Star Formation News Letter#298 1-5
⿇⽣有佑(ASIAA)An analytic expectation of α ina gravitoturbulent
thindisks,
disk isas gravity inherently acts on nongravitationallyunstableet al. 1999). Additionally, recent work by Raﬁkov (2016)
We consider
self-gravitating disk in withthe kinematic viscosity ν=2.5 H6Ω for all simulations, as
en by Gammie(2001):a non-magnetized,
suggests that shocks are not a dominant source of heat inlocal scales (Balbus & Papaloizou 1999).
shearing box approximation. Accordingly, the disk is modeled
seen in Equation (5), but ultimately
the suchheatingof thepassive disks
as those
considered here.
4 small 1 radial-azimuthal patch of the disk,
locally onasimulation
willbedominatedbythedissipationofshocks
a=
(12)
.
2.2.
Thermodynamics
transformed fromcoordinates (r, θ, f)producedto- 1) tcylindrical
9 g (gglobalcW
by the collapse of self-gravitating ﬁlaments
and Stratiﬁcation
2.3. Verticalz) co-rotating
the disk
local Cartesian coordinates(x, y,
Propermodelingof diskwith
cooling
iscomplexclumps.
Theevenheat without
generated by the dissipation of shocks is& Chiang(2014)& compare
the standard
formulationof α allow(Goldreich
Lynden-Bell
1965).
These
assumptions
forﬂux-limited diffusion
A proper implementation of a 3D shearing box simulation
using
sophisticatedray-tracing
anddeterminedby the strength of the constant of hyperdissipation,
the local
propertiesof thevalues
disk
while
requires vertical stratiﬁcation of the gas density. If this is notuationthe(9))modelingwith one of
basedonschemes,
density-weighted
of thefollowing
dependingsigniﬁcantly
on the local temperature
so in addition to our standard collection of simulations
the stress,
evolutionof thatfragments
that
form
whendisk
using
periodiccorrectly initialized, the simulation will adjust on its own,
andof themidplane to atmospheressure andand ﬁndwhile density
thedensity-weighted
α′ isfromspanning
resolution and coolingcausing
timescale,
we include
a heatingsmall and cooling as the disk swells
boundary
conditions.
Using
this
model,
therelevant
conservaundesired
rapid(Hubeny
1990;
Raﬁkov2005):
3
3
actor of 1.25–2
higher,usual
formulation
closely
Figure 1.
Surfacethe
densitymaps
of a pair of more
our medium-resolution(N = 512of) simulations
runs. On the left
is a various
simulationdissipation
with short β=2cooling,
illustrating the clearc
samplewithvaluestonotetion
equations
are
shown
in
Equations(3)–(5)
with
terms
for
The Astrophysical Journal, 848:40 (10pp), 2017 October 10
formation ofexpectationa fragment. On
the Fromright isEquations
a simulation(9)withβ=10 coolingshowing steady gravitoturbulence.up or contracts. Thus, we assume the disk begins in hydrostatic
ows the theoretical
(12).
and
2
the effect on fragmentation.
qWvx yˆ Sascswell
the Coriolis effect 2W ´ u and centrifugal force
4 viscous
equilibrium with self-gravity), one can compare theoretical expectationsof(t ) ,
In fpractice,
this may(13be) overestimating the heating resulting
as heating thatH andterms Ctcin=the
The Astrophysical Journal, 848:40 (10pp), 2017 October 10
Baehr, Klahr, & Kratt(ggenerated- 1equation.
) simulations,9genergyzs (T 4 - Tirr4 )the
forcoolinggravitationallydisksses in thefoundgravitoturbulent
state with the unstablestresses
1 dP It is2 wellfrom strong shocks generated by self-gravity.
Table
1
=
-W
z
4
p
G
r
(
z
)
dz
.
(
17
)
¢
¢
critical Toomre
wavelength
needsthatto as
be resolved by at least¶ris important¶r to note
our simulations.
It
understood
thatThree-dimensionalin outerfor
disk regions,diskatheating
is dominatedr dz Resolutions
Simulations
VariousN3, Initial 0Toomre- elements(rusuch) = fragmentation,(3) f (τ)=τ+1/τ
qWxwhere+tofD (ra) local constant,σ avoid
is ·theStefan–Boltzmann
resolution
described¶tstress,ycription offour
viscousα¶doesnot necessarily
model
Criteria
Q,
andCoolingTimes
β0 accretion (D’Alessio
stellar irradiation instead of viscous
0 by
0
opticalnumber
depth τ,ofTirr is the reference bytemperature
and adiabatica maximum
ToomreThe work
initialdistribution is determinedvitationallyby
disks,
gravity inherently
acts on nonet al. 1999).Simulation
Additionally,Grid
recentbyverticalRaﬁkovdensity(2016)
3¶unstableuP¶u asindex
Cells (N )Q
βFragmentation
0γ.
aboveofas heata dimensionless,differential equation,u=-&
qWPapaloizoux+ u · 1999).
+ qWvx yˆ - 2W
suggests that shocks are not arewriting
dominantthesourceinal scales (Balbus
dx r to a fragment requires that thermal
Contraction
¶t
¶y
2563
1 & Chiang2(2014):No
followingShi
passivesuchpressure
as those consideredhere.
T== 0.25.
(24) disks Q256t2
2563
1
10
No
supportlTdoes
ofQ256t10
overdense(4)´ u -not F counter+ fn (u) the self-gravity
2.2. Thermodynamics
5123 d 2r
1 - 2 ⎛ dr
22
No⎞
perturbations. Heat generated through viscous Q512t2
heating
and
g
2
˜
˜
2
2.3. Vertical Stratiﬁcation⎜ 10⎟ + Q 0 No
+ 1
r˜ 2 - g + r˜ 3 - g = 0.
(18)¶ss cooling¶disk
1
Q512t105123
roper modelingofiscomplexeven
without2
shock
dissipation
shouldbereleasedonacoolingtimescale
2
⎝
⎠
(
u
·
)
(
S
(
))
(
)
q
x
rn
W
s
2
f
s
5
+
=
L
+
dz
r
dz
h
˜
˜
˜
3
c
Our
simulations
containalmostexactly
one
criticalToomreG512tp5
256
0.676
0.5
No
properimplementation
shearing box simulation
ng sophisticatedray-tracing
andenoughﬂux-limited
shortpressure supportA frombuilding
up, or of a 3D
rT to keep3diffusion¶t¶y3
G256t1256
0.676If this 1is not No
wavelength
and withaonresolutionof temperature
Ndynamical
=2563 cellsineach(seerequiresverticalstratiﬁcationofWe
the3usegasandensity.
emes, depending
signiﬁcantly
the local
isothermal
approximation to the polytropic equation
shorterthana few
timescales
Equation(2)).
G256t2
256
0.676
No
T
direction,ourminimum
resolution
easilymeets
thisresolution
correctly
initialized,thesimulation
will
adjuston
its 2 own,
densityHere,of uthedisk
frommidplanetoatmospherea β-prescription
is velocity
implemented in Pencil
using
a
3
=(vx, vy + CoolingqΩx, vz) withis theﬂow plus shear
of
state
for
which
Equation
was derived (g = 1, K = cs2 ),G256t10256
0.676
10 (18) No
criterion
withT=0.008,
decreasing
byafactorof
one-halfcausingundesiredrapid
heatingandcoolingasthediskswellsbeny in1990;
Raﬁkov2005):
3
Newtoniancooling
scheme,the local box, ρ is the gas density, ands is thegas entropy.
S0 = 2Hr2. Solving
andG512t2512 assume 0.676
Yes for vertical hydrostatic3 2
3up or 3contracts.
Thus, we assume512
the3 disk begins
whenheatincreasing
the resolution
=512N3=1024
.
=to2N
rnS
Viscousis generated, with andrate-of-strain
G512t50.676in hydrostatic
5
Nowe ﬁnd
equilibrium
includingself-gravity
2 by
2
2
S
cs by
with
self-gravity 5123
r ((c13- cs,irrequilibrium) at orBoss(2017)
onlyβ-coolingconsiderfragments
tensorand4 radiatedofaway
af (simple
sprescription
G512t10
0.676
10
No
tcThe
= S,simulations
t
)
,
)
L
=
,
(
14
)
4
5123 znear9gthis
criterion,
and are (thus(g in- resolution
1) s (T 4 2.2.
d 2r˜0.676 1 ⎛ dr˜20⎞22Λ, described
Section-T2No
g - 1potentially
) tc
irr )
dP
