Star	  Forma)on	
  Newsle0er	
  No.256	
  6本目–10本目	
麻生 有佑	  (東京大学	  D1)	

becomebiggerinisaoursimulations,thepericentre
passage.
This
given
by
fit formula is valid.
counters with solar-typestars.
However,
generalisation
to mordiscenvironments
sizes. Therefore,
the
Kobayashi & Ida (2001) developed distantan analyticalestimateby
forthe rinitial
encounterscommonin 0.4clusteryields muchperi
Sizes	  of	
  protoplanetary	
  
d
iscs	
  
a
2er	
  
s
tar-­‐disc	
  encounters	
  dtially= 100 AU
. and 200 AU discs have to deqof
the size of the inner disc region, where thetoovelocity
big discdispersion
sizes. The
di↵erence
1 + m12 1/2
0.3 between the simulation result
Andreas	
  Breslau,	  Manuel	  Steinhausen,	  Kirsten	
  Vincke,	  and	
  Susanne	
  Pfalzner	  the disc material
after
an encounter
is andstill thelowenoughto form
where
the
final
size
of the200
AU disc
1/3
approximation
is
up
to
&
20 %,
theofdi↵erence
to thiFigure4bshows
thecomparison
the
sizes
approxi
planets (see their Eq. (31)). They obtained
0.2
ple
an
encounterwitha massofour
1/2 approximationEq.
up(8)to(thin,⇡ 80%.lines)
For
equal
stars
12
grey
with
the
simulation
0.5
1massratio
2 results
3 m(th4fi!
!
(イントロ)	
  1/4
periastronlines).
For
we AU
showreduces
only the curves
for distancethreeformula Eq. 4 simplifies
to clarity
distanceof 500the sizeof marperi 5/4
m12 + 1r• planet
/
.
(5)
(0.3
(solid),9.0 (dashed)
and 90.0(dotted)).
Evidentl
ほとんどの星はクラスターでできるので、エンカウントは大事。	
  
to
⇡
150
AU
while
the
initially
100
AU(7d
rinit
m12 2
r
=
0.28
·
r
.
for
prograde,coplanarencounters,
thisanalytical
appro
Fig.
4:
Disc
sizes
from
our
simulations
(b
final
peri
• 同質量エンカウントでは1/2–1/3	
  r_periとわかっていて、太陽系は30	
  AUで密度減少。	
  Thereexistsarelatively
simpledepe
regarded
as upperthe actual
turberperiastron
forlimit,a) anbecause
equal mass
pert
region is definedcan
dif-be only	
  Even though the size of this planet formingThisformulacanreproducethenumerical
resultsslightly
bet
betweenfactorandof onetwo dashedsmalleronthe(dotted
mass
ratio
betweentheandencounteri
grey aline)
1/3(shortferently than our disc size, the mass dependence is similar toare
thetypicallyestimate.
(内容)	
  ter thewithperiastrondeviations
. 10%
also
long
star
(mriastron) andthetheperiastron
distanceaswelldashedas distanceour grey
new linfit(rm12 0.32 dependence of Eq. (4). However,depen12(seeInaddition,deJuan
Ovelaretal.
(2012)
suggest44a). Nevertheless,aby
generalisationof ofanytheofwiththese•dence10 of個の粒子で円盤を作り、放物軌道のエンカウントで円盤のサイズ変化を見る。	
  line).
b) perturbers
0.3mass(soltheir analytical approximationinisFig.
strongerthan thatofmassgrey
scribedfitencounter
formulaform
theloss ina an
to estimate
the resulting
ratio independent approximations
toexpression
other
than
90.0
(dotted)solar masses
compared
toent
numerical results.
•ourエンカウント後の円盤半径は面密度の勾配が最大となる半径(aとeからradial	
  pequal-massrobability)。	
  Using themass-loss
by Olczak
et al. (2000.32 errors.
counters can obviouslytotremendous
with
(grey
c)discperturbers
sumingtheEq.
encounter
stripsthe .outerlayers, trfinal lead
=that
0.28
· m(8)· rlines).
• 初めが100	
  AUと200	
  AUを計算し、重なる範囲では	
  
12
peri
90.0
(dotted)solar
massescompared
to t
Recently,deJuan
Ovelaretal.
(2012)
derived
an
upper
limi
equal to r/r for a mass surfac
with previous approximations that M/M should be•5. Comparison
粘性やdisk-­‐diskエンカウントはviolentな場合しか効かない。	
  
1
with
Eq.
(9)
lines).
the
disc
/ as
r the
.(greyWith
Eq. (4)etthaof the disc size afterwithin
an encounter
distancedfrom
at Olczak
whichbyeq limited
Again,
the
final
disc
sizes
are
•Figure
面密度勾配が最大になる位置には幅があり、SEDフィットではその中の内側に合う。	
  oneobtains
for the discsize
after an encounter:4a shows a comparison of thegravitational
numerical results
force(solidof theperturbing
stardominates
at the
time
o
the
discs
do
not
grow.
In
the
plot
the
fit
fu
•line)過去のサイズ推定ではどれも過大評価している。	
  to the often used approximations (seeSect. 1)passage. This is given by
pericentre!1.2  200
initial0B(1/3
sizerof theinitially
discs. C⇣ AU⌘0.1- 2short dashedline,
1/2 rperi - drBperi M
1
1
final
B
rperi
= BB@proximations
1 of the fit function,
ln 2.8canrp onlycuto↵the
numerical
rfinal = rperi and rfinal = rperi(6)
obviously
be appli
d
=
.
(8
rinit
M2 + 0.5Meq
132

the curves
bend smooth
1 + m12 1/2 from the fit8 since
91
r

>

>

⇣ ⌘3/2>>
Mof
Ar<=CCCCsizes
1 the final
The
deviations
disc
⇥
exp
r
0.5
CA . by>>p
Figure 4b shows the comparison
of
the
sizes
approximated
>
>
;
:
M2of
+ 0.5M
from withthe results
the 1simulations.
Eq. (8) (thin, grey lines)
the simulation
results (thick,areblack
sizeFigure(i.e.only
5 shows
AU
an
AU
disc
4c
that
Eq.initially(9)also100
only
an ratiouppelines). For clarity weshow
theforcurvesforisthreemass
thedisc sizes
encounters.
Ontheone hand,
5–500
and after. 10% for mass
ratiosmat12this= 0c(0.3 (solid), 9.0 (dashed)
and90.0(dotted)).
Evidently,
leasplainedbyon
the thefact, orderthat in distantencounters,
where
n
are
still
of
the
uncertaintyoffor prograde, coplanar
encounters,
thisanalytical
approximation
removed from the disc, the disc can shrink by angula
can be only regarded
asremoval.
upper
limit,
becausedisc
size
validityofOn
ourformulaisrestrictum
the fitotherhand,theouractualsizealso
definitionvia
are typically betweenafactor
of
one
and
two
smallerthanthiofsteepest
surfacerfinal
> 0.2
rinit .density makes it possible, that a sestimate.

