Star	  Forma)on	
  Newsle0er	
  #272	
  6-­‐10本目 	
麻生 有佑	

Filaments	
  in	
  the	
  Lupus	
  molecular	
  clouds	
  M.	
  Benede(ni	
  et	
  al.	  (2015)	

Øetフィラメントは大・小質量で広く見られ、Hershelが高密度コアとの相互作用を解明。	
  edettinial.

Number of branches

磁場との角度	00

t kinematics

50
100
150
Branch direction (degree)

Number of filaments

0remain unclear. The far-infrared Herschel maps are a pow0.1
1.0
10.0
erful dataset forthis kindspineof study
since(pc)in these maps both
Filament
lengthfilaments and compact dense cores from which stars formcan
20 be easily identified. In particular, the Herschel compact
sources represent dusty dense cores that can have di↵erent
15
natures,
indeed they can be young stars still embedded intheir parental envelope, cores without an internal source but
10 enough to eventually form a star, or unbound cores
densethat may eventually dissipate. The presence of a protostar
5 internally accretes from the dense core can be revealed
thatby emission at wavelengths shorter than 100 µm that devi0
ates fromthe grey-body spectralenergy distribution typical
1020
1021
1022
of the emission at longer wavelengths. Therefore, -2
a detection
Average filament column density (cm )in the PACS 70 µm map can be used to identify the proto200
stars. The further distinction among the starless cores of the
Figure 8. Distribution of the deconvolved width of the filaments
gravitationally bound structures that are potential sites of

Number of filaments

umn density regime is not only valid for the
red in70filaments but is a property also of the
Lupus 1
Lupus 3as testified
by the probability distribution
60
Lupus 4s (see Sect. 4 for a further discussion).
50 that, in the three clouds both thenotingedian values of the analysed filament param40
milar (see Fig. 8). This result is in agreement
ved similarityof the overall star formation30
he three subregions of the Lupus complex.
20 allows us to sum together the filaformity
rom the10 three regions, in order to improveelevance of the subsequent analysis.

Number of filamentsØ Lupusは150-­‐200	
  pcで、フィラメントがはっきりしていて、OB	
  associa)onがある。	
  20
Ø Herschel	
  Gould	  Belt	  SurveyでLupus	
  
1,	
  3,	
  4の70,	  160,	
  250,	
  350,	
  500	
  umを取得。	
  15
Ø 加えて、Mopra, CS	
  (2-­‐1),	
  HPBW=35”,	
  ΔV=0.1	
  km/s,	
  σ=0.4	
  K	
  10tして36”分解能で柱密度マップを作成。	
  Ø 70	
  um以外のSEDをgrey-­‐body	
  ﬁØ 柱密度マップのヘッセ行列(∂i∂j5f)の固有値が、2.8σ以上でフィラメント。	
  Ø フィラメントの柱密度はPlummer-­‐like関数でp=1.8	
  (cf.	
  磁場なしp=4)。	
  
0
0.01
0.10
1.00
Ø 柱密度が小さく、ac)veなAquilaなどよりもnon-­‐star-­‐formingなPolarisに近い。	
  y, comparing
the filaments in the Lupus comFilament deconvolved width (pc)f other molecular clouds (Arzoumanian et al.
20Ø CSはLupus	
  1,	
  3の高密度領域で検出され、収縮を示す速度勾配は見られなかった。	
  he Galactic plane (Schisano et al. 2014), theLupus 1
15
Lupus 3have thetypicalwidthbutashorterlengthØ フィラメントと磁場は平行か垂直が多いà磁場がフィラメントの形成維持に寄与。	
  Lupus 4
rtantly, a low column density. Approximat10
Ø with星なしコアはほぼフィラメントの中心にあるが、コアを含まない低柱密度フィラメントも
filaments
a cylinder, a fixed observed
5
all column
density
imply
M. Benedettini
etalsoal. a small averageあるà高柱密度に育つはず。	
of the material arranged in filaments. In Lu-

owever, the di↵use background is negligiblen Fig. 7, indeed practically all the dense maextinctions larger than 2 mag is arranged inpart of filaments lying in regions of very low
at Av < 2 mag, especially in Lupus 1 andand 3). Considering the low contribution ofnts, we estimate an uncertainty on the deaments column density of at most a factor

柱密度プロファイル	Filaments	
  in	
  the	
  Lupus	
  molecular	
  clouds	  柱密度プロファイル	11

Filaments in the Lupus molecular cloudsM.	
  Benede(ni	
  et	
  al.	  (2015)の続き	

100

Table 3. Parameters of the PDF fitting. For the log-normal function: the column density at the peak <N >, the width and the
maximum M ; for the power law tail: the exponent s.