1 G512t20+ )Q 0Yesr˜ + r˜ 2 = Figure0, 1. Surface density(19maps) of a pair of our medium-resolution (N3 = 5123) runs. On the left is a simulation with short β=2 cooling, illustrating the cle= -W2 z - 4p1024
G 3 r (z ¢)dz
dz20.676¢. - r˜ ⎜⎝ dz˜ 2⎟⎠ (17G1024t2
Self-gravity
by solving
Poisson equationsusceptible istomodeled
fragmentation
due theto numericalerrors. Addiformation of a fragment. On the right is a simulation with β=10 cooling showing steady gravitoturbulence.
h
˜
30
r
dz
2
Figure 2. Evolution of the average vertical density (left) and average vertical tempe
G1024t5
1024
0.676
5
No
ere σ is thetionally,
Stefan–Boltzmann
constant,fis(τ)=τ+1/τ
fora non-zerocs,irronly
where
proportional
tobackgroundtemperthe Toomre
roughly describes
the feeding
2length
3
F
=
4
p
G
r
,
(
6
)
averagesat different
2
G1024t10
1024
0.676
10
No
unstable disk
simulations,the times.
pGfor
S0gravitationallywhere r˜ = ris/rdetermined, andS0 ), Q 0 = cfoundcal depth zone
τ, Tirrofisan
theunstablereference
temperatureandAstrophysicaladiabatics,0 W /that
ature,
corresponding
toconstantwhich
as
0 , z˜ = z / (cs,0The irradiation,
initialvertical
distribution
by/pG
clump
which Themay
or somemay not
fragment
Journal,848:40 (10pp),
2017density
October
10Baehr, Klahr,
Table 1
G1024t20
10243
0.676
20
No
critical Toomre wavelength
needs&toKratterbe resolved by at least2
Three-dimensional Simulations at Various Resolutions N3, Initial Toomre
ex γ. in Fourierby &transforming
the2011),surfaceﬁnd rewritingtheh = H / (cdifferential
demonstratedby
Lin and&density
Kratter(2016)
addsa additional
stability
The approximation ofverticallythe aboveas a dimensionless,further space(Kratter
Murray-Clay
is nottonecessarily
four theresolution
elements to avoid such fragmentation, describeds,0 / pG S0 ). equation,
Criteria Q0, and Cooling Times βContraction
to aatindicativefragment
requiresthat thermalpressureby a maximum Toomre
potential
the scaleofofa wavenumber
k andtransforming
the and tcShi
againstsmall
scale
density
perturbations,in as number ofis a&β-coolingfollowing
Chiang (2014):stratiﬁed initial density creates some small oscillations
lengthfragment.
Simulation
Grid Cells (N3)Q0βFragmentatio
port does
notback
counterthe space.
self-gravityof overdense
solution
into real
The solution
to the Poisson
Table 1. The
threedifferent
coolingtimescalesareselecteddx
2
Q256t2
2563
1
2
No
2
T=
= 0.25.
(24)
urbations.
Heatin generated
throughd r˜gassuming- 2 ⎛ dr˜ a⎞ criticalof β∼3.
For β=2,
equation
Fourier spaceis 4. viscous
2 - g + 2 r 3 - g value
3Q 2 r˜fragmentation
Q256t10
2563
1
10
No
Results heating and
lT
⎜
⎟
+
+
=
0.
18
(
)
˜
3
0
ck dissipation should be released on a cooling timescale
Q512t2512
1
2No
2⎝ dz˜ ⎠fragmentation inhthe classical scenario of 2D disk
weexpectdzr
˜˜3
Q512t10
512
1
10
No
)
2pGr (k , tsimulations
mentionedof our 3D
rt enough toAskeeppressureup, or3
Oursimulations
containalmostexactly
one
criticalToomreF (kabove,) = preliminary- from2 building(7)self, tsupport.
fragmentation (Gammie 2001) and for β=5, 10, 20, we
G512tp5
256
0.676
0.5
No
3
3
3
setup wereconducted
at
our lowestof an isothermal approximation to the polytropic equation
We userter than gravitatinga few dynamicaltimescales(seeEquation(2)). resolutionk
G256t1
256
0.676
1
No
expect a stable gravitoturbulent disk, but are also concerned wavelength and with a resolution of N =256 cells in each
G256t2
2563
0.676
2
No
Na3β-prescription
=2563, whichis the same effective
thestate
2D for which Equation (18) was derived (g = 1, K = cs2 ),direction, our minimum resolution easily meets this resolutionoling with
isit implemented
in Pencil resolution
using a as ofwith the possibility of non-convergent effects, where fragmen- criterion with T=0.008, decreasing by a factor of one-half
In 2D
simulations,
G256t10
2563
0.676
10
No
2 is useful
2 to smooth the self-gravity
=1024
of
Baehr
&
Klahr
(2015).
When
simulations
withN
3
wtonian cooling scheme,
G512t2
512
0.676
2
Yes
S0 =is2H
r . Solving
andassume tationfor verticalhydrostatic
3
3
3
3
possibleforcoolingtimescales
longerthan
β=3.
potentialatsmall
scales.
When
using
a
Fourier
method,thiswhenincreasingtheresolutiontoN
=512andN
=1024.
3
G512t5
512
0.676
5
No
initialized with Q0=1 and β<3, these simulations showno3
equilibrium
includingself-gravity
weﬁnd
Using this lower value of Q0=0.676 immediately resulted The simulations of Boss (2017) only consider fragments at or2
2
G512t10
512
0.676
10
No
means
limiting theincludedin the static
calculationof togravitationallargely
for tensr (instability,
cswavenumbers- cs,irr) remaining
3
G512t20
512
0.676
20
No
near this resolution criterion, and are thus potentiallyintheunstable
behavior
expected
from
local
disk
instability
L =to
,
(
14
)
2
3
the hundreds
potential
excludethose
corresponding
togravitational
2
G1024t2
1024
0.676
2
Yes
of (gorbital
susceptible to fragmentation due to numerical errors. Addi1 ⎛ dr˜ ⎞2 22- 1) tctimescales. Self-gravity is not strong d r˜simulations.
3
G1024t5
1024
0.676
5
No
While
Q
=0.676
isnecessarytoinitiate
GI
due
(19)
attraction
smallerthan a pressure
scale height.
tionally, the Toomre length only roughly describes the feedingenoughat scales
to excite
gravitationallyunstablemodes.This
Atis our dz 2 - r ⎜⎝ dz ⎟⎠ + Q 0 r˜ 0+ h r˜ = 0,
3
G1024t10
1024
0.676
10
No
˜
˜
˜
3
3
to
the
verticallystratiﬁed
density(see
Figure2),iteventuallyzone of an unstable clump which may or may not fragment
2 usedmedium
in 2D toresolution
ascribeto thehowever,our still, wedisk;
foundthat Q0as
=1
ofthickness
N =512
G1024t20
10243
0.676
20
No
ere cs,irr
is proportional
to a anon-zerobackgroundtemper2 as GI develops because the vertical structure of further (Kratter & Murray-Clay 2011), and is not necessarily asettlesto Q=1
showsnoevidenceforgravitational
instabilities,
suggesting
simulations
includeaverticallystratiﬁed
density
distribution,
r
=
r
/
r
Q
=
c
W
/
p
G
S
where
,
,
,
and
z
=
z
/
(
c
/
p
G
S
)
˜
˜
0
s,0
0
0
e, corresponding to some constant irradiation, which ass,00length indicative of a fragment.
this&isnotresolution-dependent
effect.
For this hreason,
2 the disk becomes much less stratiﬁed as the disk warms up andTable 1. The three different cooling timescales are selecte
therethatshouldbeKratterno aneed
for smoothing
in thesesimulations.
= H / (cs,0/Q
pGrises.
S0 ). This
monstrated
byLin(2016)
adds additional
stability
The isapproximationoftheverticallyshown in Figure 3, where the box-averaged
assuming a critical fragmentation value of β∼3. For β=24. Resultsa state,value withcloseinternal
to what is
we use we
a new
value
of Qequation0=0.676,
Finally,
use
an
ideal
of
inst small scale density perturbations, and tc is a β-coolingstratiﬁed initial
densitystability
creates somesmall starts
oscillationsas
we expect fragmentation in the classical scenario of 2D dis
Toomreparameterat thein initial
unstable As mentioned above, preliminary simulations of our 3D selftypicallydisksenergyò, andassumed
speciﬁc forheat
ratioofγ:ﬁnite thickness (Kim et al. 2002;
fragmentation (Gammie 2001) and for β=5, 10, 20, w

