsthisevolution.
Duringthegravitational
collapseofplot.
we recorded about 13 mergers in total. This kind of interactions
the fragment (Fig. 14a), the mass of theinner⇡ 3byauincreased,
can only
be captured
simulating
and resolving the full hydrodynamics
ofafragment,
andnot by a sub-grid particle model.
れる現象のため。下は軌道進化
2consistent with theuntil a value of a few 10 M was reached,
Changes in the orbit due to gravitational interactionof frag- an
creasethat are unconnectedby a spiralarm are somewhat more
results of(a) Bhandare et al. (2018).
Thisments
high-density
inner
region(b)complex, less frequent and more difficult to determine.Collisions
A generalis 10:
shown
in Figs.
13b
andthe secondary
picture, however,byis provided
by panel B1 of Fig. 11:pact
two fragFig.
(a) Orbitsalso
of fragmentswith a life
longerthan 114b,kyr, dur-surroundedparam
ing the time interval [6, 10] kyr, for run x8. (b) Orbits of all the ments approach, and their gravitational interaction slows down
the merge
disk (thecorrespondtosimulated
the midplaneand verticalin and accelerates
fragment 1, therefore
moving it to acuts
lower orbit,
fragments
with a figures
life longer than
1 kyr, during all thefragment 2, moving
to a reader,higher orbit. thePanel B4 provides
anthe increa
time,
run x16. Thefield,
fragmentrespectively).
identification number isAs
locatedthefordensity
a reference
for ittheof 16 and sp
at the starting point of the orbit, and the color code is the same example of this kind of interaction: just after the orbitsondary
29 crosseach other,
16 slows
down and gets
into a collision orbit
asthe one usedcircle
in Figs. 8 inand 9.
yellow
Fig. 13b indicates the
inner
3 au
(roughlytheplainedwith the central massive protostar, while 29 gets accelerated
into insize of the first core), and the yellow acircle
in
both
panelsof
14higher orbit. The moments leading to the orbit crossing,howwe record
The orbits presented here, however, do not take into account ever, are another example of the e↵ects of a gravitational interaccan only
indicates
assumedsizecoresof aandfragment,
forandthe
calculationthee↵ects of the theformationof second Larson
the fate tion: inused
panels B2
B3, wesee how fragment 29, originallyin bofthat entermass.
the numerical sink cell. A more detailed a low orbit, migrates towards fragment 16 and vice versa,
until
dynamics
offragmentsits (total)
discussion is presented in Sect. 7.2.
they cross each other and the scenario illustrated as t in panel0

B1 is reached. The example provided here comes from theChang
data
of run x4, but we also observed a similar behavior inrun
x8,thaments
6.6. Interactions(a)(b) Some of these interactions
but without the orbit crossing.
havecomplex,also been observed previously in 2D simulations in thecontext
6.6.1. Fragment–fragment interactionsofplanetformation
(see,
e.g.,
Zhu
et
al.
2012).
The
outcomeof hFig. 10: (a) Orbits of fragments with a life longer than 1 kyr, dur- picture,
Fragments interact with each other in two distinct ways: they these interactions (a change in the orbit or a merger) depends
ments apptime interval[6,and10] kyr,
run x8.
(b) Orbitsof allcan merge or change orbitsing
due theto gravitational
interaction
on theforapproachvelocities
and the mass
ratiotheof the interacting
angular momentum transfer.
fragments.
Intheexamplegiven
inpanels
B2–4,
themasseswere
fragments with a life longer than 1 kyr, during all the simulated fragment
Mergers (panel A1 of Fig. 11) occur when the fragments comparable.
time,infor
run x16.
fragment identification number is located fragment
have a close encounter, usuallya collision
orbit.TheAs shown
example othestarting
in the example provided inatthe
panels
A2, A3point
and A4ofof theFig. orbit, and the color code is the same
11, fragments 42 and 40 areinacollisionorbit
andmerge.
The
6.6.2.
Fragment
interactions
withspiralarms
andthe
29 cross e
as the one used in Figs. 8 and 9.
masses of the fragments combine, as shown by the spike in themassive protostar

6.5. Fragment dynamics: orbits

The rest of Sect. 6 will be devoted to the study of how fragments move in space, their interactions with their environment,
and their substructures. First, an overview of the orbits is presented. In Fig. 10, the orbits of long lived fragments (> 1 kyr)Fig. 12: InteractionsFig.
of 12:
theInteractions
fragmentsofwith
the spiral arms, and with the forming protostar modeled as a central sink cell. The orbit
the fragments with the spiral arms, and with the forming protostar modeled as a central sink cell. The orbit
in panel A4 is plotted
for aA4
windowof for2 kyr,
with ofthe2 fragment
marking
starting
point.point.
in panelis plotteda windowkyr, with theIDfragment
ID themarking
the starting(5)

Fragments間の相互作用など(4)fragment周囲の詳細構造

マージャー，相互作用…
A&A proofs: manuscript no. frag-main-arxiv
fragment–fragment interactions

Fig. 13: Secondary disk with its spiral arms around (a) frag(b)ment 11 of run x8, and (b) fragment
12 of run x16. The background map represent density in the midplane (using the same
Fig. 13: Secondarycolor
diskscale
withas its
aroundthe spiralrest of arms
the figures),and(a)
the fragarrows show thement 11 of run x8, comovingand (b) fragment
12The
of central
run x16.
Theprotostar
back- is locatedvelocity field.
massivebeyondthe bottom
the plotted areas
in bothground map represent
densityin theof midplane(usingthe cases.
sameThe yellow
circle(b) figures),has a radiusandof 3theau. arrows show thecolor scale as the rest
ofinthe(a)gravitygrav. interaction

2
1

comoving velocity field. The central massive protostar is locatedbeyond the bottom of the plotted areas in both cases. The yellow
6.8. Comparison to observations
circle in (b) has a radius of 3 au.

B
1gravity

1

2

3

4

Fig. 14: Vertical structure of fragment 12 and its close surroundings (run x16). The yellow circle has a radius of 40 au. The den(b) Density,t =as7.12
kyr of the figures.
sity uses the samecolor scale
the rest

G. André Oliva and Rolf Kuiper: Modeling disk fragmentation and multiplicity in massive star formation

migration

fragment destruction mechanisms

thermal expansion

Article number, page 13 of 22

2
A

B

C

7.1. Central temperature of the fragments

1

Fig. 15: Temperature of the fragments with life span longer than
200 yr, for run x8. The gray box indicates the hydrogen dissociation limit.

Fig. 17: Fragment destruction mechanisms.

We must, however, discuss the e↵ects of the inner bound- star. This process can also trigger fragmentation, as was the caseary conditions (size of the central sink cell) on these accretion of the spiral arm that gives rise to fragment 59 shown in Fig.
1 is only allowed to cross the
2 sink cell in3
4
bursts. Since matter
6A4. 6.8.2. Accretion burst event in G358.93-0.03
wards, we are not taking into account how outflows a↵ect theFig.
12: Interactions
the fragments
withthe spiralshowsarms,asandforming
protostarmodeledasstructure
a centralofsink
cell.accretion
The usingorbit burst were obshows theverticalaccreted
mass. Someoffragmentsthat thesimulation
ac-with theFigure
Disk14substructuresassociatedtoa fragment,aninpanelinto
A4theis plotted
forcoulda windowof 2 kyr,the fragment
the starting
the highest
resolution
dataset. When the fragment is forming
cretedsink cellalso only
be inwith
an ellipticalorbit,ID marking
servedand point.
reported
in Chen et al. (2020), for the high-mass
as discussed in Sect. 7, specially if they have already undergone (Fig. 14a), it has a spherical-like shape. Fig. 14b, however, shows
youngstellarof theobject
G358.93-0.03.
The13a:flaring
event was restructure
secondarydisk shown in Fig.
thesecond collapse, so they are less susceptible to shearing and sub- the verticalportedin gets
Sugiyama
et al. with(2019).
Chendensity
et al.in(2020) performed
indeedflattened down,
the highest
sequent accretion. These considerations could make strong lu- fragment

rian disk around a proto-O star. The main object MM1a, is re- is bigger, and the central star is more massive).
However,
there
Article number,
page 13 of
22
一方で，壊れるメカニズムも（右）ported to be ⇠ 40 M (with between 2.2 and 5.8 M attributed to are several warnings that should be taken into account. From thethe disk, and the rest, to the protostar), and the fragment MM1b results indissolution
Ilee et al. (2018), spiral
the mass
ratio of the diskshearing
and the priarm transport
is reported to be ⇠ 0.6 M , located at around ⇠ 2000 au from mary is between 0.055 and 0.145. In our simulations, the mass
MM1a.
of the central massive protostar at ⇠ 16 kyr is ⇠ 20 M (cf. Fig.
we observe it gets partially dissolved into the disk, absorbed intoa spiral arm, absorbed by other fragments or it is sheared apart.
An example of this behavior is provided by panels C1 and C2 ofFig. 17.

19). We calculated the mass of the disk including the fragments
Fragments
frequently
developa secondarywith spiraland spiralarms(integration
ofdiskdensityin a arms,
cylinder of 1500 au in
embeddedintheprimary
disk,
as
shown
in
Fig.
13.
The
figuresradius and 20 au in height), and the mass of the background disk.
show the comoving velocity field, v v ,bg e , where v ,bg is theThemassprofileof theofdisk
includingis comparable to the
angularvelocity
the primary
disk.substructures
In Fig. 13a, we obof secondary
the primary,
expectedfroma fragmenting
disk; howservemassa typical
disk, aswiththe densest
and hottest
region ever,(fragment)in
its
center.
We
also
observehowconverging
if substructures are excluded, the massAof the disk increases
flows form spiral arms. Converging flows form frequently whenmore slowly. After ⇠ 16 kyr, the mass of the background disk isshearing and turbulent motion (due to activity of fragments and5M, which
means
mass
ratio
of ⇠
other ⇠
spiralarms)
producesa regionawith
a net
outwardflow0.25.
that In addition, thesurvivingfragment(94)
in global
run x8is transport.
located at ⇠ 1500 au fromencounters
the inward
radial flow
from
mass
the primary,althoughat canthe also
endbeofdrifted
the simulation
it is moving
Spiralarms in secondarydiskso↵ theoutwards.
mass
fragment
is of thea deorder of a few solar
fragment,as shownThein Fig.
13b.ofThe
spiral arm94
encounterscelerating
inwardflow that thismakesvalue
it driftincludes
apart. As athe
result,the of the secondary
masses,althoughmass
calculated
disk.mass plot (Fig. 8) shows a decrease, since the mass ofthe spiral arm is lost from the fixed integration domain used. If
Giventhetomassof mostthe mass
fragments
produced in
the spiral arms
are thatboundedthe fragment,theofplottedofB
our simulations
isoscillation,of the orderof 1 Mthe, thethe fragment
only shows an
but frequently
spiralobserved positionarm getsspiralreal mass described in Ilee
andabsorbed
size of by
theotherdisk,
wearms,thinkprovoking
that theascenario
loss inwith a plausiblyconsequent betemperature
et theal. fragment,(2018) could
obtainedvariation
with a setup similar toover time. This mechanism provides a way to transfer back somematterours.
from fragments to the disk or the central massive proto-fragmentは星になるのか：温度が十分高くなってるもの有り(左)Article number, page 15 of 22

Panels B1–4 of Fig. 12 show two examples of accretion
bursts. Both the infall of matter through a spiral arm, as shownin panels B1–2, and the complete accretion of a fragment (panels B3–4), produce accretion bursts. The accretion of a fragment,
however, produces a much sharper and brighter peak in luminosity compared to accretion through a spiral arm. Accretion bursts
are also accompanied by overall increases in the temperature of
the disk, that we term temperature flashes, which typically last⇠ 30 yr and heat up the fragments and spiral arms, as we discussed in the previous section.

6.7. Secondary disks(6)

These destruction mechanisms severely a↵ect the lifetime offragments, if they are in their hydrostatic core phase, and showthat sub-grid sink particle models may overestimate the number

Accretion onto the central massive protostar is not a smoothprocess,
as depictedin the accretion rate shown in Fig. 4f. There
otherinteractions
are many discrete accretion events, caused by infall of matter
through a spiral arm, or the complete accretion of a fragment.
The transformation of gravitational energy into radiation is madein the form of accretion-driven bursts, sudden increases in theluminosity of the forming massive star (see Fig. 2b). This phenomenon was reported theoretically in the context of massive
star formation by Meyer et al. (2017) and Meyer et al. (2019),
where a system of magnitudes was also developed to describe
them.