all pixels
on-filaments pixels
off-filaments pixels

Ø Lupus	
  1の柱密度が他より小さい側が多いのは、Upper-­‐
Scorpiusの超新星爆発に掃かれたから。	
  Ø 高柱密度はフィラメント上に集中していて、power	
  law	  
à重力収縮	  et al. 2011; Schneider et al. 2013, 2015; Alves de Oliveira etØ 高柱密度領域はクランプ状で、半径分布の冪が急で、al. 2014; Tremblin et al. 2014; Könyves et al. 2015).
Comparing the PDF of the three clouds, it is evident
that the PDF of Lupus 1 extends to much lower column
ﬁlamentary	
  collapseよりclumpy	
  collapseを示す。	
  density, and has a peak at a value lower of about a factorof two compared to the other two clouds. This characterisØ 高柱密度側が少なく、確かにLupusはmid	  Mthe型星が中心で他のtic is partially due tofact that in Lupus 1 we mapped
not only the denser part of the cloud but also a large areaof its more di↵use surrounding medium. Indeed, about the
領域より小さい星が多い。	
  75 per cent of the field is composed of pixels at very low
column density (A < 1 mag), while it is not the case forØ 単位長さ当たりの質量を測ると、大部分がサブクリティカル。しthe other two clouds. The very low column density of thedi↵use material around Lupus 1 can be related to its pecuかし、星形成は起きており、Bonnor	
  Ebert質量を超えるコアがliar position.
This cloud is at the edge of an HI shell left
over from a supernova event in Upper–Scorpius. The dynamics of HI and CO toward Lupus 1 are consistent with
サブクリティカルフィラメントにある	
  the molecular cloud being compressed by the HI shell (deGeus 1992; Tothill et al. 2009). This scenario is supportedà局所的な重力不安定	  by the morphology of the dense gas shown by the Herschelcolumn density map, with the gas at A > 1 mag confinedin the Lupus molecular clouds
in a thin layer parallel to the edge of the HI shell (see FilamentsFig.
Ø 非熱的線幅からMline/Mline,vir<<1でトロイダル磁場が必要。	
  1) surrounded by the very low density medium swept by thewind of the supernova. On the other hand, Lupus 3 and 4
Ø フィラメント形成には自己重力より磁場が効くだろう。	
  are further from the ridge of the shell and their dense mate2)

Ms

Lupus 1
5.1⇥1020
0.23
0.16
-2.4

Lupus 39.7⇥1020
0.17
0.23
-2.4

10-2

Lupus 48.2⇥1020
0.14
0.26
-2.6

Probability<N (H2 )>(cm

10-1

10-3
10-4
10-5

10-6
1019

1020
1021
1022
N(H2) Column Density [cm-2]

1023

100

10-1

all pixels
on-filaments pixels
off-filaments pixels

Probability

10-2

v

10-3
10-4
10-5

10-6
1019

1020
1021
1022
N(H2) Column Density [cm-2]

1023

0

10

v

-1

10

all pixels
on-filaments pixels
off-filaments pixels

13

Probability

10-2

線密度	

rial is more distributed. The cloud morphology revealed by
10.0
10-3
the Herschel column density maps once again indicates therole of the Scorpius–Centaurus OB association in the star
10-4
formation history of the Lupus complex.
A peculiarity of the PDFs of the Lupus clouds is that100
10-5
the values of the peak and the maximum of the column densities are systematically lower than those found in active
10-6
regions such as Orion and Aquila, and appear to be much
1.0
1019
1020
1021
1022
1023
more similar to the values found in Chamaeleon and PoN(H2) Column Density [cm-2]
50
laris (Schneider et al. 2013; Schneider et al. 2015; Alves deFigure 13. PDF of the Lupus 1, 3 and 4 clouds. The black hisOliveira et al. 2014), regions with low or null star formation
togram represents the distribution of all the pixels of the map, theactivity. Remarkably, in the Lupus clouds the peak of thered, dashed histogram the distribution of the pixels belonging to
PDFs is at H2 column density equivalent to visual extincfilaments excluding pixels around dense cores and the blue dottedtion less than 1 mag, the lowest value found so far in the0histogram the distribution of the pixels not belonging to filaments
PDF analysis
density maps of star
forming regions
0.1
1.0 of column10.0
100.0
0.1excluding pixels around dense cores. The log-normal and power-1 at visual extincbased on Herschel data, that usually peak
100
1000
Branch mass per unit length (Msun pc )law fit to the PDFs are also shown as continuous blacklines.
tion larger than 1.5 mag. These low values of the H2 column

Flux (Jy)

Number of branches

150

Hierarchical	
  fragmenta)on	
  and	  collapse	
  signatures	
  in	
  a	
  high-­‐mass	
  starless	
  region	
  H.	
  Beuther	
  et	
  al.	  (2015)	

Ø 大質量星形成の初期条件は、大質量星なしコアか、星なしコア段階はないほど急速かもわかっていない。	
  18310-4. The
bottom-left and middle panels show in color the HerschelBeutheral. 2013b, linear and log stretch for clarity, respectively). TheØet分裂の仕方、ガスの運動、ビリアル比、乱流フローの存在などがこの分野の興味。	
  BO continuum observations starting from 4σ and continuing in 1σ stepsØ ジーンズ長(<0.1	  pc)を分解した観測が必要。	
  ottom-middle panels presents the 3 mm continuum data from Beuther et al.
+
H. Beuther
et al.: Hierarchical H
fragmentationand collapse signaturesmm	
  (0.6”x0.49”)とN
with a Ø
1σ 4.9	  valuekpcにあるIRDC	  of 0.08 mJy beam1−18310-­‐4の1.07	
  . The bottom-right
panel
then
shows
2 (3-­‐2)	
  (1.13”x0.5”)をPDBIで。	
  3σ and continuing in 1σ steps with a 1σ value of 0.6 mJy beam−1 . The
図は70	
  
um,	
  1.2	
  mmの単一鏡と3.2	
  mと1.07	  mm thewith thesame contour
levelsbut a diﬀerent color m
stretchto highlightのPdBI。54000	
  AUから2700	
  AUスケール。	
  rresponding
synthesized beams.
The 70 µm
PSF is 5.6′′ .