The fragmentation criteria in local vertically stratified self-gravitating disk simulations
Hans Baehr, Hubert Klahr, and Kaitlin M. Kratter• 外側で惑星を作るには重⼒不安定。Q~1では冷却が効き、β=t Ω=3が臨界だが、２D計算では定まらない。
• Local 3Dで冷却と分裂の関係を調べる。磁場なし、共回転shearing box、初期厚みは静⽔圧平衡。
ò

Q =0.676, β=2
分裂

Q =0.676, β=10
重⼒乱流ò緑が単⼀分裂。

⾼さ⽅向に広がると安定化する。

oxcar smoothed with a kernal of 40.

case, as the
maximum
density
crosses
only tofall radiusbelow again
later,
ﬁftieththe scaleheight
h 50this, a valuefragmentouterof rfrag
andwhereas thepressure-modiﬁed
Hillthethresholdis moreconsistentin delineating
a power-law
index offragment
density
distribution
k. Then,the most natural extension of that work and our res
betweengravitoturbulenceandfragmentation.
e threshold
This threshold criteria in local vertically stratified self-gravitating
The density.
fragmentation
disk simulations

inserting the fragment mass into Equation (25) and assuming
their ﬁndings in this regard.
pport stabilizes a fragment againsth50  andrfrag , wethen solve
forKratterthe central density ρh:
Hans
Baehr,
HubertKlahr,
KaitlinM.
の続き
Recent work has focused on
numerical
effec
susceptible to tidal shear. Starting
The Astrophysical
848:40 (10pp), 2017 October 10
Baehr, Klahr, & K
rfrag=2/3 H. With this, we ﬁnd that for an The
overdensity
inJournal,our(10pp),
Astrophysical Journal,
848:402017 October
10
Baehr, Klahr, & Kratter
3
3
3
3
k
Klee et al. (2017)
Ninﬂuence=512 on non-convergence.
N =256
gment has a radius that is a fraction
simulations to withstand 3tidal
f (3 - disruption,k ) M* ⎛ rfrag ⎞ as is shown in
実線：最⼤密度• 分裂の評価は２DではRoche⾯密
rh =
(27)
⎜
⎟.
numerical oversteepening could be responsible fo
3
Figure 7, it must satisfy
⎝
⎠
4
p
R
h
50
点線：平均温度
度だが、３Dなのでpressure-estimation of overdense peaks resulting in fra⎛ Mfrag modified Hill条件。
Through our use of sixth-order hyperdiffusion,
(25)
⎜
⎟ R,
expect oversteepening to be a signiﬁcant factor.
⎝ 3M ⎠*
Hill条件ﬁnd that dissipation of angular mo(2017)
density. Equationdisk(27)aroundwill serveas our threshold
which, central
for a protoplanetary
a solar-mass
star,•
分解能が悪いと分裂しない(ßPencilは数値散SPH methods removes shear support from region
e central star, R is the location away
-10g that-the
3 maximum density
densityfor our simulations,provided
1.2
´
10
cm
resultsinadensities
of
at
50
au
and
逸が⼤きい？)。
ﬂow velocities and as this depends on resolution, fr
actor determinedby the choice of
is−11
above
this−3thresholdseveraltimescales,thuswith
separating
1.5×10g cm
at 100forau.
Comparing
thisourbecomes easier with increasing resolution.
ﬁning• theHill条件が１周期続けば分裂と思えば、低分
fragment mass as thefragments
fromtheoverdensities
thatin have
not7, weyet seecollapsed
simulations
and
with
Roche
density
Figurethat
While our results strongly suggest converge
radial shells,enough.
解能でのsink cellにすると良いかも。
Figure 8. Timeseries of the maximum surface density in a set of simula
this density
threshold more adequately delineates between
Figure carried
8.fragmentation
Timeseriesof the maximum
surfacein a setsimulations
lowest resolution
isand Qdensity
suppressedduout at resolution
N =256=0.676.
Theoffaintdashedlin
Finally, we wish to apply our fragment
threshold,carriedout
resolution Ntemperatures
=256 andcorrespondingQ =0.676. The
faintdashed linesareFigure 7. Fragment threshold densities r(dashed line) and ρ(dottedthe atbox-averaged
to theappropriate
densityThe
AstrophysicalJournal,848:40(10pp),
2017
October
10Baehr,
Klahr,&
Kratterr
Figure7.
Fragment
thresholddensities(dashedline)
andρ(dottedthebox-averaged
temperatures
correspondingtotheappropriate
density
curve
fragments
and non-fragments.
A disk withfrom
thetemperatures3
3for=512 simulations
for longer
run times. Theline) compared3with our N as
cient
resolutionbothand
3D models,by color.
The 3
black2D
dashed lineis the pressure-modiﬁed
Hill densitysim
cri
Equation(27), to our simulations,needtoNwhich
=256
,not
3D,
β=2
Ncolor.
=256
, 2D,
β=2
=512
simulations
longer run
times.
The
line)
compared
withweouris
Nby
The blackdashed
line
rfrag
Roche
thresholdclearly
not anappropriateforthresholdin thenon-fragmenting
deﬁnedby Equation(28).is the pressure-modiﬁed Hill density criterion⎛ r h ⎞k 2
Roche thresholdisclearlyanappropriate
thresholdinthenon-fragmenting
deﬁnedbyEquation(28).
case, as the maximum at
density
this value
only to fall below
againTurklater,
results
et al. (2012), which found thin) these extract
simulations
will havean aspectratio case,
H/R≈0.11
50crosses
the density
proﬁleof a fragment.
ﬁndthat
athresholdr h ⎜ ⎟ r dr,(26
as whereastheWemaximum
density crosses
thisonly isto
fall below
againofthe pressure-modiﬁed
Hillvaluemoreconsistent
inlater,delineating⎝⎠whereasthepressure-modiﬁed
Hill
thresholdismoreconsistentindelineatingthemost natural extension of that work and our results sup
between gravitoturbulence and fragmentation. velocity ﬂuctuations
50
suppressed
the andformationofthe most naturalextension of that work
our results support
fragment scales
withau.k=0.7theseto adensities
fragmentof
au and H/R≈0.16
at 100With
andradius
aspectbetweengravitoturbulence
and fragmentation.
•r ⼀旦不安定になれば２D(+⾼さを想定した
their ﬁndings in this regard.
their ﬁndings in this regard.
Recentwork
has
focusedon
numerical
effects
anddynamos
Jeans
lengthis andnottheirrer =2/3
With andthis, we ﬁnd thatmagnetic
for an overdensity
in our Recentwhen
work hasthe
focusedon numericaleffects
ratios, we approximate threshold fragment masses
of
5H.M
r =2/3
H. Withthis,J weﬁnd that for an overdensity in ourinﬂuence on non-convergence. Klee et al. (2017) foundsmoothed self-gravity)も３Dも同じ。
simulations to withstand tidal disruption, as is shown ininﬂuenceon
non-convergence.
Klee
et
al.
(2017)
found
7 at 50 and 100 au, respectively.
simulations
tidal disruption,least
as is 64
showngridinnumerical
oversteepening
could be responsible
for thatthe ocells.
Atoversteepening
higherresolutions,theresultFigure to7, itwithstandmust satisfy
15
M
numerical
couldbe
responsible
for
the
overJ
Figure 7, it must satisfy
estimation of overdense peaks resulting in fragmenta• ３Dでは⼩スケールも捉えられるが、⾃⼰重
estimationof overdense
resultinginclearfragmentation.
with
fragm
M* standard fragmentation
Throughourscenario,
use ofpeaks
sixth-order
hyperdiffusion,
we doApplying the density threshold to our low-resolution
r .M
25.57
,
(28)Through
our
use
of
sixth-order
hyperdiffusion,
we doDengnot e*r h . 25.57 3 , R(28)
expectoversteepening
tobeasigniﬁcantfactor.
⼒には効かない。
β=2 and a lackof fragmentation
evident
atet β=
expect(2017)
oversteepening
a signiﬁcantal.
R
simulations, which failed to form sustained fragments
ascanﬁnd thatto bedissipationof factor.
angularDeng
momentumwhich, for a protoplanetary disk around a solar-mass star,(2017) ﬁnd that dissipation of angular momentum in
SPH methods removes
shear asupport
fromregions withwhich, for a protoplanetary disk around-The
a solar-mass
star,
3
prescription
isas thisnottruesubstituteresults in a densitiesof 1.2 ´ 10 10g cm-βatcooling
50 au andSPH
methods
removes
supportfrom
regionswithhigh
be seen in Figure 8, simulations with very shortﬂow velocities
andsheardepends
on resolution,
fragmenta
results incoolinga densities timesof 1.2 ´ 10-10g cm-3 at 50 au andﬂow
velocities
and
as
this
depends
onresolution,
fragmentation
⾃⼰重⼒を過⼤評価、
1.5×10g cm
at 100 au. Comparing
this
with
our
cooling,
only a becomes
simpleeasier parametrization
with increasing resolution. of the
1.5×10 density
g cm
at 100 a
au. Comparing
this with our(β = 1, 0.5) surpass this threshold. If the maximum
easier withincreasing
resolution.
• ３Dだとこれまでの２Dより分裂に⼤きな質
simulations and withof
the Roche density in Figure 7, we see thatbecomesWhile
our results
stronglysuggest convergence, atsimulations and with the Roche density in Figure
7,
we
see
that
While
our
results
stronglysuggestis convergence,at toourins
physics.
The
use
of
a
ﬁxed
backgroundterm mayha
少しハイコントラスト。
thisdensity
thresholdmoreadequately
delineates
betweenlowestresolution
fragmentation
suppressedduefragment
cansurpass
thiscriticaldensity
for
more
than
an
orbit,
this density threshold more adequately delineates between
resolution
fragmentation
is suppressed
due to similar
insufﬁ-to量が必要。
fragments and non-fragments. A disk with the temperatures aslowestcient
resolution
for both 2D
and 3D models,convergence(Riceet Turkal.both2012),
thus
onesimilarmustbeand non-fragments. A disk with on
the temperaturesas3Dmodels,to theit can be considered a fragment even if itfragments
isinsimulations
subsequently
results of foret 2D
al. and(2012),
which found
that
turbu
these
simulations will have an aspect ratio H/R≈0.11 at 50cient resolution
resultsvelocityof Turkﬂuctuations
et al. (2012),
which
found
that
turbulent
in
these
will
have
an
aspectratio
H/R≈0.11
at50
the formationof small sà分裂後も⼤きいはず。L1448
au and H/R≈0.16 at 100 au. With these
densities and aspectis not lost if suppressed
convergence
this formation
term
is
remov
velocity
ﬂuctuations
suppressedsmallscale bH/R≈0.16
at 100cell
au. With these densities and aspectdisrupted. Thus, thisIRS3Bがそう。
threshold may provideauaandusefulsinkmagnetic
dynamos
when thetheJeans
length ofis notresolved
ratios, we approximate threshold fragment masses of 5 M andmagnetic
dynamoswhentheJeans lengthis notthe
resolvedbyratios, we approximate threshold fragment massesof 5 M2016).
andKratter
However,assimulations
using
βat
least
64
grid
cells.
At
higherresolutions,
results
follow
15 M attoo
50 and100 au,formation criterion for simulations with resolution
lowtorespectively.
least 64
gridcells.
At
higherresolutions,theresults
follow
the
15 M atApplying
50 and 100theau, density
respectively.
standard fragmentation scenario, with clear fragmentatio
thresholdbackgroundto our low-resolutionstandard
fragmentation
scenario,
withsupports
clear
fragmentation
at
it
our
un
Applying
the density
thresholdto sustained
our low-resolutionas irradiationβ=2
andconverge,a Withlack suchof fragmentation
evident
atthisβ=5,
10,
fragment.
simulations,which
to form
Figure 9. Left: map ofsurface density
fromfailed
a low-resolution(N = 256fragments) 3D run with can
efﬁcient
coolinga short coolingtimescale,setupisβ=2Theand βaβ=2.
lackoffragmentation
evidentatβ=5,
10,20.
simulations,which
failedtoformsustainedfragments
ascancoolingprescription
is
not
a
true
substitutefor
realin Figure8, simulations
withofvery
shortcooling
times
expected to fragment,bebutseeninsteadshows sheared
self-gravitatingﬁlaments
typicalofgravitoturbulence.
Right:
mapofsurfacedensityfroma2D
simulation,
which
the
physics.
Theβcoolingprescription
is
not
a
true
substituteforrealistic
be caseseenfailsin Figure8, simulations
withvery shorttimesself-gravity. The
cooling,only
a simpleparametrizationof modelsthe underl
similar to the 3D
to fragment,
but is slightly
clumpier
due tocoolingthe stronger
simulation
shown
on the rightis the same as the
from