Fig. 14: Vertical structure of fragment 12 and its close surroundings (run x16).
yellow
circle hasa radiustoofthe
40general
au. ThedenObservations of the massive young stellar object G11.92–0.61
ThisTheseems
to be speciallycompatible
results
周フラグメント円盤にもspiral形成，鉛直方向の円盤構造も見えてる
6.8. Comparison toMM
observations
1 reported in Ilee et al. (2018) show a fragmentedsity
Keplex8, butlaterscalein timein the observations
uses intherunsamecolor
as(thethedisk
restreportedof the figures.

rian disk around a proto-O star. The main object MM1a, is re- is bigger, and the central star is more massive). However, there
6.8.1. G11.92–0.61ported
MM to
1 be ⇠ 40 M (with between 2.2 and 5.8 M attributed to are several warnings that should be taken into account. From thethe disk, and the rest, to the protostar), and the fragment MM1b results in Ilee et al. (2018), the mass ratio of the disk and the priA&A proofs: manuscript no. frag-main-arxiv
reported tobe ⇠ stellar
0.6 M , object
located ataround ⇠ 2000 au frommary is to
between0.055 and
0.145. In ourtosimulations,
theresults
mass
Observations of theismassive
young
G11.92–0.61
This seems
be speciallycompatible
the general
MM1a.
the later
centralprotostarat ⇠ 16 kyrinis the⇠ 20observations
M (cf. Fig.
MM 1 reported in Ileeet al. (2018) show a fragmented Keple- in run x8,ofbut
inmassive
time (thedisk reported

Fig. 11: Fragment-fragment interactions. In panels A3 and B4, the fragment ID is shown at the starting point of the orbit. In the caseof panel A3, the time window shown in the orbits is 1.3 kyr; and in the case of panel B4, 1.2 kyr.

accretion bursts(b) Density, t = 7.12 kyr

6.8.1. G11.92–0.61 MM 1

2

core and potentially allow a temperature increase and continuation of the evolutionary process.
Fragments of sizes of a few solar radii would be unresolvablewith our current simulation setup. However, since their compactness would also provide stability, it would be safe to add a subgrid particle model in order to study their behavior. Before thesecond collapse happens, however, fragments are just hydrostaticcores with strong interactions with the disk, spiral arms and otherfragments. Some of these interactions are strong enough to destroy them. The next sections describe these mechanisms, andconsider the e↵ects that our simulation setup with a central sinkcell have on the number of companions that are formed according to the simulations.

A(a) Density, t = 5.88 kyr(b)

7.2.1. Fragment destruction mechanisms(a)Fragments that move in an eccentric orbit near the central primary protostar with high speeds experience shearing, which typically causes their destruction, as illustrated in panel A1 of Fig.
17, and exemplified by panel A2. A similar process can be foundin simulations on fragmentation in protoplanetary disks, as described in Lichtenberg & Schleicher (2015). It is also common
in this scenario that some matter of the fragment gets accreted by
the central protostar; sometimes forming a “ring-like” accretion
structure like the one discussed in Sect. 5. In the particular example of panel A2, however, matter is not accreted. The shearedmaterial expands and gets absorbed by spiral arms, providing
converging flows needed for further fragmentation according to
the mechanisms discussed previously.
Spiral arms can also cause a mass loss to the fragment bytransporting matter along them (Fig. B1 of Fig. 17), eventuallydestroying the fragment. As an example, fragment 43 of run
x8, shown in panel B2, is drained by a spiral arm that is being
stretched, and delivers the material to fragments 32 and 40.
Another fragment destruction mechanism occurs as a consequence of temperature flashes associated with accretion bursts(described in Sect. 6.6.2). Fragments and spiral arms are heated
up by the temperature flash. This triggers thermal expansion,
which in turn lowers the density and central temperature of thefragment, compared with the values before the flash. If the fragment had an already low temperature and density, this thermal
expansion and cooling can take the fragment below the detection threshold. After manually following the remaining matter,merger(a) Density, t = 5.88 kyr計算の分解能依存性

A&A proofs: manuscript no. frag-main-arxiv

mdiplane density

run x1run x2run x8run x4run x16z [au]
600
300
0
-300

time evolution

x [au]

04

8 12
t [kyr]x [au]

16 20 04

8 12
t [kyr]x [au]

16 20 0disk formation epoch4

8 12
t [kyr]fragmentation epochx [au]

16 20 04

8 12
t [kyr]quiescent epoch

0
60

0
30

0

00
-3

60
-6 0
00

0
30

0

00
-3

60
-6 0
00

0
30

0

00
-3

60
-6 0
00

0
30

0

00
-3

60
-6 0
00

0
30

0

00
-3

-6

00

-600
x [au]

16 20 04

8 12
t [kyr]16 20

no data available

Fragmentation の詳細には迫れない

Toomre Q
number of fragments

ローカルなジーンズ長を分解しないとonly spiral arms

only spiral arms

Fig. 20: Convergence of di↵erent quantities with resolution. The midplane density data was taken at t = 7 500 yr for all the maps intheexact source unit
(e.g. a collisional
disc or cometary
low mid-infrared(MIR)
excessesinwards
and steep
grain
size
star-grain
separation
vector, debris
respectively.
Material
migratingthrough
Poynting-Robertson
In this paper we investigateapotential
mechanism
2017). Transient
dynamical
upheavals,
suchas the disintegration). We then followFthe= Fevolving
size
, and
(1)
distributions(Sezestre,
Augereau& atThébault2019),
grav + Frad(PR)
drag andpiling up
the sublimationzone
cannot2.1.1
Forces
Theto location
combinede↵ects of radiation pressure andto generate NIR excesses acrossdiversetypes
andHeavystellar
Bombardment,
could
supply (Bonsor
materialofthegrain.
and Latemay
requirespecific
systemarchitectures
produce enough hot dust to reproduce observations, since
where FF is thetotal
force and Fgrav and Frad are
43: Gas trapping of hot dust around etmain-sequence
stars
the
veryRaymond
inner regionsof thesystem;however,such induce
PR-drag
a
force
on
the
grain:
al.
2014;&
Bonsor2014;
Faramazetal.
In the absence of radgas, the dust grain is subject to gravity
ages, without requiring specific systemarchitecturesor remain near the sublimation
the timethat small grains
those
due
to gravity and radiation, respectively. The
eventsare tooshort-lived
to explain
theas frequency2017).
Transientdynamical
upheavals,
suchthe(Tim D. Pearce⋆, Alexander V. Krivov
andMark
Booth)
andradiation
forces.
Its equation of motion isregion
is
too
short
(van
Lieshout
et
al.
2014;
Sezestre,
exceeding constraints on MIR
dust
migratingofHeavy
observations(Bonsor,Raymond& Augereau2013). 2.1.1 Forcesgravitational force isLate emission:
Bombardment,
could
supplymaterialto✓◆Augereau & Thébault 2019). Trapping grains via theMaterial
migratinginwards
Poynting-Robertson
the veryinner
regionsof thethe throughsystem;however,suchinwards
underradiation
forcessublimates
near
star,
ṙ
v
In the absence of gas, theF dust
grain
is subject
to gravity
Di↵erential
Doppler
E↵ectisine↵ective
against PR-dragdd【内容】幅広いSpタイプ，ageの主系列星（おおよそ1/5）で見られる，
=
F
+
F
,
(1) (3)grav
radGM? m ,
(PR)andpiling up toat thesublimation
zone cannot F
=
|F
|
1
r̂
eventsaredragtooshort-lived
explainthefrequency
grav
radradiation forces. Its equationof motion
is
Fgrav
=
r̂,
(2)
(Sezestre,
Augereau& Thébault 2019), and andwhilstreleasing gas which then traps
subsequent
grains.
These
2
c
c
r
produce enoughhot dust
to reproduce
observations,sinceof observations(Bonsor,RaymondAugereau2013).
where F is the total force and Fgrav and Frad are
謎めいた近赤外線の輻射超過の謎に迫る。落下してきたダストが蒸発す
magnetic
trapping
has&been
proposed(Rieke, Gáspártimethat small
grainsremainnear the sublimation
hot grains, the source of Material
thethenear-infraredemission,
migratinginwards
through
Poynting-Robertson
where
G, M⇤ , m,
and r̂ are thegravitationaldue
to gravity
andr radiation,
respectively.
Theconstant,& Ballering
2016)
the e↵ectivenessof the mechanismthoseis
where
the ratio
ofisFdust
radiation
to the andF=+grainFrad ,mass,pressure(1)
ることによって発生するガスによりダストが円軌道化＆安定化させられgrav
regionis tooshort(vanLieshout
et al.zone
2014;
Sezestre, is gravitational
(PR)
drag
and
pilingup
atthesublimation
cannotstar
mass,
star-grain
separationforce
unclear(Kral
et al.
2017a; Kimura et al. 2020).
are held on stable orbits by gas.
The
idea
was
briefly
Augereau&
Thébault2019).
Trapping
grainsvia the whereforce,
produceenoughhot
dust
toreproduce
observations,sincestar-grain
unit
gravitational
theseparation
dust
velocity,is thed isandṙdrespectively.
Frad
are radial
F is v
the
total
force
and
Fgravvector,
In
this
paper
we
investigateapotential
mechanism(1)
ダストにる機構を新たに提唱。比較的少ない質量供給で観測可能な輻射超過
explored before (Lebreton ettheal.time2013),buttherequiredDi↵erential
DopplerE↵ect
is ine↵ective
against PR-drag those due to gravity
thattosmall
grainsremainnearacrossthe sublimation
The andcombinede↵ectsof radiationpressure andradiation,
respectively.
The
generate NIR excesses
diversestellar typesof
and
GM
m
?
component
v
,
r̂
is
the
radialunit
vector
and
c
is
the
d
F
=
r̂,
(2)
(Sezestre,
Augereau&
Thébault2019),
andwhilstgrav（量，寿命）が作れる上，サイズが自動的に一定に揃う予言が観測的特
region
is
too
short
(van
Lieshout
et
al.
2014;
Sezestre,
PR-draggas quantity appeared too high to becompatible
withgravitational
force is induce a forcer2Frad on the grain:
ages,
without requiring
specific system architecturesor
働く力：magnetic
trapping 2019).
has been
proposed(Rieke,Gáspár
speed
ofmigrating
light (Burns, Lamy & Soter 1979). Radiation
Augereau& exceedingThébault
Trapping
grainsvia theconstraintsonMIR
emission:dust
observations (Su et al. 2016).
WeDoppler
perform
detailed
徴（中間赤外での超過量が近赤外に比べて少ない）を説明できる（太陽where G, M⇤ , m, r and r̂ are the gravitational✓◆ constant,& Ballering
2016)
the ise↵ectivenessof the mechanism
isDi↵erentialE↵ectine↵ective
againstPR-draginwards under radiation forces sublimatesnear
the star,ṙdcircular
vd andpressure
counteracts
gravity,
so=
a |F
grain
on
aseparation
orbit
βは輻射圧と
GM
?m
star
mass,
dust
grain
mass,
star-grain
|
1
F
r̂
(3)
unclear
(Kral
et
al.
2017a;
Kimuraetal.
2020).
grav
radanalyses and show that the(Sezestre,gas quantities
neededare
Fgrav =r̂,(2) ,Augereau
Thébault2019),
and whilstgrains. These型の場合）ようになった（ただし，A型星に関してはまだ）。
releasing &gaswhich thentraps subsequent2ccr
star-grain
separation
unit
vector,respectively.
hasareducedvelocity
In
this
paper
we
investigateapotential
mechanism
magnetic
trapping
has beenGáspár 重力の比
hot grains,
the proposedsource of (Rieke,
the near-infraredemission, The combined e↵ects of radiation pressure andmuch smaller than the previous
estimate.
where G, M⇤ ,wherem, r and isr̂ aregravitational
constant,
thetheratioof radiationpressure to theto generate
NIR
acrossofdiverse
stellar types& Ballering
2016)
theexcessese↵ectivenesstheis andare heldonstable orbits
by mechanism
gas. The idea
was briefly
inducea force
Fstar-grain
the grain:
radvonstar PR-dragmass, dust
grain
mass,
andṙd is the radial
The
work
is
laid
out
as
follows.
In
Section2
wegravitational
force,
dust
velocity,
ages,
without
requiring
specific
systemarchitecturesord is the separationunclear
(Kral
et
al.
2017a;
Kimuraetal.
2020).
【背景】
explored before (Lebreton et al. 2013), but the requiredpstar-grain
separation
unit
vector,component of vd , r̂ isrespectively.
the radial unit vector and c is theexceedingconstraintsonMIR
emission: mechanism
dust migrating
this paper
weinvestigateapotential
describe the evolution of dust In
grains
close
to
the
star
✓
gas quantity appeared too high to be compatible withv=v
1,ṙ ◆ pressure(4)
Hot
dust trap
KepdThe
combinede↵ectsofradiation
and
speed
of
light
(Burns,
Lamy
&
Soter
1979).
Radiation
inwards
underradiation
forcessublimates
near
the
star,
v
• AFGKの主系列星の20%が近赤外線超過を示す
to generate NIR
excessesacrossdiversestellar
types
and
d
d
observations(Suet gasal. 2016). We perform detailed= counteracts|F| the1gravity,Fradr̂ a grain, on a circular(3)
gravonin the absence of gas. In Section
3
weoutlineourPR-drag
induceaforce
Fgrain:
pressure
so
orbit
rad
releasing
gas
which
then
traps
subsequent
grains.
Theseccages, withoutanalyses
requiringand
specificarchitecturesor needed areshow systemthat thegas quantities
and temperature
T velocity.
by P = ⇢kB T /(µmu ). Substituting
2.
is
the
Keplerianorbitalwherev
Kep• 星のごく近傍の1000Kくらいのダストの存在を示唆
hasareducedvelocityhotgrains,thesourceofthenear-infraredemission,exceedingconstraintsonMIR
emission:
dust
migrating2
model, and show that grains can becometrappedinpreviousamuch smaller
than theestimate.
4⇡s⇢dof
ds, where
dust Hotgrain
density,yields in ga
where
is dm
the= ratio
radiationpressure
to dustthe trapped✓◆ ⇢d is the
W
are
held
on
stableorbits
by
gas.
The
idea
was
briefly
inwards
underradiation
forcessublimates
near
the
star,
ṙ
v
輻射圧の効果でダストはゆっくり回転ddthesublimation
rate
as
The
work
is
laid
out
as
follows.
In
Section2
we• 説明の難しい様々な特徴
gravitationalgas disc. We examine the implicationsof
oursimulations,|Fgravv| d is1the dustr̂velocity,
Frad = force,, ṙd is the(3)radialptwexplored
before(Lebreton
etal.
2013),buttherequired
releasing gas describe
which thentraps
subsequent
grains.
Theseccthe evolution of dust grains close to the starv=d ⇢k= BunitvTKep1u ). Substituting, c is the(4) Nume
componentof vd , r̂ istheradialvectorandw
andtemperature
T
by
P
/(µm
2.2
includingobservational
comparisons,inSection4.
We
gas
quantity
appeared
too
high
to
be
compatiblewith• より長波長側の超過の有無とはあまり関係なし
hot grains, thesourceofthenear-infraredemission,s
Sublimation
2 (Burns, Lamy & Soter 1979). Radiationin the absence of gas. In Section 2.1.2
3 we outline
our
gas
speed
of
light
where
is
the
of
radiationpressureto⇢eqthe
sin
dm
=
4⇡s
⇢ratio⇢d Keplerianis ds
the dust
grainyieldsd ds, whereobservations
(Su
et
al.
2016).
We
perform
detailed
kBdensity,
Td velocity.
istheorbital
where
v
are
held
on
stableorbits
by
gas.
The
idea
was
brieflyKepWe
impleme(2)昇華：熱力学的な考察から温度の関数でdiscuss the results in Section 5, and conclude
in Section
model, and showthat grains can become trapped
inpressurea the sublimation. orbit(7)
counteracts
gravity,so a=grainṙdonathecircularcorate
asgravitational
force,
v
is
the
dust
velocity,isradiald• MIRの超過量が著しく少ないSEDやPolarizationの観測は，ダスト
dt2⇡µmu ⇢danalysesandshow that
the2013),gas quantities
needed are
two-dimensio
explored
before(Lebreton
et
al.
but
the
requiredgas disc. We examine the implicationsof oursimulations,ahasthea reduced
We
implement
component
ofsublimation
vd , r̂velocity
is the radialprescription
unit vector and of
c is Lebreton
the
6.
much
smallerthantheprevious
estimate.
withvariablegas quantity including
appeared observational
too high to becomparisons,compatible withsSoterT
in Sectionspeed
4.
Weof light2.1.2
サイズがsteepで昇華領域すぐ外側にあることを示唆→星のタイ
Sublimation(Burns,Lamy&1979).
RadiationThisisequivalent
toEquation
17
ofLebretonetal.
(2013)
サイズの進化
single
dust
g
et
al.
based
on
that
of
Lamy
(1974).
Particles
The (Su
worketis al.
laid2016).
out asWe
follows.
In Section
2 (2013),
weobservations
perform
detailed
k
T
⇢
ds
in
B
eq
d
p
discuss the results in Section 5, and conclude in pressure
Section counteracts
if nogas=discpresent.
The
densitygravity,so a isgrain
on a circularorbitof(7)evaporating.
completely su
describetheevolutionof
dust
grains
close
to
the
star
v
=
v
1
,
(4)
analyses
and
show
that
the
gas
quantities
needed
are
Kep
d
th
dt
2⇡µm
⇢
We
implementthesublimationprescriptionofLebretonu
プとダスト存在領域の半径には相関あり
devaporate hasfroma grainat attemperature
Td at6.
γは昇華の効率gas
saturation pressure,⇢eq , ais rate
found froma thea reduced
velocity
distance of