amount of bound mass is located in the low density reAndreas Breslau et al.: Sizes of protoplanetary discs after star-disc encounters(a)final discsize [AU]150.0

cer par(3)oplanefinition
only ofseveralmethodsity andwer law
ation ofges, theity falls
l 1998).
c’s surp in thes methntrast in

r an ene partiee casedo notdial diserefore,cle disresenta-

bservace denn be obpplyinga and e.
s yields
Whenwith the(3) onegnostics(p = 1)

rongestt of theatistical
ve to belied.
rber onhe cor-

100.0

(b)

50.0

50

m12
= 3: 0.30
Fig.
The parameter
space of encountersoccurringin a star
1.00
5.00
50.00
500.00cluster like the ONC (full height and open to the right) comparedto the parameter space of our simulations (grey area) and thevalidity area of our fit formula (grey, not ruled area). For further
details
100 see text.
200 300
500
1000
2000 3000
periastron distance [AU]3. Resultswith linear dependence on the periastron distance can describe
Fig. 2: Final thisdisce↵ectsizes
versusperturber periastron for some peronly
approximately.
It is (values
also important
to note,that numbers
in contrast at
to close,
peneturber mass ratios
shownby thethe lines)
trating encounters,
disc sizefor
changein distantisfrom our simulations(blackthesquares
initially
100encounters
AU discs
not mainly caused by a real truncation of the disc. Mostly, theand diamonds
forinitially200
AUdiscs)
comparedto
ourfit
forsize change is dominated by the redistribution of disc material
mula (Eq. 4, towards
grey, dotted
the hostlines).
star. This redistribution results in smaller discsizes even when no material is lost at all.
Figure 3 shows where our fit formula can be applied. The
axesnumericalare chosen toresultscover thetypicalwe present the
inencounter
absoluteparametervalues,spaceassuming
for an ONC-like star cluster. The grey area shows the paramean initial disctersize
of
100
AU
(blacksquares).
For
comparison,
space covered by this study. Right from the solid bent line,
the diamondsencounters
represent
discs
with
havesome
almostexemplaryno e↵ect on results
the mass,for
angularmomensizeAU.
of a As
disc.long
Rightasfrom
the dashed bentline, it thecanan initial sizetumofor200
an encounterchangesbe assumed
have alsoa negligiblethee↵ect.
The
sizes of the discs
with that
bothencounters
initial sizes
significantly
resulthorizontal, dashed line depicts the parameter space of Hall et al.
ing sizes are(1996)
approximately
thedotsame.
Since
the discs
do notwhile the black
marks thesimulations
by Kobayashi
1
become bigger
our Insimulations,thearea
final
arediscs
limited& Idain(2001).
the black shaded
the sizes
remaininghave
0.2 rTherefore,
10 %discof theirinitialparby the initialsizes
discbelow
sizes.
thethanfinal
sizes
of iniinit or have lessSinceAUthe discs
simulations
area maybe encounters,
influenced bytially 100 AUticles.
and 200
haveintothis
deviateafter
low resolution or the hole in our discs, we excluded them. The
where the final
size ofgrey
thearea
200depicts
AU discis & 100range
AU.forFor
examremaining
the parameter
which
our
ple an encounter
withisa valid.
mass ratio of m12 = 0.3 and a periastron
fit formula& Idathe(2001)an analyticalfor
distance of 500Kobayashi
AU reduces
sizedevelopedof an initially
200estimate
AU discsize ofinner disc100
region,velocity dispersion ofto ⇡ 150 AU thewhilethetheinitially
AUwheredisc theis unchanged.
the disc material after an encounter is still low enough to form
There exists
a relatively
dependence
planets(see their Eq.simple(31)). Theyobtained of the disc sizeon the mass ratio between theand the disc-bearing!1/4 encountering
!5/4
rperi
m12 + 1star (m12 ) andthe/ periastron
distance(r) which can be deperi
rplanet
.
(5)
2
rinit
m12of
scribed by a fit formula
the form

Figure 2 gives an overview of the results of our parameter study.
(The actual values can also be found in Table A.1 in the Online
Material.) For clarity and better comparability to observations

than· rour discsize, the mass dependence is similar to (4)therfinal = 0.28 ·ferently
m120.320.32
peri .

シミュレーション結果。	
  横軸は近点距離。	
  円盤サイズの決め方。	
   縦軸は最終円盤半径。	
実線は粒子数分布。	
  
破線は質量分布。	

Fig. 1: a) Face on view of a disc after an encounter with m12 = 1
and rperi = 2 rinit . For clarity, the particle angles have been decorrelated to destroy the spiral arms. The vertical lines mark the disc
diameter (= 2rdisc ) as obtained with our disc size definition.
b) Corresponding initial (thin) and final (thick) particle (solid)
and mass (dashed) surface density distribution (all lines aresmoothed). The vertical line shows the final disc size as obtainedwith our disc size definition.

responding initial (thin) and final (thick) time averaged surface
density distributions for in initially constant particle (solid) and/ r 1 mass (dashed) distribution. The vertical line shows the final disc size as obtained with our disc size definition. It can beseen, that the vertical line matches the points of steepest gradientin both final density distributions.
To determine the statistical deviations of our disc sizes we
performed ⇡ 100 simulations of one encounter with di↵erent random seeds for the initial particle distribution. Because
smaller radial bins for the surface density computation requirea longer smoothing length (as mentioned above) and vice versa,
we found a bin width of 0.01 rinit as a good compromise between
resolution and smoothing. The statistical deviations are then also
on the order of 0.01 rinit .