1 3

⎞1 3

M
We use γ= 5/3
makes *f=r hwhich. 25.57, 4, whereas a softer choice(28)of
3
R resulting in a slightly higherγ= 7/5 would mean f= 16,

3

3
3

3

3
M. ‐ Hill

M. ‐ Hill

Roche

Roche

3
3

3

0

0

frag

frag

h

−11

J

−11

−3

3

−3

J

J

3

J

3

(β = 1, 0.5) surpass this threshold. If the maximum density of acooling, only a simple parametrization of the underlying= 1,fragment
0.5)
surpass
this tothreshold.
thedensity
maximum
densityaruns
The use of a ﬁxed background term may have an e
Baehr & Klahr(β(2015),
but scaled
mimic
theIfsize
andresolutionof the3Dan
presentedphysics.
in this paper.
candown
surpass
this criticalfor morethanoforbit,

2017)

Deuterated methanol on Solar System scale around the HH212 protostar
E. Bianchi, C. Codella, C. Ceccarelli, V. Taquet, S. Cabrit, F. Bacciotti, R. Bachiller, E. Chapillon, F.
Gueth, A. Gusdorf, B. Lefloch, S. Leurini, L. Podio, K. L. J. Rygl, B. Tabone and M. Tafalla

A&A 606, L7 (2017)• prestellarでダスト上のCがD化分⼦にà原始星期に放出、つまり歴史を保存。
• さらに円盤形成のショックでも変化するので原始星の惑星形成領域を⾒たい。
observations are then crucial to measure the D/H ratio within
A.1. Examples of line profiles in T scale (not corrected for the
50–100 au from the protostar, that is, in the region hosting them dilution):
species and transitionsClassare reported. The0,
verticaldashed•
HH212,
Orion
(450
pc),
分⼦円盤(M*=0.2-0.3
R~60
protoplanetary discs. Mo,
Dust grains
and icesAU)。
may also be a↵ected
stands for the systemic V velocity (+1.7 km s , Lee et al. 2014).
by the accretion shock near the centrifugal barrier, therefore weand blue curves are for the Gaussian fit. In the spectrum of theBand
7,doublet
メタノール,
Cycle 1, 0.43 km/s,
0.4“; Cycle 4, 0.87 km/s, 0.15”
le 1•(1 –0ALMA,)A CH OH transition,a CH DOH
containdo not know the deuterium fractionation at small scales.
the (5 –5 )e1 and the (5 –5 )e1 transitions is also shown (see13CH
e A.1).
4 spectraOH
the (7 –6)A CH OH and the (8 DOHが12本、E–
The HH212 star-forming region in Orion (d = 450 pc) is an• In Cycle
5本、CH2
up=17-438 K、円盤形成領域で初検出。
SO transitions are also3
shown.
B

1

LSR

1,1

0,0

4,2

3,2

13

3

2

4,1

3,3

1,7

1,6

3

2,6

2

ideal laboratory for studying the jet-disc system. The HH212mm Class 0 protostar is driving a bright, extended, and bipolar molecular jet extensively observed using IRAM-NOEMA,
SMA, and ALMA (e.g. Lee et al. 2006, 2007, 2008,22015, 2016,2017a,b;Codella16‒2 et al. 2007; Cabrit et al. 2007, 2012). A molec17
ular disc was revealed2in HCO+ , C17 O, and SO emission, using
the first ALMA cycles with‒2
angular resolutions of ⇠000. 6. Velocity gradients have been detected along the equatorial plane consistent with a rotating disc around a 0.2–0.3 M protostar (Leeet al. 2014; Codella et al. 2014; Podio et al. 2015). A disc witha radius
60 au has indeed been imaged by Lee et al. (2017a),
A&A
606, L7of(2017)
who observed the dust continuum emission at 850 µm. Finally,
Codella et al. (2016) and Leurini et al. (2016) suggested that
HDO and CH3 OH emission is likely associated with outflowing
gas, and possibly with a disc wind. To conclude, the HH212 region is the unique Class 0 protostellar region where a bright jet,a compact rotating disc, and signatures of a disc wind have been
revealed. In this Letter, we exploit ALMA Band 7 observations
with an angular resolution down to 000. 15 to obtain the first measurement of methanol deuteration in the disc formation region.