Hot Dust Evolution
without gas

•
•
•
•
•

the absenceof previous
gas. In Section
3 we outline our gas
fomuchinsmaller
than theestimate.
et al.Clausius-Clapeyron(2013), based onequationthat of Lamy (1974). Particles
ThevariableistheKeplerianorbitalvelocity.
wherev
かなり短い時間で昇華，吹き飛ばされないのはなぜか？
This Kepisequivalentfrom
to Equation
Lebreton et al.T(2013)
model,
and
show
that
grainscanbecometrapped
in
a
re
The
work
is
laid
out
as
follows.
In
Section2
weevaporateapgrain17atoftemperatured at a rate instantaneou
2 HOT DUST EVOLUTION IN THE
if no gas disc is present. The density of evaporatingdegas disc.
We examineof toourthesimulations,describe
the evolutionof thedustimplications
grains closestarρeq: 飽和蒸気圧に
v
=
v
1
,
(4)
✓
◆
✓
✓
◆
◆
Kep
d
the
scale
fac
P
1
Collisional ABSENCE
cascade は時間がかかりすぎて無理
eq
2 observational
HOT DUSTEVOLUTION
IN THEgas at saturation pressure,⇢eq , is foundfrom the Td
OF A GAS
DISC
⇢
Td
eq
includingcomparisons,inSection4.
We
in the absence of gas. In Section 3 we outline our gas
p
f
=
,
(5)
2.1.2
Sublimation
forconvergen
log10 equation
log10= B A Peq
, (8)
evap
おけるガス密度，3
ABSENCE
OF
A
GAS
DISC
Clausius-ClapeyronistheKeplerianorbitalvelocity.
where
v
g
cm
K
K
Kep
fevap
= Tpd
,
(5) for g
discuss
the resultsin Section
and conclude2⇡µm
model,and showthat grains
can 5,
becometrappedininSectionau kB
results
Commet ー ダストサイズ分布が説明できない
2⇡µmu kBof
Td LebretonWe
implementthesublimationprescription
We first describe the evolution
of
hot
dust
close
to
the
6.
gas disc. We examine
implicationsof our simulations,described in
We first thedescribe
the evolutionof hot dustTclose
to thedにすごく敏感where◆ A and ✓B ◆are1 material-specificquantities
✓
✓
◆
2.
et
al.
(2013),
based
on
that
of
Lamy
(1974).
Particles
where
f
is
the
flux
of
particles
evaporating
from
the
where
f
is
the
flux
of
particles
evaporating
from
the
evap
⇢
T
T
includingobservational
comparisons,inSection4.
We
evap
一時的なダスト放出（Gianteqd (Lebreton et al.
d 2013); for carbon,
star intheinfluenceabsence of a ofgas disc, under the influenceofSublimation
determined
empiricallystar in the absence impactなど）：寿命短すぎ
of a gas disc, underthe
2.1.2evaporate
log10grain
log
=
B
A
, (8)
10
at
a
rate
from
a
grain
at
temperatureT3dsurface,
P
and
µ
are
the
saturationpressure
and
eq
W
g cm
K = 7.2294 pressure
Kdiscuss the resultsin Section
5, andconclude inThis
Section
A
=
37215
and
B
(Zavitsanos&
Carlsonradiation
forces andsublimation.
evolutioncannotgrain
surface,
P
and
µ
are
the
saturation
andeq
radiation forces and sublimation.
evolutioncannotmolecular
weight ofevaporating
material
respectively,
PR効果によるダスト落下：ダストの量が稼げない
the1973;
sublimationprescriptionof Lebreton
PR
Sezestre,
Augereau& Thébault2019).
Hence ⇢eq
6. 2 Thiskeep
hot dust
close
to theINstar
for long enoughWeto implement
be
HOT
DUST
EVOLUTION
THE
where
Aevaporating
B arematerial-specificquantities
molecular etweightofmaterialbe
2.3 Result
mbasedisisandtheunit
krespectively,
is the Boltzmannal. (2013),
on atomic
thatof mass
Lamy(1974).
extremely
sensitivetoT .and Particles
P※SED modelから，Carbonのダスト考える

Hot dust trapped in gas around main-sequence4
ガスがない時のダスト進化(G2starstype)  






vgas = vKep⌘⌘    




cs =




  



Figure 1. Evolution of solid carbon grains of di↵erent
initial sizes orbiting a G2 star, if no gas is present. The
qualitative evolution is independent of initial grain size. First,
grains migrate inwards under PR-drag, maintaining circularorbits (Stage I). When grains approach the star they begin
to sublimate over a narrow distance range (Stage II). As
grain radii decrease theirvalues increase, and radiation
forces cause their orbital eccentricities to grow (Stage III).
Eventually grains leave the system. The Figure is very similar
to Figures 4 and 5 in Sezestre, Augereau & Thébault (2019).
The dashed line is at rs = 0.022 au, where grains of all initial
sizes have lost 50 per cent of their mass through sublimation;
this is taken as the gas input location in later modelling.
Note that dust arbitrarily originates at 1 au on this figure,but provided it starts exterior to the sublimation region thefundamental results are unchanged.

3.1

(9)

vKep

(10)

and cs is the isothermal sound speed, given by





⌘,

✓ Mamajek◆2星の放射はPecaut &(2013)から引っ張ってくる
cs





1

where
本論文では，太陽型の場合(G2)とA型星(A0)を場合を扱う。


pGrain evolution model with gasskB Tgas
.
µmu

(11)

Stage
I: assumed
Poynting
Since
gas isto beRobertson効果による落下
produced by dust sublimation,
its molecular weight µ is assumed to be that of the dust.
Stage
II: 昇華点を超えて急激にサイズが小さくなるFor
the parametersin our model the factor ⌘ ⌧ 1, so thebulk gas velocity is approximately Keplerian.
Stage
吹き飛ばされるサイズに達すると一気に外に飛んでいく
For aIII:thin
disc the midplane gas density ⇢gas isrelated to surface density ⌃ by
⌃
.
2⇡H

(12)

cs
,
⌦

(13)

⇢gas = p
The scale height H is
H=

where ⌦ is the bulk gas orbital frequency. For gas
viscosity ⌫ we employ the Shakura & Sunyaev (1973)
prescription⌫ = ↵cs H,(14)where ↵ is a dimensionless quantity smaller than unity.
The appropriate value of ↵ is unclear (Kral et al. 2016;
Kral & Latter 2016; Moór et al. 2019), and so we leave it

vKep
disc;
properties may be simplifications, but shouldp somevgas = vKep
1 to⌘,demonstrate the viability(9)
sufficeof the model.
and cs is the isothermal sound speed, given by
We assume the disc to be much less massive than thewherestar, but sufficiently dense for gas to behave viscously. Wesalso impose that the disc is vertically thin and isothermal.
kB Tgas✓ cUsing◆
these
assumptions
we can describe2.
(11) the gas with a
css =
µmu
thin protoplanetary
disc model⌘⌘(10) summarised in Armitagev(2010).
Kep
Since gas is assumed to beThe
producedby dustbulk
sublimation,
gas undergoes
circular motion about theisothermal
soundspeed,
given
byand cs isitsthe
molecular weight µ
is assumed
to be that ofcauses
the dust.
star,
where pressure-support
the bulk gas velocity
For the parameters invgas
ourtomodel
the factor⌘ ⌧than1, sothetheKeplerian orbital
be slightly
smallersbulk gas velocity is approximately
velocity vKep : Keplerian.