Article number, page 3 of 9

Simulation results (m = 1)
1.0
the central
areasof the discs. For typical viscosity v
1/3 periastron distanceperiastron
distancee↵ectedarea1/2
istheregion within . 0.2 rinit . Only in
0.9
0.28 periastron distanceviolent interactions the disc size is reduced to such low
0.8
For these cases viscous forces would have to be in prin
0.7
cluded.
As can be seen in Table A.1, this is, for exam
case0.6for equal-mass stars in penetrating encounters cl
0.7 rinit . For typical disc sizes on the order of some 100
0.5
Bally
et al. 2000; Andrews et al. 2009), such encou
relatively
rare in ONC-Type clusters (Olczak et al. 2006
0.4
dition, for such destructive encounters the material tha
0.3
bound is usually < 20 % of its initial mass and its struc
not 0.2
resemble0.5a disc as 1such. In thesecases
5 defini
2
3
4 theperiastronquestionable.
distance [r ]disc size is anyway highly(b)
1.0 additional approximation is that the case whereAnof thestars was surrounded by a disc was considered.
0.9
been done for simplicity of description. In principle,
disc0.8encounters the sizes could be larger because disccould
0.7 be transferred from the perturbing star to the disstar and replenish the disc. Pfalzner et al. (2005a) sho
0.6
=
0.30
9.00
in caseboth mstars
aresurroundedby90.00
discs, mostly an
0.5
approachcan be used as usually captured material is dclose0.4to the star. In addition, the amount of captured ma
small compared to the disc mass as such. Therefore in m
0.3
the final
disc size is little influenced by captured mateexceptionisagain 1the casewherethe encounter
is ver
0.2
0.5
2
3
4 5
10
and the remnant disc periastronmass very
distancelow.
[r ](c) Furthermore, the outcome of a disc-disc encounter
1.0
influenced by the dependence of the disc mass and siz
0.9
stellarmass. Observations give no conclusive answe
0.8
question.
If the disc size scales in some way with thmass,
the situation can occur that the perturber has a mu
0.7
mass, and therefore has a bigger and possibly more masm =(see0.6e.g. Andrews
et1.00al. 2013). In90.00
this case the amoun
terial0.5 captured by the primary could be comparable tohigher than that of its remaining disc.
0.4
We have chosen the point of highest surface density
0.3
as definitionof the disc size (see Sect. 2.2). However
encountertheregionwhere
thedisc’s surface
density d
0.2
0.5
1
2
3
4 5
10
nificantly spans someperiastronrangedistance(see Fig.
[r ] 1b). The inner bou
this region would correspond better to the disc sizes ob
Fig. 4: Disc sizes from our simulations (black lines) versus perSED fits, where the size is usually defined as the point, w
turber periastron for a) an equal mass perturber compared to 1/2
surfacedensitytransitsfroma power-law
to thesomething(dottedgreyline) and1/3 (shortdashedgrey line) of
peIf we distancehad defined
discnewsizes
as the(longinnerboundariastronas wellour
as ourfit formuladashedgreyline). b) perturbers
withresults
0.3 (solid),
9.0 be(dashed)andthandensity-drop
region, thewould
smaller
90.0(dotted)solar masses
compared toifthedisc sizestheobtained
actualdefinition.
Conversely,
definingsize
as twith Eq. (8) (grey lines). c) perturbers with 1.0 (solid) and
where
the
surfacedensity
falls
below
a
certainthresho90.0 (dotted) solar masses compared to the disc sizes obtained
12

final disc size [rinit]ar being
pproacherial areor a renamical

he innerhe mass

(a)

200.0

過去の推定方法との比較。	
  一番上の右の破線が今回のフィット。	
  それ以外は全て過大評価。	
Even though the size of this planet forming region is defined dif-m12
dependence of Eq. (4). However, the periastron dependence of their analytical approximation is stronger than that ofAgain, the final
disc sizes
are limited by the initial disc sizes, as
our numericalresults.

the discs do not grow. In the plot the fit function is limited by the
initial size of the initially 200 AU discs. Close to the sharp upper

init

final disc size [rinit]

at least
at rinit
riastron12

init

final disc size [rinit]of protoplanetary discs after star-disc encounters

12

init

An	
  ALMA	  Con9nuum	  Survey	
  of	
  Circumstellar	
  Disks	
  in	
  the	
  Upper	  Scorpius	
  OB	
  Associa9on	
  
John	
  M.	
  Carpenter,	
  Luca	  Ricci	  and	  Andrea	
  Isella	
  (イントロ)	
  • 円盤散逸のタイムスケールはクラスターでdisk	
  frac)onを比べて測られてきた。	
  • IRは~1	
  AUを見るのに対してsub	
  mmは外まで見える。	
  
	
  
(内容)	
  
• ALMA,	
  880	  µm	  • Upper	
  Scorpius,	  K-­‐M	
  13/20個検出,	
  Class	  II,	
  5–11	
  Myr,	
  	
  M*=0.1–1.6	
  Mo,	
  d=145	  pc	
  • Taurus	
  (1–2	
  Myr)と比較するためにフラックスからMdustを計算。	
  • log	
  Mdust/ME=0.68+1.01log	
  M*/Moを得る、Taurusでも傾きは1.1。	
  • Upper	
  Sco.にはM0.5–M3に対応するM*の天体がないà分布のブレイク?	
  • IRのdiskはM*が小さいほどたくさんあるàM*を揃えてTaurusと比較。	
  • M*がM0.5より軽い組ではMdustはTaurusより25%小さい。	
  • M*がM3より重い組ではTaurusとの違いは微妙。	
  ∆δ [arcsec]

J155624.8-222555

J155706.4-220606

J155729.9-225843

J155829.8-231007

contours = -1, 2σ-2, 2σ-2, 2σ-2, 3, 10, 20σ

J160357.6-203105

J160421.7-213028

J160525.5-203539

J160532.1-193315-2, 3, 6, 9σ-2, 3, 30, 130σ

-2, 3, 6σ-2, 2σJ160600.6-195711

Sco PMS 31

J160622.8-201124

J160643.8-190805-2, 2σ-2, 3, 6σ-2, 2, 4σ-2, 2, 3σ

J160702.1-201938

J160823.2-193001

J160827.5-194904

J160900.0-190836-2, 2σ-2, 3, 30, 60σ-2, 2, 4σ-2, 3, 7, 11σ

2 J160900.7-190852 J160959.4-180009 J161411.0-230536 J161420.2-190648
1
0-1-2, 3, 30, 60σ-2, 2, 3σ-2, 3, 10, 20σ-2, 3, 30, 120σ-2
2 1 0 -1 -2∆α [arcsec]

20天体中13天体で連続波を検出。	

Fig. 3.— Dust mass as a function of stellar mass for the 20 stars in the Upper Sco sample. Sources with 880 µm continuum detections
are denoted by circles, and 3σ upper limits to the 880 µm detections are indicated by triangles. The dashed lines shows constant ratios ofdust mass to stellar mass of 0.01ζ and 0.001ζ, where ζ = 0.01 is the dust to gas ratio. The shaded region shows the correlation between

Upper	
  Sco.のMdustとM*の関係。	

ig. 1.— Contour maps of the ALMA 880 µm continuum emission for 20 K-M type stars in Upper Sco. Each map is centered on the
dust where
mass solid
andanddisk
mass derived by Andrews et al. (2013) in Taurus, where the width of the region shows the 0.7 dex spread about thelar position after correction for proper motion. The contour levels are indicated in the lower right for each panel,
dottedbest fit relation.
tours indicate positive and negative flux densities, respectively.