単一鏡の4つのコアがさらに分解された。	
  rM andTable 2. Projected nearest neighbor separations
(”)

(AU)

3mm data
mm1–mm2
2.9 14200
mm1–mm3
7.1 34900
1mm data
mm1a–mm1b 0.94400
mm2a–mm2b 0.5
2600
mm2a–mm2c 0.7
3500
mm2b–mm2c 1.1
5500
mm3a–mm3b 1.5
7600
mm3a–mm3c 2.5 12000
mm3b–mm3c 2.4 11900
Uncertainties are ≈0.1′′ or ≈490 AU.

Hierarchical	
  fragmenta)on	
  and	  collapse	
  signatures	
  in	
  a	
  high-­‐mass	
  starless	
  region	  H. Beuther et al.: Hierarchical fragmentation and collapse signatures

H.	
  Beuther	
  et	
  al.	  (2015)の続き	

Ø Herschelで見るとmm2に付随する成分が見られ、波長でピークがずれている。	
  Ø L~16	
  Lo,	
  Tdust~15	
  Kと推定され、大質量星はできてないと考えられる Fig. 2. Re-calibrated Herschel PACS images at 70, 100 and 160 µm (from left to right). The scaling in the three panels is from -3.8
to 4.0, from 5.0 to 17.6, and from 33 to 45 mJy pixel , respectively. The 3.2 mm continuum contours are from 3σ and continuing in(Mgas~800	
  Mo)。	
  2σ steps with a 1σ value of 0.08 mJy beam . A scale-bar and the 3.2 mm synthesized beam are shown in each panel, and the threemain sources are labeled in the bottom-left panel. The 70, 100, and 160 µm PSFs are 5.6 , 6.8 and 11.3 , respectively.
Ø この小さなLは原始星よりも大きな面への質量降着で説明されるので、70umで見えるof the extended 70 µm emission of the hosting molecular cloud sion peak is more than 4 . Although this is less than the beam
(Figures 1 & 2). Although the extinction contrast decreases at of the 70 µm image, as mentioned in §3.1, source peak positions
mm2もやはり初期、星形成開始直後の段階にある。	
  100 µm, we still perceive the central parts as an infrared dark can be determined to much higher accuracy than the nominal
cloud (IRDC). At 160 µm, the extended emission in the sur- spatial resolution φ (down to). Hence, we think that there
roundings is not so dominating anymore, and emission structures is a real shift in peak positions when going to longer wave	
  emerge from the inside of the IRDC.
lengths. This may be explainable by the combined action of two
eﬀects.
5–3
6–3。	
  First, the 160 µm data trace colder dust expected in the
At the north-westernborderof と1.5x10
the IRDC silhouette, wenoØ 単一鏡と3	
  mmから平均密度を出すと2.5x10
	
  
c
m
	
  
c
m
deeperinterior of the IRDC, compared to the 70 µm wavelength
tice a faint emission point source at 70 µm which also persists range. Second, the 160 µm beam is around 11. 3. It thus conat 100 µm. In the previous data reduction products we used in volves emission from larger areas, and therefore may comprise
T=15	
  KでλJ=1000	
  AU,	
  4000	
  AU,	
  MJ=0.37	
  M(2012)
o,	
  and
0.15	
  
Ragan et al.
Beuther M
et al.o	
  (2013a), this source was emission from mm1 (dominating) and mm2 (minor contribunot that apparent. We attribute the diﬀerences to the use of tion), while the finer 70 µm beam of 5. 6 can still distinguish
the newest
Scanamorphos
algorithms and the inclusion of the AØ 観測は3.2	
  mmの距離が数10000	
  AU,	
  1.07	
  mmの距離が~5000	
  U	
  (mm2
Table	  )。	
  between(associated2
with70 µm emission at its north-west
gyro-correction information (Sect. 2.2) in the current data re- side) and mm1 (without noticeable 70 µm emission).
duction. In order to determine accurate positions, we referencedà古典的な熱的ジーンズ分裂	  the PACS maps with the Spitzer/MIPSGAL (Carey et al., 2009)24 µm data. We did not use individual MIPSGAL maps for refer- Table 3. Far-infrared fluxes of mm2
ence, but relied on the recently released MIPSGAL 24 µm pointØ 質量は3.2	
  mmで18,	
  36	
  Mo、1.07	
  mmで2.2,	
  
