Star	  Forma)on	
  Newsle0er	
  #266	
  1-­‐5本目	
麻生 有佑	

Forma)on	
  of	
  prestellar	
  cores	
  via	
  non-­‐isothermal	
  gas	
  fragmenta)on	
  Formationof prestellar cores via
non-isothermal gas fragmentation
3
S.	
  Anathpindika	  (2015)	
Table 1 Physical parameters for the two cases.

!
" !
" !
• 分子雲中でのコアの形成過程を
Serial n̄
n̄
gas

a

2.5×1022.5×1022.5×102

1
2
3

icm

Tgas
[K]

Ticm
[K]

125
125
125

40
100
150

131
328
491

Ptherm
kB

b

1.0
2.5
3.75

Pgrav
kB

Pext
kB

"

h0 c
[pc]

0.63662
1.592
2.388

1.63662
4.092
6.138

0.572
0.905
1.108

d
Ntot
×105

6.4
7.21
7.61

havg e[pc]

Mgas f
MJeans

0.044
0.052
0.055

1.4
0.6
0.36

a Number density for gas and the ICM listed in columns 2 & 3 in units of [cm−3 ].

b Components of pressure listed in columns 6, 7 & 8 in units of 104 ×[K cm−3 ].
c Scale-height for the slab

d Total number of particles including those representing the ICM.
e Average smoothing length for gas particles.
fM

J eans is the thermal Jeans mass calculated for the initial gas temperature, Tgas .

Formation of prestellar cores via non-isothermal gas fragmentation

Pext

ICM

Pext

Pext

R
y
SLAB
Pext

The slab was characterised by radius, R = 2.5 pc,
uniform initial number density, n̄ = 250Table
cm−31, Physicalgas tem-parameters for the two cases.
! scale!
" !
"perature, Tgas , anda thickness, y =
the
b"
Pgrav
Tgas2h0 ,Twhere
Pext
h0 c
Pthermicm
Serialn̄icm
gas slab has[K] below.kB
kB
kB
[pc]
height,h0 , forn̄thebeen [K]calculated
Val2
2.5×10125parameters40
131
1.0 listed
0.63662 1.63662 0.572
ues of1the relevant
physicalhave been
2 1. For
2.5×10
100
328
2.5
1.592
4.092
0.905
in Tablea slab2 in 125
pressureequilibrium,
the pres125
491 the3.75
2.388
6.138
1.108
sure 3exerted 2.5×10
by the 2ICM
, Pext ,150
balancesthermalpressure, Ptherm , and the gravitational pressure, Pgrav ,a Numberwithinthedensity
slab soforthat
gas and the ICM listed in columns 2 & 3 in units of [cm−3 ].

3

d
Ntot
×105

6.4
7.21
7.61

havg e[pc]

Mgas f
MJeans

0.044
0.052
0.055

1.4
0.6
0.36

b Components of pressure listed in columns 6, 7 & 8 in units of 104 ×[K cm−3 ].

P

Figure 1. A sketch of the gas-slab of radius, R, and height, y,confined by the ICM has been shown in this cartoon. The small
ICM exerts pressure, pext , externally on all faces of the slab asdemonstrated by the direction of arrows.

2 Initial conditions
The set-up for our simulations is simple and consists ofa uniform-density slab that is marginally gravitationally super-critical in case 1 (slab mass approximately
1.4 times the initial thermal Jeans mass), and gravitationally sub-critical (slab mass only a fraction of
the initial thermal Jeans mass) in the remaining twocases (see Table 1). The slab is circular with radius,R, and is in pressure-equilibrium with the inter-cloud
medium (ICM), that confines it. Note that particles
in the slab and the ICM were so distributed that the
number-density of particles across the slab-ICM inter-=P+ Pgrav = Pint + GΣ2g

c Scale-heightext
for the int
slab

(1)

d Total number of particles including those representing the ICM.

