星形成ゼミ
SFN #292 (41-45本目)
百瀬宗武（茨城大・理）41. On the methanol emission detection in the TW Hya disc:the role of grain surface chemistry and non-LTE excitation
S. Yu. Parfenov, D. A. Semenov, Th. Henning et al. (MNRAS, 468 (2): 2024-2031)
https://arxiv.org/abs/1703.03748【CH3OH分布を求める上で背景とした円盤モデル】• g/d=100, ダスト最大粒径 amax = 1mmのもと，観測から得られたダスト
質量や質量降着率と整合的なもの。
• 85化学種，600化学反応を含み，ガスの熱収支も解くことで，3.9au200auの範囲の温度分布をガス・ダスト独立に得る。

【背景】ALMAにより初めて原始惑星系円盤からCH3OH輝線を検出
The Astrophysical Journal Letters, 823:L10 (7pp), 2016 May 20（Walsh et al. 2016; 下図)。
The Astrophysical Journal Letters, 823:L10 (7pp), 2016 May 20

Table 1
Methanol Transitions

Walsh et al.

Transition

Frequency(GHz)

Upper Level Energy(K)

Band 650 –4 0 (E)
5-1–4-1 (E)505 –4 04 (A)241.700
241.767241.791

47.9
40.4
34.8

Band 7211−202 (A)312−303 (A)413−404 (A)817−808 (A)304.208305.473307.166
318.319

21.6
28.6
38.0
98.8

photons. These model calculations motivated a successful
ALMA proposal, which has resulted in the ﬁrst detection ofgas-phasemethanol in a nearby protoplanetary
disk (TW Hya,
241GHz付近(Band6)の3遷移，及び54 pc), the results for which are reported here.

310GHz付近(Band 7)の4遷移のデー
2. OBSERVATIONS

タをuv平面でstackingしS/N向上。
The young star, TW Hya, was observed on 2015 January 02

with 39 antennas and baselines from 15 to 350 m (project2013.1.00902.S,
I. C. Walsh). The quasars
J1256-0547 and左はBand P.7のChannel
map.
J1037-2934 were used for bandpass and phase calibration,
respectively, and Titan was used for amplitude calibration. The
Figure 1. Channel maps for the stacked observed B7 CH OH line emission. The white contours show the 2.5σ, 3.0σ, 4.0σ, and 5.0s levels for the CH OH data andthe gray contour shows the 3s extent of the 317 GHz continuum. The black cross denotes the stellar position, and the dashed gray lines show the disk major and minor Band 7 (B7) methanol transitions listed in Table 1 were
axes. The synthesized beams for the continuum (open ellipse) and line (ﬁlled ellipse) emission are shown in the bottom left panel.
targeted using a channel width of 122 kHz (corresponding to0.12 km s−1). A continuum-only spectral window at 317 GHz
triggered by energetic photons or particles or by energy
Because the methanol chemistry applicable to disks remains
released during exothermic chemical reactions (reactive
relatively unconstrained, we adopt a parametric approach to (with a total bandwidth of 2 GHz) was also covered. The total
desorption, e.g., Garrod et al. 2006). The rates for such
constraining the location and abundance of gas-phase methanol on-source observation time was 43 minutes. All data were selfprocesses remain relatively unconstrained except for a small set
in TW Hya. Methanol is assumed to reside in three differentz r - 0.1,
0.1 - z r - 0.2,
and calibrated prior to imaging using CASA version 4.3 and theof molecules and reaction systems (e.g., Westley et al. 1995;
verticallayers:0.2 - z r - 0.3, where z and r are the disk height and radius,Öberg et al. 2009b; Fayolle et al. 2011; Bertin et al. 2013;
continuum band at 317 GHz, and using a timescale of 20 s (≈3
respectively (dashed lines in Figure 3). A small grid of models
Fillion et al. 2014; Cruz-Díaz et al. 2016; Minissale
was run in which the inner and outer radii of the emission were times the integration step). This increased the dynamic range ofet al. 2016). It also remains a possibility that gas-phasevaried (in steps of 10 au), in addition to the fractional
chemistry contributes to the gas-phase abundance (e.g.,
the continuum data by a factor of »30 . Self-calibration using
abundance of methanol (relative to H2). Ray-tracing calculaCharnley et al. 1992; Garrod3
et al. 2006). For example, thetions were performed using LIME (LIne Modelling Engine, the continuum around the methanol lines between »304 andrate coefﬁcient for the OH + CH3OH gas-phase reaction was
only recently determined to be rapid at low temperatures (<100Brinch & Hogerheijde 2010) assuming LTE, a disk inclination
K, Shannon et al. 2013; Acharyya et al. 2015).
and position angle appropriate for TW Hya (Hughes 307 GHz gave almost indistinguishable results. The rms noiselevel achieved for the 317 GHz continuum following imaging
3
with CLEAN (Briggs weighting, robust = 0.5) was 0.10 mJy
beam−1, with a peak signal-to-noise ratio (S/N) of 4200. The
3

3【本研究の内容】TW Hya 円盤モデルに基づき，複数の化学反応モデル

によりCH OH分布を求め，non-LTE輻射輸送計算に基づく模擬観測から実際の観測が再現できるものがあることを確かめた。

• 中心星や環境からのUV, Walsh
Xrayも考慮。
et al.
0 5 × 0 5 (-89 ). Following self-calibration, the line data
were continuum-subtracted and imaged to the same velocity
resolution as the B7 data. An rms noise »5 mJy beam−1 perchannel was achieved in the dirty channel maps at all threefrequencies.
A signiﬁcant3 signal was neither found in the individual
channel maps of the B7 data nor the B6 data. The three B7 data
sets at »304 , 305, and 307 GHz (corresponding to the lowest
energy transitions) were concatenated into a single measurement set following velocity regridding and then imaged using
CLEAN with natural weighting (i.e., “stacked” in the uv
3 resulted in a synthesized beam of 1 4 × 0 73
domain). This(-84 ) and an rms noise of 2.0 mJy beam−1, which is a factorof »2 increase in sensitivity. A single round only of additional
CLEANing was performed. Signiﬁcant methanol emission isdetected across six channels (23s ) from 2.45 to 3.35 km s−1
reaching a peak S/N of 5.5s . No signiﬁcant signal was foundin the stacked and imaged B6 data.

【CH OH分布の導出】• Gas-grain chemistry を計算できるコード (ALCHEMIC）• CH OHはダスト表面で主に作られる。COのhydrogenation，OH-CHのラジカル間反応など。

• ダストからの脱離：reactive desorption(下図b)だけでなく，CRによって励起されたH2からのUVによるphoto-desorption(c) が重要。それを考3. RESULTS

3.1. Detection of Gas-phase Methanol
慮しない場合(d)は，気相に十分CH
3OH供給されず。
Methanol in the disc of TW Hya

2025

The channel map for the stacked B7 data is presented in
Figure 1. The inclination and position angle of TW Hya (7 and335 , respectively; Hughes et al. 2011) are such that emission
from the northwest and southeast is respectively blueshifted
and redshifted in velocity, with respect to the systemic velocity(2.9 km s−1, Hughes et al. 2011; Andrews et al. 2012). This
kinematic structure is evident in the methanol channel map. In
all channels in which emission is detected, the peak is offset
from the stellar position, indicating that the emitting methanol
is possibly located in a ring; however, there is signiﬁcantemission (23s ) at the source position. The detected emission
appears to be compact compared with the extent of thecontinuum emission (»100 20 au). This may be due to the
low S/N, but we cannot exclude a real drop in the CH3OH
abundance in the outer disk.
Figure 2 shows the extracted line proﬁle (dark−3reddashed−1 estimated for the ‘E
Figure
1.
The
log
of
methanoldesorption
rates
in
cm
s
diff /Eb = 0.4’ disc model. The rates are shown only in the disc regions withlines in left
panel) within the 3s contour of the continuum,−15
XM >is10marked. (a) by
CRP
rate. (b)Reactive1.desorption
without taking into accountwhich
thedesorption
gray contour
in Figure
The peakrate.
ﬂux(c) Photodesorption rate. (d) Photodesorption rate estimated −15
the secondary
photons
CRP
excitation
H2 . The
black contours denote the gas-phase CH3 OH abundance of 10 .
densityfor theUV
stackedlineproduced
proﬁle byis 33
mJy
and theofrms
noise
is 6.5 mJy, resulting in a S/N of 5.1.

Figure 3. TW Hya and DM Tau disc models. Left and middle columns show relative methanol abundances (wrt H2 ) computed with the physical models of
Gorti et al. (2011) and Kama et al. (2016), respectively. Right column shows the methanol abundances computed with the DM Tau disc model taken from
Semenov & Wiebe (2011). The black contours denote the methanol abundance of 10−12 .