8

10

TaurusとのMdust分布の比較。M*が大きい側(左)ではMdustに差がある。	
  Fig. 4.— Left: Cumulative distribution of the stellar masses for the Taurus (grey) and Upper Sco (black) samples for stellar masses

nd magnetic field perpendicular to eachthat the tangential component of the magnetic field
discussion of oblique shocks. Here weshock planeis reversed
inmbipolar	  the post-shock
region. Thes
Forma9on	
  
o
f	
  
M
agne9zed	  Prestellar	
  
C
ores	
  
w
ith	
  
A
D
iﬀusion	  ck equations and write them in a more
solutions are commonly specified as intermediate shocks
tailedjump
conditions.
and	
  Turbulence	  Wu 1987; Karimabadi 1995; Inoue & Inutsuka 2007). A
plane-parallelshock
these two field-reversal solutions, we notice that rf,exp
Che-­‐Yu	
  Chen	  and	
  withEve	
  Cuniform.	
  Ostriker	
  preρ0 and ionization-recombination equiapproaches the hydrodynamic jump condition (rf,hydro =he shock front is in the x–y plane, thewhen θ → 0, and rB,exp (θ), 2 is smaller in magnitude than
(イントロ)	
  the z-direction (v0 = v0 ẑ), and the upsolutions when θ < θcrit . Thus, we classify this set of sol
s in• themass/ﬂux比で重力収縮が決まる。ISMでは磁場が強く、星では弱いが間の変化は
x–z plane, at an angle θ to therf,exp (θ), 2 and rB,exp (θ), 2 as the quasi-hydrodynamic s
未だ謎。	
  + B0 cosθ ẑ) such that Bx = B0 sin θ isThis quasi-hydrodynamic solution can create gas compr• 準静的なambipolar	
  iﬀusionでは10t_ﬀかかり(観測2–5t_ﬀ)、GMC内はﬂowがある。	
  nt perpendicular
to the flow. dTheparammuch stronger than the regularly applied fast shock con	  m valueof the Mach number and plasma
and may be the reason that when θ < θcrit , even ideal
CO12
therefore become(内容)	
  simulations can generate shocked layers with relatively• 両側のﬂowに対して傾いた磁場を想定し、ショックを解く。	
  mass-to-flux ratio (see Sections 4 and 5 for more details)
B02
1
1 1
0
n~103	
  cmof–3ではM>10	
  oが必要で観.
(1), • m/fの臨界値はM/ΦB=1/2π√Gだが、B~10µm,	
  
≡
=
The
definition
θcrit can beMderived
from Equatio22β0測されるコアの1Moで収縮するにはambipolar	  8πρ0 cs
βx sin θ
2
diﬀusionが必要。	
  which turns
negative when 1 − (2 cos θ/β0 M2 ) >1 − (2rf (θ) cos2 θ/β0 M2 ) < 0:
• ideal	
  HD,	
  等方収縮では、あるθより大きい(ﬂowと磁場が垂直側)とpost	  shockで磁MHDshocksMare
described
by compres場が大きくなり、ISMà星の磁場の弱まりに合わない。	
  nd magnetic
field:
β0 M2
22
cos θ > cos θcrit =.
B
stream⊥,downstream2r(θ)
f crit• , シミュレーションではθと電離度χがパラメーター。	
  r B⊥ ≡.
(2)
B⊥, upstream
ream• 磁場が強いとコアはゆっくりでき、磁場に垂直なフィラメントができる。	
  Using Equation (5) and considering only the terms ∼M• 磁場が弱いとambiがあって中心部が良く圧縮されコアがすぐできる。	
  becomes0) and(A14) in CO12, we have√2
• 中間の磁場だと磁場に沿ったサブフィラメントネットワークができる。	
  cos θcrit
β0 M
"2 !
,
≈
2
sin
θ
2
θ
sin
2 cos2 θ
crit
2
=
M
+
1
+
or
√
β0 M2
β0
β0 M
2
"!
"2
sin θcrit +sin θcrit − 1 = 0.

• 密度が107	
  cm–3を超えたときにコアの物理量を測ると、密度、サイズ、質量、磁場、CFE,	
  CMF,	
  質量とサイズの間の冪、は大体観測と合っている。	
  • コアの質量とサイズはθとχに依存しない。	
  • χが大きいとambiは起きないがコアはできたà非等方収縮	
  Figure 13. Close-up view of magnetic field (pink lines) and gas velocity (black arrows) over column density (color map) projected to the x–z plane (left panel) and•ideal	  M
HDでは磁場に垂直な方向には集まらず、磁場に沿った方向に集まる。	
  x–y plane(right panel)a forming
at lines)different
from model
A20ID.
The
regionshown
here isindicated
the white
in Figure7. Thesize
Figure13.
Close-upviewaroundof magnetic
fieldcore(pink
andtimes,gas velocity(blackarrows)overcolumndensity(colormap)byprojected
to dashed
the x–zbox
plane(left panel)andthe box
N panel)×N ×
N isaLforming×core
4R at different
× 4R times,, whereand R The arecalculatedusingisEquations
and(36),dashedrespectively.
velocity! Lmodel A20ID.
!
x–yofplane(rightaroundfromregionshown here
indicated (31)by thewhite
box in The
Figure7. Thevectors
size
density-weighted) = L (v (i,andj, k)ρ(i,
j,are
k))/
ρ(i, j,k). Weused thesame
as in the left
panel
in Figure3 toof•arethe box
N × N × Naverages
is L over×the
4R box, i.e.,
× 4Rv (i,,jwhereR
calculatedusing
Equations(31)
andmethod(36), respectively.
The
velocity
vectors
磁場に沿った円柱を考えると臨界質量が1.3	
  Msameoとなり、観測されるコアに合う。	
  ! the length of!
the magnetic fieldlines.over
Thethemagnetic
field
velocity
vectors
both
Note thatthethevectorright3panel
aredraw
density-weighted
averagesbox, i.e.,v line(i, spacingj ) = and(v (i, j, k)ρ(i,thej, k))/
ρ(i,j, k).
Weindicate
used thestrength.
methodas inleft scale
panel ininthe
Figuretotimes larger
thanin thepanel infieldorder
better show
thelength
gas movement.
The pre-shocksupersonicthe inearlierstages(firstdraw
the magnetic
fieldlines.
Theleftlinetospacing
and theof the velocity
vectors bothindicate inflows
strength.along
Notethethatz-direction
the vector inscale
the right
panel•istwotwo
また、post	  smagnetic
hockの磁場はpre	
  shockの動圧で決まるので、コアの(臨界)質量がθやχに依
plots
inleft panel)
hereintoorder
focustoon
the post-shock
dynamics.
is twotimes
largerthan inare
theomitted
left panel
bettershow the gas
movement. The pre-shock supersonic inflows along the z-direction in the earlier stages (firstcolorinversionof thisis hereavailablein thejournal.) dynamics.
two(Aplots
left panel)
are figure
omittedto focusononline
the post-shock(A(notecolorらないことも説明できる。	
versionof
thisfigureisavailable
intheonlinejournal.)Combining Equations (31), (33), and (34) yields
that up to a factor 3/4, this is the same as Equation (15)).
x