Gas Diskの導入

ダスト流入→ダストの昇華→ある半径でデルタ関数的にガス発生，そkB TgasFor a thingas density
cs =disc the midplane.
(11) ⇢gas isu RAS, MNRAS 000, 1–19cµm
2002
related to surface density⌃ by
れが粘性拡散してできる平衡回転円盤を
Since gas is assumed to be produced by dust sublimation,考える
ns of di↵erent
its molecular weight µ is assumed
to be⌃that of the dust.


density evolution equation for a thin,viscousgas disc
radiusrs , and(x) is the Dirac Delta Function.
(Lynden-Bell & Pringle 1974; Pringle Combining1981) with an
Equations 14 and 15 shows viscosity
Hot dust trap
additional term for mass input (e.g.
Kralproportional
et al. 2016) to distance;in
to be
to explicitly show this
is
in
s

Ṁ
˙
(3) ガスの面密度時間発展＆ガス発生
=
(r
r
),
⌃
dependence, we define2⇡r⌫ ⌘s V r where V is a parameter

independentof r. We assume the disc to be in steady
⌘
@⌃
3 @
Ṁin
1/2
˙ in , that˙ in0.= Making
state,
such
@⌃/@t
=
(16)
+
⌃
= where⌫⌃r
r1/2(r thesers ),atsubstitutions
(17)
⌃
is
the
gas
mass
input
rate
the sublimati
Ṁ
in
@t
r @r
@r
2⇡rs
and expanding Equation 16 yields
˙ in is the r
(x)
is
Delta
Function.
is the Diracgas mass input
rate atthe sublimationin thes , and
where t is time andradius⌃surfacedensitywhere
input Ṁ
rate.


@ ⇣

rs , and (x) is the Dirac Delta Function.
Gas is added to the disc by dust sublimation,
2radiuswhich@⌃r Ṁ14in and 15 shows viscosity
2 @ ⌃ Combining
Equationshappens over a very narrow radius range;
wetherefore
2r
+
7r
+
3⌃
+
(r rs ) = 0. (18)2@rto be proportional@r
to r
distance;s 3⇡V to explicitly show thiswrite
Hot dust trappedin gas aroundmain-sequencestars
5
dependence,
wedefine
⌫
⌘
V
r
where
V
is
a
parameterThis is a second order inhomogeneous linear di↵erentialof r. We assume the disc to be in steadyequation,independent
with the solution
state, such that @⌃/@t= 0. Making
these substitutions
and expanding Equation
16 yields

Ṁin
r
✓
◆

˙
(r rs ),
(17)
⌃in =
C1
C2
rs
Ṁin
2⇡r
s
(12)
⌃=
+ 3/2
1
✓(r rs ). (19)
2
@⌃
r
@
⌃
Ṁ
r 2r2r3⇡V r+ 3⌃ +rin (r r ) = 0. (18)+7r
where Ṁin is the gas mass input rate at the sublimations@r2@r
rs 3⇡V
radius rs , and (x) is the Dirac Delta Function.
Here C1 and C2 are constants to be determined, and ✓(x)This is a second order inhomogeneous linear di↵erential
Combining Equations 14 and 15 shows viscosity is the Heaviside
stepfunction.
equation,withthe solution
to be proportional to distance; to explicitly show thisCombining Equations 14 and 15 shows viscos
to be proportional to distance; to explicitly show t
定常状態ならdependence, we define ⌫ ⌘ V r where V is a parame
independent of r. We assume the disc to be in stea
state, such that @⌃/@t = 0. Making these substitutio
and expanding Equation 16 yields
F.
⇢gas = ps present. The
For the parameters in our model the factor⌘ ⌧ 1, so the2⇡Hrain size. First,
bulk gas velocity is approximately Keplerian.
taining
circularThe
scaledischeightHmidplane
is

For
a
thin
the
gas density ⇢gas is
tar they begin
related to surface density ⌃ by
(Stage II). Ascs
In general, an equation of the form of Equation 19
2
and radiation
,
(13)
H
=
dependence,
wedefine
⌫
⌘
V
r
where
V
is
a
parameter✓ in r ◆by considering
Hot dust trapped in gas around main-sequencestars 42⌦
has
its
constants
CandC
determined12↵erentow (Stage III).
C1
C2
rs
Ṁin
independent of r. We assume the disc to be in steady⌃srs ). (19)


⌃
=
+
1
✓(r
2

p
.
(12)
=
⇢
gas
3/2
of
et.isThe
very similar
where ⌦ is the bulk2⇡H
gas orbital frequency. For gas state, such that @⌃/@t = 0. Making these substitutions the homogeneousr equivalent
3⇡V
r

s rEquationr 18, which is theFirst, (2019).
hébaultcase if ṀHere
Armitage(2010) tostatesthat for anda thinin =C0.and
viscosity ⌫ we employ the Shakura& Sunyaev (1973) and expanding Equation 16 yields
C2 are constants
be determined,✓(x)1pircularinsof all 
initialThe scaleheight H isdisc extending
to the surface
of a slowly-rotating star, avgas = vKep 1 ⌘,(9)prescription
is the Heaviside
step function.
2
ghbeginsublimation;@⌃r Ṁinsimple solution
to the anhomogeneous
equation
equation of theform of is
Equation 19
2@ ⌃

In general,
2r
+
7r
)
=
0.
(18)
+
3⌃
+
(r
r
I).
As
where
s
ater modelling.
cs
has its constants C1 and C2 determined by considering@r2@r
rs 3⇡Vdiation(13)
H = ⌫, = ↵cs H,
on this figure,(14) This is a second order inhomogeneous linear di↵erential! 18, which is thethe homogeneous equivalent rof Equation
⌦
✓
◆
e
III).
2
tion region theR⇤states that for a thincase if Ṁin = 0.ṀArmitage(2010)
acccs
equation,withthesolution
similar⌃h = to the surface
1
,
(20)a
⌘ ⌘ quantity(10)
where ⌦
is thegas orbital
frequency.
For thangas unity.
where↵ isbulk
a dimensionlesssmaller
discextendingofaslowly-rotating
star,
v
3⇡V
r s
1
2
in rKep(2019).
viscosityThe⌫ weemploy the
ShakuraSunyaev(1973)
appropriate
valueof ↵ is&unclear(Kral
et al. 2016;


r ◆
✓
simple solution to the homogeneous equation is
s
C
C
r
Ṁ
3/2
1
2
in
s
initialistheisothermal
soundspeed,
given
by
and
c
 sprescription
Kral & Latter
2016; Moór et al. 2019), and so we leave it
⌃=
+ 3/2
1
✓(r rs ). (19) where Ṁ
acc is the accretion rate of gas
r
3⇡V r
r
r
mation;! the star, andronto
free for this analysis.
s
R⇤ to
Ṁacc
R⇤ isFigure
the starradius(Armitage2010).
We
defineC1theanddelling.
2. Themidplanegasdensityrelativethat atHereC
1 and C2 are constants to be determined, and ✓(x)
⌃
=
1
,
(20)
We
assume
the
disc
to
be
optically
thin,
such
that
h
olution
1 C from
2 this,kTBgas
figure, in the
3⇡V
r
r
dust
sublimation
radius,forsteady-stategasaroundaG2
star.
noting that Equation 20 is a simplification(14) (11) is the Heaviside step function.
⌫is=the↵csblackbody
2
cH,
.
s =
its
temperaturetemperatureµmu
Here actual
the gas massrate fromclose
sublimation
is assumed
toon thegas input
properties
to thestar would
In general, an equation of the form of Equation 19 and theis theaccretion
gasstar.
onto
thedashedstar, and
wheretoṀthebe similaraccretion
raterate
ontooftheThe
acc gaswhere ↵ is a dimensionless quantity smaller than unity.
has
its
constants
CandC
determinedbyconsidering
12
be complicatedbyvariousfactors.
SuchaWe
simplification
Since gas is assumed to✓be producedby
dust
sublimation,
◆
line
marks
the
sublimation
radiusr(takentobedefine
0.022 au),
R
is
the
star
radius(Armitage2010).
C1 ands⇤
1/4⇣⌘
The appropriate value of ↵ is unclear
(Kral
et
al.
2016;
1/2
the
homogeneous
equivalentofEquation
18,
which
is
the
L
rbe that of the dust.
⇤
is justified
here
because,as welater 20show,
dust does
its molecularweightµisassumed
to
where
mass
is inputted.
C
from
this,
notingthat
Equation
isasimplification
2gas
T
=
278
K
,
(15)
gas
Kral & Latter 2016; Moór et al. 2019),
and sowe leave itcase if Ṁin = 0. Armitage (2010) states that for a thin
L
au
For
the
parameters
in
our
model
the
factor
⌘
⌧
1,
so
the
1 farther2
not driftandmuch
inwardthanclosers andso stardoeswould
nottheactual gas
properties
to the
discextendingtothesurfaceofaslowly-rotating
star,
a
free
for
this
analysis.
t around thebulk gas velocity is approximately Keplerian.
bethe
complicatedby various
factors.
encounterinner regionof thedisc. Such a simplification
simplesolutiontothehomogeneous
equation
is
and
L
are
the
star
and
solar
luminosities
where
L
We
assume
the
disc
to
be
optically
thin,
such
that
⇤


d maintainedtheFor a thin disc the midplane gas density ⇢gas isin
is justified Equation
here because,
asintowe latershow, dust
does
Substituting
20
Equation19
andrespectively.
The
gas
being
optically
thin
means
that
is theblackbodytemperature
occurs overits
a temperature
relatedto surface
density
⌃ by
drift
much
fartheris inward
rs anddoes not!
r
formof thisdensityshown thanon Figure
2. soFinally,in The not(1) ガスの回転速度(2) ガス粘性と
ガス温度

d
H
b
li
w

 

@⌃
r Ṁ
@ ⌃
2r
+ 7r
+ 3⌃ +(r r ) = 0. (1
@r
@r
r
3⇡V
静水圧平衡からFi
This is a second order inhomogeneous linear di↵erentdu中心面密度求めたHe
equation, with the solutionbe 

鉛直方向は静水圧平衡とし，ガス温度は
黒体の輻射平衡温度で与える

(1

C
C
⌃=
+
r
r

Ṁ
3⇡V r

✓

1

r

r
r

◆

✓(r

r ).

lin
T
wh

in
a

(1

Th
int
a

Here C and C are constants to be determined, and ✓(is the Heaviside step function.
In general, an equation of the form of Equation⇥
has its constants C and C determined by consideri
thehomogeneous
equivalentofEquation
18,
which
is
t
このガス中でダスト進化を調べると。。。
⇥
case if Ṁ rewriting= 0. theArmitage(2010)
statesthatfor a thsurface density
in termsof that at
rs yields

As well as sublimating, grains embedded in gas can growgrain embedded in gas oftheusame2⇡µm
kB Tgas molecular weightasWematerial
accretes onto
them. ofContinuingwithaccrete particles
at a ratein gas can grownow consider
the e↵ectthe above
gasthedisc on
As well as sublimating,grains embedded
where facc is the flux of gas particles accreting onto theprescription of Lebreton
et al.
(2013)
andLamy(1974),
a
F
=
F
+
F
+
F
,
(25)
grav
gas
rad
migrating dust. The grain equation
ofvdmotionin theas (26)
material accretes onto them. Continuing with the
v
⌘
v
.
gas
grain embedded in gas of the same molecular weight will
grain and Pgas is the gas pressure. Combining this withpresenceof gasatisa rateprescription of Lebreton et al. (2013) and Lamy (1974), a
accreteparticles
Equation 6 for sublimation, the grain mass changes at ais the gas drag force. This force is related towhere Fgas disc ontion in the

gas

(25)