13.7	
  &M
oなのでM
source catalogue (Gutermuth
Heyer,
2015). Corresponding
Jとは桁で違う。	
  positions in the PACS maps were determined by employing PSF
photometry using IDL/Starfinder (Diolaiti et al., 2000). The necØ 乱流線幅でMJを出せば増えるが、観測された線幅はmm1aで<0.3	
  km/s。	
  essary adjustments were shifts on the order of 1.1–1.6 . For
the previous Herschel data products (with uncorrected pointØ 密度分布を冪にすると質量は最大20倍増え、距離も増えるはず。	
  ing) we had to use a shift of almost 4 (Beuther et al., 2013a).
This supports predictions that the absolute pointing error of
Herschel data can be brought down to a level of ∼0. 9 1σ ifØ N2H+	  (1-­‐0)は線幅は狭く、それぞれのコアに複数成分あり、ガスの収縮と思われる。ビ
all the recent corrections for the pointing product are applied(Sánchez-Portal et al., 2014). This 70 µm point source is thus located very close to mm2. Interestingly, the compact emission
リアル質量も小さい。à乱流は小さく、収縮しているのだろう。	
  seen at 160 µm is shifted towards the center of the IRDC andHence, the PACS data show tentatively that at least object
−1

−1

′′

′′

′′

′′

φ
S /N

′′

′′

′′

′′

′′

basically coincides with the mm1 location (Fig. 2). The uncertainties of the peak positions are on the order of 1′′ for 70

λ
S
(µm)
(mJy)
70
90
100
357
1
160
≤339
32302
0.9
Flux uncertainties at 70 and 100 µm are ∼10%.
1
Upper limit from the residual flux toward mm2 after subtracting thepoint source centered on mm1.
2
From Beuther et al. (2013a) with an accuracy of ∼15%.

mm2 may not be totally starless anymore, but that star formation processes might have begun at its north-western border.

StarBench:	
  The	  D-­‐type	
  expansion	
  of	
  an	
  HII	
  region	
  T.G.	
  Bisbas	
  et	
  al.	  (2015)	

Ø 計算機シミュレーションは解析的な計算を超えて複雑な系を理解できるが、しかし、それぞれに適応範囲があり、共通のテストで比較が必要。	
  àHII	
  regionのD-­‐type	
  expansionのベンチマークテスト、比較するコードはtable	
  1。	
  Ø ioniza)on	
  frontを超えてイオン化が進み、イオンの音速よりも早く拡大àR-­‐type	
  (Rareﬁed)	
  Ø 内側の圧力でイオンの音速よりも遅く拡大à	  D-­‐type	
  (Dense)	
  Ø D-­‐typeの解析解は厳密なRaga	
  et	
  al.	  (2012)があって、earlyな近似Spitzer	
  solu)onと慣性を入れたHosokawa	
  &	
  Inutsuka近似というのがある。Ragaはlateにも拡張した。	
  
S TAR B ENCH: The D-type expansion of an H II region

Table 1. Participating codes in this project.

Code name

Code representative(s)Kind

AQUILINE

Williams
Arthur
BaczynskiWünschWilliams
Tremblin
MackeyHaugbølle & Frostholm
Geen & Rosdahl
KuiperHubber & Bisbas
Haworth

Grid
Grid
Grid
Grid
Grid
Grid
Grid
Grid
Grid
Grid
SPH
Grid

CAPREOLE -C 2 -R AY
FLASH - FERVENTFLASH - TREERAY
GLIDE
HERACLESPIONRAMSES - LAMPRAYRAMSES - RT
SEDNA
SEREN
TORUS

Early Phase
1D
3D

Late Phase
1D
3D

X

X
X
X
X

X
X
X

X
X

X
X
X
X
X

X
X
X
X
X
X

X
X

X
X
X
X

5

Ø 比較は、イオンも中性粒子も等温で、接触面の扱いはそれぞれで、重力も磁場もない。earlyとlateをテスト。	  Mesh motion

Mesh geometry1

Eulerian
Eulerian
Eulerian
Eulerian
Lagrangian
Eulerian
Eulerian
Eulerian
Eulerian
Eulerian
Lagrangian (SPH)
Eulerian

Uniform AMR radial
Uniform cartesianUniform cartesianUniform cartesianUniform radial
Uniform radial
Uniform radial (1D) cartesian (3D)
Uniform cartesianUniform cartesianUniform radial
Equal mass
Uniform radial

1 Refers to the test problem presented in this paper and not to the general capabilities of each code.

0.02
0.04
0.08
0.14

0.536
0.717
1.009
1.343

0.530
0.707
0.996
1.324

2.488
3.848
3.679
2.848

3.26
3.59
4.35
4.29

6.1
4.2
2.6
1.7

StarBench:	
  The	  D-­‐type	
  expansion	
  of	
  an	
  HII	
  region	
  T.G.	
  Bisbas	
  et	
  al.	  (2015)の続き	

3.3
1.4
0.4
0.2

Figure 5. Comparison between Eqns. 8 (Raga-I), and 11 (Ra
1D participating codes. The black dashed line corresponds
B ENCH Eqn. 28. We additionally plot the Spitzer and th
Inutsuka (HI) expansion laws for reference.