x

y

y

z

z

mag,cylmag,cylth,sphth,sph2Dth,sphth,sph2D

mag,cyl3D
kmag,cylk 3Dth,sphkth,sphkThethatcriticalmass
Mmag,cyl
πRis2 L
ρpsascanthen be(15)).
written(note
up toa factor
3/4,=thisthesameEquationmag,cyl2
as
The critical mass Mmag,cyl = π R Lmag,cyl ρps can then be written
"
#2 "
#
as
R 2 Bps
Bps
R
"
"
#
#
. (32)
Mmag,cyl = 2 √ = 1.2 M⊙
R 2BpsG
B
R pc2
0.05
50ps µG. (32)
Mmag,cyl = √= 1.2 M⊙
0.05 pcto transverse
50 µG contraction
This cylinder2is G
gravitationally stable
unless
L ! is2Rgravitationally(Mestel & Spitzer
However,
contractionThiscylinderstable1956).
to transverse
contraction
alongLthe
lengthof the&cylinder
is unimpededby contraction
the magnetic
unless! 2R(MestelSpitzer 1956).
However,fieldtheandlength
will ofbe theablecylinder
to overcomepressurebyforces
providedalongis unimpeded
the magnetic
thatandLmag,cyl
exceeds
theovercome
thermal Jeans
length,which
is truefield
will beable topressure
forcesprovidedin Lgeneralforobliqueshocksin
typicalconditions
under
that
exceeds
thethermalJeans
length,
which
is
true
mag,cyl
The longitudinal
will produce
in consideration.
general for oblique
shocks incontraction
typical conditions
underanapproximatelyTheisotropic
core ofcontraction
radius R whendensityanhasconsideration.
longitudinal
willtheproduceincreased by isotropica factor core of radius R when the density has
approximately
increased by a factor
Lmag,cyl
ρ′
,
(33)
=
′
ρ ρps Lmag,cyl
2R
,
(33)
=
ρps
2R
and at this point transverse
contraction
would no longer bemagnetically
impeded.
For
thecore towould
have nosufficientand at this point transverse contraction
longer selfbe
gravity to overcome
this sufficient
point, the selfradiusmagnetically
impeded. thermal
For thepressure
core to athave
wouldtohave
to be comparable
to Rth,sph
gravityovercome
thermal pressureat (seethis Equation
point, the(12)):
radiuswould have to be comparable to Rth,sph (seecs Equation (12)):.
(34)
R ∼ Rth,sph = 2.3 √
′
cs
.
(34)
R ∼ Rth,sph = 2.3 √ 4πGρ
4π Gρ ′

Combining Equations (31), (33), and (34) yields
Bps 2
(35)
ρ ′ = 0.19 2 2
B4πc
ps s
(35)
ρ ′ = 0.19
4π cs 2and14. Space–time diagrams for varying magnetic obliquity and ionization, showing the x (left panels), y (middle√panels), an
Figure2
2componentsof the gas velocity averaged aroundand# "core in#each model, normalized by the total velocity vtot = vx + vy +" a collapsing
2 It is evident thatis the same as in Figure
anisotropic
condensation
along the magnetic field (x-direction) initiates core formation in
Bps −1
T
cs13.
#−1 "
# .
"
(36)
R = 5.3 this2 figure =0.05 pc(A color version of √B
T10 K
csGBps is available in the
50psonlineµG journal.).
(36)
R = 5.3 √= 0.05 pc
50 µG
10 K
GBps
Substituting
Equation condensation(36) in Equation(32), explain
the minimumIn
addition, anisotropic
also helps
whyThis is equivalent to Equation (24
mass
will
be
magneticallythecorethatmassesarebothquite
similarfor andHDthermallyand MHDmodels,2.8. GO11 also pointed out that ρ0
Substituting
Equation(36)
in Equation(32),
thesupercritical,
minimumallowing
for beanisotropic
condensation
along B,magnetic
will
be fieldandindependent
ofboththemagneticallyangle
between
upstreammassthat will
andthermally
supercritical,
to GΣGMC 2 for a gravitationally bou
andconverging
flow. Notecondensationthat Equation
(37)
only
depends
onallowing
for anisotropic
along
B,
will
be
GMC. Thus, using Equation (28) of GO
"
#−1 "
#2
T shock,
cs 4 field strength. B
the post-shock magnetic
Forparameter αvir , Equation (38) would b
ps a magnetized""##
Mcrit = 14 magnetic= 1.3 M⊙−12 . (37)
4
the post-shockbalancetheB
T10 pre-shock
cs3/2
psµG
G
B2 ps pressure must
50
K
$
%2 $
Mcrit = 14
= 1.3 M⊙ 2 . Therefore, Equation. (37)(37)
momentum
flux:
T
ΣGM
G3/2BBpsps /8π ∼ ρ0 v0 50µG
10 K
Mcrit = 2.8 M⊙
canThus,
be expressed
as contraction can lead to low-mass supercriticalanisotropic
10 K
100 M⊙
cores,
with values
comparable
those
formed inour simulaThus,
anisotropic
contraction
can tolead
to low-mass
supercritical
11
tions.with
Equations (38) and (39) suggest that M
cores,
values comparable
tothoseformedinour"#−1/2simula11
n0
cs 4
of
magnetic field direction upstream,tions.
= up
2.8to!
= 2.1 M⊙
Mcritthat
11 Notefactors(35)–(37)can−33 ρ ofv the2 order of unity, Equations
magnetic
field strength upstream. Tha
1000
cm
G
0 taking
0
Bps andrequiringthat thecan
density
11 equivalently
Note thatupbe
to obtained
factors ofbytheorderB$
of=unity,
Equations(35)–(37)post-shock
regions (assuming that th
%
′
2
#and
" (11)–(12)Equationssuch that
Rth,sph∼ Rmag,sph
ρ → ρ in be−1
equivalently
obtainedby
B =(14)–(15)Bpsthat
the density
T and isrequiringv0takingsupercritical at large scales), the crit
and
M
∼
M
.
′
th,sphmag,sph×.
(38)
and (14)–(15) is such that Rth,sph ∼ Rmag,sph
ρ → ρ in Equations (11)–(12)1 .km s−1
10 K
by the dynamical pressure in the cl
and Mth,sph ∼ Mmag,sph
17
18
17