• 13CH3OH過去のCH3OHでLTE回転温度、柱密度(CH DOHも)。
• 13CH3OH: (6.5±2.1)x10 cm , CH DOH: (1.1±0.2)x10 cm‒2。
Fig. 1. Left panel: HH212 protostellar system as observed by ALMA• 12C/13C=70とし、D/H=(2.4±0.4)x10
Band 7 (Codella et al. 2014). Blue and red contours plot the blue- andredshifted SiO(8–7) jet overlaid on the continuum at 0.9 mm (black con• IRAM, Perseus, Class 0ではD/H~0.5
tours). Positions are with respect to the coordinates reported in Sect. 2.
The filled ellipse shows the synthesised beam (HPBW): 0 . 61 ⇥ 0 . 45.
• Tdust~12 K in Perseus, >16 K in Orion。Orionのホットコアでも他より1桁低い。
Central panels: zoom-in of the central region as observed by ALMA-

A.2. Rotation diagrams for 13 CH3 OH (upper panel) and CH2 DOH
wer panel). An emitting region size of 000. 19 is assumed (see text).
parameters Nu , gu , and Eup are the column density, the degener-

•
•
•
•

2. Observations
HH212 was observed in Band 7 with ALMA using 34 12 m antennas between 15 June and 19 July 2014 during the Cycle 10000Band 7 Cycle 1: 13 CH3 OH(130,13 –121,12 )E and CH2 DOH(90,9 –81,8 )e0
integrated over ±4 km s 1 with respect to the vsys = +1.7 km s 1 , (black
contours and grey scale). First contours and steps are 5 for 13 CH3 OH
2 beam 1 km s 1 ) and CH2 DOH (35 mJy
2 beam 1 km s 1 ). The(15 mJy
130000
HPBWs are 0 . 52 ⇥ 0 . 34 (PA = 64 ) for CH3 OH and 000. 54 ⇥ 000. 35(PA = 65 ) for CH2 DOH. Right panel: zoom-in of the central region,as observed by ALMA-Band 7 Cycle 4, showing the 13 CH3 OH(121,11 –
120,12 )A emission integrated over 10 km s 1 around vsys (black contours
and grey scale). First contours and steps are 5 (20 mJy beam 1 km s 1 )and 3 , respectively. The HPBW is 000. 15 ⇥ 000. 12 (PA = 88 ).

CH DOHの北成分はSO のblue。
⾚、⻘、マゼンタとも90x45 AU。
±1 km/sの勾配はジェットと逆。
r~0.1“は円盤半径に近いので降着衝撃波か。
3. Results and discussion
3.1. Line spectra and maps

LkCa 15
TW HyaUX Tau A
V4046 Sgr

167
140
63
77

3.9
0.3
1.4
<0.1

0.25
0.04
0.27
<0.04

16.7
8.3
5.3
1.4

K3
K6
K2
K5

2.0
1.5
1.0
2.4
1.7

0.69
0.43
0.09
0.35
0.26

2.9
3.3
11.1
6.7
6.3

K4
M2
K7
K0
K7

No
No
No
No

Espaillat et al. (2010); Andrews & Williams (2005)
Torres et al. (2006); Weintraub, Sandell & Duncan (1989)
Herbig (1977); Andrews & Williams (2005)
Quast et al. (2000); Rosenfeld et al. (2013)

Chemical enrichment of the planet forming region as probed by accretion
Richard A. Booth and Cathie J. Clarke

EG Cha
TWA 7
V1086 Tau
V396 Aur
V397 Aur

Weak T Tauri stars
Mamajek et al. (1999)
Torres et al. (2006)
Herbig & Bell (1988)
Herbig & Bell (1988)
Steffen et al. (2001)• 惑星形成化学。星への降着領域に近く、原⼦になるので存在量がわかりやすい。ダスト⽳の影響。
主にHST,
F5-M2型星、25CTT, 5 WTT, NV 1238.88-1242 Å, CIV 1548.28-1550.8 Å, SiIV 1393.8-1402.88 ÅThe•1.3 mm
flux has been extrapolated
from the 880 µm flux.
The 1.3 mm flux has been estimated by extrapolating the far-infrared SED.
The•line profilesof the sources marked ‘Yes’ may be affected by outflows.
同じデータの過去論⽂あり(Ardila+ʼ13)。

a The 1.3 mm flux has been renormalized to mJy at a distance of 140 pc.

bThe Si:N, Si:C and C:N hot gas line flux ratios are from Ardila et al. (2013).
cde

塗り：⽳なし、枠：⽳あり、三⾓：上限
星：分⼦流的ラインプロファイル
M型、F-G型、K型
点線：WTTの1σ
WTTで規格化。

•
•
•
•
•
•

Accretion and chemical evolution
SpTと分⼦流は無相関。WTTより広分散。
モデル：grain growth, radial drift, 乱流粘性、拡散、粘性加⽳ありでSi/N, C/Nが低い。
熱、照射、M=10 Mo/yr, α=10
ß⽳の縁に粒⼦トラップ、Cも運ばれない。
Species (X)Tbind (K)aCase 1b : X/H
Case 2c : X/HàCは主に耐⽕(CO2)、Nは主に揮発(N2)。
↖Cは平衡↗0.5 × (N/H−NH3 /H)
N2473, 757–764 (2018)
770
0.5 × (N/H−NH3 /H)
MNRAS
⽳なしではSi/N, Si/Cが1.3 mmと相関。
CO
850
0.45 (1 + fCO ) × C/H
0.65 × C/H
CH4
1300
0.45 (1 − fCO ) × C/H
0ß進化して1.3 mmもSiも減る。
CO22575
0.1 × C/H
0.15 × C/HFigure 1. Flux ratios of Si, N and C normalized to the WTT sample mean against the flux at 1.3 mm normalized to the distance of Taurus (140 pc). The 1σ
deviations of the WTT sample are shown by the black dashed lines. Filled circles denote full discs, while large hollow symbols refer to sources with known
large cavities. Triangles denote upper limits. The sources with line profiles that may be affected by outflows are marked with stars. The spectral type of the
2. theBindingenergies and volume mixing
sources is shown by point colour: M-stars are in magenta, F and G stars in cyan and K stars in black. Note that for the cavity source VTable
4046 Sgr,normalized‒8ratios of chemical species adopted‒3 (from Madhusudhan, Amin & Kennedy 2014;
Booth
et
al.
2017).
Si/N ratio (0.03) lies below the bottom of the figure.
dot,int

oaded from https://academic.oup.com/mnras/article-abstract/473/1/757/4157283
stitute of Earth Sciences, Academia Sinica user
November 2017

2
2

NH3
H2 O
Carbon grains
Silicates

2965
5700
–
–

0.07 × N/HO/H – (3 × Si/H + CO/H + 2 × CO2 /H)
0
Si/H

0.07 × N/HO/H – (3 × Si/H + CO/H + 2 × CO2 /H)
0.2 × C/H
Si/H

a We use binding energies Collings et al. (2004), Garrod & Herbst (2006), Martı́n-Doménech et al. (2014) and Fayolle et al. (2016).