et al. 2016). For consistency with W16, the test calculations with theGorti et al. (2011) disc model and parametrized CH3 OH distributionof W16 were performed assuming a distance of 54 pc. By adding
line specific intensities in the all pixels of the synthetic images, we
obtained the synthetic integrated CH3 OH spectra.
LIME produces images at a single spectral frequency without taking into account the averaging within the spectral channels as inreal observations. We have checked how this averaging affects thesynthetic spectra following the procedure given by Cleeves et al.
(2016). We performed calculations of the synthetic spectra with aspectral resolution of 0.015 km s−1 , 10 times higher than our initialresolution and the resolution of the W16 data, before averaging theresults of these computations back to the resolution of 0.15 km s−1 .
The resulting synthetic peak line flux densities do not vary by morethan 3 per cent due to the averaging, a variation that is significantly
lower than the ratio of the rms noise (6.5 mJy) to the peak flux
Figure 4. The zeroth moment maps obtained for the 31 − 30 A−+(305.473 GHz) transition with the ‘Ediff /Eb = 0.77’ (left-hand panel) anddensity (33 mJy) in the spectrum of W16. Thus, we assume the‘Ediff /Eb = 0.4’ (right-hand panel) disc chemical models. The colour bars
averaging can safely be neglected.
−+
denote the intensity in 10−6 Jy pixel−1 km s−1 .
(304.208 GHz),
W16 considered the Band 7 21 − 20 A
(305.473 GHz), 41 − 40 A−+ (307.166 GHz) transi31 − 30 A−+ diﬀ
tions (hereafter, B7 lines) and Band 6 50 − 40 E (241.700 GHz),
5−1 − 4−1 E (241.767 GHz), 50 − 40 (241.791 GHz) transition 2). In the case of the ‘Ediff /Eb = 0.77’ model, the CH3 OH
diﬀ
bintions (hereafter, B6 lines). The difference in the maximum speemission is mainly concentrated within a thin ring, while in the
2030
S.
Yu.
Parfenov
etal.
cific intensity of the synthetic images for these lines between thecase of the ‘Ediff /Eb = 0.4’ model, it is distributed over a larger‘Ediff /Eb = 0.77’ and ‘Ediff /Eb = 0.4’ models does not exceed
image area (see Fig. 4).
45 per cent. The spatial distribution of the CH3 OH emission, howThe line flux densities Fν in the spectra obtained with theever, is significantly different, primarily caused by the difference in‘Ediff /Eb = 0.77’ model are lower by a factor of <9 than thosethe methanol column densities NM between the models (see Secobtained with the ‘Ediff /Eb = 0.4’ model (see Fig. 5). The difference【CH3OH生成における未知量: ダスト表面における拡散効率】【輻射輸送計算・模擬観測】• 拡散エネルギー/束縛エネルギー = Ediﬀ / Ebin でパラメータ化。

• LIMEを用いたnon-LTE計算 → CASAに• Ediﬀ が相対的に小さいほど，拡散しやすく反応が促進される。

よる模擬観測。

• 最近の室内実験も考慮，2つの場合を計算。
• 下図 (a) が拡散しにくい場合，(b)が拡散しやすい場合の気相CH3OH
分布。(b)の場合は低温下でも効率的に生成。結果，外側で柱密度が高くなる(d)。(c)は(b)の時の固相CH3OH分布。
2026• TW Hyaに合わせた円盤モデルではガス密度が比較的高く，ほとんどの遷移がLTEとさほど変わらない。
• 右図：異なるE

での積分強度。

• 下図はE /E=0.44での模擬観測チャ

ンネルマップ。

S. Yu. Parfenov et al.

MNRAS 468, 2024–2031 (2017)

Figure 2. (a) and (b) The log of relative gas-phase CH3 OH abundance with respect to the H2 density in the ‘Ediff /Eb = 0.77’ and ‘Ediff /Eb = 0.4’ disc models.
(c) Same as (b) but for grain surface (ice) CH3 OH. The most right panel shows gas-phase CH3 OH vertical column density in the ‘Ediff /Eb = 0.77’ (solidline) and ‘Ediff /Eb = 0.4’ (dashed line) chemical models and grain-surface (ice) CH3 OH vertical column density in the ‘Ediff /Eb = 0.4’ model divided by 107(dotted line).

強度や分布をまずまず再現。
円盤物理モデルの細かな違いより，
Ediﬀ/Ebinの選び方（メタノールの生成効率）が大事。

model of similar complexity from Walsh et al. (2014). As noted in
Parfenov et al. (2016), this discrepancy can be due to the relatively
low grain-surface diffusion rates assumed by Semenov & Wiebe(2011), with the ratio of diffusion to binding energy Ediff /Eb of
0.77 for surface species. In this study, however, we consider surface
reactions with faster diffusion rates with Ediff /Eb = 0.4, close to the(Tsukagoshi et al. 2016) or a local gas density depletion (Teague
et al. 2017).
3 R A D I AT I V E T R A N S F E R C A L C U L AT I O N S
For the LRT calculations, we have used the LIne Modelling Engine

Figure 8. The synthetic channel maps for the stacked B7 data calculated with the ‘Ediff /Eb = 0.4’ TW Hya disc chemical model. White contours show 2.5σ ,3σ , 4σ and 5σ levels for the B7 data. Grey contour shows the 3σ level of continuum emission at 317 GHz. Dashed lines denote minor and major disc axes
and the black cross denotes the stellar position. The synthesized beams for the continuum and line data are shown as open white and filled black ellipses,
respectively.

One of the main parameters of chemical models that influence the abundances of complex species is Ediff /Eb (see e.g.

by the Russian Science Foundation (project no. 15-12-10017). DAS
acknowledges support fromthe Heidelberg Institute of Theoretical

42. Dynamical histories of the IC348 and NGC1333 starforming regions in Perseus
Richard J. Parker and Catarina Alves de Oliveira (MNRAS, 468 (4): 4340-4350)
https://arxiv.org/abs/1703.08547【使用したデータ】

Dynamical histories of IC 348 and NGC 1333

4341

NGC 1333 star-forming regions in the Perseus giant molecular
cloud from Luhman, Esplin & Loutrel (2016) to determine the spatial structure and relative spatial distributions of the most massive
stars compared to other stars and brown dwarfs.
The paper is organized as follows. In Section 2, we describe
the data sets used; in Section 3, we outline the methods used toquantify the spatial distributions and in Section 4, we present theresults for IC 348 and NGC 1333. We compare these results to
N-body simulations of the evolution of star clusters to constrain theinitial density of both regions in Section 5. We provide a discussion
in Section 6 and we conclude in Section 7.

• Luhman et al. (2016)によって報告された最新データ（右図）。赤点は大質量順に10個の星の分布。

【背景】星団の空間構造のCharacterizationは，以下の量でよくできる• メンバー数：478 for IC 348 and 203(Cartwright & Whitworth 2004; 2009)。

for NGC 1333。等級・減光量・スペmは 『minimum spanning tree (MST) 全ての星を線分でつないだ中で長さの総計が最小になるもの』の枝の平均長The statistical separation
analysis of star clusters
595 = 星同士の平均距離
sは normalized
lengths

MSTの例(Cartwright &Whitworth 2004より)

2 DATA S E T S
クトル型がほぼ全て導出。
For the observational sample, we adopted the most recent census of
IC 348 and NGC 1333 clusters presented in Luhman et al. (2016),
where tens of new low-mass stars and brown dwarf candidate members have been confirmed spectroscopically. Additionally, Luhman
et al. (2016) have classified spectroscopically several previously
known members, resulting in an unprecedented census with a number of members of 478 for IC 348 and 203 for NGC 1333. In bothclusters, all members have measured magnitudes and an estimateof extinction, as well as a spectral type, except for 19 members of
IC 348 and 41 members of NGC 1333.
To estimate the masses of the members of the clusters, we first
converted spectral types to temperatures, adopting the temperature
scale
from Schmidt-Kaler (1982) for stars earlier than M0, and theMSR
scale from Luhman et al. (2003b) for sources with spectral type between M0 and M9.5. For the L dwarfs, we applied the scale proposed
by Lodieu et al. (2008). The bolometric luminosity was calculated
by de-reddening the magnitudes of the targets with the extinction
law from Rieke & Lebofsky (1985), using a distance to the clustersof 300 pc for IC 348 and 235 pc for NGC 1333, and bolometric corrections from Pecaut & Mamajek (2013), Herczeg & Hillenbrand(2015) and Dahn et al. (2002). Masses were derived from the evolutionary models (Baraffe et al. 1998; Chabrier et al. 2000; Siess,Dufour & Forestini 2000) according to each target’s location on
the HR diagram. For the lowest mass brown dwarfs (spectral types
later than ∼M8), luminosities become more uncertain both in thedata and the models, and therefore masses are derived only fromtemperatures using the models from Chabrier et al. (2000).
In Fig. 1, we show the positions of the objects in IC 348, andin Fig. 2 we show the positions of the objects in NGC 1333. In
both plots, the 10 most massive stars in each region are shown by
the large red points. Both regions have been extensively surveyed,
and we show the areas that are observationally complete by thedashed lines. In IC 348, this corresponds to an area with radius
14 arcmin from the central star BD +31 643 and in NGC 1333 thearea covered by the Chandra X-ray Observatory Advanced CCD
Imaging Spectrometer (ACIS-I). In addition to the full data sets, we【各星団の特徴づけ】

1. Q値：空間分布が球対称かフラクタ
ルか，またそのべき指数・フラクタ
ル次元は？
2. Λ

：mass segregation ratio。特定の質量集団についてMSTをとり，※ mやsだけだと，球対称分布を仮定した時のべき指数や，フラクタル形状を仮

その長さが星団全体のMSTのそれと定した時のフラクタル次元はよく見積れるが，両者の区別ができない。Qにする

同様の性質を持っているかを調べる。

ことで，球対称かフラクタルかが判別できる。

3. Σ-m：個々の星の周辺での星密度【本研究の内容】若い(1-3Myr)星団，IC348とNGC1333に含まれる星々のデータから，Qによる構造解析や星質量によるsegregationの有無，星Figure 4. Minimal spanning trees for (a) ρ Ophiuchus, (b) IC2391, (c) IC348, (d) Taurus and (e) Chamaeleon.

柱密度の揺らぎを解析。さらにN対シミュレーションと比較して形成初
Mean values of Q for the various types of artificial star cluster
are recorded in Table 1 (column 5). For artificial clusters with asmooth large-scale radial density gradient (type 3Dα), Q̄ increases
from Q̄ ≃ 0.80 to 1.50 as the degree of central concentration increases from α = 0 (statistically uniform number-density) to α = 2.9(n ∝ r−2.9 ). For artificial clusters with fractal substructure (type FD),Q̄ decreases from Q̄ ≃ 0.80 to 0.45 as the degree of subclustering
increases from D = 3.0 (uniform number-density, no subclustering)

期条件を探った。

Using Fig. 5, we infer that Taurus, IC2391 and Chamaeleon havesubstructure with notional fractal dimensions D = 1.5, 2.2 and 2.25.
In contrast, ρ Ophiuchus and IC348 appear to be centrally concentrated, with radial density exponents α = 1.2 and 2.2. These

Figure 1. Map of objects in IC348. The red points indicate the 10 most
massive stars. The area within the dashed line is the 14 arcmin radius fromthe centre, which is observationally complete (Luhman et al. 2016).