The AstrophysicalChen
Journal,785:69 (20pp), 2014 April 10& Ostriker

The Astrophysical Journal, 785:69 (20pp), 2014 April 10

Astrophysical Journal, 785:69 (20pp), 2014 April 10

C

Chen & Ostriker

parameter that controls ambipolar diffusion effects in our
simulations, following CO12. We use typical values of themean neutral and ion molecular weight µn and µi of 2.3mH
and 30mH , respectively, which give the collision coefficient(see Equation (20c)) between neutrals and ions α = 3.7 ×
1013 cm3 s−1 g−1 .
The physical parameters defining each model are ρ0 , v0 =|v0 |, B0 = |B0 |, θ , and χi0 . We set the upstream neutral number
density to be n0 = ρ0 /µn = 1000 cm−3 in all simulations,consistent with typical mean molecular densities within GMCs6(e.g., Larson 1981; Williams et al. 2000; Bot et al. 2007; Bolatto
et al. 2008). We choose the upstream B0 = 10 µG as typicalof GMC values (Goodman et al. 1989; Crutcher et al. 1993;
Heiles & Crutcher 2005; Heiles & Troland 2005) for all our
Figure 2. Schematic configuration for our simulations.
simulations. To keep the total number of simulations practical,(A color version of this figure is available in the online journal.)
we set the large-scale inflow Mach number to M = 10 for
all models. Exploration of the dependence on Mach numberof ambipolar diffusion and of core formation has been studied√in previous simulations (CO12 and GO11, respectively). For
three-dimensional velocity dispersion δv = 3 · δv1D at theour parameter survey, we choose θ = 5, 20, and 45 degrees
e of the simulation box would beto represent small (θ < θcrit ), intermediate (θ > θcrit ), and"!
large (θ ≫ θcrit ) angles between the inflow velocity and cloud√ πGαvir 1/4 1/2 1/2 1/4
magneticChen
field.
For each θ , we conduct simulations with χi0 = 3,
v(L(20pp),
3 10
M cs ρ0 Lbox 1/2 . (22)box ) =
85:69
2014 April& Ostriker
15
10, and ideal MHD to cover situations with strong, weak, and no
ambipolar diffusion. We also run corresponding hydrodynamicemphasize the influence of the cloud magnetization instead ofsimulations with the same ρ0 and v0 for comparison.
perturbation field, our simulations are conducted with 10%
A full list of models is contained in Table 1. Table 1 also−1
he value δv(Lbox ), or δv = 0.14 km s with αvir = 2. With
lists the steady-state post-shock properties, as described iner δv(Lbox ), simulations can still form cores, but because
Section 2.1. Solutions for all three types of shocks are listed-self-gravitating clumps can easily be destroyed by strong
for the θ = 5◦ (A5) case. For the θ = 20◦ and θ = 45◦
ocity perturbations and no core can form before the turbulent
cases, there is only one shock solution. Also included inrgy dissipates, it takes much longer, with corresponding
Table 1 are the nominal values of critical mass and radius forher computational expense.
Figure 4. Similar to Figure 3, but
for model A5X3 withsymmetric
upstream magnetic field
nearly parallelto
to the(θ = 5 ) and low ionization underfraction (χFigure= 3).5. Similar to Figure 3, but for model A45ID, with 45 angle between upstream v and B, and ideal MHD.
spherically
volumes
beinflow
self-gravitatingthese(A color version of this figure is available in the online journal.)(A color version of this figure is available in the online journal.)
steady-state post-shock conditions, as discussed in Section 2.2
3.2. Model Parameters(small θ and/or small χi0 ) (seeand strong(large θ and/or(11),large (12),filaments
perpendicular
the magnetic
field.“thermal”
The timescales
Equations(14),
and to(15)).
Bothhydrodynamic solution. This is a direct evidence omeasured
the average density
within the z = 0.5 pc ± ∆x layer
χi0 ) magnetic effects in the shocked gas. The thickness of theat which compressed layers become
gravitationallyunstableand“magnetic”
criticalmassesarelisted.
In
mostmodels,of a transient stage of ambipolar diffusion (CO12
at
t
=
0.3
Myr
for
model
A5X3
and found that this overdense
A schematic showing our model setup is shown in
Figure2.
post-shock layer is very different for these two extreme cases.
and start to form cores also differ. Note that in the
cases
with
5
−3
Table 2 lists the physical properties of the poslayern ≈ 1.4
× 10 cmlayer, which exceeds the steady-MHD
Especially at early time (0.3M
Myr), structureis alsodifferentand ambipolar
diffusion(Figures3,and4),hasa highlycompressed
>
M
M
≫
M
indicatingthatthesimulation box is 1 pc on each side and representsaremag,sphth,sphmag,sph⊙measured at t = 0.2 Myr, as well as the corresp
shockregion.
jump condition
predicted
in these two cases, with stronger magnetic effects producing
forms in the center of the post-shock
Quantitatively,
we in Table 1 even for the quasipost-shock regions are dominated by magnetic support, andn within a GMC where a large-scale supersonic converging
109either ambipolar diffusion
or anisotropic condensation would
w with velocity v0 and −v0 (i.e., in the center-of-momentum
be needed to form low-mass supercritical cores, as discussedme) collides. The z-direction is the large-scale inflow direcin Section 2.2. On the other hand, the quasi-hydrodynamic, and we adopt periodic boundary conditions in the x- andshock solution for models with θ < θcrit (i.e., A5 cases) has
rections. We initialize the background magnetic field in the
Mmag,sph < Mth,sph < M⊙ downstream. If this shock solution
ud, B0 , in the x–z plane, with an angle θ with respect tocould be sustained, then in principle low-mass supercriticalconvergent flow. For simplicity, we treat the gas as isothercores could form by spherical condensation of post-shock gas.
at temperature T = 10 K, such that the sound speed is
In order to collect sufficient statistical information on the= 0.2 km s−1 . The neutral density within the cloud, ρ0 , is

v

B

v

x

y

z

◦

i0

◦

↑左は磁場が弱いとき、右は磁場が強いとき	
  	  ←θとχでコアができたときの違い	Figure 8. Statistical distribution of core mass (left) and size (right) from all models combined.
(A color version of this figure is available in the online journal.)

質量とサイズはパラメー
ターに依らない。	

Figure 9. Median (diamond) and ±25% values (vertical bars) of core mass, size, average magnetic field, and normalized mass-to-flux ratio for different model

The Astrophysical785:69(20pp),
2014
Aprilhigher
10
Chenangle& Ostriker
parameters. InJournal,
each figure
fromleft toright,
X corresponds to increasing ionization, and larger A corresponds to larger
θ , or increasing pre-shock(upstream) magnetic field Bx = B0 sin θ parallel to the shock front. The dashed line in the core size plot (bottom left) indicates the lower limit (0.015 pc) of resolved
core size; for our simulations, 0.015 pc ≈ 3∆x.

磁場に沿った方向に流れてくる非等方収縮	cores found in the simulations did not form isotropically. We
discuss this further in Section 6.
To further investigate the relationship between core masses
and sizes, we binned the data set by log Lcore and calculate
the average core mass and mean density for different model

We note in particular that for the θ = 20◦ and θ = 45◦ ideal
MHD cases, the masses in Figures 8 and 9 are more than anorder of magnitude lower than the limits for a spherical region
at post-shock conditions to be magnetically supercritical, as
listed in Tables 1 and 2. This implies that the low-mass bound14