ガスがある時のダスト進化
(G2
type)
We do not consider turbulent motion in the gas,grain
hence
embedded in gas of the same molecular P
weight will
gas

p
f
=
,
(
rate
acc
the
gas
velocity
v
is
the
bulk
velocityfromEquationv, the grain velocity relative
gas to the gas:accrete particles at a rate Hot dust trapped in gas
aroundumain-sequencestars 7
2⇡µm
k
T
B
gas
赤線がガスあり，グレーがガスなし
s related(1)toダストに働く力： 9. F
= FgravP+
Frad Equation+ Fgas , 4, for a grain(25) on a circulargas
Combiningwithpfacc =,(31)  2⇡µmu kB Tgas
orbit



dm
2
where
f
is
the
flux
of
onto
where Fgas is the gas drag force. This force is related to (fgas particles
accP
fevap ) µmuaccreting
,
(32)
=
4⇡s
gas

acc
f
,
(31)
v
⌘
v
v
.
(26)
acc = p dt
gas
d
where
f
is
the
flux
of
gas
particles
accreting
onto
the
v,
the
grain
velocity
relative
to
the
gas:
ガスダストの相対速度差：acc
grain and Pgas
is uthegas pressure. Combining this w
⌘
⇣p
2⇡µm
kB Tgasp(26)
grain and Pgas is the gas pressure.
 disc therefore evolves as
v = Combining
vKep
1this⌘with 1,(27)
and grain6radius
in a gas
Equationforsublimation,
the
grain
mass
changesaWe
donot
considerturbulentmotion
in
the
gas,
hence
Equation 6 for sublimation, the grain mass changes at a
where f
is the flux of gas particles accreting onto thegas, hence
acc
rate
考えている円盤モデルでは，現実的なダストサイズで
β
>
η
v
⌘
v
v
.
(26)

rate
gas
d
the
gas
velocity
v
is
the
bulk
velocityfromEquationm Equation
so dust gas
on a circular orbit is slower than gas if >grain⌘ (e.g.
and Pgas is the gas pressure.
Combining
thispwiths
n a circular （ダストの方がガスよりゆっくり回転），抵抗則はEpstein⇢eq changes⇢gas atTgas
Takeuchi&
Artymowicz
2001).
In
ourparameterspace
9.
CombiningwithEquation
4,
for
a
grain
on
a
circularEquation
6 for sublimation,
the grain
a /Td
kB Tdmassds
We do not consider turbulent
motion
in
the
gas,
hence

.
(33)
=
5
4
dm
⌘
⇠
10
to
10
,
with
the
smallervaluescloser
to
the
rate
2
dt dm
2⇡µmu
⇢d
orbit
the gas velocity
the bulk
Equation
gas is(facc
f4evap )velocityµmu , from (32)= v4⇡s
2 








dt
star.
A
of
10
corresponds
to
a
grain
radiusofseveral
(f
f
)
µm
,
(
=
4⇡s
acc
evap
u
   
9. Combining with Equation 4, for a grain on a circular
dt
This
is
equivalent
Equation
17andofgrey Lebreton
millimetres
aroundaG2
star
orseveralcentimetresfor
Figure 3. Evolution of an initially 10 µm radius solid carbon to
grain orbitinga G2 star. Redlines show evolutionet
in al.
,
(27)
and
grain
radius
in
a
gas
disc
therefore
evolves
as
⌘
⇣
orbit
(2) ダストの成長（凝縮）：熱力学から定式化pdmp2
the presence and absenceof a gas disc, respectively.
The gas density at r = 0.022 au is ⇢ (r ) = 10g cm , and the disc(2013),
noting
that
we
do
not
require
gas
and
to
an
A0
star;
for
gas
quantities
consideredin
thispaper,
(f
f
)
µm
,
(32)
=
4⇡s
u is initially too large to couple
Ṁ ). The grain
to gas,dust
so itsfollows the density profile on Figure 2 (Equation 22,acc
with Ṁ =evap
v = vKep
1 ⌘
1
,
(27)
and
grain
radius
in
a
gas
disc
therefore
evolvesasdt
early evolution is identicalto the gas-free case; the grain migrates inwards under PR-drag and begins to sublimate near the star.
> ⌘ (e.g.
have
the same
temperature.
such
are
not
coupledtogasanyway.
Hences large ⇣grains⌘
However, once the grain becomes sufficiently
small it starts
to couple to the gas, which draws the grain away from the star andpppprotects it from further sublimation and eccentricity excitation. The grain is eventually trapped on a circular orbit just exterior⇢⇢T/Tmeter space
kB
T
ds
eq
gas
gas
d
vin=thevparameter
1
⌘
1
,
(27)
d
space
where
gas
drag
may
be
importantandgrain radiusa gas
therefore
asthe right-hand plots, emphasising
Kep
to the sublimation
region, where ingas dragbalancesdisc
PR-drag.
Note the break inevolves
the time axes on.
(33)=
so dustdton a circularorbit
isslower
than
gas
if
>
⌘
(e.g.
the speed of sublimation in comparison to drift.
soser to the
2⇡µm
⇢
p
u
d
> ⌘, and so dust moves more slowly than gas acrossthe
Hot dust trapped in gas
around main-sequencestars 8s of several⇢⇢
T
Takeuchi
Artymowicz
2001).
In
ourparameterkTdsso dust on a&circularorbit
isslower
than
gas
if
>
⌘ (e.g. spaceeqgas
gas /TdBdsregion of interest.
p3.2.2 Criteria for dust trapping and growthis only valid(noting that taking the magnitude of F.
(=
ダストがあるサイズ，距離で安定化！！
5
4
This
is
equivalent
toEquation
17
ofLebreton
et
al.
'
&
'&
3.2
Results
inthepresenceofgas
imetres for
if
>
⌘,
as
satisfiedfor
ourparameter
space).
Similarly,⇢⇢
T/T
Takeuchi&
Artymowicz
2001).
In
ourparameter
space
eq
gas
gas
d
⌘ ⇠ 10to10 The, withthe smaller
valuescloserB Tddrag formalism
dependsongrain
size toandtheGas v.
has Iftwo dsmain e↵ects on dust:kdragand growth.
dt
2⇡µm⇢todshrink at a rate



u
PR-drag
causesthesemimajor
axis
.
(33)
=
(2013),
notingthat
donotrequire
gas
and
dust
to
5
4we
this paper,Growth is simple; if gas is dense enough, sufficient
4 withhas
⌘
⇠
10
to
10
,
the
smallervaluesclosertothedtonto the2⇡µm⇢dgas model, we now describe the
the
grain
radius
s
⌧
,
where
is
the
gas
mean-freeu through

star.
A
of
10
corresponds
to
a
grain
radiusofseveralmaterial accretes
grain to o↵setthat lost
Havingimplemented
the
ガスがないと，離心率が大きなまま，近日点付近でどんどん昇華が進み，や
have the same
temperature.
way. Hence

4 
da
GM

sublimation. Equation 33 shows that a grain will grow if

=
2
.
(37)
star. A of 10path,corresponds
to
a
grain
radiusofseveral

then
drag
is
in
the
Epstein
regime.
The
mean
free
dt
ac
evolutionof
dust
grainsinthepresence
of
gas.
This
is
equivalent
toEquation
17
ofLebretonetmillimetres arounda G2 star or several centimetresfor
e important
がて吹き飛ばされる。
p
p Equation 17
This is equivalent
toof Equations
Lebretonal.
millimetresa G2 star or several
centimetres forEquating
36 and 37etand substituting
F from around
path
is
⇢
T
>
⇢
(T
)
T
.
(34)
s across the gas quantities considered in this paper,
Equation30, a notgrain willbe trapped if gas
the localandgas(2013),
notingthat
wedorequire
dust
an
A0
star;
for

ガスがあると円軌道化。昇華線の内側に入っても昇華でサイズが小さくほど(2013),
noting
that
we
do
not
require
gas
and
dust
to
an A0 star; for gas quantities consideredin this paper,
density satisfies
Regarding gas drag, Equation 30 shows that the drag






)
force direction depends
on thegrain velocity
relative
to
have
the
same
temperature.

such
large
grainsarenotcoupledtogasanyway.
Hence
3.2
Results
inthepresence
of
gas
have
the
same
temperature.
such
large
grainsarenotcoupledtogasanyway.
Hence
ガス抵抗がより効くようになり，外に移動してやがて安定に。
p
gas, and in our parameter space gas moves faster thanand v. If
µmu


(GM )
s 1

p
⇢
.
(38)
=
⇢
p
dust
(Section
3.1.2).
Gas
dragtherefore
draws
the
grain
=
,
(28)
3.2.1
Generalgrain
evolution
inthepresence
of
gas
in
the
parameter
space
where
gas
drag
may
be
importantintheparameter
space
where
gas
drag
may
be
important
c
r
v
+
v
v
s mean-free
Having implementedthe gasmodel, we now
describe
away from the star, whilst PR-drag draws it towards
PR効果で落下後，昇華線の外側で止まった場合でも，ダストが成長し，PR
2 ⇢gasthe
the star. Hence a grain becomes trapped when gas drag
> ⌘,
soso
dust
moves
more
slowlythangasacrosstheFinally, Equation 22 relates the local gas density at radiuse mean free>⌘, and
and
dust
moves
more
slowlythangasacrosstheevolutionof dustgrainsinthepresence
of
gas.


balances
PR-drag.

Gas can trap grains larger
the blowout
exterior
r to thatthan
at the sublimation
radius, ⇢ size(r ). Figure
4効果で結果的にさらに内側に落ちてくる。結局，成長も昇華もしない領域＝
whereis the collisional cross-sectionof the gas. Even
We now calculate the gas density required to trap
regionofinterest.
shows the gas density at the sublimation radius required
region of interest.


to
the
sublimation
region,protecting
furthergrains. The
axis a ofpresence
a grain subject
3.2
Results
in
the
of
gas
16
2 osculating semimajor
to trap
grainsof di↵erent sizesthem
at di↵erentfrom
distances,andcm gravity
substitutingµ size= 12.01
10 to two-body on grains = 1 cm,
 andThe dragfor
formalism
depends
andv. If ⇠昇華線付近に滞留（左の図参照）
plus
an
additional,muchsmaller
3.2
Results
insothepresence
gas or grow.
the distancesat which grains ofwill sublimate
Gas
'
&
'&
sublimation
andpreventing
theirejectionfromtheThe drag formalism depends on grain size and v.perturbing
If force instantaneously evolves as
can trap grains just exterior to the sublimation region if      



















s

in

gas

18

s

3

acc

gas

(

(

!

!

!

!



!

!

!

!



!#



!

!

!#



!"

!#

!

!"

gas

gas

eq

d

gas

d

gas

d

5/2

2
th

⇤

3/2

2





!

!"



!



!

!

!



!

$%&








!

!"





$%&

!#

!

!

!

    

!

!

!

⇤





gas

!

!

!

!

!

!



!

!



s

and vertical axes show gas density at rs , rather than local density; the local density
The plots show the analytic arguments in Section 3.2.2 and agree with simulation
rains around the blowout size can be trapped for very long periods just exterior tohe blowout radius for solid carbon is 0.5 and 5 µm for G2 and A0 stars, respectively).
s (rs ) is larger for A0 stars than G2 stars, because the sublimation radius is farther
an those shown will not be trapped, because they experience an inwards drag force
ains eventually lie at the corresponding point in the grey region regardless of theirtion 3.2.2.

Hot dust trapped in gas arou   

















 


















   






















  





  































Figure 5. For a given gas density, the final size and distance ofa trapped grain is independent of its initial parameters. Shownis the evolution of solid carbon grains of various initial sizes
around a G2 star, in the presence of a gas disc with density
10 18 g cm 3 at 0.022 au. Black lines show the evolving grain
radii (left-hand vertical axis) versus distance. The shaded grey
area shows the local gas density (right-hand vertical axis). The
black circle shows the final grain parameters at the end of thesimulations, which are independent of initial grain size.

     





  

nd distances ofentual trapping
nitial grain size.
hat, for a givenof dust depends
he initial grain
rties of trapped
mulations; lower
being trapped
uantities result
he star.

最初のダストサイズによらないfrom the star.
nterior to thends on Figure
imate; as they
more e↵ective
Likewise, grains
he sublimation
gure 4) woulds, then migrate
ns would thenthe star, androcesses cause
ded regions of
sublimate, andhe actual timeodelled physical

滞留ダストのサイズはガス密度だけで決まり， 











Figure 6. The final radii and distances of trapped grain
populations from simulations with di↵erent gas densities.
Labels show log10 [⇢gas (rs )/(g cm 3 )], where ⇢gas (rs ) is thegas density at the sublimation radius. Dashed lines show grain
blowout radii; grains smaller than this cannot be trapped bygas. Note that the trapped grain parameters are independentof initial grain sizes and depend only on gas quantity, as shown
on Figure 5.