NH3
H2 O
Carbon grains
Silicates

2965
5700
–
–

0.07 × N/HO/H – (3 × Si/H + CO/H + 2 × CO2 /H)
0
Si/H

0.07 × N/HO/H – (3 × Si/H + CO/H + 2 × CO2 /H)
0.2 × C/H
Si/H

Chemical enrichment of the planet forming region as probed by accretion
Richard A. Booth and Cathie J. Clarkea We use binding energies Collings et al. (2004), Garrod & Herbst (2006), Martı́n-Doménech et al. (2014) and Fayolle et al. (2016).

b, c Volume mixing ratios adopted from Madhusudhan et al. (see e.g. 2014), with solar elemental abundances (Asplund et al. 2009).

の続き

fCO2 is the fraction of CO2 molecules in ices. The NH3 abundance of 0.07 follows Bottinelli et al. (2010) and Piso et al. (2016).

Mdisk,int=0.1 Mo, Rint=100, Case 2

d/g⽐

最⼤粒⼦

• 揮発分⼦はダストに乗ってきて、スノーラインにたまる。内側からSi, C, N。CはCO2に多く、COもCO2になる。

CO2
NH3

CO
N2

Figure 2. Evolution of the dust fraction, ϵ, maximum grain size, a, and gas phase chemical abundances for a 100 au disc. The C/H and N/H ratios arenormalized to the solar values.

フェイスオン円盤でフラックスを計算。
argue that, based on the work presented here and in Kama et al.
• モデルはSi/N-1.3mmの相関、特に右上を再現。
実線：Case 1, 破線：Case 2, 点線：無反応(2015), the carbon-locking is not the main driver for the chemical
two important snow lines: CO and N at a large radius and CO andNH closer in: however, theMyr)。
fraction of C residing in CO is large
evolutionof the inner regions of protoplanetary discs. As discussed• Si/Nが⾼いとNが来てないので若い(~0.5compared with the fraction of N in NH and thus the net effect isin Booth et al. (2017), in the absence of detailed chemical models
that carbon is more rapidly conveyed to the inner disc than N. In
thatradial drift, we gain some confidence in the simple• include
⾼い[C]/[N]で⾼いC/N輝線⽐を再現。
Fig. 2, the difference between C and N is further enhanced becausemodels from the fact that they span the range of behaviours seen in
the conversion of CO to CO at the snow line results in extra C
thedetailedchemicalmodelsofEistrupetal.
(2016).
•Fig. 原⼦輝線⽐と存在量⽐の相関を⽰唆。
being deposited at the CO snow line.
2 shows the typical evolution, using a disc with an initial
We now show this sorting of atomic abundances can explain
mass
of⽳なしと思われていても、1.3
0.1 M⊙ , a radius of 100 au and the Case 2 ‘equilibrium’•
mmが強くSi/N
the main feature of the Ardila et al. (2013) data if one interpretschemistry. The physical evolution is typical for models of this kind,the flux ratios as indicating the abundance ratios. We note that thewith theが低いものは⽳ありの可能性。
mass of the gas decreasing due to viscous accretion, whileabundance evolution of the accretion flow can already be inferred
it spreads outwards in radius. In comparison, the dust mass evolves
A. Boothdeposited further out. The C and N profiles762
are each R.
controlled
by and C. J. Clarke
2

2

3

2

3

2

2

more quickly due to growth and radial drift, leading to the decreaseof both the dust-to-gas ratio and disc size (as determined by, e.g.
the radius outside of which the dust is smaller than 1 mm).
The dust evolution is associated with the transport of volatiles
which make up the icy mantles of the grains, which are carried as
the dust migrates. These ices are deposited by desorption at theirrespective snow lines while the grains continue to drift towards thestar. CO and N2 are left farthest out, at 30–40 au, leading to spikes

from Fig. 2 because the abundance of accreting material tracks thatat the inner edge of model. This is also true of the dust, which
is well coupled to the gas at the inner edge due to its small size
(thus, the dust-to-gas ratio normalized to its initial value gives the
Si abundance relative to solar). The 1.3 mm flux for the models isderived assuming a Weingartner & Draine (2001) composition. The
FigureSame as Fig.for
1, with the addition of model tracks which show the ratio of the atomic species accreted on to a star with dots placed every 0.5 Myr.
q = 33.(appropriate
grain size distribution is n(a)da ∝ a−q da, withThe line colours denote the initial disc outer radii: 50 au (blue), 100 au (orange) and 300 au (green). The cases 1 and 2 ‘equilibrium’ models are shown by solid
an evolved dust population; Birnstiel, Ormel & Dullemond 2011)

初期半径50, 100, 300 AU

and dashed lines, while the dotted line shows the Case 2 ‘no reactions’ model.

New binaries in the ε Cha association
Cesar Briceno and Andrei Tokovinin••••若い星の連星率は円盤分裂、IMF、円盤の寿命、連星系での惑星形成につながる。
Taurus, Cha Iなど孤⽴系でOrionより2倍PMS⼩質量連星が多いà⼒学散逸か、いや、環境で初期率が違う。
εChaは110 pcと近い、35-41個のメンバー、3-5 Myr。
separation 4-300 AU, 37メンバーの最⼤調査。SOAR 4.1 m 南⽶。Iバンド、788 nm, FWHM=132 nm, 0.33”。

The Astronomical Journal, 154:195 (9pp), 2017 November

⾃⼰相関

重⼼を揃えた

Briceño &• AO Spekleイメージング。
• パワースペクトルàフーリエ変換して⾃⼰相関関数。
• ⾃⼰相関の環上で検出限界測定(5σ)。
• パワースペクトルを点源ｘリファレンスでモ
The Astronomical Journal, 154:195 (9pp), 2017 November
Briceño & Tokovinin
デルフィット。
ピークを揃えた

検出限界
実線：中央値
Figure 1. Example of the speckle data processing for the well-resolved binary
VWCha. The top row shows the central fragments of images, in the negative
scale: the ACF (a), the SAA image (b), and the centered image (c). The bottom
row shows the data in the Fourier space: the power spectrum and the reference

Figure 1. Example of the speckle data processing for the well-resolved binary

Figure 2. Detection limits for 20 faint unresolved targets recorded with 2×2
binning and 0.1 s exposure time. The thick curve shows the median detection

New binaries in the ε Cha association
Cesar Briceno and Andrei Tokovininの続き

Figure 3. Images of six newly resolved binaries with faint companions displayed on an arbitrary negative scale. The separation is indicat
each image, the companions are marked by arrows. Cha-13 and TYC 9238-612-1 are average images in closed AO loop, the rest are SAA