分布(Σ)を，質量(m)の関数として表す。

Figure 2. Map of objects in NGC1333. The red points indicate the 10 most
massive stars. The area within the dashed lines is the ACIS-I field from
Luhman et al. (2016), which is observationally complete.

Cartwright (2009) and combines the normalized mean edge lengthof the minimum spanning tree (MST) of all the stars in the region,m̄, with the normalized correlation length between all stars in theregion, s̄. The level of substructure is determined by the following
equation:
m̄
.
(1)
s̄
A substructured association or region has Q < 0.8, whereasQ=【IC348の結果】【N体計算との比較】 Dynamical histories of IC 348 and NGC 1333

4345

Table 1. Summary of the N-body simulations used in this work. The columns show the star-forming region, number of stars, theIMF used (either the data from Luhman et al. 2016 or the Maschberger 2013 IMF), the radius of the star-forming region, rF and the
median initial local density this radius results in, ρ̃ini .

• Q=0.98，N(r) ∝ r -2.5の中心集中した球対称分布で説明。

• 星団と同数の星を仮定したIMFに沿って含ませ，数値計算から期待さ
Region

IMF

NstarsrFρ̃ini• ΛMSR：顕著なmass segregation の兆候はない（下図a,b）。

れるprimodial substructure を真似た分布で初期配置。

• Σ-m：星密度が高いところにもっとも大質量の星は存在？ (c)• 初期速度分散に対するαVir = 0.3；手を離すと収縮を始める。

Dynamical histories of IC 348 and NGC 1333

4343

IC 348
IC 348
IC 348
IC 348

425
425
425
425

Observed (Luhman et al. 2016)
Observed (Luhman et al. 2016)
Maschberger (2013)
Observed (Luhman et al. 2016)

0.5 pc
1.5 pc
1.5 pc
3 pc

NGC 1333
NGC 1333

150
150

Observed (Luhman et al. 2016)
Maschberger (2013)

0.5 pc
0.5 pc5000 – 10 000 M⊙ pc−3
100 – 500 M⊙ pc−3
100 – 500 M⊙ pc−3
10 – 60 M⊙ pc−3
500 – 2000 M⊙ pc−3
500 – 2000 M⊙ pc−3

Dynamical histories of IC 348 and NGC 1333

4345

Table 1. Summary of the N-body simulations used in this work. The columns show the star-forming region, number of stars, theIMF used (either the data from Luhman et al. 2016 or the Maschberger 2013 IMF), the radius of the star-forming region, rF and the
median initial local density this radius results in, ρ̃ini .
RegionNstars

IMF

rF

ρ̃ini

IC 348
IC 348
IC 348
IC 348

425
425
425
425

Observed (Luhman et al. 2016)
Observed (Luhman et al. 2016)
Maschberger (2013)
Observed (Luhman et al. 2016)

0.5 pc
1.5 pc
1.5 pc3 pc

5000 – 10 000 M⊙ pc−3
100 – 500 M⊙ pc−3
100 – 500 M⊙ pc−3
10 – 60 M⊙ pc−3

Figure 5. N-body simulations of star-forming regions containing 425 stars undergoing cool-collapse with stellar masses from the Luhman et al. (2016) sample
NGC 1333
150
Observed (Luhman et al. 2016)
0.5 pcfor IC 348 and initial stellar densities of 5000–10 000 M⊙ pc−3 . In panel (a), we show the evolution of the Q-parameter; in panel (b), we show the Q−"MSR
NGC
150(2013) by the plus signs, open circles
0.5andpc
plot and in panel (c), we show
the1333
Q−#LDR plot. In panels (b)and (c), the simulation data at Maschberger
0, 1 and 3 Myr are indicatedcrosses, respectively. In all three panels, the blue diamond symbol shows the observational value at 3 Myr. The dashed horizontal line in all panels indicatesthe boundary between a substructured (Q < 0.8) and a smooth (Q > 0.8) distribution, and in panels (b) and (c) the vertical dashed lines indicate "MSR = 1(no mass segregation) and # LDR = 1 (no enhanced surface densities), respectively.

Figure 3. Data for IC348. Panel (a) shows !MSR as a function of the NMST most massive stars. !MSR = 1.1, which is probably not a significant deviationfrom unity. Panel (b) shows !MSR as a function of the NMST least massive objects. Again, the deviation from unity is not likely to be significant. Panel (c)shows the median surface density for the most massive stars (red line), cluster average (blue line) least massive BDs (orange line). Deviations from the median
are not significant (KS test p-values of 0.49 and 0.20, respectively). The Q-parameter is 0.98 (centrally concentrated).

and s̄ = 0.64. This is a less centrally concentrated spatial profile
the orange line. The surface density ratio for the most massive stars
than is measured for the full data set, and corresponds to a uniform
is " LDR = 1.77, but a KS test between the two populations gives
distribution. Again, this is unsurprising as we are pruning the more
D = 0.25 and a p-value of 0.49 so that the two populations sharedistant objects from our determination of Q.
the same underlying parent distribution. Based on this, we cannot-2.5
conclude that the most massive stars reside in areas of higher than
average surface density.
4.2.2 Mass segregation ratio, !MSR
If we compare the surface densities of brown dwarfs to the surface
MSR.
4344
R. J.
Parkerand C.region,
Alves
Oliveira
densityof thewholestar-forming
wede
have
" LDR = 0.82,
In Fig. 4(a), we show the evolution of !MSR as a function of the NMST
which suggests that the brown dwarfs reside in areas of lower thanmost massive stars in the subset, which is compared to the MSTs
average surface density. However, the KS test between the twoof objects randomly drawn from the spatial distribution shown in
distributions has D = 0.33 and the p-value is 0.20, again suggestingFig. 2. !MSR = 1.2+0.4−0.3 for the NMST = 10 most massive stars, andthat the two populations share the same underlying distribution.
also does not deviate from unity if we consider fewer (e.g. NMST = 4)
Previous studies have suggested that the most massive objects inor more stars.
IC 348 have significantly higher surface densities than the lowest
We then show the !MSR ratio for the NMST least massive objects
mass objects (Kirk & Myers 2012), and this gradient is also visually(brown dwarfs) in Fig. 4(b). !MSR = 0.9+0.2−0.3 for the NMST = 10
apparent in our data set. The conclusion in Kirk & Myers (2012)least massive brown dwarfs and this plot suggests that these objects
was drawn from analysing a sample of 232 objects, which was split
are not more or less spatially concentrated than the stars in IC 348.
into two bins (high and low mass). This may introduce an inherent!MSR ∼ 1 for the ACIS-I completeness field, suggesting that ourbias if one of the subsets in question (e.g. the most massive stars)
results are not influenced by the inclusion or otherwise of outlying
contains stars in regions of higher or lower density, because one isobjects.
then not comparing a subset of objects to an ‘average’, such as the
low-mass stars (0.08–1.0 M⊙ ) in the sample.
We measure " LDR = 1.42 for the objects within 14 arcmin of the
4.2.3 Local surface density ratio, " LDR
centre,
and
as
for
the
full
sample,thedifference
betweenthesurface
Figure 4. Data for NGC1333. Panel (a) shows !MSR as a function of the NMST most massive stars. !MSR = 1.2, which is probably not a significant deviation
The
localthesurfacedensitya functionof mass
is shown forall (c)ofdensities
the (b)most
massivecomparedto thewhole
region objects.
as a functionof theNMST
least massive
Again,
deviationfrom asunity
is not likely
to be significant.
Panel
from
unity.of
Panel
shows
!MSR stars
the(bluestarsline)
in oursampleinBDs
Fig.(orange
4(c). The
mediansurfaceforis notthesignificant.
We findsimilarconclusions
when
the averageshows
median surface
densityfor themost massive
starscomparing(red line), cluster
least
massiveline).
Deviations
fromdensity
the medianarenot significant
test substellar
p-values ofobjects
0.92 andto0.22,
The Q-parameter
0.89 (centrally
theiswholecluster isconcentrated).
shown by the blue dashed line, the median forsurfacedensities(KSof thethe respectively).
whole region.

500 – 2000 M⊙ pc−3
500 – 2000 M⊙ pc−3

IC 348【NGC1333の結果】

IC 348は100-500M⦿pc-3，• Q=0.89，N(r) ∝ r

NGC1333は500-2000M⦿pc-3•Λ

の中心集中した球対称分布で説明。

Σ-m：mass segregation や分布の違いの兆候なし。

の初期密度で星団の特徴再現。

Figure 6. N-body simulations of star-forming regions containing 425 stars undergoing cool-collapse with stellar masses from the Luhman et al. (2016) sample
for IC 348 and initial stellar densities of 100–500 M⊙ pc−3 . In panel (a), we show the evolution of the Q-parameter; in panel (b), we show the Q−"MSR
plot and in panel (c), we show the Q−#LDR plot. In panels (b) and (c), the simulation data at 0, 1 and 3 Myr are indicated by the plus signs, open circles andcrosses, respectively. In all three panels, the blue diamond symbol shows the observational values at 3 Myr. The dashed horizontal line in all panels indicatesthe boundary between a substructured (Q < 0.8) and a smooth (Q > 0.8) distribution, and in panels (b) and (c) the vertical dashed lines indicate "MSR = 1
Figure 5. N-body simulations of star-forming regions containing 425 stars undergoing cool-collapse with stellar masses from the Luhman et al. (2016) sample(no mass segregation) and # LDR = 1 (no enhanced surface densities), respectively.

for IC 348 and initial stellar densities of 5000–10 000 M⊙ pc−3 . In panel (a), we show the evolution of the Q-parameter; in panel (b), we show the Q−"MSR
histories
348 and NGC
and inarepanel
(c),
show
the
In 5.2
panels(b)andwith(c), oftheIC
simulation
data at1333
0, 1 and4347
3 Myr are indicated by the plus signs, open circles andTheplot
simulations
evolvedforwe
10 Myrusing
theQ−#kira integrator
Comparison
IC
348
LDR plot.Dynamicalin the crosses,
Starlabrespectively.
environment (Portegies
Zwart etal. 1999,
2001).
In all threepanels,theblue diamondsymbolshows
the observational
value theat 3initial
Myr. The dashed horizontal line in all panels indicates
In Figs 5–7,
we show
the simulations
set up to constrain
We do not include stellar evolution in the simulations as neither
density
of
IC
348.
In
all
three
figures,thebluediamondsymbolcorthe boundary between a substructured (Q < 0.8) and a smooth (Q > 0.8) distribution, and in panels (b) and (c) the vertical dashed lines indicate "MSR = 1
IC 348 or NGC 1333 contains stars massive enough to evolve sigrespondsdensities),to the observed
value for IC 348 at its current age (3 Myr).
(noinmasssegregation)and # LDR = 1 (no enhanced surface
respectively.
nificantly
the first
10 Myr.