 




Figure 7. The gas ca
substantially slow theibe created in collisionThis plot shows the r
grain from simulation
disc. The dashed line s
in the absence of gas
grain that interacted w
even once it is well-cl
0.05 µm in radius, and(just exterior to the sub

SEDの予言ガストラップが有効となるのにダスト同士の衝突・破壊なども考慮
Hot dust trapped in gas around main-sequence stars

必要なMass flow

そんなにべらぼうに大きくない

  















 












  


















14





! 1
r
For gasp
R⇤23⌫) (e.g. より現実的な場合，ダストの寿命など色々面白い話はあったが飛ばすṀacc = 3 2⇡ ↵⇢gas (rs )cs (rs )H (rs ) 1
.
rs
(47)
This equates to 9 ⇥ 10 12 M yr 1 ↵[⇢gas (rs )/10 16 g cm 3 ](45)
for dust trapped around a G2 star, and6 ⇥ 10 10 M yr 1 ↵[⇢gas (rs )/10 16 g cm 3 ] for thataround an A0 star.
mescaleCombining all three mass loss processes, sustainingar anda gas trap requires a mass input rate of
erefored dust⇢
er than⇢gas (rs )111Ṁ = 2 ⇥ 10
M yr ↵ 1 + 0.5
ars. As
10 16 g cm 3
mation(48)
r, thenfor 10 11 M of 1 µm grains trapped around a G2 star,in thisandviscous⇢⇢gas (rs )101Ṁ = 1 ⇥ 10
M yr ↵ 1 + 6
10 16 g cm 3
(49)
for 10 9 M of 10 µm grains trapped around an A0
ntain astar. These mass inflows are small, equivalent to aout the⇠ 1 km radius comet fully sublimating per year if ↵ ⇠ 1.
comets,However, unless ↵ is small they still exceed the dust
xteriormass inflow into the inner Solar System, estimated ass. The5 ⇥ 10 14 M yr 1 (Grün et al. 1985). These low massby twoinflows imply that the mechanism may be common acrossre lost,a diverse range of stellar systems, but is not necessarilyubiquitous unless ↵ is small.
s likely
It should also be noted that gas trapping is









 








  




 


  

Figure 8. Simulated SEDs for the gas-trap scenario. Three dust populations are modelled: trapped grains, dust migrating inwards
from an external source, and unbound collisional ejecta released by trapped grains. Solid black lines are combined fluxes for all
three populations, for di↵erent values of the gas viscosity parameter ↵. For high viscosities (↵ ⇠ 0.1) trapped grains have short
lifetimes, since collisions rapidly deplete trapped dust; in this case large dust inflows are required, and the dust SED is dominatedby migrating grains. For smaller viscosities the required dust inflow is reduced, and the dust SED tends towards trapped grains
alone (dashed black lines). Escaping grains make negligible contributions (black dotted lines). Hatched regions show di↵erences
between edge-on and face-on systems. The G2 and A0 star fluxes are the thick yellow and blue lines, respectively. Vertical bands
mark 2.2 and 8.5 µm; to reproduce typical observations, the 2.2 µm dust flux should be at least ten times that at 8.5 µm. The
model reproduces observations for Sun-like stars, provided ↵ . 10 2 . For A-type stars the 8.5 µm flux is too large, because gas
cannot trap sub-blowout grains. The ejecta fluxes qualitatively di↵er, since G2 ejecta sublimate before escaping, whilst larger A0ejecta survive and are blown out of the system. The data are for gas densities at the sublimation radius of ⇢gas (rs ) = 10 19 g cm 3 .
The G2 star model shows 10 11 M of 0.5 µm radius grains trapped at 0.03 au, with a dust source at 1 au. The A0 star modelshows 10 9 M of 5 µm radius grains trapped at 0.2 au, with a dust source at 6 au. All fluxes are scaled such that the 2.2 µm
flux of trapped grains alone is 1 Jy.

These results agree with Kirchschlager et al. (2017),
who aimed to reproduce NIR and MIR excesses assuming
pure graphite dust populations of a single size anddistance. They were able to constrain hot dust locations
for two Sun-like stars: 0.013 0.06 au for hot dust around⌧ Ceti (0.46 L ), and 0.035 0.52 au for that aroundHD 22484 (3.0 L ). Since thep gas trap location is set
by dust temperature, rs / L⇤ and so these inferred
dust locations are consistent with our prediction thatgas trapping occurs at distances of 0.02 0.03 au fromG2 stars. If the observed dust around ⌧ Ceti is at
the outermost location expected from gas trapping,then the hot grains must be . 0.5 µm in radius (theirtrapped grains cannot get hot enough to explain the high
NIR flux relative to that at MIR. Whilst smaller grains
emitting primarily in the NIR would be created throughcollisions at the trap location, their flux contribution issmall since they either rapidly sublimate or quickly blowout of the system.
Again, our results agree with Kirchschlager et al.
(2017). Of the 9 A stars they analysed, all haveinferred hot dust locations compatible with our result of
0.1 0.2 au for an
p A0 star (again, having scaled the trap
distance as rs / L⇤ ). The gas trap model can therefore
reproduce the inferred location of hot dust around A0
stars. However, Kirchschlager et al. (2017) infer that theG2型星はまずまずOK，A0型星はMIRがまだちょっと大きい

ダストをトラップするのに必要なガス量はALMAの[CI]検出限界より相当下

813
028
092

−42.21249223335−42.20670598232−42.20732210284

#37

791
804
709

667
624
605

970
1124
855

T.Yu. Magakian1 , T.A. Movsessian1 , H.R. Andreasyan1 , J.Bally2 and A.S. Rastorguev3,4
Byurakan Observatory of the Nat.Acad.Sci. of Armenia, Byurakan, Aragatsotn prov., 0213, Armenia; 2 Departmentof Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO,USA; 3 Faculty of Physics, Lomonosov
Moscow State University, Leninskie Gory 1, bldg.2, Moscow, Russia; 4 Sternberg Astronomical Institute, Lomonosov
Moscow State University, Universitetskii prospect, 13, Moscow, Russia
1aparDR2.
blue,
d are

http://arxiv.org/pdf/2008.13411

Herbig-Haro flows around BBWo 192E (GM 1-23) nebula

SL 4 dark cloudo 192Co 192D, GN 08.51.1.01
o 192B, GN 08.50.5

Accepted by MNRAS

Most probable

Distance, pc
Min

Max

865
968
1028
958
962

839
768
1004
876
880

893
1301
1053
1055
1060

HH天体のケーススタディ

E-mail contact: tigmag at sci.am
We studied a small comet-shape reflection nebula, located in the dark cloud SL 4 in the Vela Molecular Ridge cloud C,
known as BBWo 192E (GM 1-23), and a young infrared cluster embedded into the nebula, for the evidences of recent
star formation. We obtained the images of BBWo 192E in Hα and [SII] lines and in SDSS i’ with Blanco telescopeat the Cerro Tololo Interamerican Observatory to discover new Herbig-Haro (HH) flows. 2MASS and WISE surveys
were used for the search of the additional member stars of the cluster. We also studied proper motions and parallaxesof the cluster members with the aid of GAIA DR2. Five new groups containing at least 9 HH objects tracing several
distinct outflows were revealed. A previously unreported reflection nebula and a number of probable outflow sourceswere found in the infrared range. The proper motions allowed selecting eight probable member stars in the visualrange. Their parallaxes correspond to a mean distance 800 ± 100 pc for this cluster. The bolometric luminosities ofthe brightest cluster members are 1010 L! (IRAS 08513−4201, the strong source in the center of the cluster) and 2 to
6 L! for the five other stars. The existence of the optical HH flows around the infrared cluster of YSOs suggests thatstar formation in this cloud is on-going around the more massive HAeBe star. By its morphology and other features
this star-forming region is similar to the zone of star formation near CPM 19.
Accepted by MNRAS
http://arxiv.org/pdf/2009.00642

Accretion discs with non-zero central torque
Chris Nixon1 and Jim Pringle1,2
School of Physics and Astronomy, University of Leicester, Leicester, LE1 7RH, UK; 2 Institute of Astronomy,
Madingley Road, Cambridge, CB3 0HA, UK

1E-mail contact: cjn at leicester.ac.uk

Figure 9. Eight stars with close PM and distances, which are theprobable members of BBWo 192E cluster, are marked by whitesquares on the color image of the field, taken from DECaPS survey.

We present analytical and numerical solutions for accretion discs subject to a non-zero central torque. We express
this in terms of a single parameter, f , which is the ratio of outward viscous flux of angular momentum from the innerboundary to the inward advected flux of angular momentum there. The standard “accretion” disc, where the central
boundary condition is zero-torque, is represented by f = 0. A “decretion” disc, where the radial velocity at the inner37

the brightest cluster members are 1010 L! (IRAS 08513−4201, the strong source in the center of the cluster) and 2 to
6 L! for the five other stars. The existence of the optical HH flows around the infrared cluster of YSOs suggests thatstar formation in this cloud is on-going around the more massive HAeBe star. By its morphology and other features
this star-forming region is similar to the zone of star formation near CPM 19.

#38
2

Accepted by MNRAS
http://arxiv.org/pdf/2009.00642

f = 0 (accretion)

-2

-4

-6

-1

0

log R

f = 0.1

log Σ

log Σ

E-mail contact: cjn at leicester.ac.uk
-1

0

log R

1

f = 1.0

t = 0.0001
t = 0.001
t = 0.01
t = 0.1
t=1

0

-2

-4

-2

-4

-1

2

0

-6

1

log R

f = 10.0

0

log R

1

f = 100.0

t = 0.0001
t = 0.001
t = 0.01
t = 0.1
t=1

0

log Σ

0

-1

2

t = 0.0001
t = 0.001
t = 0.01
t = 0.1
t=1

-2

-4

Chris Nixon1 and Jim Pringle1,2
School of Physics and Astronomy, University of Leicester, Leicester, LE1 7RH, UK; 2 Institute of Astronomy,
Madingley Road, Cambridge, CB3 0HA, UK

2

t = 0.0001
t = 0.001
t = 0.01
t = 0.1
t=1

Accretion discs with non-zero central torque
1

-2

-6

1

0

log Σ

t = 0.0001
t = 0.001
t = 0.01
t = 0.1
t=1

-4

2

-6

f = 0.01

0

log Σ

0

log Σ

2

t = 0.0001
t = 0.001
t = 0.01
t = 0.1
t=1

-2

-4

We present analytical and numerical solutions for accretion discs subject to a non-zero central torque. We express
this in terms of a single parameter, f , which is the ratio of outward viscous flux of angular momentum from the innerboundary to the inward advected flux of angular momentum there. The standard “accretion” disc, where the central
boundary condition is zero-torque, is represented by f = 0. A “decretion” disc, where the radial velocity at the innerboundary is zero, is represented by f → ∞. For f > 0 a torque is applied to the disc at the inner boundary, which37
feeds both angular momentum and energy into the disc. This can arise, for example, in the case of a circumbinary
disc where resonances transfer energy and angular momentum from the binary to the disc orbits, or where the discis around a rotating magnetic star which can allow the disc orbits to be accelerated outwards at the magnetosphericradius. We present steady-state solutions to the disc structure as a function of f , and for arbitrary kinematic viscosity
ν. For time-dependent discs, we solve the equations using a Green’s function approach for the specific case of ν ∝ R
and provide an example numerical solution to the equations for the case of ν ∝ R3/2 . We find that for values of f < 0.1
the disc solutions closely resemble “accretion” discs. For values of f > 10 the solutions initially resemble “decretion”
discs, but at sufficiently late times exhibit the properties of “accretion” discs. We discuss the application of this theory
to different astrophysical systems, and in particular the values of the f parameter that are expected in different cases.
Accepted by New Astronomy

-6

-1

0

-6

1

log R

-1

0

2

1

t = 0.0001
t = 0.001
t = 0.01
t = 0.1
t=1

0

log Σ

log R

-2

https://arxiv.org/pdf/2008.07565

Solving grain size inconsistency between ALMA polarization and VLA continuum in
標準降着円盤モデルを
the Ophiuchus IRS 48 protoplanetary
disk
Satoshi Ohashi1 , Akimasa Kataoka2 , Nienke Van der Marel3 , Charles L. H. Hull4,5 , William R. F.
Dent5 , Adriana Pohl6 , Paola Pinilla6 , Ewine F. van Dishoeck7 and Thomas Henning6-4

中心境界のトルクが０でない時の
RIKEN Cluster for Pioneering Research, 2-1, Hirosawa, Wako-shi, Saitama 351-0198, Japan; National Astronomical
Observatory of Japan, 2-21-1 Osawa, Mitaka, 解析解の導出とTokyo 181-8588, Japan; Department of Physics and Astronomy,
University of Victoria 3800 Finnerty Road, Victoria, BC, V8P 5C2, Canada; National Astronomical Observatory
現実へのアプリケーションに関する議論
of Japan, NAOJ Chile, Alonsode Córdova 3788, Office 61B, 7630422, Vitacura, Santiago, Chile; Joint ALMA
2

1

-6

-1

0

log R

1

3

4

Figure 2: The time-dependent disc solutions given by (28) for different values of f as indicated in the top left corner of each panel. The different lines correspond to thetimes shown in the legend in units of tν = R2add /ν(Radd ). The initial behaviour in each case is the same, and differences begin to appear once the disc has spread and begins
to interact with the central boundary condition. For f = 0, the surface density at Rin is zero, while for all other cases the value is non-zero. The disc outer boundary is at
infinity, and thus in each case the discs spread outwards over time. For f ! 0.1 the solutions are similar to the accretion disc ( f = 0) case. For f " 10 the solutions are
similar to the decretion ( f → ∞) case. The corresponding numerical solutions for this case (with an outer boundary at a finite radius) are plotted below in Fig. 4.