(e.g. Whitworth et al. 1994), where the gas surfacefM
thermalJeans
masscalculated forTthe
gas temperature, Tgas .
J eansΣisdensity,= n̄µhgas
temperature,correg the
0 . Thegas ,initial
sponds to sound-speed a, so that the scale height forathe slab, h0 = √2πGn̄µ(Ledoux 1951; Lubow & Pringle
The slab was characterised by radius, R = 2.5 pc,
2001). The length of the fastestPext
growing mode
uniform initial number density, n̄ = 250 cm−3 , gas temICM in a cooling medium
perature, Tgas , and thickness, y = 2h0 , where the scalePext is,
Pextheight, h0 , for the slab has been calculated below. Val! γ πa2 "1/2e
λf ast =(2)
ues of the relevant physical parameters have been listed
γGµn̄ Rin Table 1. For a slab in pressure equilibrium, the presy polysure exerted by the ICM, Pext , balances the thermal(Vázquez-Semadeni et al. 1996); γe , is the eﬀective
SLAB curve shown intropic exponent, i.e. slope of the coolingpressure, Ptherm , and the gravitational pressure, Pgrav ,within the slab so that
Fig. 2, which for our choiceof the initial gas density, n̄,Pextturns out to be ∼ 0.9 where as, γ = 5/3, is the adiaPext = Pint + Pgrav = Pint + GΣ2g
(1)
batic
gas constant. The equilibrium pressure at density,
Figure 1. A sketch of the gas-slab of radius, R, and −3
height, y,n̄,confinedaccordingto ICMthe cooling
7500
K cm The. We
by thehas been curve
shown isin thiscartoon.
small(e.g. Whitworth et al. 1994), where the gas surfaceperform
three
realisations
with diﬀerent
choiceofslabtheas
ICM exerts
pressure,
pext , externallyon all facesof thedensity, Σg = n̄µh0 . The gas temperature, Tgas , corredemonstrated
by the directionof arrows. thermal pressure,initialgas temperature,and therefore,
sponds to sound-speed a, so that the scale height fore Average smoothing length for gas particles.

Forma)on	
  of	
  prestellar	
  cores	
  via	
  non-­‐isothermal	
  gas	
  fragmenta)on	
  S.	
  Anathpindika	  (2015)続き	
TIとGIの成長率を調べた。ωとkの分散関係。	
  初期に重力的にsuperなcase	
  1ではGIが発達。	
  速度、密度の分布やMss-­‐size関係も調べている。	
  
	
  
	
  
・・・	
  
	
  
	
  
	
  
	
  
まとめると、	
  
分子雲は安定で低温、安定で高温、不安定な3つが混ざっている。	
  フラグメントは熱的不安定で始まりフィラメントができ、質量降着や合体で重力不安定を起こしてコアができる。	
  これらの不安定性によって、dense	
  coreなどでよく観測されるような弱い速度場が得られる。	
  
16

[
3

2.5

log10(ω/[Myr-1])

2

1.5

1

(TI)t=0.01 Myr(GI)t=0.01 Myr(TI)t=2.2 Myr(GI)t=2.2 Myr(TI)t=4.1 Myr(GI)t=4.1 Myr

0.5

0

20

40

60

80
k/[pc-1]

100

2.2

120

140

(TI)t=0.01 Myr(GI)t=0.01 Myr(TI)t=2.21 Myrs
(GI)t=2.21 Myrs
(TI)t=6.1 Myrs
(GI)t=6.1 Myrs

2

ω/[Myr-1]

1.8

1.6

1.4

1.2

1

0.8

20

40

60

80
k/[pc-1]

100

3

120

140

(TI)t=0.01 Myr(GI)t=0.01 Myr(TI) t=4.51 Myrs
(GI) t=4.51 Myrs

2.8
2.6
2.4
log10(ω/[Myr-1])

Schmidt, W., Kern, S.A.W., Federrath, C & Klessen, R.,
2010, A&A, 516, 25
Schneider, N., Bontemps, S., Simon, R., Ossenkopf, V., Federrath, C., Klessen, R. S., Motte, F., André, Ph., Stutjki,
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Schneider, N., Csengeri, T., Hennemann, M., Motte, F.,
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Schneider, N., André, Ph., Könyves, V., Bontemps, S.,
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Tohline, J., Bodenheimer, P & Christodoulou, D., 1987,
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Truelove, J. K., Klein, R. I., McKee, C. F., Holliman, J.,
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Anathpindika, S