NGC1333

MNRAS 468, 4340–4350 (2017)

Figure 8. N-body simulations of star-forming regions containing 150 stars undergoing cool-collapse with stellar masses from the Luhman et al. (2016) sample
for NGC 1333 and initial stellar densities of 500–2000 M⊙ pc−3 . In panel (a), we show the evolution of the Q-parameter; in panel (b), we show the Q−!MSR
plot and in panel (c), we show the Q−"LDR plot. In panels (b) and (c), the simulation data at 0, 1 and 3 Myr are indicated by the plus signs, open circles andcrosses, respectively. In all three panels, the blue hexagram symbol shows the observational value at 1 Myr. The dashed horizontal line in all panels indicatesthe boundary between a substructured (Q < 0.8) and a smooth (Q > 0.8) distribution, and in panels (b) and (c), the vertical dashed lines indicate !MSR = 1(no mass segregation) and " LDR = 1 (no enhanced surface densities), respectively.

238

F. C. Pignatale et al.

43. Size and density sorting of dust grains in SPH simulationsof protoplanetary discs【ガス円盤中ダストの振る舞いに関する基本概念のまとめ】(式1) サイズsd ，密度ρd のダスト粒子に対するF.C. Pignatale, J.-F. Gonzalez, Nicolas Cuello et al. (MNRAS, 469 (1): 237-254)
https://arxiv.org/abs/1703.10385

Stopping time (ts)とaerodynamic parameter (ζ)

【背景】始原的隕石コンドライトは，(1)コンドリュールのサイズ，(式3) 落下がもっとも効率的に起こるサイズ sopt :(2)Fe/Si比，(3)鉄全体に占める酸化鉄の割合に，クラスごとの特徴有。

ts = ΩK-1を満たす場合で，Figure 1. Average diameter of chondrules in different groups of chondrites.
Figure adapted from Palme & Jones (2003) and Scott & Krot (2005).

density of the considered dust particle. Moreover, the value of sopt
midin the mid-plane, sopt
, can be written as

238

F. C. Pignatale et al.

mid
sopt
= √

!g
2πρd

(4)

,

(Fouchet, Gonzalez & Maddison 2010), where ! g is the gas surface
midon the particle intrinsic density isdensity. The dependence of sopt
also evident.
The different response to the gas drag of dusty aggregates withdifferent sizes and densities is thought to have contributed to thedetermination of the physical and chemical properties of the pristine complex aggregates in our early Solar system: chondrites(Scott & Krot 2003; Cuzzi & Weidenschilling 2006). Chondrites
are undifferentiated meteorites, which are characterized by the presence of chondrules, small spherules 0.01–10 mm in size (Scott& Krot 2003). Chondrites host other components: (i) calcium–aluminum rich inclusion (CAIs), made of refractory material, (ii)Figure 1. Average diameter of chondrules in different groups of chondrites.
Figure 2. Fe/Si ratios for different groups of chondrites normalized to CI
olivine aggregates, characterized by fine olivine grains,
Figure adapted from Palme & Jones (2003) and Scott & Krot (2005).amoeboid chondrites,
which are assumed to be the solar standard. This figure is adapted
metals andfrom
refractorycompounds,(iii) metallic grains (Fe–Ni)
Palme & Jones(2003).
density of the considered dust particle. Moreover, the value andof sopt(iv) matrix, an unequilibrated volatile-rich mixture (MacPhermidin the mid-plane, sopt
, can be written as
son 2003; Scott & Krot 2003; Scott 2007). Chondrites are among!gmidthe(4)
oldest rocks known. They retain radiometric ages corresponding
sopt = √,2πρdto the first few Myr after calcium–aluminium rich inclusions [whose(Fouchet, Gonzalez & Maddison 2010), where ! g is the gas surface
formation dates at 4567.2 ± 0.6 Myr ago (Amelin et al. 2002)], andmidon the particle intrinsic density isdensity. The dependence of sopt
thus record events that occurred at the beginning of the Solar system
also evident.
The different response to the gas drag of dusty aggregatesformation.
withdifferent sizes and densities is thought to have contributed to The
the formation of chondrules was an ongoing process that ocdetermination of the physical and chemical properties of thecurredpris- from the formation of CAIs and lasted 3 Myr (Connellytine complex aggregates in our early Solar system: chondrites
et al. 2012). The size of chondrules varies within each clan as well
(Scott & Krot 2003; Cuzzi & Weidenschilling 2006). Chondrites
as between different chondrite groups (Rubin 2010), see Fig. 1.
are undifferentiated meteorites, which are characterized by the presence of chondrules, small spherules 0.01–10 mm in size There(Scott is a general size–density correspondence between chondrules,& Krot 2003). Chondrites host other components: (i) calcium–
metallic grains (Fe–Ni) and sulphide grains, within the same groupaluminum rich inclusion (CAIs), made of refractory material,of (ii)chondrites, for which (ρs)chond ∼ (ρs)metal ∼ (ρs)sulph (Benoit,
amoeboid olivine aggregates, characterized by fine olivine grains,
Akridge & Sears 1998; Kuebler et al. 1999). Size sorting and size–
metals and refractory compounds, (iii) metallic grains (Fe–Ni)
density sorting due to gas drag in different scenarios (local turand (iv) matrix, an unequilibrated volatile-rich mixture (MacPherbulences, large disc scale turbulences, jet-flow) are some of theson 2003; Scott & Krot 2003; Scott 2007). Chondrites are among
the oldest rocks known. They retain radiometric ages corresponding
proposed mechanisms to explain the chondrule size distribution,
to the first few Myr after calcium–aluminium rich inclusions [whose
the assemblage of the chondrite components, and the size–density
formation dates at 4567.2 ± 0.6 Myr ago (Amelin et al. 2002)], andcorrespondence
betweenchondrules,
metallic
grains(Fe–Ni)andFigure 3.
Urey–Craig
diagram illustrating
the ratioof oxidized
versusthus record events that occurred at the beginning of the Solar system
metal+sulphidesilicon,in different
groups of chondrites.
sulphide grains,
within ironthe tosame
groupof chondrites(ClaytonValues
1980;
formation.
are 1998;
expressed
in mole ratio.
This1999;
diagramCuzzi
is adapted
Righter, Liffman
Drake &
The formation of chondrules was an ongoing process thatoc- et al.
BenoitKuebler
et al.
et fromal. 2001;
Scott (2006).
curred from the formation of CAIs and lasted 3 Myr (Connelly
2005; Zanda et al. 2006; Jacquet et al. 2012).
et al. 2012). The size of chondrules varies within each clan as well
Chondrites
exhibit different degrees of elemental fractionaAnders 1970). The Fe/Si ratio of chondrites normalized to CI
as between different chondrite groups (Rubin 2010), see Fig. 1.
tion,
for
examplein their(Larimerchondrites (whose
Fe/Simetal–silicate
ratio is close to content
the solar value)varies&There is a general size–density correspondence between chondrules,(1)コンドリュール
粒径Figure 2. Fe/Si ratios for different groups of chondrites normalized to CI
chondrites, which are assumed to be the solar standard. This figure is adaptedfrom Palme & Jones (2003).

(3)酸化鉄含有量【用いたSPH法の概要】• ガス円盤は最初に適当なパラメータの静水圧平衡円盤を置き，8000yr進化を追って安定させる。α=0.01。r=20-400auの範囲。
• 8000yr後に，ガス上に以下の化学組成を持ったダストグレインを投240 F. C. Pignatale et al.

(2)Fe/Si比入。初期サイズは10μmで一定。
Figure 3. Urey–Craig diagram illustrating the ratio of oxidized versus
metal+sulphide iron to silicon, in different groups of chondrites. Values
are expressed in mole ratio. This diagram is adapted from Righter, Drake &Scott (2006).

Anders 1970). The Fe/Si ratio of chondrites normalized to CI
chondrites (whose Fe/Si ratio is close to the solar value) varies
according to the chondrites group (Palme & Jones 2003; Scott &Krot 2005), see Fig. 2. Moreover the ratio of oxidized iron andmetallic iron+sulphides to silicon, changes for different chondrite
groups, Fig. 3. The chemical and physical properties of chondrites
suggest that chondrites formed, accreted and evolved in distinct discregions and at different times, within different chemical reservoirs(Scott & Krot 2005).
Aerodynamic sorting, photophoresis, magnetic properties, grain
aggregation and heating processes, both in large (disc, eddies)and small (chondritic parent bodies) scales, are among thesuggested theories to produce the observed trend (Larimer &Wasson 1988a,b; Kuebler et al. 1999; Moore et al. 2003; Wurm,
Trieloff & Rauer 2013; Cuello, Gonzalez & Pignatale 2016).