各モデルと解析解の差。

Ø Early	
  1-­‐D)	
  	
  コード同士は合い、時間が経つとSpitzer	  solu)onからH-­‐I近似に移る。	
  the positions
predicted ofby theexpressions
S TAR B ENCH: ThetoD-type
expansionan analytical
H II region
11

Section 2. Table 4 gives the mean position of the ion
with the standard deviation (columns 2 and 4) as well
Table 3. This table shows results from the ‘early phase’ test (see 5.1.1).
and standard deviation for the maximum density reach
Column 1 shows the time. Columns 2 and 4 show the mean position of the
6 and 7). The relative difference around ⟨RIF ⟩ is ! 2%
ionization front, ⟨RIF ⟩ with the corresponding standard deviation, σ, forIn this late phase test, the position of the ionizatio
1D codes. Columns 3 and 5 are the respective for 3D codes. Columns 6nates as predicted by Eqn. 8 (Raga-I) since the H
and 7 show the mean maximum density of the shock front ⟨ρmax ⟩ and its
in pressure equilibrium with the pressure of the neut
standard deviation, σ, for 1D codes only.
Indeed, as shown in Table 4, the mean stagnation r
sured at t = 3.0 Myr) as given by all six participatt⟨RIF ⟩
σ/10−3⟨ρmax ⟩/10−19
σ/10−19⟨RIF ⟩ = 2.359 pc (standard deviation σ = 0.032 pc
(Myr)
(pc)
(pc)
(g cm−3 )(g cm−3 )from this mean value) which gives a relative error of ∼
1D
3D
1D
3D
1D
1D
compared to Eqn. 14.
The shell thickness is a function of resolution, w
0.005
0.373
0.378
2.059
2.76
5.7
3.6
0.01
0.430
0.430
3.180
2.96
5.9
3.0
the thickness
obtained expansion
by TORUS is oflargerS TAR B ENCH
: The D-type
an than
H IIthe
rego
0.02
0.536
0.530
2.488
3.26
6.1
3.3
(i.e. 1024 cells, compared to a maximum of 40960 us
0.04
0.717
0.707
3.848
3.59
4.2
1.4
The shell develops rapidly and becomes geometrica
0.08
1.009
0.996
3.679
4.35
2.6
0.4
t = 0.05 Myr. As seen in Fig. 4, the thickness is rema
0.14
1.343
1.324
2.848
4.29
1.7
0.2
ilar as calculated by all six participating codes. The shthicker over time as observed for t " 0.2 Myr. The leFigure 5. Comparison
Eqns.
8 (Raga-I),
and 11 (Raga-II)for theventuallybetween
becomesa detachedexpandingcompressio
1D participating
codes.ofThedasheddensity
line corresponds
to theS TAR
the value
theblack
maximumρmax drops
downto
B ENCH Eqn. 28. We additionally plot the Spitzer and the Hosokawa
which is the density of the undisturbed neutral medium
Inutsuka (HI) expansion laws for reference.
beginning of each simulation).
Figure 5 shows the position of the ionization front
compared with Eqns.8 (Raga-I) and 11 (Raga-II). Fo
to the positions
predicted
the analyticalexpressions discussed
we alsoplot thebySpitzer
and Hosokawa-Inutsuka
equatii
Section 2. Table
gives
theetmean
positiontheofcodes
the ionization
fron
shown4byRaga
al. (2012b),
initially follo
with the standard
deviationand 4) aswell
as thetowar
meation predictedby(columns
Eqn. 11 2however
they‘relax’Figure 3. Position at which the ionization fraction is xi = 0.5 as calculated
deviation
the maximum
densitybalancereachedpredicted(columnnationradiusfor
expectedfrom pressure
by the 1D participating codes. The upper panel compares the codes andwithstandard
S TAR B ENCH
: The
D-typeexpansionof an
H IIis !
region13
and7). Thedifference
around⟨R
2% in allcase
IF ⟩ temporarily
Therelative
positionof the ionization
front
expandthe Spitzer (Eqn. 9; solid gray line) and the Hosokawa-Inutsuka (Eqn.6 13;
late phaseradius
test, thepositionof theinwards.
ionization
front stagdashed gray line) equations. The lower panel shows the realtive error found In thisstagnation
beforerelaxing
Accordingt
between the numerical solution and either of the two analytical equations
nates as predicted
8 (Raga-I)
H IIofregion(2012b), by
thisEqn.
‘overshoot’is duesince
to thetheinertia
the H i(solid lines correspond to the errors due to the comparison with the Spitzer
in pressure equilibrium
the apressureof the neutral
Here, wewith
providesemi-empiricalequationmedium(whic
equation, while dashed lines due to the Hosokawa-Inutsuka equation). Indeed, as ‘S
Figure7.
Fig.
5 stagnation
for thethe
3D position
participating
co
shown
Table
4, As
theinmean
radius of(mea
TAR Bin
ENCH
equation’)predictingthsured at t front= 3.0forMyr)as given
allforsixt participating
this latephasebytest∈ [0, 3] Myr.codes
The Si⟨RIF ⟩ = 2.359
pc (standard
deviation σ = 0.032 pc or ∼ 1.3%
equationhas the form:
developin thewhere
theofshockin thefrom this meanvalue)firstwhich
givesplaces
a relativeerror∼ 2.2%
whe
Rpropagating=14.
RII +parallelfSB (RIto−the
RIIgrid), and that if a differenSBcompared toEqn.
thethickness
3D datacube
taken, theinstabilitieswhich
are notis in
The shell
is a isfunctionof resolution,whesuggeststhat forthese than
two codes
the instab
the thicknessstrongly
obtainedby TORUS
is larger
the otherresultodd-eventype,tofirstdescribedofby
Quirkused(1994).
Th(i.e. 1024 cells,
compareda maximum
40960
in PION
can be cured
by introducing
extra
numerical diffusion
The shell develops
rapidly
and becomesgeometricallythick bschemewhenstrongshock
is detected
parallel tot = 0.05 Myr.
As seenin aFig.
4, thethicknessis remarkably
simttion, byor using
hybrid Riemann
which
switc
ilar as calculated
all six aparticipating
codes.solver,
The shell
becomeRiemannsolvertheMyr.
Roe solverused byCA
thicker over usual
time asobserved
for t(e.g.
" 0.2
The leading
shoc
R AY) toaa detachedmore diffusive
Riemannsolver suchas aneventually becomes
expandingcompression
wave,
aninsideshocks. density ρmax drops down towards ∼ ρ
the value of the
maximum
Figure6 shows
the comparisonof the analyticalwhich is the densityof theundisturbed
neutral medium(i.e. at thØ Late	
  1-­‐D)	
  	