2.2
2
1.8
1.6
1.4
1.2
1

20

40

60

80
k/[pc-1]

100

120

140

number in a MC could possibly influence filament propboundary particles that prevent SPH particles fr
erties, we leave this aspect of the problem for future
caping. Unlike the gas and the ICM particles, theinvestigation. Other free parameters in the set-up were,ary particles are dead and do not contribute t
Stability	
  of	
  ﬁlaments	
  in	
  star-­‐forming	
  clouds	
  and	  the	
  forma)on	  of	
  prestellar	
  cores	
  in	
  them	  the length of the cylinder, L= 5 pc, contrast, D=10,
forces. The layer of dead boundary particles wa
S.	
  Anathpindika	  and	  J.	
  Freundlich	  2015)	
betweenthe initial gas(density
within the cylinder andto simply hold the gas+ICM particles in the bits surrounding medium, the average initial gas density
prevent them from diﬀusing away. Particles wit
within the cylinder, n̄gas = 600 cm−3 and the initial
set-up were initially stationary as no external v
フィラメントの力学的安定性を他の論文より現実的に調べる。	
  mass line-density, (Ml )init . This choice of gas density
field was introduced.
isalso
consistentwithdensities
found
in
a
typicalstar(i) 等温一様密度ではなくcooling	
  func)onも含めたエネルギー方程式を解く。	
  forming cloud (e.g. André et al. 2013). The temperature(ii) 初めから動的ではなく、圧力平衡	
  
3.2 Numerical method : Smoothed Particof the confining medium is calculated by using the conHydrodynamics (SPH)
dition of pressure-balance at the surface of the cylinder.
(iii) 重力的にsupercri)calな必要があるか調べる。	
  The initial radius of the cylinder was calculated using
Simulations were performed using our well teste• 初期条件は、重力収縮せず一様密度で周囲と圧力平行にある筒。	
  Eqn. (4) above. Though simple, this set of initial condialgorithm, SEREN, in its conservative energy
tions is suitable for the extant purposes of studying the• 筒は半径方向に収縮し、軸上にジーンズ長間隔でコア(105cm-­‐3)ができる。	
  (Hubber et al. 2011). The SPH calculations in th
origin of the density profile and the temperature produe to the artificial c
Stability of filaments in star-forming clouds
and the formation of prestellar cores in also
them includepcontributions• R~0.1	
  pcになり、密度分布はOstriker	  1964)と合う。(Plummer-­‐like;	
  
=2)	
  9
file of a typical filament and (theformation of presteltivity prescribed by Price (2008), to avoid any sp
lar cores along cthe
length ofS(r)で評価。	
  this filament. Parameters• 重力的な安定性をSturges	
  riterion	
  numerical artefacts possible due to the creatio
used in the realisations performed in this work havegap between multi-phase fluids. An SPH particle,
àずっとsub-­‐cri)cal	
  beenS(r<R)<1で自由落下していない。	
  listed in Table 1. Sinusoidal density perturbations
work, had a fixed number of neighbours, Nneibs
alongthe length
ofcoresthein theminitial distribution9 of gas were
Stabilityof filaments in star-forming clouds andthe formationof prestellar
温度も一様ではない。	
Gas cooling was implemented by employing theimposed in five simulations; see Table 1. These perturfunction given by the equation below,
bations were imposed by revising particle positions, xp ,! −1.184 × 105 "Λ(Tgas )to x′p , such that the following expression was satisfied,= 107 exp+
ΓCR
Tgas + 1000
ALJeans
xp = x′p +sin(kx′p )2π! −92 "#
cm3
1.4 × 10−2 Tgas
(Hubber et al. 2006), where the wave-number, k =TgasnπLJeans , the integer, n = 1, 2 for respectively, the funda(Koyama & Inutsuka 2002). Constant backgroun
mental mode and the second harmonic; A = 0.1, is theing due to cosmic rays is provided by the heatin
amplitude of perturbations.
Figure 5. As in the plot shown in Fig. 1, this is the radial disFigure 8. Same as the plot in Fig. 3, but now for the cores thattion, ΓCR = 2 × 10−26 erg s−1 . The temperatur
The numberof gas filament
particlesin 2.a simulation are caltribution of gas density within the collapsing filament at diﬀerent
form in the post-collapse
in realisation
epochs in realisation 2.
SPH particle is calculated by revising its interculated according to ergy. The equilibrium temperature, Teq , attaine
distribution of gas density within the collapsing cylin"
drical cloud which,that
3 remarkably !similarVto
1 thoughinit
small
SPH particle corresponds to equilibrium· Nneibs· is3relatively ,Ngas= 2 for· the isothermal
shown
in Fig.
filament,
8
4πhshallow (Plummer-like; p = 2 in Eqn. (11)). avg(init)
The radial
ueq , and the timescale, τ , over which energy is
100000t=0.002 Myr
t=0.1 Myrt=0.2 Myrt=0.3 Myrt=0.4 Myrt=0.5 Myrn/[cm-3]