5

Observatory, Alonso de Córdova 3107, Vitacura, Santiago, Chile; 6 Max Planck Institute for Astronomy, Königstuhl
17, 69117 Heidelberg, Germany; 7 Leiden Observatory, Leiden University, P.O. Box 9513, NL-2300 RA Leiden, The
Netherlands

is around a rotating magnetic star which can allow the disc orbits to be accelerated outwards at the magnetosphericradius. We present steady-state solutions to the disc structure as a function of f , and for arbitrary kinematic viscosity
ν. For time-dependent discs, we solve the equations using a Green’s function approach for the specific case of ν ∝ R
and provide an example numerical solution to the equations for the case of ν ∝ R3/2 . We find that for values of f < 0.1
the disc solutions closely resemble “accretion” discs. For values of f > 10 the solutions initially resemble “decretion”
discs, but at sufficiently late times exhibit the properties of “accretion” discs. We discuss the application of this theory
to different astrophysical systems, and in particular the values of the f parameter that are expected in different cases.

#39

Accepted by New Astronomy

大橋さん，一言解説をお願いします。

https://arxiv.org/pdf/2008.07565

Solving grain size inconsistency between ALMA polarization and VLA continuum in
the Ophiuchus IRS 48 protoplanetary disk

10

Ohashi et al.

Satoshi Ohashi1 , Akimasa Kataoka2 , Nienke Van der Marel3 , Charles L. H. Hull4,5 , William R. F.
Dent5 , Adriana Pohl6 , Paola Pinilla6 , Ewine F. van Dishoeck7 and Thomas Henning6
RIKEN Cluster for Pioneering Research, 2-1, Hirosawa, Wako-shi, Saitama 351-0198, Japan; 2 National Astronomical
Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan; 3 Department of Physics and Astronomy,
University of Victoria 3800 Finnerty Road, Victoria, BC, V8P 5C2, Canada; 4 National Astronomical Observatoryof Japan, NAOJ Chile, Alonso de Córdova 3788, Office 61B, 7630422, Vitacura, Santiago, Chile; 5 Joint ALMA
Observatory, Alonso de Córdova 3107, Vitacura, Santiago, Chile; 6 Max Planck Institute for Astronomy, Königstuhl
17, 69117 Heidelberg, Germany; 7 Leiden Observatory, Leiden University, P.O. Box 9513, NL-2300 RA Leiden, The
Netherlands
1E-mail contact: satoshi.ohashi at riken.jp
The protoplanetary disk around Ophiuchus IRS 48 shows an azimuthally asymmetric dust distribution in (sub)millimeter observations, which is interpreted as a vortex, where millimeter/centimeter-sized particles are trappedat the location of the continuum peak. In this paper, we present 860 µm ALMA observations of polarized dust emission of this disk. The polarized emission was detected toward a part of the disk. The polarization vectors are parallelto the disk minor axis, and the polarization fraction was derived to be 1 − 2%. These characteristics are consistent
with models of self-scattering of submillimeter-wave emission, which indicate a maximum grain size of ∼ 100 µm.
However, this is inconsistent with the previous interpretation of millimeter/centimeter dust particles being trappedby a vortex. To explain both, ALMA polarization and previous ALMA and VLA observations, we suggest that thethermal emission at 860 µm wavelength is optically thick (τabs ∼ 7.3) at the dust trap with the maximum observablegrain size of ∼ 100 µm rather than an optically thin case with ∼ cm dust grains. We note that we cannot rule outthat larger dust grains are accumulated near the midplane if the 860 µm thermal emission is optically thick.
Accepted by ApJ
https://arxiv.org/pdf/2007.15014.pdf

Modeling disk fragmentation and multiplicity in massive star formation
G. André Oliva1 and Rolf Kuiper1
1Institute for Astronomy and Astrophysics, University of Tübingen, Auf der Morgenstelle 10, 72076, Tübingen,

Figure 6. Same as Figure 5 but assuming two populations of dust grains. The 5 cm dust grains are located at the continuum
peak with an azimuthal width of w = 18 . The 140 µm dust grains are distributed in a larger crescent with the azimuthal
width of w = 41 .

image of this model for the ALMA 440 µm observations
is discussed in Section 5.1. The dust settling parameterof fset = 10 is used.
Figure 6 compares the images of ALMA Band 7 polarization and our model. Similar to Figures 2 and 5,
the polarization vectors are parallel to the disk minor
axis. The polarization fraction shows ⇠ 0.5 2.0% andit decreases to ⇠ 0.5% at the continuum peak. This isbecause only the 5 cm dust grains are located at this region, which do not produce the scattering-induced polarization. Our large beam size cannot spatially resolve theour model is lower than the observations even though
we use a maximum grain size of 140 µm, which is themost efficient to produce the polarization. Therefore,
dust grains with a maximum grain size of ⇠ 100 µm
may need to be located also in the continuum peak unlike our model. Furthermore, such 100 µm sized dust
grains need to dominate the continuum emission to reproduce the polarization fraction as shown in Figure 5.
These conditions may be unlikely because the larger dust
grains will be more concentrated on the dust trap (Birnstiel et al. 2013). Furthermore, it may also be difficult tothe effects of spatial resolution and to compare our high-resolution results with previous lower resolution studies in
the literature, we perform the same simulation for five different resolutions, each of them with a factor of two lower
resolution than the predecessor run.
Results: The cloud collapses and a massive (proto)star is formed in its center, surrounded by a fragmenting Keplerianlike accretion disk with spiral arms. The fragments have masses of ∼ 1 M! , and their continuous interactions withthe disk, spiral arms and other fragments results in eccentric orbits. Fragments form hydrostatic cores, surroundedby secondary disks with spiral arms that also produce new fragments. We identified several mechanisms of fragment
formation, interaction and destruction. Central temperatures of the fragments can reach the hydrogen dissociation
limit, form second Larson cores and evolve into companion stars. Based on this, we study the multiplicity predictedby the simulations and find ∼ 6 companions at different distances from the primary: from possible spectroscopic
multiples, to companions at distances between 1000 and 2000 au.

#41

若い星団のメンバーをGaia DR2で同定して6

Pang et al.
力学状態や将来の進化を議論

Accepted by Astronomy & Astrophysics
https://arxiv.org/pdf/2008.13653

Different Fates of Young Star Clusters After Gas Expulsion
Xiaoying Pang1,2 , Yuqian Li1 , Shih-Yun Tang3,4 , Mario Pasquato5,6 and M.B.N. Kouwenhoven1
Department of Physics, Xi’an Jiaotong-Liverpool University, 111 Renai Road, Dushu Lake Science and Education
Innovation District, Suzhou 215123, Jiangsu Province, P. R. China; 2 Shanghai Key Laboratory for Astrophysics,
Shanghai Normal University, 100 Guilin Road, Shanghai 200234, P. R. China; 3 Lowell Observatory, 1400 W. Mars Hill
Road, Flagstaff, AZ 86001, USA; 4 Department of Astronomy and Planetary Sciences, Northern Arizona University,
Flagstaff, AZ 86011, USA; 5 INAF-Osservatorio Astronomico di Padova, Vicolo dellOsservatorio 5, 35122 Padova,
Italy; 6 INFN- Sezione di Padova, Via Marzolo 8, I35131 Padova, Italy
1E-mail contact: Xiaoying.Pang at xjtlu.edu.cn
We identify structures of the young star cluster NGC 2232 in the solar neighborhood (323.0 pc), and a newly discoveredstar cluster LP 2439 (289.1 pc). Member candidates are identified using the Gaia DR2 sky position, parallax andproper motion data, by an unsupervised machine learning method, StarGO. Member contamination from the Galactic
disk is further removed using the color magnitude diagram. The four identified groups (NGC 2232, LP 2439 and two
filamentary structures) of stars are coeval with an age of 25 Myr and were likely formed in the same giant molecular
cloud. We correct the distance asymmetry from the parallax error with a Bayesian method. The 3D morphology
shows the two spherical distributions of clusters NGC 2232 and LP 2439. Two filamentary structures are spatiallyand kinematically connected to NGC 2232. Both NGC 2232 and LP 2439 are expanding. The expansion is moresignificant in LP 2439, generating a loose spatial distribution with shallow volume number and mass density profiles.
The expansion is suggested to be mainly driven by gas expulsion. NGC 2232, with 73 percent of the cluster mass
bound, is currently experiencing a process of re-virialization, However, LP 2439, with 52 percent cluster mass being
unbound, may fully dissolve in the near future. The different survivability traces different dynamical states of NGC
2232 and LP 2439 prior to the onset of gas expulsion. NGC 2232 may have been substructured and subvirial, while
LP 2439 may either have been virial/supervirial, or it has experienced a much faster rate of gas removal.
Accepted by ApJL
http://arxiv.org/pdf/2008.02803

39

Figure 2. General properties of identified member candidates. (a) The color magnitude diagram of Gaia DR 2 absolutemagnitude MG (adopting Gaia DR 2 parallax) for candidate stars identified by StarGO. Red and blue dots are candidate
members of LP 2439 and NGC 2232. The purple and green dots indicate candidates of the purple and green groups in Figure 1 (c).
Crosses indicate field contaminants that are excluded from further investigation. The PARSEC isochrones of 25 Myr and 100 Myr
are overplotted as the black solid curve and grey dashed curve, with E(B V ) = 0.07 mag (Lyra et al. 2006) corrected andsolar metallicity assumed. The black dotted curve is the PARSEC isochrone of 25 Myr adopting the same reddening but asupersolar metallicity of [Fe/H]=0.32 (Monroe & Pilachowski 2010). The asterisks indicate binary candidates. The red outlined
grey shaded asterisk corresponds to the grey shaded bin in panel (c). Uncertainties of colors are indicated with horizontal error
bars. The typical G magnitude error is 0.002 mag. (b) The spatial distribution of member candidates after CMD cleaning. The
symbols and colors of member candidates are identical to those in panel (a). Members cross-matched with previous catalogs:
Cantat-Gaudin et al. (2018), black open circles; Kounkel & Covey (2019), black crosses; Liu & Pang (2019), orange open circles.
(c) is the RV histograms for LP 2439 (red), NGC 2232 (blue), the purple group and the green group. (d) shows the propermotion vector plot with colors and symbols the same as panel (a) for member candidates.

Figure 2 (c)), di↵erent from the majority in LP 2439.
Considering its location along the binary sequence (thefollow-up spectroscopy may further constrain the natureof these stars.