Spitzer	
  View	
  of	
  Massive	  Star	  Forma9on	
  in	
  the	
  Tidally	
  Stripped	
  Magellanic	
  Bridge	  C.-­‐H.	
  Rosie	
  Chen,	
  Remy	  Indebetouw,	
  Erik	  Muller,	
  Akiko	
  Kawamura,	
  Karl	  D.	
  Gordon,	  Marta	  Sewi	
  lo,	  Barbara	
  A.	
  Whitney,	
  Yasuo	
  Fukui,	
  Suzanne	
  C.	
  Madden,	  Marilyn	
  R.	
  Meade,	  Margaret	  Meixner,	  Joana	
  M.	
  Oliveira,	
  Thomas	
  P.	
  Robitaille1,	
  Jonathan	
  P.	
  Seale,	  Bernie	  Shiao,	
  and	
  Jacco	
  Th.	
  van	
  Loon	  (イントロ)	
  • 大質量星はUVや星風で環境を変えるので、銀河の環境がMassive	  Star	  Forma)onへ与える影響を調べるにはYSOが良い。	
  • LMCとSMCが200	
  Myr前に衝突してできたBridgeがあり、潮汐系であり、また金属量も小さいという特徴を持つ	
  (Bridge:	
  1/5–1/8	
  Zo,	
  LMC:	
  1/3	  Zo)。	
  • HI,	
  H2の柱密度は大きく、CO	
  1–0で分子雲も8個同定されている。	
  
(内容)	
  
• Spitzer	
  (3.6–24µm)にSuper	
  COSMOS	
  Sky	  Surveyと2MASSの可視とNIRを使用。	
  • [8]	  vs	
  [4.5]–[8.0]のColor	
  Magnitude	
  Diagramを使って[4.5]–[8.0]>2,	
  [8.0]<14–([4.5]–[8.0])という条件でYSOを決定。	
  • さらにSEDがYSOかlate-­‐type銀河かでYSOを絞る。	
  • 26個のYSOをSEDで分類↓	
  
Type	
  I:	
  エンベロープからの放射あり。Ksより短波長で見えない。	
  Type	
  II:	
  円盤あり。可視で暗く、赤外で明るい。	
  Type	
  III:	
  ほぼ星。	
  • 中心星、ﬂared	
  disk,	
  ﬂa0ened	
  回転エンベロープ、bipolar	
  cavityを含むモデルでSEDフィット。	
  • パラメーターはM*,	
  Ltot,	
  Mdot,env,	
  Mdisk,	
  age,	
  Av	
  • Mdot,env/M*とMdisk/M*から進化段階を分類↓	  • Stage	  I:	
  >10–6	
  yr–1,	
  Stage	
  II:	
  <10–6	
  yr–1かつ>10–6,	
  Stage	
  III	
  <10–6	
  yr–1かつ<10–6	
  • 26個のYSOのうちsingleとわかった17個についてTypeとStageを比べると	
  • Type	
  I,	
  I/II	
  -­‐-­‐-­‐	
  Stage	  <1.6,	
  Type	  II,	
  II/III	  -­‐-­‐-­‐	
  Stage~2.0	
  • Type,	  Stage	
  IIIは見つからなかった	  (LMCにはいる、金属量が少ないとダスト散逸も速い)。	
  • M*は最大で10	
  MoでLMCの17–45	
  Moほど重くない。	
  • Bridgeと同じM*の範囲で可視で見える個数を比べると、Bridgeで81%,	
  LMCで56%。	
  • foregroundの減光はともにAv~3.4à分子雲のダストは同じくらいある。	
  • 星周ダストの減光のMdot,env,	
  Mdustに対する分布もBridgeとLMCで同じ。	
  àBridgeの方がclumpyだから散乱光で短波長が良く見える	
  (進化も速い)。	
  
•
•
•
•

SFEを調べるためにあるN(HI)の範囲で見つかるYSOの割合をピクセルの個数比で調べた。	
  N(HI)が大きい比εも大きい。εはN(HI)が大きい側でLMCの1/3だが、小さい側では2倍。	
  N(HI)が大きいと低金属量なので星形成の効率が下がるのだろう。	
  N(HI)が小さいと潮汐力によって星形成が誘発されるのだろう。	
  Young Massive Stars in the Magellanic Bridge

28

Chen et al.

Chen et al.

19

N(HI)マップとCOからの分子雲。	
  
	
  
CMD:	
  赤がYSO	  他は銀河や主系列星。	

Fig. 3.— [8.0] vs. [4.5]−[8.0] CMD of all sources detected in the Bridge. Expected loci from AGB stellar models (Groenewegen 2006) aremarked with filled cyan squares; only models for a stellar luminosity of 3000 L⊙ are plotted and hence these loci can shift vertically from
1.2 to −3.3 mag for the luminosity range of AGB stars. The criterion to exclude normal and AGB stars is shown in short-dashed lines andthat to exclude background galaxies in long-dashed lines. Sixty YSO candidates are found in the upper right wedge that has the minimum
contamination from stars and background galaxies. These candidates have been through detailed examination using multi-wavelength
images and SEDs. Candidates that are most likely YSOs are marked with additional red open circles and non-YSOs with green crosses.
In addition to these YSOs, the same examination procedures are carried out on 1028 sources in the corresponding lower wedge to identify
lower mass or more evolved YSOs.
that are most
likelyI)YSOs
markedmappedwith additional
magentaopen
circles.
Fig.Candidates
11.— (a) Histogramsof N(Hat 44arepositionsin CO surveysof theBridge(dotted lines; Fukui et al. in preparation) andat which eight molecular clouds are detected (solid lines; Mizuno et al. 2006). Despite the sparsity of CO observations in the Bridge, it
shows that the chance of detecting CO is larger at higher N(H I). (b) Histograms of all H I resolution elements (dotted lines) and thosecontaining YSOs (solid lines) in the Bridge.

横軸:	
  エンベロープによる減光	  縦軸:	
  Mdot,envとMdust	.— (a) Aint versus Ṁenv and (b) Aint versus Mdust of YSOs in the Bridge (filled circles). For comparison, YSOs in two LMC
mplexes (open triangles; Chen et al. 2009, 2010) are also plotted. Ṁenv and Mdust in this figure are not scaled with respective
ust ratios for the LMC and Bridge so that the comparisons among parameters are all based on dust masses. YSOs in the Bridge
imilar distribution in the inferred amount of circumstellar dust compared to in the LMC, even though the optical counterparts arequently detected in the former than the latter.

あるN(HI)を持つピクセル数と、そのN(HI)に含まれるYSOの数。	

Fig. 4.— SSS B images and SEDs of two CMD-selected YSO candidates that are most likely galaxies. The observed SEDs of these
two sources (filled circles), are not well fitted by YSO models (black and grey lines). Instead, they have SEDs similar to galaxies and areresolved into a spiral galaxy (a) or appear extended (b).