10000

1000002

t=0.002 Myr
t=0.1 Myrt=0.2 Myrt=0.3 Myrt=0.4 Myrt=0.5 Myr
t=0.6 Myrt=0.8 Myr
p=2

1000
1.8

1.6
1.4

n/[cm-3]

Mcore/[MSun]

10000

1000

1.2
100
0.01
1

0.1
r/[pc]

1

0.8
0.6
0.4
0.2

100
0.01

0.1
r/[pc]

1

0
0.5

0.55

0.6

0.65

0.7
0.75
t/[Myr]

0.8

0.85

0.9

0.95

1

0.8

variation of the stability factor, S(r), within the collaps-

S(r)

0.6

ing cylinder for this realisation has been shown in Fig. 6.
PASA (2015)

This plot is qualitatively similar to the one produced forFigure 14. Radial distribution of the density averaged gas temperature within the post-collapse globule in realisation 8 at thetime of termination of calculations (t = 2.5 Myrs).

Stability	
  of	
  ﬁlaments	
  in	
  star-­‐forming	
  clouds	
  and	  the	
  forma)on	
  of	
  prestellar	
  cores	
  in	
  them	
  S.	
  Anathpindika	  and	  J.	
  Freundlich	
  (2015)	
• ガスの温度を上げて初期にsub-­‐cri)calな場合も調べた。	
  à細くなるのではなく押しつぶされた。	
  • 高密度フィラメントを作るためには少なくともcri)cally	
  stable	
  (S(R)~>1)でなければならない。	
  • S(R)~1の状態は10	
  Kの等温一様密度を仮定すると重力的にsuper-­‐cri)calに見える。	
  • 自由落下していなくても軸上にコアはできる。	
  • フィラメントで観測されるPlummer密度分布は地場なしでも作れる。	
  • 解析的にもPlummer密度分布から自由落下しないとわかる。	
  • 観測的にもフィラメントで自由落下でないインフォールを示すフィラメントの例がある(DR21,	
  Perseus	
  MC,	
  Serpens	  MC)。	
  • 自由落下でないとすると、極端に強い減光を示すフィラメントがないことや、フィラメン
トの幅がどの領域でも同じことを説明できる。	

Mopra	  CO	
  Observa)ons	
  of	
  the	
  Bubble	
  HII	
  Region	
  RCW120	
  Loren	  Anderson	
  et	
  al.	  (2015)	
••••

よく知られたHII	
  regionの円状バブル構造は一様膨張を示す。	
  しかし、球殻では説明できず<10	
  pcの薄いシート内でできた2次元のリングとするものも。	
  バブルの幾何は誘発的星形成の理解にとって重要(2Dリングではあまりできない)。	
  – 28 –RCW	
  120	  (d=1.3	
  kpc)は20のClass	
  I/IIを含むがバブル(D=3.8	
  pc)の中心に2個しかないà2Dリングか?	
  • Mopraで12CO,	
  13CO,	
  C17O,	
  C18O。速度分解能は0.7	
  km/s。	
  • Hαで見える吸収は手前にあるはずで、球状膨張していれば青方偏移しているはず。	
  • 吸収部(Absorp)on)、吸収なし(No	  Absorp)on)、両方(Interior)、PDRでスペクトルを比較。	
  – 22 –