  コード同士は合い、Raga-­‐Iは慣性を考慮してないので少しの間過小評価(↘図)	
  àStarBench方程式を提案。	
  Ø Early	
  3-­‐D)	
  
SPHで粒子数が少ないとピーク密度が低く、シェルが厚くなる。H-­‐Iとのずれは<4%、Spitzerとのずれは>5%。	
  Ø Late	
  3-­‐D)	
  SPHでは真空にもゆっくり流れ込む問題(contact	
  discon)nuity	
  problem)が起こった。どのコードも1Dと同じくどの解析解とも完全には一致しないが、StarBench方程式には<2%で合う。	
  
	

The	
  growth	
  of	
  planets	
  by	
  pebble	
  accre)on	
  in	
  evolving	
  protoplanetary	  discs	
  Bertram	  Bitsch,	
  Michiel	
  Lambrechts,	
  and	  Anders	
  Johansen	
  (2015)	
Ø ガス惑星は円盤にガスがあるうちにでき、岩石惑星はそれより長くかかる。	
  Ø 大きさ微惑星に小さな微惑星が堆積すると、円盤の寿命より時間がかかる。
ßpebbleを考慮すると短くなる。	
  Ø ガスを集め始める質量は、微惑星に対して決めにくく、pebbleは簡単(H/rが大き
いと大きい)。	
  Ø 惑星形成はこれまでpopula)on	
  synthesisで研究されてきたが、惑星移動速度
や円盤中の固体の量など疑わしい仮定を含んでいた。	
  Ø disc	  evolu)on,	
  2D輻射流体(粘性加熱+輻射冷却)、radial-­‐driu-­‐dominated	
  approachでpebbleが形成、微惑星は(t0,	
  r0)にpebble	
  transi)on	
  massを1個手で入れる、微惑星へのガス降着、解析トルク方程式でtype-­‐I移動、ギャップが開けば粘性type-­‐II移動、円盤の寿命は3	  Myr。(ßいろんな人たちのモデルを導入)	
  A&A proofs: manuscript no. Planetgrowth
Planet category
Ice planet
Ice giant
Cold gas giant
Warm gas giant
Hot gas giant

Planetary mass
0.1ME < MP < 2ME
MP ≥ 2ME and Mc ≥ Menv
Mc < Menv
Mc < Menv
Mc < Menv

Orbital distancerf > 1.0 AU
0.1 AU < rf < 1.0 AU
rf < 0.1 AU

Table 1. Definition of planets used in this work. We distinguish the main classes of planets (gas giants, ice giants, and ice planets) only by mass
惑星の定義。cは惑星のコア、envは大気。	
and mass ratio between core and envelope. The subcategories
for gas giants are defined through their orbital distances, which we do not apply forThe	
  growth	
  of	
  planets	
  by	
  pebble	
  accre)on	
  in	
  evolving	
  protoplanetary	  discs	
  Bertram	  Bitsch,	
  Michiel	
  Lambrechts,	
  and	  Anders	
  Johansen	
  (2015)の続き	

e accretion in evolving protoplanetary discs

A&A proofs: manuscript no. Planetgrowth

3.0x106

惑星進化の例。	

100

1000
10.0

2.5x1062

1

t0=2 Myr0.1
r0 = 5.0 AU
r0 = 10 AU
r0 = 15 AU
r0 = 25 AU
r0 = 40 AU
r0 = 50 AU
tD=3.0Myr
Σpeb at 2 Myr

0.01

0.001
0.1

Σ

0.1

t0 peb[yr]

M [ME]

1

Zは円盤中の固体の割合。	
  Zが小さいと右上の黒が
増える。	

20.0

10

[g/cm ]

100.01

2.0x106

1.5x106

100
Z=1.0%
5.0
10

1.0x106

MP in ME

1000

1.0

0.1 0.51
0.5x106
1

5

10

20

30 40 50r [AU]