【本研究の内容】原始惑星系ガス円盤の中に，いろいろな組成を持ったダストグレインを初期条件として配置し，それが合体成長しつつガス抵
抗を受けながら分布を変えていく（沈殿・中心落下）様子をSPH法で解き，その様子を考察することで上記の起源をえる手がかりを得たい。
MNRAS 469, 237–254 (2017)
metallic grains (Fe–Ni) and sulphide grains, within the same groupof chondrites, for which (ρs)chond ∼ (ρs)metal ∼ (ρs)sulph (Benoit,
Akridge & Sears 1998; Kuebler et al. 1999). Size sorting and size–
density sorting due to gas drag in different scenarios (local turbulences, large disc scale turbulences, jet-flow) are some of the
proposed mechanisms to explain the chondrule size distribution,
the assemblage of the chondrite components, and the size–density
correspondence between chondrules, metallic grains (Fe–Ni) andsulphide grains, within the same group of chondrites (Clayton 1980;

according to the chondrites group (Palme & Jones 2003; Scott &Krot 2005), see Fig. 2. Moreover the ratio of oxidized iron andmetallic iron+sulphides to silicon, changes for different chondrite
groups, Fig. 3. The chemical and physical properties of chondrites
suggest that chondrites formed, accreted and evolved in distinct discregions and at different times, within different chemical reservoirs(Scott & Krot 2005).
Aerodynamic sorting, photophoresis, magnetic properties, grain
aggregation and heating processes, both in large (disc, eddies)(式4) 特に密度成層しているガス円盤での中心面では• ダストの衝突合体はLaibe+(2008)の処方箋に従う。
100%合体，同じ化学組成同士のみ合体（すぐに分布がspeciesごとにバラけるので良いと言っている）。
• 破壊は入っていない。

Table 1. Dust distribution from Pollack et al. (1994) describing thechemical composition for large discs with related wt% and intrinsic
densities. Ratios between groups of different species are also shown.
Group

Dust species

wt%

Density(g cm−3 )Fe

Metallic iron
Troilite

1
6

7.87
4.83

Si

Olivine andpyroxene

25

3.46

org

Refractory organics
Volatile organics

25
4

1.5
1

H2 O

Ice

39

0.92

RatiosH2 O/Si
Fe/Si

1.56
0.28

In order to account for the different chemical species, we modified the SPH code described in Barrière-Fouchet et al. (2005) by【結果のハイライト】
1. ダスト投入直後に，ρdが異なること
による組成層構造(Fig. 4左上，sdが成長するより早く起こる)
2. 成長してsoptmidに達すると落下。動
径方向の組成勾配が発生(Fig. 5も)
3. 時間が経つと ζ でダスト分布構造が
242
F. C. Pignatale et al. Fig. 7)。
支配されている(式4,same size (ζ i differs only because of their intrinsic density). From
Dullemond & Dominik (2004),

沈殿時間
Z
4 σ ρg cs=,
tsett =
2vsett
3 m $k(6)

A second phase of vertical settling【ダスト分布断面図の時間発展】
inner discand, at later times, in thesettle towards the mid-plane, remixing
dust. This second stage of vertical sethe evolution of the aerodynamic para(ρdsd)-1=ζ-1
MNRAS 469, 237–254 (2017)【ダストサイズの半径依存性の時間発展】

Figure 5. Edge-on view of the spatial evolution for icy (black), silicate (red), sulphide (green) and iron (blue) grains at four evolutionary stages. Species aresuperimposed for ease of reading. A fast dust vertical settling is followed by an efficient dust radial drift. The effects of different dust chemistry in determining
the rate of settling and drift are evident.
Dust sorting in protoplanetary discs 245

橙: 水氷のsoptmid
茶: 鉄のsoptmid

Fig. 7 the icy particles for which ζicy < ζsil , are the particles that
populate the icy contour of the disc in Fig. 5. As grain growth
proceeds, ζ of the lighter material on the surface of the disk increases and becomes comparable to the values that characterized
the denser material at earlier stages. We have a superimposition ofthe ζ values with ζ icy ∼ ζ sil and the vertical settling of the lightermaterial becomes more efficient. This phase of settling is, thus,
size driven.
The introduction of lighter material into the mid-plane is more
efficient in the inner zone of the disc (see Fig. 5). At the end of
our simulation and in the inner ∼80 au, all the icy particles are
introduced in the denser mid-plane. In the outer part of the disc a
vertical chemical sorting can still be noticed. This behaviour is dueto the lower growth rate in the outer disc [see Fig. 4, and Laibe et al.
(2008)], where smaller and lighter icy grains will remain coupled
to the gas longer.

3.3 Radial drift
After the first ∼40–50 kyr, the radial drift of the dust starts to become
extremely efficient for the denser grains (see Fig. 5). We see a radialsorting of chemical species with time. The outer disc becomes
depleted in heavy particles in t ∼ 50 kyr. Fig. 8 shows the surface
density of different species at the end of the simulation: the discoutside ∼110 au is iron depleted, outside ∼200 au sulphide depleted
and outside 250 au silicate depleted. The regions beyond 250 au are
ice rich. The different maximum values of the surface densities are
due to the differences in the initial amount that characterizes eachspecies.
As reported in the introduction, the dust radial drift is driven by
the optimal drift size proper to each dust particle (see equations 3
and 4). In Fig. 4, we reported the evolution of the radial profile
mid
for water ice and iron at different evolutionary stages. Ironof sopt
particles have a smaller optimal drift size than water ice particles.
Looking at Fig. 4 it can be seen that the smaller optimal drift sizefor iron particle is leading to a radial chemical sorting of the dust.
Similar to iron, sulphides and silicates follow the radial drift dictatedmid. Not all the water-ice particles in the outer disc reachby their sopt
their optimal drift size by the end of the simulation, making theradial drift of ice overall less efficient.
Fig. 9 tracks the radial drift (top), s/sopt (middle), with sopt calculated using equation (3), and the size (bottom) as a function oftime for three particles with different intrinsic density (water-ice,
silicate and iron) which are located at the same position at the beginning of the simulation. As the growth proceeds, the iron particle
reaches the s/sopt = 1 point before the lighter particles and starts
to drift inward more efficiently. Lighter particles keep growing inplace before reaching their optimal size and starting to drift towards
the inner regions of the disc.

【ダストζ分布：氷と鉄の比較】

MNRAS 469, 237–254 (2017)

Figure 4. Radial size distribution for icy (black), which comprise water ice, volatile organics and refractory organics, silicates (red), sulphides (green) and iron(blue) particles at four evolutionary stages. Species are superimposed for ease of reading. The two curves represent the optimal drift size for water ice (orange
with open squares) and iron (brown with open triangles), calculated using equation (4). Grain growth proceeds faster in the inner zones than in the outer zones.
Moreover, the optimal drift size is a function of the intrinsic density of the dust. Thus, denser grains will have a smaller optimal drift size compared to lighter
grains. Since grains are growing, denser particles will start their radial drift at earlier stages in the outer disc, leading to a radial chemical sorting.

Figure 7. Aerodynamic parameter for icy (black) grains and silicates (red) grains at four evolutionary stages. The double tail for the icy grains is caused by
the fact that we are considering all the three icy populations (water ice, volatile organics and refractory organic) that have intrinsic density 0.92 ≤ ρ d ≤ 1.5.
When the size of the grains with different density is comparable, the heavier grains separate from the lighter grains and start to settle towards the mid-plane.
As the lighter grains grow, their aerodynamic parameter increases and they start to behave as heavier grains and settle towards the mid-plane. After t ∼ 50 kyr,the vertical chemical separation of grains in the inner disc out to 80 au is lost.

In order to quantify in more details the change in the chemistry
in the whole time range, we report in Fig. 11, from left to right, thetotal time of the simulation. Moreover, these plots will give us an
idea of the chemical composition of the dust from which aggregates【その他】• SPHなので個々の粒子の履歴を追える。
• 組成の分離・サイズ分離が同時並行で進むので，この線で考えていけば，
コンドライトの起源の謎にも迫れるかもね。

44. A Multi-Wavelength Analysis of Dust and Gas in the
SR 24S Transition Disk

【13CO, C18O(J=2-1)】

The Astrophysical Journal, 839:99 (11pp), 2017 April 20※ 分子雲成分の混入で，vlsr = 2.7-4.05km/s
Pinilla et al.
では放射がよく捉えられていない。

P. Pinilla, L. M. Perez, S. Andrews et al. (ApJ, 839: 99)https://arxiv.org/abs/1703.09227【本研究の内容】SR24S，SR24NのALMA Band 6観測。SR24Sについて
は，先行研究であるBand 9データと合わせ，ダスト連続波の詳しい構造やSpectral Index分布をデータから導出。SR24S円盤の穴の生成機構や
SR24Nのダスト上限値（<0.12M⨁）の意味を議論。
The Astrophysical Journal, 839:99 (11pp), 2017 April 20

Pinilla et al.