Fig. 1.— H↵ emission of RCW 120 from SuperCosmos (Parker et al. 2005). The map covers
the same area as our Mopra observations, and is 200 square, centered at (`, b) = (348.282 ,0.498 ), and oriented in Galactic coordinates. The north and west directions are indicated.
The location of the ionizing source (from Martins et al. 2010) is identified with a small green
cross and the location of “Condensation 1” is identified with a green circle. Absorption↑Hαで黒く吸収が見える。	

Mopra	  CO	
  Observa)ons	
  of	
  the	
  Bubble	
  HII	
  Region	
  RCW120	
  Loren	  Anderson	
  et	
  al.	  (2015)続き	à❌4つとも似ていた(-­‐10	
  km/sの凹みはセンスとしては逆)。	
  • チャネルマップでは、blueからredで内側、PDR、内側と明るいはず。à❌	
  • moment	
  2で内側ほど速度分散が大きいはずà❌	  • PV図で環状に見えるはずà❌	  • しかし、吸収が見えるので2Dではないはずで、速度分解能が足りないのだろう。	
  • Stromgren半径を用いた球殻膨張の解析解。膨張速度は~1.2-­‐2.3	
  km/s。	
  • 乱流速度1.5	
  km/s、膨張速度1.0	
  km/sのモデルが合う(1.5	
  km/sでは合わない)。	
  – 29 –– 31 –– 30 –

pectra from the four apertures defined in the text and in Figure 7. So thecan be better seen, we normalized all spectra to a peak corrected antennaTA⇤ , of 1 K.

Mopra	  CO	
  Observa)ons	
  of	
  the	
  Bubble	
  HII	
  Region	
  RCW120	
  Loren	  Anderson	
  et	
  al.	  (2015)続き	
• 8.0	
  µmで見るとPDRの外にダスト温度がエンハンスされた場所がいくつもある。	
  • 東西のエンハンスは-­‐8.9	
  km/s	  (青コントア)のCOの隙間に、南は-­‐6.0	
  km/s	  (赤コントア)のCOのクランプの間にある。	
  • 北東に開いている部分も-­‐6	
  km/s	  (赤コントア)のCOがないところに合う。	
  • 北東も含め、バブルは多孔質になっていて光子が漏れている。(Anderson	
  et	
  al.	  2010の確認)。	

g. 14.— (Left) Dust temperature map of RCW 120 derived from Herschel data, showg temperature enhancements outside the PDR. Red contours show 13 CO emission a
6.0 km s 1 (antenna temperature values of 1.4 and 2.0 K), while blue contours show 13 CO

down to V ≃ 12.6 .

2 Observations
and results
Resolved	
  photometry	
  of	
  the	
  binary	  components	
  of	
  RW	
  Aur	  S.	
  An)pin	  et	
  al.	  of(2015)	
Multicolor
imaging
RW Aur was performed on November 13/14, 2014 with a newly
installed 2.5 meter telescope (Fequiv = 20 m) of the Caucasus observatory of Lomonosov
Moscow State University at the mount Shatzhatmaz1 in course of test precommissioning
observations aimed at checking the image quality provided by the instrument. The telescope was equipped with a mosaic CCD camera manufactured by Niels Bohr Institutebased on two E2V CCD44-82 detectors (pixel size 15 µm) and a set of standard Bessel
UBV Rc Ic filters from Asahi Spectra Co.
In course of observations the image quality with FWHM between 0.5 and 0.7 arcsec
was routinely obtained confirming the excellent optics quality of the instrument, deliveredby the REOSC company of Safran group, France (Poutriquet et al. 2012). The binary was
clearly resolved (see Fig. 1): the wings of a brighter component image contribute < 7 %to the central intensity of a fainter component in all bands. This time of year at the site
is known to be characteristic of exceptionally stable atmospheric turbulence conditions(Kornilov et al. 2014), so this result was not unexpected. The exposure time varied from
5 sec in the Ic band to 300 sec in the U band, the middle date of measurements is JD
2456975.56.

Forma)on	
  of	
  complex	
  organic	
  molecules	
  in	
  cold	  objects:	
  the	
  role	  of	
  gas	
  phase	  reac)ons	
  Nadia	  Balucani,	
  Cecilla	
  Ceccarelii	  and	
  Vianney	
  Taquest	  (2015)	

2

Balucani et al.

4Balucani et al.