イメージ

The Astronomical Journal, 154:195 (9pp), 2017 November

Briceño & Tokovinin

パワースペクトルTransitional Disk (TD). Murphy et al. (2フリンジか伸びで検出。
is variable in Cha-13, though the line pwide, with a 10% width of ~170 km s-1
accretion rate of ~10-11 M: yr-1. These
resemble those of other TDs, like
新しく⾒つかった連星(Espaillat et al. 2008). In addition toは10個。
(2013) ﬁnd a number of other emission
The Astronomical Journal, 154:195 (9pp), 2017 November
Briceño & Tokovinin
Cha-13, like He I, [N II]l6548 6583, [SFigure4.
Power
spectraofthree
resolvedclosebinaries
displayedontheTable 3others, leading them to suggest the gap• εChaの中⼼にある同名の三重連星。
Detection Limits for Unresolved Targets
logarithmic scale. The separation is indicated in the lower left corner; theby jet/outﬂow activity. Our discovery
inserts in the lower right corners show the central fragments
the ACFs.
• of外は反時計、内は時計回り。
Name
rmin
Dm (0. 15)
Dm (1 )
∼90 au raises the alternative interpretatio
(″)
(mag)
(mag)
related to the binarypair。
nature of the syst
• つながれたｘと□がouterHD 82879
0.04
1.6
5.1
1200 au , a companion can truncate th
in 2000. The subsystem Ba,Bb was also unresolved at SOAR in
CP-68 1388
0.04
2.2
4.8
A-Bはサブシステム(a,b)のせいでよ
TYC 9414-191-1
0.04
1.6
4.3
2014 and 2015, although at DJ = 0.3 mag it •shouldbe easily
separations of few tens of au, the di
RX J1123.2-7924
0.04
1.9
3.4
detectable. It is possible that the pair Ba,Bb becamecloser (itsfrom the inside (Manoj et al. 201
2MJ11432669-78...
0.10
0.9
2.2
ろよろしている。
Figure 3. Images of six newly resolved binaries
with faint companions displayed on 0.04
an arbitrary negative scale.1.7
The separation is indicated4.0
in the lower left corner of
RX J1147.7-7842
estimatedperiodis∼70years).
The
pair
AB
moved
very
littleChamaeleon I, Daemgen et al. (2016each image, the companions are marked by arrows. Cha-13 and TYC 9238-612-1 are average images in closed AO loop, the rest are SAA images with or without AO.
RX J1149.8-7850
0.04
2.1
4.3
•
サブはあと数年で周期が決まる。
its discovery in 1994; its estimated period is ∼400 years.
statistically signiﬁcant difference in
RX J1150.4-7704
0.04
1.8 Murphy et al. (2013)
4.6 also ﬁnd thatsinceTransitional Disk (TD).
Hα
2MJ11550485-79...
0.10
1.7 though the line proﬁle
3.3 itself is not very
is variable in Cha-13,
It is not a member of the association, but deﬁnitely a young
between single and binary systems;
consistent with a low
wide, with a 10% width
T Cha
0.04
2.4 of ~170 km s , 5.1
object;Murphyetal.
(2013)
attribute
it
to
the
Cha
I
group.
Itissystems with separations 1100 au show
accretion
rate
of
.
These
characteristics
closely~
10M
yr
RX J1158.5-7754B
0.04
2.0
4.2
•
連星率はG0か⼩質量では0.1
perspeciﬁcallyresemble those of other TDs, like CVSO-224 in OrionCXOUJ115908
0.10
2.2
2.3
of accretion activity. More
(Espaillat et al. 2008). In addition to Hα, Murphy etnot
al. featured in the Gaia DR1, so its true membership is still
HD 104237E
0.04
1.6of other emission lines
4.6 in their spectra of(2013) ﬁnd a number
TDs shows that close to 38% can b
difﬁcult to ascertain.
decade separation。矮星と同程度。
2MJ12005517-78...
0.04
1.4
II]l6548 6583, [S II2.6]l6716 6731, amongCha-13, like 2017年の⾃⼰相関
He I, [NFigure 4. Power spectra of three resolved close binaries displayed on theothers, leading them0.7
to suggest the gap may
HD 104467
0.04
6.1 have been cleared 11186-7936.
interactions between a close binary co
2MASS J11183572-7935548 (Cha 13,
logarithmic scale. The separation is indicated in the lower left corner; theby jet/outﬂow activity.
of a companion at•
A,
B型は全て。0.6
per decade
USNOB-120144-78...
0.10
2.0 Our discovery 2.9
inserts in the lower right corners show thecentral fragments of the ACFs.
∼90 au raises the alternative interpretation that the TD statusiswhile the remaining
proportion are likely
I=12.22
mag, M4.5) is a new 0 92 binary. Murphy et al.
CXOUJ120152-78...
0.10
2.0
3.2
related to the binary nature of the system. At separations of
RXJ1202.8-7718
0.04
2.5
4.5
(2013)
suspected
RV
variability,
which
might
mean
that
it
is
like
disk
photoevaporation,
grain grseparation。
1200 au , a companion can truncate the outer disk, while atin 2000. The subsystem Ba,Bb was also unresolved at SOAR in
J1204.6-7731
0.04
2.3tens of au, the disk
4.5could be truncated= 0.3
2014 and 2015, although at DJ RX
mag it should be easily
separations of few
triple, because thearcsec
new wide pair has a period of ∼2 kyr. In
interactions (Ruíz-Rodríguez et al. 20
detectable. It is possible that the2MJ12074597
pair Ba,Bb became closer (itsfrom the inside 2.5(Manoj et al. 2011).
0.10
3.6 Indeed, studying
estimated period is ∼70 years). The
pair
AB
moved
very
littleChamaeleon
I,
Daemgenetal.
(2016)
ﬁnd
that
there
is
a
Figure5.
Tentative
orbitsofthetriplesystem
òCha
with
axis
scale
in
their Spitzer
study
ofouter
Chamaeleon,
Manoj et al. (2011) classify
accretion activity and excess infrared
RX J1207.7-7953
0.04
2.6
3.9
since its discovery in 1994; its estimated period is ∼400 years.
statistically signiﬁcant difference in the (イラストnotaccretor arcseconds.
fraction
Only a fragmentof theorbit is forplotted; publication)
its wavy trajectory
yet
ready
RX J1216.8-7753
0.04
2.4 binary systems; in
4.6 particular, binary
It is not a member of the association,
but deﬁnitely a young
between single and
this
as
a
Weak-lined
T
Tauri
star
based
originate in one or two circumprimary
reﬂects
thestarwobblecausedby the inner subsystem.
Crossesandsquareson the modest Hα
RX J1219.7-7403
0.04
1.8 1100 au show a4.2
low ∼6% incidence
object; Murphy et al. (2013) attributeit to the Cha I group. It issystems with separations
connected to the orbit by dotted lines denote the measurements of the outerequivalent width of 11 Å reported in literature low
circumbinary disk? Has the gap in this Tof accretion activity.
a recent study ofemission24
not featured in the Gaia DR1, so
its true membership is still
2MJ12210499-71..
0.04
1.7More speciﬁcally, 5.1
-1

-11

:

-1

CN rings in full protoplanetary disks around young stars as probe of disk structure
P. Cazzoletti, E. F. van Dishoeck, R. Visser, S. Facchini and S. Bruderer• ガスリングは化学を含め、形以上の価値がある。
P. Cazzoletti et al.: CN rings in full protoplanetary disk
• CNは13CO並みに明るく、円盤表⾯のPDR。ALMA TW Hyaで初めてリングを分解。構造か化学か？
uscript no. cazzoletti_2017
Fig. 5: Ray-traced images of the CN emission rings in models with 10 M , = 0.3, h = 0.1 disks around a T Tauri and a Herbig• 2次元熱化学モデルDALI、exp.
tail、冪スケール
star. The ring in the Herbig disk is clearly more
extended than that around the T Tauri star. The images are not convolved with any
Table 1: Parameters of the disk models in the main grid.
beam, and the resolution is set by the size of the cells in the spatial gridding of the disk (⇠ 2.5 AU). For the ray-tracing, the disks
ハイト。T
are assumed
to be at aMC。存在量とT
distance of 150 pc.
⽩線：τ=1dustは2D
gas (冷却＋加Parameter
Range熱)は⾃⼰無撞着。
Chemistry
化学でリング[C]/[H]
1⇥10
Fig. 9: Dependence of the CN ring location on the total disk mass
• of化学モデルは気相反応、イオン化、光解離、紫外[O]/[H]
3.5⇥10Fig.
8:
DependencetheCN
integrated
flux
on
the
total
disk
in the models.
[N]/[H]
1.6⇥10線、X線、宇宙線、PAH、粒⼦表⾯化学、凍結、
mass
for
disks
aroundT
Tauri(upperpanel)
andHerbig(lower[PAH]
10 ISM abundance
A&A proofs: manuscript no. cazzoletti_2017
panel)
stars.
For
each
value of , the range highlighted by the
昇華を含む。
Physical structure
shaded area is due to the variation of hc . The fluxes are mea1
main reactions that dominate the formation of CN are• The
緑点線の⾼さ。
0.1, 0.2, 0.3sured by assuming the disks are at a distance of 150 pc. The
instead
CNピーク半径h0.1, 0.2 radvalue measured for TW Hya and rescaled for the distance of the • H2*はUVによる振動励起。
R
60 AU
↓
M
10 , 10 ,models
10 , 10 , is
10 also
M shown.
N + H⇤2 ! NH + H Fig. 2: (a) Abundance of CN in a 10 M , = 0.3, h (4)f0.99= 0.1 disk s
沈殿粒⼦だけ0.2
with the green dot. The shape of the distribution (5)of the outer
C+ + NH ! CN+ + H. marked
models. The white line shows the ⌧ = 1 contour of the CN (N = 3 2
same wavelength. The green dotted line marks the location of the ver
0.2
H
Stellar spectrumgasin• CNはOに破壊されるが温度依存なし。

ite
ze.