【ダスト連続波(λ=1.3mm) 観測結果】

Figure 3. Left panels: channel maps of the 13CO (top panels) and C18O (bottom panels) emission in SR 24S from 0 to 9.45 km s−1. The spectral resolution is1.35 km s−1 and the rms is around 1.4 mJy beam−1 per channel for both lines. The contour levels are 20%, . . . , 100% of the peak of the dust-continuum emission.
Right panels: 13CO and C18O (J=2–1) spectrum by integrating over a circular area centered at the location of SR 24S and with a radius of 1″.

et al. (2014). We summarize the properties of each image incavity and a ring. The 1.3 mm emission strongly decreases
inside the cavity where the ﬂux is reduced by around 85%. In
Table 1. The continuum emission is detected with a signal-tocontrast, the 0.45 mm emission shows a shallower cavity, withnoise ratio (with respect to the peak) of 146 for the 0.45 mm
the emission reduced by about 24% compared to the peak ofdata and 256 for the 1.3 mm data (see Table 1). The total ﬂux atemission. In addition, the position of the peak of the ring is0.45 mm is 1.9 Jy and at 1.3 mm it is 0.22 Jy. Calculating thelocated further out at 1.3 mm. However, this contrast anddust disk mass from 1.3 mm ﬂux, and assuming the same
location of the cavity can be affected by the beam convolution
opacity and temperature as for SR 24N, we obtain thatand a more detailed analysis of the intensity proﬁles is done inPinilla et al.
The Astrophysical(11pp),
2017 April
Mdust,SR 24SJournal,~ 3.0 ´839:99
10-4 M
a 20
dust disk ratio: , implying
the visibility domain in Section 4.1.
between the southern and the northern component of 2840 .
Nonetheless, Equation (1) assumes optically thin emission,
3.2. Gas emission
which may not be the case for SR 24S, especially close to thelocation of the ring (see. Section 4.2). If only part of theBoth 13CO and C18O (J=2–1) lines are detected, but areemission is optically thin, the dust mass for the disk aroundaffected by foreground absorption from the nearby dark cloud.
SR 24S is underestimated, which increases the dust mass disk
In particular 13CO is more contaminated than C18O because
ratio between the southern and the northern components.
C18O is more optically thin than 13CO. Figure 3 shows the
Taking the total ﬂux at each wavelength, the integrated
channel maps of the 13CO and C18O emission in SR 24S from 0
spectral index is given by amm= ln (F1.3 mm F0.45 mm )to 9.45 km s−1. In addition, the 13CO and C18O (J=2–1)
ln(0.45 mm 1.3 mm) = 2.02 0.13 (the error includes aspectrum is shown in Figure 3, which is obtained by integrating
calibration uncertainty of 10%), which is lower than the value
over a circular area centered at the location of SR 24S and withpreviously reported (Pinilla et al. 2014) based on SMA anda radius of 1″. These channel maps conﬁrm the presence of
13
ATCA observations at 0.88 and 3.0 mm (Ricci et al. 2010;
CO and C18O in the SR 24S disk, but also the effect of theAndrews et al. 2011). This low value may indicate grain
foreground absorption, in particular in the channels of 2.7 andgrowth and/or a small cavity, but most likely arises from4.05 km s−1. Thus, the asymmetry of the double-peaked
13
18
Figure 4. Zero-momentmapemissionof CO as(leftdiscussed
panel) andinCSection
O (middle
disk
SR 24S.
levelsare due
20%,to. .this. , 100%of the peak of the
optically thick
4.2. panel) of the transition
velocity
proﬁleforThebothcontour
lines islikelyforegrounddust-continuumFigure
emission.
Rightpanel:thenormalized
ﬂuxﬂuxalongnormalized
the PA of theboth zero-moment maps. For comparison the ﬂux of the continuum emission is
2 alsoshows
continuum
to diskthe from absorption.
overplotted.peak of emission at 0.45 and 1.3 mm of a radial cut along the
Figure 4 shows the zero-moment map for 13CO and C18O
PA of the disk (obtained in Section 4). Both proﬁles reveal aobtained from −1.35 km s−1 to 10.8 km s−1, where the※ 積分強度図：星の位置にピークが来ているようである。

Figure 1. ALMA dust-continuum observations of the SR 24 system at 1.3 mm, with a resolution of 0 18×0 12. The contour lines in the left panel correspond to
3sN , where sN = 75 m Jy beam-1 is the rms measured at the location of the north component. The right panel corresponds to a zoom-in of the image centered at thelocation of the south component SR 24S.

【SR24Sダスト円盤の複数波長マップと長軸の輝度分布】
Figure 2. Continuum observations of the transition disk SR 24S. Left panel: ALMA continuum map at 0.45 mm. Middle panel: ALMA continuum map at 1.3 mm.
Speciﬁc details are summarized in Table 1. For both maps, the contour levels are 10%, 20%, . . . , 90% of the peak of emission. Right panel: normalized continuum
ﬂux at 0.45 and 1.3 mm along the PA=24° of the disk (error bars are also included, which are of the size of the points).