Fig. 12.— (a) Histograms of all H I resolution elements in the LMC (black dotted lines) and those containing YSOs (black solid lines,
Gruendl & Chu 2009). Similar histograms for the Bridge are shown as red dotted and solid lines. (b) ϵ as a function of N(H I) for the20−2coiled radio spirals in K
(between 0.01 and 1.0) with the points of CO 2-1 Ipeak
teresting case study sug
map for S1 (hc = 0.15) and S3 (hc = 0.27), but not forCOspiralsin the disk
Spiral	  arms	
  S2,
in	
  and
the	
  
isk	
  of	
  spiralHD	
  1with42527	
  
from	
  
CO	
  3-2
emission	  lines	  with	
  fordneither
the points
of CO
Ipeak
S1 could be fit withmap. In order to further reduce the parameter space, aALMA	
  an embedded companio
second set of fits was run fixing as well the value of hc
on the model s
ValenSn	
  ChrisSaens,	
  Simon	
  Casassus,	  SebasSan	
  Perez,	
  errit	
  darkvan	
  grayder	
  Plas	  acationnd	
  Francois	  to 0.15.
The best
fit models
are shown
in G
solid
strained. An object halines in Figure 3b and d; the inflection point in the spiral
Menard	  (2012) and re-detectedcurves represents the best fit location of the planet. The⇠12 AU. Extending S1values of the best fit rc , ✓c , and 2 are given in Table 1.
firm a possible relation(イントロ)	
  Sweepingfrom 0.15 (Perez et al. 2014) to 0.30
a gap as large as 140 A• transi)on	  d(qiskは惑星形成と関わり、非対称、warp,	
  スパイラルはcompanionの証拠。	
  = 0.6) does not significantly change 2 (relative
to the(e.g. Dodson-Robinson
spread of values for di↵erent spirals) and the value of the• HD	  142527はNIRでギャップやスパイラルが見つかっている。	
  both the relatively poo
other parameters. On the contrary, the best fit param	  (1) and (2) and their v
eters depends strongly on hc ; a di↵erence of a few huna di↵erent cause.
(内容)	
  dredths induces significantly di↵erent results, confirmSimulations in the codegeneracy
noted byCO	
  Muto• ALMA	  12CO	  ing
2-­‐1	
  the(1”x0.7”),	
  3-­‐2	  (already0.6”x0.4”)と13	
  2-­‐1	   et al. (2012)
shown that two-armed
and Boccaletti et al. (2013). Since 2 depends on the• 南側は分子雲の吸収があるので北側に注目。	
  be induced by stellar eestimated error bars, which are not independently de2001; Quillen et al. 2
スパイラルを3つ検出	  (S1はNIRでも検出されている)	
  2
4•
Christiaensal.
termined, we
usetoet comparedi↵erent models rather
Augereau & Papaloizou
2
最も外のS2では輝度温度、励起温度は11–15	
  でCOがdeple)onしていないので、
ing•S1 andS2 in the CO 3-2
Ipeak map
(Figure3c). Unr(✓), so thatobtained K
witheach equation
notthanassesstheirstatisticalsignificance.
The
best should
fit spireproduce the large sca
certainties in the measured positions of the spirals werebe mutually compared.
2
ral
appearsS2slopesanda ofS3
providedustが少ないか赤道面にある。	
  set to max{binsize, quarterof thebeam size}.toWebethenS1, while
The similar
S3 andS1 may suggestvalues
that S3 is
ral observed in the diperform least-squares fits a
to factor
each spiralof
independently
prolongating
S1. Conversely, models for S2 and S3 do notseveral times
larger.
• two温度からスケールハイトとdisk	
  asharespect	  ra)oが計算できる。	
  duction from one of its
usingdi↵erent parametric formulae, as follows.
the same
slope, even though the point-symmetricformula
by to
the
work
The polar coordinates (✓, r)Anotherof an acoustic
wave cre- suggested
of S2 with respect
the theoreticalstar roughly coincides
with ofS1
the• byradial	
  	
   disk). Tidally indu
ated
a planet, c
atut上の極大点でスパイラルを決めて、2種類のモデルでフィット	
  location(✓c , rc(2011)), on a gaseous
disk
and S3 (dasheddark gray curvein Figure3b). wake
Kim
approximates
the
shape
of
the
spiralcan be approximated by (Muto et al. 2012, and referand vanish within a fe
2.3.3. Comparison
with NIR SpiralArms to an
by an embedded planet
on a circular
orbit
ences
therein):(Muto+2012,	
  Kcreatedim	
  2011)。	
  very recent encounter o
Although S2 and S3 had•not S1は良くフィットできたが、S2とS3はでbeen detected before, a	  ✓(r) = ✓c + sgn(r rc) Archimedean spiral: spiral arm similar to S1 hadalready been reported in
the disk periodically ex
NIR H and K bands by Fukagawa
et al. (2006). Also inh
きていない。	
  ( ✓ ◆ csuch object has been d
✓ ◆ ↵
NIR,
in Ks-band (Casassus etal.
1+r(✓)closer-in= a✓observations
+b
(2)
r
1
1
r
2012), L’-band (Rameau et al. 2012), H- and K-bands⇥
Gravitational instab• 大きさも異なり、原因が違うのかも。	
  
rc
1+
1 ↵+
rc
polarimetric intensities (Canovas et al. 2013; Avenhaus
et al.r2014),
independently
tolaunching
the detection ofraspiwherewithrp•theスパイラルの原因としてエンカウント
nario able to create a✓◆ ) a corresponds to
p /Mall
p led
1
1
ral
structures
closertothestar,
originating
at
the
outer
(1) and Mp its Mach number, and b is aof the planet
structure (see e.g. Bosedge of the gap. In Figure 3 we register the contour crests
1+
1 ↵ dius+はないが、重力不安定はあり得る。	
spiralbestof Fukagawa
et al.each(2006, spiraltheir Figure
2),
constant. Parametersfrom
forthethe
fit ofarecharacterized by Toom
where hc is the disk aspect ratio at radius rc . It is as-

as well as2the most prominent spiral feature from Casas-

ピーク図ではスパイラルがわかるが、速度と速度分散ではわからない。	

Spiral arms in the disk of HD 142527

5

Figure 1. Moment maps for CO 2-1 and CO 3-2. Respective beam sizes are 0.96⇥0.72 and 0.63⇥0.40 arcsec2 . North is up and east is to
he left. x and y axis indicate angular o↵set from the star along R.A. and Dec. from the position of the star. A continuum contour at
80 mJy beam 1 (half-maximum, from Casassus et al. 2013b) is overplotted in light gray. Velocity-integrated intensity maps: a and e. For
CO 2-1 and CO 3-2, the 1 noise levels are respectively 14 and 17 mJy beam 1 ; and the color scales are both normalized to 20 . The 3
ontour is shown in white. Peak-intensity maps: b and f. With Ipeak maps, the mean of the noise is non-null; it equals respectively 27 and2 mJy beam 1 for CO 2-1 and CO 3-2. The 1 values are respectively 11 and 15 mJy beam 1 ; and the color scales are both normalizedo 40 . The relevant contour, mean(noise)+3 , is shown in white. Velocity centroid: c and g. Velocity dispersion: d and h.

スパイラルを決めた点とベストフィットモデル	

Figure 2. CO 2-1 Ipeak maps: unsmoothed (a), smoothed using two (b) and smoothed using four (c) shifted datacubes. Legends followrom
Figure1b. Theofrestof theobserved
paperinimplicitly
shows
Ipeak
smoothed
four1bshifted
datacubes.
Figure3. Modellingthe spirals
the CO 2-1 andCO 3-2
Ipeak maps
maps. Legends
followusingfrom Figureand f . For
comparison,