5

10

15

20

25

30

35

40

45

0.1

50

Fig. 2. Growth tracks of planets that accrete pebbles in an evolving pror0 [AU]toplanetary disc. The big black circular symbols indicate the final mass
Fig. 4. Final masses of planets (total mass M = M + M ) as a function of formation distance r and formation time t in the disc. Planets thatare below the dark blue line have reached pebble isolation mass and can accrete gas. All planets that are below the white line have M < M ,and position of the planets at tf = 3 Myr, meaning that the planets exindicating that they have undergone runaway gas accretion. The yellow line marks the pebble production line; planets below the yellow line cannot
have formed by pebble accretion, because the pebbles have not yet formed at the insertion time of the planet. The black lines indicate the final
perience 1 Myr of evolution. The small black dots indicate 2.2, 2.4, 2.6,
orbital distance r of the planet. Each point in (r , t ) corresponds to the final mass of one individual evolution track as shown in Fig. 2. The whitecrosses indicate the initial orbital positions and times for the planetary evolution tracks shown in Fig. 2.
and 2.8 Myr. In the example of the purple line (r0 = 10 AU), the planet
reaches 0.1 AU before the final disc lifetime, and we stop the simula-In the late stages of the disc (t > 2 Myr), the region of out- we show that the formation of diﬀerent planetary types is draward migration is located at ∼ 3 AU and can hold planets of up matically diﬀerent when adopting too simplistic a disc model.
tion. The diﬀerent coloured lines indicate diﬀerent planetary evolutions,to a few Earth masses (Fig. 1). This means that ice giants stop
their inward migration there, explaining the pile-up of ice giants
which correspond to diﬀerent types of planets, where
we
have
an
ice
giE
3.4. Influence of pebble surface density
in this region of parameter space.
ant, a hot gas giant, a cold gas giant, one more ice giant, and two iceWe want to note that Fig. 4 does not give a percentage ofwhat kind of planets should exist around other stars. Figure 4 The metallicity in pebbles Z has a strong influence on the outplanets starting from inside out (see text). The grey line indicates theinstead shows what kind of planet would form if an initial seed come of planetary systems (Lambrechts & Johansen 2014). A
planetesimal with M(eq. 5) was placed in the disc at r and higher metallicity in pebbles will allow for faster growth of thesurface density of pebbles in the disc at 2 Myr and ends at the ice line
t for a disc that lives, in total 3 Myr, around a solar type star. planetary core, resulting in a larger core. However, the pebble
mass (eq. 16) reduces in time as the disc evolves andslightly interior to 1 AU, where the pebble surface density changes. . We can learn from Fig. 4 that gas giants are more abundant if an isolation
planets form, keeping the final core mass from being twice asØ 比較として微惑星降着では固体は全て微惑星と仮定するのでZ=8%(MMSNの8倍)で、コア形成に時間がかかるので円盤寿命を5	
  Myとしても、
Mp>10M は8AU以遠にできない。	
  Ø 太陽系再現について、gas	
  giantとice	
  giant2つずつのNice	
  modelの初期条件を再現できた。	
  
P

c

env

0

0

c

f

0

trans

env

0

0

0

early formation scenario is invoked and that hot gas giants haveto form early and fairly close to the central star, while cold gas
giants can form at later times and further out in the disc. In situ
formation of gas giants is not possible. For later formation times(t0 > 2 Myr), the final mass of the planet becomes lower, because the isolation mass becomes lower as H/r drops, resulting
in smaller planetary cores. A smaller planetary core then prolongs the contraction time of the gaseous envelope, allowing theformation of planets that have Mc > Menv at 2 Myr, because theplanets have a shorter total evolution time. Considering that themost common observed exoplanets are small (MP < 10ME ), alater formation time for planets is favoured by our planet formation scenario.
These results emphasise the importance of an evolving discstructure that is not a simple power law. We discuss planet formation via pebble accretion in the MMSN in Appendix C, where

議論:	  Myr, because
our total disc lifetime is 3 Myr.
Fig. 2 the evoluØ dM/dt<2x10–9	
  MIno/yrで止めないと大きく結果が変わる。観測的制限を待つ。	
  tion tracks of the planets and the pebble surface density Σ at 2
Myr areØshown.
The surface density of pebbles Σ is calculated
太陽系の完全な再現には惑星大気のオパシティと複数の惑星を考える必要あり。	
  #through eq. 12, which depends on Σ . Therefore the bumps inØby 木星に希ガスが多いことも、遠くで遅くにできたと思えば、我々のモデルで説明できる。	
  Σ caused
the transitions in opacity (Bitsch et al. 2015) translate into bumps in the pebble surface density. As the gas surface
微惑星モデルでは形成が遅すぎて現れない”ice	
  planets”という種類を予想。	
  density Ødecreases
and evolves in time, so does the pebble surface
density. The starting mass of the planets is diﬀerent at diﬀerentØbecause
popula)on	
  synthesisモデルのような不自然な仮定なしに、合理的な結果が得られる。	
  locations,
it is set by the pebble
transition mass, which
peb

peb

g

g

Article number, page 10 of 23

depends on the disc’s aspect ratio (eq. 5).
Planets that manage to reach their pebble isolation mass con-high for discs with twice the metallicity in pebbles. Lower metallicity in pebbles slows down the growth of the core of the planet,
resulting in lower core mass, because the isolation mass drops intime owing to H/r decreasing in the longer time that is needed
to build the core. This change in the mass of the core will theninfluence the gas accretion onto the planet, because a larger planetary core can contract its envelope in a shorter time than asmaller planetary core. The mass of the cores of these planetsin a Z = 1.5% disc is ∼ 20 − 30ME , which is about a factor ofthree to four too low to explain the amount in heavy elements
for Corot-13 b, 14 b, 17 b, and 23 b, which have solid cores ofaround 100ME (Moutou et al. 2013).