channels contain signiﬁcant emission (25s , with s = 1.4
we assume an axisymmetric disk (Figure 2), and thus we focus
−1
−1
13
4
mJy beam per 1.35 km s channel). For CO, inside a circle
on ﬁtting the real part of the visibilities. The Fourier transform of(leftandtransition
C O (middle
panel)
the Thetransition
disk
SR
24S.
The 20%,contourare100%of thethepeakof theruv =uf cos. .levels
i. +vf ,20%,u. f. ,peak
=
u cos
f+
v sin
f and
where
with
anel)panel)of the
disk
SR of
24S.
contourlevelsare, 100%
of .theofnormalized
ﬂux along
theofPAdisk frominsidethe same
circle∼0of the7 radius,
theboth zero-moment maps. For comparison the ﬂux of the continuum emission isof the disk from −1both zero-moment
maps. For vcomparisonof fthecontinuum
emissionf +ﬂuxv cos, andi and f being
the isinclination and
f = - u sin the−1
is ∼0.5 Jy beam km s , and approxiposition angle of the disk, respectively.
mission comes from the inner part. ThisTo ﬁt the morphology of the disk, because the visibilities andat 【ダスト詳細構造の解析】
the (2
center
withs =
a 1.4
value ofwe assume an axisymmetric disk (Figure 2), and thus we focus
5s , withemissioncontinuum maps reveal a cavity at the two wavelengths, we
1
13
and
rms
ofwe
the
zero-momentmapon ﬁtting thedisk
assumeanaxisymmetric(Figure2),
and thus
we
focus
=−1
1.4theFor
hannel).
CO,
insidea circlereal
partof the thevisibilities.
The
FouriertransformofThe
exploremodelswhere
intensity
proﬁlehasaring
shape.
−1• 軸対称の輝度分布を仮定，円盤中心を位相中心とすることにより，
km
sof ,SR
which
gives
signal-to-noisem circle
24S,
the total
ﬂuxreal parta symmetricbrightness
distribution
canMarkov
beexpressed
inMonteterms ofalocationonﬁttingtheofthevisibilities.
The
Fouriertransformofﬁttingisconducted
using
the
chain
Carlo
−1 and−1
he
peak
the
totalapproximately
ﬂux, respectively. the zeroth-order Bessel function of the ﬁrst kind J0 of the
km
s
,
and
am
(MCMC) method.
Theﬁrst model
we useofis a radiallytal
ﬂux
a13symmetricbrightness
distribution
can beexpressed
in terms
18
Visibilityの実部を使って円盤構造を（イメージングdeconvolutionに依存
CO
and
the
C
O
in
a
o
the
peak
of
the
m the inner part of the disk insidedeprojected
uv-distance,
such
that
symmetric
Gaussianring,
withkind
two extra
freetheparameters, forimatelyofthezeroth-order
Besselfunction
of
the
ﬁrst
J
of
the
disk
is
also
shown
in
Figure4.
For0
mission peaks at the center with a¥
Rpeak , Rwidth , Ftotal , i, PA, x0 anda total of seven free parameters(
しない形で）議論できる。具体的には…
1
ﬂux
of
the
continuum
millimeter
klizedinsidedeprojected
uv-distance,
such
that
V
(
r
)
=
2
p
I
(
r
)
J
pruv r )isrdrgiven,(2 )and the rms of the zero-moment
Real thatuv the intensity radial
0 (2
),
such
proﬁlebyy0−1 of both lines resides inside the
0
km
speak
r1The
with
a, which gives a signal-to¥⎛ (r - R peak )2 ⎞uncertainties
forthewithﬂuxrespect
are alsotoshown
2
2
2(+
the
peak
and
100
V
(
r
)
=
2
p
I
(
r
)
J
2
p
r
r
)
r
=
u
cos
i
v
where
,
with
moment
13
Real
uv
uv
f
I (0r ) = Cfuvexp ⎜rdr
-uf, = u2 cos f ⎟+,(2v)sin f and (3)
4
of
CO
and
es
of
emission
beyond00
he same circle of ∼0 7 radius, the2R widththe inclination⎝ f being
⎠
v
=
u
sin
f + v cos f , and i andandgnal-tof−1observations
−1
ise
of
the
and
they
are
not
Jy beam km s , and approxi- 2
2 of theJournal,
2 whereposition
angle
erive
the
inclination
and PA
from
the
gas
spect
to
The
Astrophysical
839:992017
20of the disk as
constant
C isrespectively.
with
ﬂux
r
=
u
cos
i
+
v
udisk,
urelatedcos f(11pp),+ vthesintotalfAprilwhere, withandcomes from the inner part.
uv This f
f =
f the
eius,
dust-continuum
Moreover, To ﬁt the morphology of the disk, because the visibilities andthe withv emission.
hecenteravalue
ofFinclination
total= -ofuthe
sinchannels,
f + vcontinuum
cos
and
i and
f Cbeing
theand narrower
thatf ,theregions
where
accumulates
becomeund absorption in fsome
maps
reveala=dustcavityatthetwowavelengths,
we (for
.
4)
¥
he
rms
of
the
zero-momentmap
pproximasses
from theposition
current observations) J0 (0) rdr
I (rlonger
exploremodelswhere
the intensity
proﬁlehasa ring shape.
Thelargergrains(and therefore
wavelengths).
Addition−1
angle ofofthe
disk,respectively.
ò0 for
s
,
which
gives
signal-to-noise
rt. Thisoneby e.g., Williams & Best (2014) andﬁtting
usingthethe
Markovchain
Montenarrower
Carlo atally, is
it isconducted
expectedthataccumulation
is radially
To ﬁt the morphology
of
the
disk,
becausethevisibilities
andand the total ﬂux, respectively.
Themethod.
cuts along
PA ofmodelthe disk
in useFigurethat theueof(MCMC)
Thetheﬁrst
we
is 2ashow
radially
13
18
longertimes
ofevolution(1
Myr),
becausemicron-sized
dust
CO
and
the
C
O
in
a
ak
of
the
continuum
maps
revealacavityatthetwowavelengths,
we
ring
is
not
necessarilyasymmetric
Gaussianaroundthepeakponentof the SR 24 system (SR 24N),symmetric Gaussian ring, with two extra free parameters, for innt
map
particles
requiremore (intimetoagrowtomillimetersizes
in the13
isk is alsoofshownin4. Fornothingtheradialdirection
particular
for
the
0.45
mm
emission),
COexplore
orFigure
C18O models(i.e.,
detection
where
theintensity
proﬁlehas
ringshape.
Thea total of seven free parameters(Rpeak , Rwidth , Ftotal , i, PA, x0 and−1o-noiseux
ofthecontinuum
millimeterof thedisk,
fromother
where
they willthen drift
towardandparts
hence
we
use twodifferent
modelsto mimicavalue of aroundﬁtting∼1.5 mJy
beam
pery0),outer
such
that
the
intensity
radialproﬁle
is
given
by
is
conducted
using
theMarkov
chain
Monte
Carlo
3つのモデルakof bothlines resides inside theasymmetric(still azimuthally
symmetric
ourively.
the radiallypressure
bump. Atring
longertimes (∼5 Myr),the since
emission(MCMC)shown
method. from
Themodelsﬁrstmodels
we⎛ﬁttinguseisbeaa)part8
2 ⎞radiallynties
aremodelfocusedontherealof the visibilities).
Ina
(
r
R
the
is
expectedtosymmetricring.
As
O infora the ﬂux are alsopeak
Iof(rtwo)these= Cextraexp ⎜ (3 )⎟ ,asymmetric
Gaussian consequence,
ring,
with
free
parameters,for•
動径方向単純ガウシアン
4 of 13CO andmission beyond
0symmetricthe ﬁrst
modelsweassumeanGaussian2
the morphologyoftrappedis expected to
e4.
4.observations
ForAnalysisand they are not
2Rthe⎝ that⎠ at dust
width
with
two
different
widthscoincidethelocationof thehe Data
FtotalRpeak ,ring
Rwidth,the, i, PA,x0 anda total of seven free parameters(beanasymmetricinradialdirection(whichcanbelimeterpeakofemission,suchthat
e. inclination
andyPA
from the gas
where
the constant
C is R
relatedwiththeﬂux of thediskasradialproﬁleis <given
bytotalDisk Morphology0), such that the intensity
mimickedassuming
inEquation(5))
atshorterR
width
width2side
the emission. Moreover,continuum⎧(r - Rispeakformed
)2
F
times
after
the
pressure
bump
(1
Myr),
becoming
alysisforthethemorphology
total• ﬁtting
2つのガウシアンを貼り
2
C
exp
for
r
R
orptioninsome ofchannels, of the⎛ (r C-⎪
⎞
peak
shown
2
(4 )
.
⎪=R peak2R width¥ )ntinuumemissionisperformedinthenarrowerandradially
symmetricatlonger
times
(∼5
Myr;
see,
fromandthe current
observations of I (r ) = C exp ⎜I-(r ) = ⎨ ò I (r )⎟J,0 (0) rdr
.
(5 )
(
3
)
CO
合わせたもの(外側の方が
2
0
2
(
r
R
)
e.g.,
two
wavelengths
separately.
We work e.g., Figure⎪RCwidth
4 fromPinillaetal.2 peak2015).for r > Rpeak
Williams& Best(2014) and
2
⎝
⎠
exp
⎪
are
not since
2R width2in Figure 2 show that thev) point
we do not assume any TheSecond,
より広がってる？)
cuts alongthe⎩ PA aofcombination
the disk
we assumeof a Gaussian proﬁle withheﬂux,
positionangle,ring
the
gasSR
not necessarily
a symmetric
Gaussianaroundthe peaknamely
inaisispower
law.
This
also
hasﬂuxeight
freeparameters,of total
the
24inclination,system
(SR
24N),
where
the
constantC
related
with
the
total
of
the
disk
as
R
,
R
This
model
has
a
total
of
eight
free
parameters:
peakwidth ,
13 these are
18free parameters of eachthe radial direction (in particular for the 0.45 mm emission),Hence,
nreover,of CO or C O (i.e., nothing
Rpeak, Rwidth, γ,, F
, i,x PA,x0y, andy0,radiallygiven by
total
F
,
i,
PA,
,
and
.
This
asymmetric ring
R
total
0
0
width2
F
−1
,
i,
PA,
x
and
y
,
being
x
and
y
(
total
0
0
0
0
F
and
hence
we
use
two
other
different
modelsto mimic a
total
fannels,around ∼1.5 mJy beam per2(⎞4⎤) trapping in⎡ (stillby theof particle= model. azimuthally
m the center taken at a2000 =16:26:58.5,C⎛ results¥ is also motivated()
rRradially
asymmetricring
symmetric
since our
peak
g
•
ベキ乗
+
ガウシアン
⎥
⎢
ions
of
(6 )
I(r(r))J0=(0Cbumps.
r +These
expreal-part of⎟ .
⎜models) rdr
radialpressureof2thedustvisibilities).
evolution
predict
As a ﬁrst approximation for the structure,models
ò0are IfocusedonﬁttingtheIn⎢⎣
2R width ⎠ ⎥⎦⎝14) and (inner diskの寄与を含む)
the ﬁrst of these models we assume an asymmetric Gaussian
5 PA
The cuts along thethe disk
Figure2 isshowthatlocation
the theofpotentialThe
motivation
ofinthismodel
toatinvestigate
Analysiswithtwoof
different
widthsthat
coincidethetheemissionfrom theinnerand its possible
withring is not necessarily
aofsymmetric
Gaussianthe peakdependency
inpeakemission,suchthat diskaround
RMorphology
24N),
wavelength.
the radial direction (inparticular
0.45 mm emission),nothing⎧ for the(r - R peak )2
orof theFor other
the ﬁts,
we
used
emcee
(Foreman-Mackey
et al. 2013),−1ﬁtting the morphology
C
exp
for
r
R
peak
⎪
2
and
hence
we
use
two
different
modelstomimica⎪
per is performed in the2R widthemissionwhichallowsustoefﬁciently
sample the parameter
space
⎨
.
I (still(r ) = azimuthally(5) inradially
asymmetricring
symmetric
since
our
2
(r - R
wavelengths separately. We work
peak )
order to maximize
thelikelihood
result for each model.
⎪

ò

ò

(
(

(

)
)

)

1.30 2mm
Table
42.15-2.67
Results from the MCMC Fitting ALMA Data

Note. Ring model (Equation (3)).

21.41-2.04

Note. iRing
(3)).
R
F
R
(au)
(au)
(Jy)
(°) model (Equation
PA (°)
Data
【結果】
The
36.62(11pp), 2017 April
ﬁxed
ﬁxed
0.45
mmAstrophysical20.66 Journal, 839:99
1.85 20
Table 3•1.30似たようなフィットのあい具合。
Results
Fitting
Data
mm
42.15
0.21 from the MCMC
46.17
21.41
Table
2 ALMA24.73
width

peak

+3.25
-3.17

+2.36
-2.49

+0.16
-0.16

+2.29
-2.67

+2.69
-2.04

+0.01
-0.02

Rpeak (au)Data Ring model (Equation
Note.
(3)).

Datamm0.45

0.45 mm1.30 mm

total

+peak
2.06 (au)20.88R
-3.02

+3.25
20.66
+2.85 -3.17
37.452.91

+2.78
-1.02

+3.16
-1.31

x0 (mas)y0 (mas)+0.30-3.170.17+0.162.900.34+0.45-1.400.97+0.33
2.640.78

Results from the MCMC Fitting ALMA Data
Rwidth (au)Rwidth2 (au)
Ftotal (Jy)i (°)
PA (°)
RwidthRipeak(au)
Rwidth (au) 35.77+1.32 FData(°)ﬁxedPA(au)(°)
total (Jy)ﬁxed
1.83+0.19
28.81+3.56
-1.57

-2.54

-0.16

+2.06
+2.36
+0.16
0.45mm
20.88
36.62ﬁxed-3.02 +2.87
1.85
+3.96
+1.13 Table
2.49
0.16 +0.01
3
16.46-2.94
25.00
0.21 0.02
45.76-0.87
Results from-1.67
the MCMC Fitting-ALMA
Data
+2.85
+0.01
+2.78
+2.69
1.30mm
37.45
0.21
46.17
21.41-2.91
0.02
-1.02
2.04

0.21-0.02

+3.56
28.81
ﬁxed
-2.54
+2.56
23.630.61+3.96+3.16
16.46
24.73
-2.94-1.31

Results from the M
x0 (mas)Rwidth2(au)+x00.07(mas)
−2.57
-0.08
+1.32 +0.30
35.77--1.57
3.17+0.08-0.17-0.540.05+1.13 +0.45
25.00-1.67
1.40-0.97+2.29
1.30 mm
42.152.67
R
(au)
Data
width (au) (5)).
peak
Note. Radially asymmetricring R(Equation

Rwidth2 (au)

Ftotal (Jy)

+2.06
+3.56
0.45
mm Ring model
20.8828.813.02
2.54
Note.
(Equation (3)).