1)
in
200
re
he
m,
ow
l.

DR
er

2

c

4

4
5

3

c

c

gas

5

4

3

2

1

2

large

T e↵

Lbol
LX

c

blue line) and HCN (cyan line) column densities calculated for the sa(greendot8 Min/year),Fig. 2a). Again, the CN
molecule is located near the CNdensity+
4000 K + UV
( Ṁ = 10
Fig. 6: Comparison between the radial CN column
profile (blue)
andto
intensity
profilethe twodisks
in Fig.
proceedsthenCNthrougha forchargetransfer
reactionwithThe
HCN(red)columndensityhasbeen shown
multipliedby 15, andis more radi
10000 K surface of the disk and between the5.hydrogenatomicmolecThe plots show
how the andemissionring follows the column density. The total gas column density is also
+ plotted in yellow+ as aHorthroughtheintermediates
HCN
and
HCNH
followed
1, 10 Lreference.
into thevdisk.
1030 erg s 1ular hydrogen layer, with HCN locatedv deeper
The verticalfollows
a Gaussian,with= -2 km/s= -1 km/s
by dissociative
recombination.
Alternatively,
NH canreact
withv = 0 km/s
v = 1 km/s
v gas
= 2 density
km/s distribution

T Tauri
Herbig

表⾯２層が観測可能。

aspect-ratio that depends on the radius as
It is worth investigating whether the increase in CN col- neutral C directly to formanCN.
Another less important route to✓R◆umn density toward the outer disk is due to decreasing UV cyanides starts from reactionsh(R) = hcof N. with CH2 and C2 H. Alter-(2)Rc+ordecreasing
temperature,orsomecombinationofparameters.
natively, reactions of N with H2 lead to NH+4 , through a seOther parameters
In order to mimic dust settling, two populations of grains are
The strongest dependence on temperature is found in the back- ries of ion-molecule reactions,
Cosmic-ray ionization
which
then
reactsofwith
C to
form
consideredfollowing
the approach
D’Alessio
et al.
(2006):
17
1
fast, therefore making the relevant timescales much barriers (London 1978; Tielens & Hollenbach 1985; Sternberg
rate per H25 ⇥per10layerss is+reactiona small one (0.005 1 µm) and a large one (1 1000 µm).
HCNH.
& Dalgarno 1995; Bruderer et al. 2012). Of particular imporExternal UV flux
G0shorter than the average age of a Class II disk.
The small-grains population has a scale height of h, while thetance to our models is the reaction of atomic N with H to form
scale heightof the more settled large-grainsis reCN is primarily destroyedby photodissociation
andpopulation
by reacNH, which in turn reacts with C or C to form CN or CN (see2.2. Grid of models
duced
to
h,
where
0
<
<
1.
The
fractionof
dust
below). The initial step has an activation energy of 12 650 K
rate
coefficientof twothepopulations
CN +isOcontrolled
reac-suran input gas and dust density structure,
the +
dust
trans- + H,
density
distributed in theby(Davidson & Hanson 1990) and would normally onlyCN
Hradiative! HCN(3)proceedtions with atomic O. Theface

Dust properties
Dust

Fig. 4: (a) Radial abundances for the most important reactants in the formation of CN (see reactions 4 and 5), along the dotted green
line in Fig.
Each curve is normalized to 1 at the location of the CN maximum. (b) H2 excitation and H⇤2 de-excitation rates along
0.005-1µm2a.
(small)the dottedline in Fig. 2a. All quantities are normalized to their value at the CN peak abundance (green dot in Fig. 2a), and1-1000µm green(large)refer to the model shown in Fig. 2a. The dashed vertical and horizontal lines mark the location of the CN peak abundance.

+

The goal of our work is to2investigate whether or not the ring-like⇤2+

CN rings in full protoplanetary disks around young stars as probe of disk structure の続き
P. Cazzoletti, E. F. van Dishoeck, R. Visser, S. Facchini and S. BrudererFig. 5: Ray-traced images of the CN emission rings in models with 10 2 M , = 0.3, hc = 0.1 disks around a T Tauri and a Herbig
star. The ring in the Herbig disk is clearly more extended than that around the T Tauri star. The images are not convolved with any
beam, and the resolution is set by the size of the cells in the spatial gridding of the disk (⇠ 2.5 AU). For the ray-tracing, the disks
are assumed to be at a distance of 150 pc.

•
•
•
•

T TauriとHerbigで半径が違う。
hcは効かない。
ψが⼤きいかUVが強いと⼤きく明るい。
粒⼦サイズを変えても半径差は数AU。

P. Cazzoletti et al.: CN rings in full protoplanetary disks around young stars as probe of disk structure

Fig. 6: Comparison between the radial CN column density profile (blue) and intensity profile (red) for the two disks shown in Fig.
= 0.2, hc = 0.1 disk surrounding a T Tauri star assuming
5. The plots show how the emission ring follows the column density. The total gas column density is also plotted in yellowf as a= 0.1 and
0.8. In these models, the higher amount of small
large
reference.
grains in the disk atmosphere lowers the intensity of the FUV
v = -2 km/s

v = -1 km/s

v = 0 km/s

v = 1 km/s

v = 2 km/s

field. Accordingly, the high CN-abundance region is moved toeven higher altitudes in the disks where G0 /ngas is similar. As aconsequence, the CN column density decreases by a factor of < 2
for the flarge = 0.8 model and by a factor of ⇠3 for the flarge = 0.1
model. However, the integrated fluxes are only ⇠20% and ⇠30%
lower, respectively, and the sizes of the rings are similar in the
flarge = 0.1, 0.8 and 0.99 models within a few AUs. The fact thatthe flux di↵erences are so small is due to the high optical depthof the CN (N = 3 2) line studied here.

幅はhcの違い。TW Hyaのフラックス、半径を再現。

3.4. Excess UV from accretion

In order to further test the impact of the UV field on the CN

Fig. 7: Simulated observations of a Mdisk = 10 2 M , hc = 0.1, = 0.2 disk around a Herbig star, inclined of 60 . The imageflux
wasand distribution, we ran an additional set of models by
14: Integrated flux of the CN (N, J)=(3-2,7/2-5/2) emission varying the excess UV due to accretion onto a T Tauri star.
simulated using the tasks simobserve and simanalyze in the CASAFig.
software.
2

δ：Cのdepletion factorSo far, the T Tauri stellar spectrum was modelled as a 4000

in a disk with Mgas = 10 M , = 0.2 and hc = 0.1 as a function of the C and O depletion. The blue dot refers to the model
where a higher gas-phase carbon abundance than oxygen is assumed. All the fluxes are normalized to the non-carbon-depleted= 1 case. The fluxes vary of less than a factor of 2.

K blackbody spectrum with a UV excess for an accretion rateof 10 8 M year 1 . The excess accretion UV is modelled asa 10000 K blackbody on a 1.65 R radius star (Kama et al.
2016). The additional accretion rates considered are 10 7 , 10 9 ,10 10 M year 1 and a non-accreting blackbody spectrum, andwe investigate the e↵ects of the di↵erent UV excess on a disk
with Mgas = 10 2 M , = 0.2 and hc = 0.1.

• CNから質量はわからない。ß少し光学的に厚く、上層だけだから。
Fig. 9, on the other hand, shows the size of the ring as afunction of M . More massive disks haveArticle
larger rings.
Thepagedif- 5 of 12
number,• CやNが少なくても、破壊源のOも少なければCNの量は変わらない。
ference between T Tauri and Herbig stars is much more evident
The integrated flux and ring size as function of accretion ratediskhere than for the flux, hinting at a strong dependence of the CN
abundance on the FUV spectrum. In particular, disks surrounding T Tauri stars show rings with sizes ranging between 10 AU
and 50 AU while Herbig disks show rings extending to more thanare plotted in Fig. 11. The observed trends presented in Fig. 11
confirm the main di↵erences seen between T Tauri and Herbig
stars. Higher accretion rates corresponding to higher UV fluxes
show higher CN integrated emission. Moreover, the radius of the