In Fig. 5 we display the final planetary masses for Z = 0.5%
(top, half the nominal metallicity in pebbles) and for Z = 1.5%
(bottom, 3/2 times the nominal metallicity in pebbles). In gen-

Triggering	
  Collapse	
  of	
  the	  Presolar	
  Dense	  Cloud	
  Core	  and	
  Injec)ng	
  Short-­‐Lived	
  Radioisotopes	
  with	  a	
  Shock	
  Wave.	
  IV.	
  Eﬀects	
  of	
  Rota)onal	
  Axis	
  Orienta)on	
  – 12 –Alan	
  P.	
  Boss	  and	  Sandra	
  A.	
  Keiser	
  (2015)	

Ø 超新星残骸は、60Fe,	
  26ALといったshort-­‐lived	
  radioisotopesを分子雲に供給する候補。	
  Ø ordinary	
  chondrite	
  (普通石質隕石)のデータは60Fe/56Fe=5-­‐10x10–7、隕石全体では1.15x10–8、非平衡普通コンドライトでは7x10–7à差をSNRで説明できそう。	
  Ø 分子雲の回転とショック伝播方向を垂直にしたモデル(2013,	
  2014は2D,	
  3Dで平行)。	
  Ø FLASH2.5	
  AMR,	
  最小グリッドは9	
  AU,	
  初めは周り10	
  Kショックフロント1000	
  K,	
  C-­‐shock,	  クーリングはΛ=9x1019(T/100	
  K)ρ2	
  erg	
  cm–3	
  s–1	  (thin	
  H2O,	
  CO,	
  H2相当)。	
  Ø 初期M=2.2	
  Mo,	
  R=0.053	
  pc, 分子雲回転はx軸、ショック伝播は–y軸、	
  Table 1. Initial conditions and basic results for the models, with varied shock speeds (vs ,in units of km s−1 ), shock gas densities (ρs , in units of the standard shock density,
3.6 × 10−20 g cm−3 ), target cloud perpendicular rotation rates (Ωc , in rad s−1 ), mass incollapsing (ρ > 10−16 g cm−3 ) region (Mc , in in M⊙ ), shock wave masses in collapsingregions (Ms , in M⊙ ), injection eﬃciencies (fi ), and approximate spin directions of resulting
disks.
Model

vs

ρs

Ωc

Mc

Ms

fi

spin direction

40-200-pr13
40-200-pr14
20-200-pr13
20-200-pr14
20-400-pr13
20-400-pr14

40
40
20
20
20
20

200
200
200
200
400
400

10−13
10−14
10−13
10−14
10−13
10−14

0.45
0.49
0.95
1.04
0.64
0.72

0.011
0.012
0.028
0.031
0.032
0.036

0.037
+ŷ
0.040
-ŷ
0.093 -ŷ to +x̂ to +ẑ
0.103 -ŷ to +x̂ to -ẑ
0.053-ŷ to -x̂
0.060
-ŷ

モデルのパラメーター	Triggering	
  Collapse	
  of	
  the	  Presolar	
  Dense	  Cloud	
  Core	  and	
  Injec)ng	
  Short-­‐Lived	
  Radioisotopes	
  with	  a	
  Shock	
  Wave.	
  IV.	
  Eﬀects	  of	
  Rota)onal	
  Axis	  Orienta)on	  今回の結果の一つ	
– 13 –Alan	
  P.	
  Boss	  and	  Sandra	
  A.	
  Keiser	
  (2015)の続き	

Ø 2012,	
  2013,	
  2014では、Rayleigh-­‐Taylor	
  ﬁngerがショックと分子雲の表面にでき、超新星でできた物質を分子雲に注入していた。	
  Ø 平行のときはinner	
  diskの軸は伝播方向と平行、outer	
  diskは歪んだ。	
  Ø 垂直にすると(今回)、inner	
  diskは3つが初期回転に垂直、3つが傾き、outer	
  diskは6つとも歪む。	
  Ø つまり、平行の時と違って、全て初期回転からずれている。	
  	
Ø ストリームをよく見ると、Rayleigh-­‐Taylor	
  ﬁngerが初期回転を超える角運動量を与え、ケプラー円盤ができると考えられる。	
  Ø warp	  diskも、追加された物質がR-­‐T	
  ﬁngerの影響を受けるため。	
  Ø 空間分解能が足りないとR-­‐T	
  ﬁngerは現れない(Li	  et	  al.	  2014)。	
  Ø R-­‐T	
  ﬁngerは超新星由来の物質を運ぶだけでなく角運動量も運ぶことがわかった。	
  Ø 生成された物質のうち分子雲に注入された割合fiは、平行のときとおよそ変わらない
が、平行の時より少し増えているのはR-­‐T	
  ﬁngerの影響が大きいから。	
  Ø 超新星が運んだ質量と分子雲質量の比3x10–4も、SNe-­‐derived	
  SLRIのdilu)on	  factor10–4-­‐10–3に一致	
  (Takigawa	
  et	
  al.	
  2008)。	
  Fig. 1.— Model 40-200-pr13 log density cross-section in the z = −1.5 ×1015 cm plane, wh
the maximum density occurs, showing an edge-on disk. Region shown is 1333 AU across
0.085 Myr. Shock propagates from top to bottom in each model. Direction of initial tar
cloud spin axis is to the right.