#42

Magnetic torques on T Tauri stars: accreting vs. non-accreting systems
G. Pantolmos1 , C. Zanni2 and J. Bouvier1
Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France; 2 INAF - Osservatorio Astrofisico di Torino, Strada
Osservatorio 20, 10025 Pino Torinese, Italy
1E-mail contact: george.pantolmos at univ-grenoble-alpes.fr
Classical T Tauri stars (CTTs) magnetically interact with their surrounding
disks,
processno.thatis thought toA&A
proofs: amanuscript
Pantolmos_Zanni_Bouvier_v2_arxiv
regulate their rotational evolution. In this work, we compute torques acting onto the stellar surface of CTTs arising
Table 1.(stellar
Varied input
parameters
global properties ofejections)the simulations.
from different accreting (accretion funnels) and ejecting
winds
and andmagnetosphericflow components.
Furthermore, we compare the magnetic braking due to stellar winds in two different systems: isolated and accreting
Case B⇤ /B0⌥⌥open hrA i/R⇤ Ṁacc / Ṁ0 ⌥acc Rt /R⇤ ⌧ sw /⌧acc ⌧me /⌧acc
open / ⇤stars. 2.5D magnetohydrodynamic, time-dependent, axisymmetricsimulationsareemployed.
both systemsa1
0.81255030
0.296
441 For 7.98... the ...
...
...
...
a
stellar wind is thermally driven. In the star-disk-interaction 2(SDI)
simulations
disk
viscous,1.625
25800the accretion
0.230
1360 is Keplerian,
12.0
...
...
...
...
...
a
3.25
1300000.1723860 T Tauri
17.6 systems... the ...
...
...
...
and resistive. Two series of simulations are presented, one for3each
system.
We find thatin classicala4 expansion,
6.5
63500010900
25.6 geometry
...
...
...
...
presence of magnetospheric ejections confines the stellar-wind
resultingin0.131
an hourglass-shaped
of...
a
5
13
2960000
0.0951
26700
33.9
...
...
...
...
...
the outflow. In addition, the formation of the accretion columns
modifies
the amountof openmagnetic
1b
1.625
45000
0.381
6550
23.4 flux exploited
0.489
3.82 1.82-0.3550.486
bby the stellar wind. These effects have a strong impact on the2 stellar
wind 139000
properties0.267
and we show
the stellar-wind
3.25
9890 that
28.1
0.628
11.9 2.64-0.4160.219
6.5the isolated
667000 ones.
0.164We also
18000
37.0
-0.3590.111
braking is more efficient in the star-disk-interacting systems3bthan inderivetorque0.861
scalings,34.7 4.04b9.75 in2220000
0.114 that28900
44.9
1.20
55.9 4.68-0.221-0.0237
over a wide range of magnetic field strengths, for each flow 4componentaSDIsystemdirectly
appliesatorque5b
135420000
52.5
1.61
74.4 4.92-0.173-0.0853
on the stellar surface. In all the performed SDI simulations the stellar
windextracts0.0873
less than41300
2% of themass accretion
rate and the disk is truncated up to 66% of the corotation
radius. All thesimulations
show
a net spin-up
torque.
In In our simulations, a negative (positive) torqueNotes. (a) Isolated-stellar-wind(ISW)
simulations. (b)Star-disk-interaction(SDI)
simulations.
towards(awayorfrom)the star(see also§3.1.1). Consequently,
order to achieve a stellar-spin equilibrium we needindicateseitherangularmoremomentum
massiveflowing
stellar
winds
disks
being
truncatedcloser ⌧sw > 0, ⌧acc < 0, and ⌧me 7 0 (for the sign of⌧me in each SDI case see also Fig. 10).
to the corotation radius, which increases the torque efficiency by the magnetospheric ejections.
Accepted by A&A
http://arxiv.org/pdf/2009.00940

Gas trapping of hot dust around main-sequence stars

円盤・Tタウリ星系のTim D. Pearce1 , Alexander V. Krivov1 and Mark Booth1

Astrophysikalisches Institut und Universitätssternwarte, Friedrich-Schiller-Universität Jena, Schillergäßchen 2-3, D07745 Jena, Germany1

磁場構造モデルから，E-mail contact: timothy.pearce at uni-jena.de
磁気制動の効果や自転進In 2006 Vega was discovered to display excess near-infrared emission. Surveys now detect this phenomenon for one fifth
化を議論
of main-sequence stars, across various spectral types and ages. The excesses are interpreted as populations of small,

hot dust grains very close to their stars, which must originate from comets or asteroids. However, the presence of suchgrains in copious amounts is mysterious, since theyrapidlysublimateor be blown
outtheoftemporalthe system.
Fig. should
1. Logarithmic
normalized
density (colormaps)
showing
evolution ofHere
a star-disk-intercation simulation. The snapshots wereafter 5, dust
10, 20, migratingand 30 stellar inwards
rotation periods,P⇤ . The
far-left panel
illustrates
the inner domain of this simulation, with the vertical white
we investigate a potential mechanism to generate taken
excesses:
underradiation
forcessublimateslines indicating the location of the truncation radius Rt (dashed black core) and corotation radius Rco (solid black core). Each plot includes magnetic
near the star, releasing modest quantities of gas whichthen traps subsequent grains. This mechanism requires neither
field lines (white lines) and velocity-field vectors. The cyan lines delimit the stellar-wind flux tube and the red lines mark the Alfvén surface.

#44
赤外線と電波の観測を組み合わせ，
メタノールのガスと氷，水氷の分布をCO分布と合わせて議論
A&A proofs: manuscript no. aanda

G. Perotti et al.: Linking ice and gas in the Serpens low-mass star-forming region

Fig. 3. L-band optical depth towards the SVS 4 sources (black). The
lines
representlaboratory
ice data
employedin thethe lines represent the CO:CH3 OH 1:1 laboratory spectrum (orange),
Fig.coloured
2. M-band
opticaldepththetowards
the SVS
4 sources(black).
Thefitting:coloured
pure H2 O (dark blue), the H2 O:CH3 OH 38% (light blue), the CO:CH
and thereproducing
total fit (magenta).
black
the CDE-corrected
Lorentzian
the pureThe
CO dashed(cyan) andthelines
totalarefit (magenta). The dashed black lines are used as a reference for ⌧=0.
3 OH 1:1 (orange),
2 starting from SVS 4 2 to SVS 4 12
used as a reference for ⌧ = 0. The cyan boxes illustrate the selectedThefitting
ranges.ofTheof thefrom
fit SVS
goodnessthegoodness
fit 2⌫ starting
4 2 to SVS 4 12 is 0.95, 0.22, 0.79, 0.32, 0.83, 0.74, 0.30, 0.25, 0.87, and 0.64.
⌫
is 0.59, 7.47, 0.55, 9.15, 0.79, 4.14, 0.72, 0.43, 0.25, and 22.5.

The spectral fitting procedure developed by Suutarinen though the O-H stretching contribution of CH3 OH necessarily
because the blue component does not constrain the methanol(2015a)
ice towards
the cluster(DevlinZamirri toet theal. 2018).
and adopted
in thissources
study stands
as 1992;an alternative
replaces some of the absorption of H2 O. The aim of this fitting
abundance, but rather that of CO2 ice (Boogert et al. 2015). commonly
The Althoughtheredcomponent
canbeassociated
with
CO:H
2O
used method to detect molecules in interstellar ices
procedure
is to determine the maximum amount of CH3 OH ice
central peak (i.e. middle component) is associated with the C-O
iceal.
(Thiet al.
2006),ettheOH
mixturetoisthethelatter,most likely(Grim et1991;
Brookeal.CO:CH
1999). 3In
contrastthat is hidden below the red wing of interstellar ices, and thus tovibrational mode of pure CO ice. It was fitted using a continuous
carrier ofofthis
feature(Cuppen ettoal.
and ofit isto explain the high CH3 OH abundances that are observed inwhich consists
fittinga polynomial
the2011),
red wing
theassumed
O- help
distribution of ellipsoids (CDE) corrected Lorentzian function
trace warmer
regions
than pureThe opticalgoodnessof thefit thewasgas-phase.
H stretchingmode andanalysingthe 2CO.
residualdepth
at, that is givenby 2⌫ at= 2 /⌫,in order to take into account irregularities in the grain shape 3.53
and µmaddressed
the thereducedfitting ⌫procedure
we adopted
to detectusing
CH3 OH,
Figure 2 shows the optical depth of the sources listed in Ta⌫ is the di↵erence
betweenthe number toof thedata3 points
match the central peak of the observations (Pontoppidan ettempts
al. where
to simultaneously
fit multiple
ice componentsµm andble 1 decomposed by analytical and experimental components
thenumberoffreeparameters
in
the
fit.
2003b).
region to find the maximum amount of CH3 OH that is hidden
using the OMNIFIT fitting utility (Suutarinen 2015b). As outbelow the The
red wing.
This approach
it possible
to condecompositionof makes
the L-bandfeatures,between
The red component, on the other hand, was fitted with

Linking ice and gas in the Serpens low-mass star-forming region
G. Perotti1 , W. R. M. Rocha1 , J. K. Jørgensen1 , L.E. Kristensen1 , H. J. Fraser2 and K. M. Pontoppidan3
Niels Bohr Institute & Centre for Star and Planet Formation, University of Copenhagen, Øster Voldgade 5−7, 1350
Copenhagen K., Denmark; 2 School of Physical Sciences, The Open University, Walton Hall, Milton Keynes, MK7
6AA, United Kingdom; 3 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
1E-mail contact: giulia.perotti at nbi.ku.dk
The interaction between dust, ice, and gas during the formation of stars produces complex organic molecules. Whileobservations indicate that several species are formed on ice-covered dust grains and are released into the gas phase,the exact chemical interplay between solid and gas phases and their relative importance remain unclear. Our goal is to
study the interplay between dust, ice, and gas in regions of low-mass star formation through ice- and gas-mapping andby directly measuring gas-to-ice ratios. This provides constraints on the routes that lead to the chemical complexitythat is observed in solid and gas phases. We present observations of gas-phase methanol (CH3 OH) and carbon
monoxide (13 CO and C18 O) at 1.3 mm towards ten low-mass young protostars in the Serpens SVS 4 cluster from the
SubMillimeter Array (SMA) and the Atacama Pathfinder EXperiment (APEX) telescope. We used archival data fromthe Very Large Telescope (VLT) to derive abundances of ice H2 O, CO, and CH3 OH towards the same region. Finally,
we constructed gas-ice maps of SVS 4 and directly measured CO and CH3 OH gas-to-ice ratios. The SVS 4 cluster ischaracterised by a global temperature of 15 ± 5 K. At this temperature, the chemical behaviours of CH3 OH and CO
are anti-correlated: larger variations are observed for CH3 OH gas than for CH3 OH ice, whereas the opposite is seen
for CO. The gas-to-ice ratios (Ngas /Nice ) range from 1 − 6 for CO and 1.4 × 10−4 − 3.7 × 10−3 for CH3 OH. The CO
gas-maps trace an extended gaseous component that is not sensitive to the effect of freeze-out. Because of temperature
variations and dust heating around 20 K, the frozen CO is efficiently desorbed. The CH3 OH gas-maps, in contrast,
probe regions where methanol is predominantly formed and present in ices and is released into the gas phase throughnon-thermal desorption mechanisms. Combining gas- and ice-mapping techniques, we measure gas-to-ice ratios of
CO and CH3 OH in the SVS 4 cluster. The CH3 OH gas-to-ice ratio agrees with values that were previously reported
for embedded Class 0/I low-mass protostars. We find that there is no straightforward correlation between CO andCH3 OH gas with their ice counterparts in the cluster. This is likely related to the complex morphology of SVS 4: theClass 0 protostar SMM 4 and its envelope lie in the vicinity, and the outflow associated with SMM 4 intersects thecluster. This study serves as a pathfinder for future observations with ALMA and the James Webb Space Telescope(JWST) that will provide high-sensitivity gas-ice maps of molecules more complex than methanol. Such comparative
maps will be essential to constrain the chemical routes that regulate the chemical complexity in star-forming regions.
Accepted by Astronomy and Astrophysics
https://arxiv.org/pdf/2008.02827

ALMA chemical survey of disk-outflow sources in Taurus (ALMA-DOT) II: Verticalstratification of CO, CS, CN, H2 CO, and CH3 OH in a Class I disk
L. Podio1 , A. Garufi1 , C. Codella1,2, D. Fedele1 , E. Bianchi2 , F. Bacciotti1 , C. Ceccarelli2 , C. Favre2 ,S. Mercimek1,4 , K. Rygl3 and L. Testi5,6,1