+1.32
35.771.57

+0.19
+0.07
ﬁxed
1.83
Note.
asymmetric ringﬁxed(Equation (5)).−2.57-0.08-0.16 Radially+0.11
1.950.45+2.85
37.452.91+1.13
25.001.67+0.01
0.210.02+0.14
1.630.34

1.30 mm+3.96
16.462.94

i (°)

PA (°)+2.87
45.760.87+2.56
23.630.61

x0 (mas)+0.08-0.540.05

Table 4
Results from the MCMC
Fitting
Table
3 ALMA Data
Note. Radially asymmetric ring (Equation (5)).
Results from the MCMC Fitting ALMA Data
Rwidth (au)
FtotalRpeak (au)γ(Jy) et al. i (°)
PA (°)
Data
PinillaRwidthR+width2
Rpeak
(au)
(au)
i (°)
Datamm0.27 (au)
+2.27
+F
0.19
+1.51
total (Jy)ﬁxed
ﬁxed(au)PA (°)
0.45
1.6421.29
1.8736.06
0.29
-1.62
0.17
-1.25
R
R
(au)
Data
width
peak
Table 4
+1.32
+0.19
+2.06
+3.56
ﬁxed
0.45
mm
35.77
1.83
20.88
28.81
a total
of
4000
steps
with
1000
set
from
the-measurement
MCMC
Fitting
ALMA
Data +2.27+ﬁxed
1.57
-0.16
-3.02
-2.54 ResultsEach+1.51+walkers.
2.91
+0.24
+1.79
+0.02
1.88
+2.14
0.45 mm
21.29
36.06
22.74-1.96
1.34-0.29
1.30 mm43.98-1.46
0.21-0.01
46.31
24.30
-1.62-1.07
-1.25
-0.86

y0 (mas)• 長波長側ほどResults
from the M
x0 (mas)
ピークが外側，幅が狭いのは共通。

+0.23x0 (mas)−4.44γ
-0.54
F
+0.07
−2.57-0.08
+0.27
+0.28
1.64
1
-1.21
-0.29
-0.45

• Eq (5)のモデルでは，やや外側に膨ら+2.85 therefore+
3.96 usedγ emcee
+F
1.13
+
0.01
+
2.87
+2.56
isDataﬁtted
separately
we
to ﬁt a totalof +1.7945.76
R
R 37.45(au) and(au)(°)
PA (°)x (mas)y (mas) +0.08
1.30 mm
16.4625.000.21i -2.91
2.94
1.67 (Jy) んでいる？
0.02
0.87
+2.9123.63-0.61+0.24 - 0.54-0.05
22.74 1.96
1.34
1.30 mm43.98-1.460Note.Power
law21.29+ ring-Gaussian(EquationThe
range
given for1.87
eachparameter
to theﬁxed
95% credible range.
The PA and -i 0.29
areﬁxed for thsixmodels(threemodelsfor(6)).
twodifferent
datasets).corresponds
To
ﬁxed
−4.44
0.45
mm
1.64
2.85
36.06
0.45
mmRadiallydataandare taken
to ring
be thesame
valuestheﬁttingof •the1.3i mmdata (speciﬁcally PA=24° and i = 46 ).
次ページもあるように，リング付近はNote.
asymmetric(Equation(5)). found from
simplify
theﬁttingprocess,
weobtained
the
PA
and
the
using
22.74
1.34
1.30 mm43.98
0.21
46.31+ ring-Gaussian
24.30(Equation (6)).
-1.21
Note.Power law
The range given1.47
for each pa
the 1.3 mm data (since it has better signal-to-noise)for
0.45 mmやや光学的に厚く，ダスト分布のサイ
data eachand are taken to be the same values found from the ﬁtting of t
Note.Powerlaw +ring-Gaussian(Equation (6)).
The range
given
for eachparameter
corresponds toto
the 95% credible range. The PA and i are ﬁxed for the ﬁtting ofmodel,
andkeep
thebest-ﬁtvaluesofthesetwoparameters0.45 mm data and are taken to be the same values found from the ﬁtting of the 1.3 mmズ依存性など議論するには苦しい。
data(speciﬁcallyPA=24° and i = 46 ).
Table
4ﬁt the 0.45 mm data.
width

peak

total

0

+2.27
-1.62

+1.51
-1.25

+0.27
-0.29

+0.19
-0.17

+1.79
-1.46

+2.91
-1.96

+0.24
-0.29

+0.02
-0.01

+1.88
-1.07

+2.14
-0.86

0

+0.23
-0.54

+0.32
-0.76

+0.28
-0.45

+0.39
-0.53

Results from the MCMC Fitting ALMA Data
• Spiralを思わせる非対称残差。

The results are summarized in Tables 2–4 and Figure 6. All
Rwidth (au)
Ftotal (Jy)
Rpeak (au)γi (°)
PA (°)x0 (mas)Data
threemodels show
that
the
peak
of
the
ring
is
locatedfarther
+0.27
+0.23
+2.27
+0.19
+1.51
ﬁxed
ﬁxed
−4.440.45 mm
1.6421.291.8736.060.29
1.62
0.17
0.54
1.25
out and becomes narrower at longer wavelength, with a
2.91
+0.24
+1.79
+0.02
+1.88
+2.14
+0.28
1.341.30 mm of around43.980.2146.3124.30-1.21differencefor -+thelocationof the peak
and
1.96
0.29
1.46∼20 au 22.74
0.01
1.07
0.86
0.45
∼10 au for the width(s). The models of the radially asymmetricNote.Power law + ring-Gaussian (Equation (6)). The range given for each parameter corresponds to the 95% credible range. The PA and i are ﬁxe
ring0.45
showthat R taken to<beRthe, creating a slightly (radially)
width2mm data and arewidthsame values found from the ﬁtting of the 1.3 mm data (speciﬁcally PA=24° and i = 46 ).
asymmetric ring with an outer tail. The model of the power law
together with a Gaussian gives a slightly steeper proﬁle for the
0.45 mm emission. The inclination and position angle obtainedwith the three models give very similar values, with meanvalues of 46° and 24°, respectively, in agreement with thevalues found by Andrews et al. (2011) and van der Marel et al.
(2015), and those in Section 2. The values obtained for the shiftof the center are very low compared with the pixel sizes fromthe observations (0 02 for the 1.3 mm observations and 0 04
for the 0.45 mm observations).
Figure 5. Observations, best-ﬁt models, and residuals for the 0.45 mm data (left panels) and the 1.3 mm data (right panels). In the observations and mode
We image the models and residuals (data-model) using
contours are every 20%, ..., 100% of the peak value (Table 1). In the residual maps (data model), the contours are every 3s (from −12σ to 12σ for the
Figure 5. Observations, best-ﬁt models, and residuals for the 0.45 mm data (left panels) and the 1.3 mm data (right panels). In the observations and model maps themodel and (u,fromv)−6σ ...,
to 100%6σ forofthe
1.3 asmm
model),
showingthenegativeobservations.
contours
with dashed lines.
identical
theactual
ALMA
contours are every
20%,coordinates
the peakvalue(Table1). In theresidual maps
(data model), the contours are every 3s (from −12σ to 12σ for the 0.45 mm
model and5from−6σ to the6σ forsynthetic
the 1.3 mm model),showingof
thethenegative
contours models
with dashed lines.
Figureshows
imagesbest-ﬁtand best-ﬁt models, and residuals for the 0.45 mm data (leFigure 5. Observations,contours
are every
the corresponding residuals. In general, the qualityof thethree20%, ..., 100% of the peak value (Table 1). In the residual−6σ to 6σ
for the 1.3As
mma model),the negativecon
azimuthalvariations.
result, showing
if an asymmetry
ariseexperiment, we found a higher amount of residuals, butmodelwith and from

【同じ解析を動径分布で見た場合】【議論】• 上パネルがモデルから求められた輝度分布（3つのモデル）。

• 中心付近でガスがさほどdeplete していないようなので，惑星が穴を• 下パネルは左から，観測された輝度分布，spectral index，輻射輸送計

開けたのだとしたら，その質量は(0.1-1Mjup)。

算に基づく中心面温度分布を仮定して算出された光学的厚み。

• ガスで中抜けにならない別の可能性としては dead zoneが作る

The Astrophysical Journal, 839:99 (11pp), 2017 April 20

Pinilla et al.

pressure bumpも考えられる。両者の切り分けには，近赤外線散乱光
で小さなダストの分布を見るのが良いだろう (dead zoneの場合はミリ波と同じサイズになるはずであると議論している)。
• 長波長側ほど幅が狭いのは，大サイズダストほど集中した分布を示すとするdust trapの予想と整合的だが，光学的厚みの効果には要注意。

Figure 6. Best-ﬁt models (from left to right: ring, asymmetric ring, and power law+ring) for the 0.45 and 1.3 mm data. For each case, the intensity is normalized to thevalue at the location of the peak of the ring.

• SR24Nはseparation 0.2” (~27au) のbinaryだが，ここでは，すでに惑
星ができているか，binaryの力学相互作用によるランダム速度増大でダストが成長できずにいるのかもしれない（ガスの兆候は観測されている）。

Figure 7. Left panel: normalized ﬂux at 0.45 and 1.3 mm of the azimuthally averaged deprojected ALMA images. The error bars are of the size of the points. Middle
panel: spectral index calculated from the best-ﬁt parameters of the intensity proﬁles at each wavelength (Section 4.1) Right panel: optical depth obtained by calculating
the brightness temperature from the continuum images and by assuming the physical temperature from van der Marel et al. (2015). The error bars are included andobtained from error propagation, taking into account the rms and the standard deviation from the azimuthally averaged ﬂux.

to conclude how signiﬁcant is the amount of residuals, and
their shapes and higher angular resolution observations are
required to conﬁrm if these potential asymmetries are real.
Zhang et al. (2016) modeled the visibility proﬁle of several
disks with multiple rings (such as HL Tau, TW Hya, andHD 163296). Applying their method to our data does not seemsuitable since there is not more than one distinctive peak in thevisibility proﬁle. However, as a test we did an experiment ofprotoplanetary disks have been resolved, where in most of
the cases the spectral index increases radially, evidencing thatthe grain size decreases for increasing radius (e.g., Banzatti
et al. 2011; Pérez et al. 2012, 2015; Trotta et al. 2013; Tazzari
et al. 2016), as expected from radial drift, as seen in dust
evolution models (e.g., Birnstiel et al. 2012).
However, for transition disks the spectral index is expected
to increase toward the outer edge of the cavity, that is, toward45. The star formation law in Galactic high-mass star-forming
molecular clouds
R. Retes-Romero, Y.D. Mayya, A. Luna and L. Carrasco (ApJ, 839: 113)https://arxiv.org/abs/1704.00068【背景】分子ガス柱密度 vs. 星形成効率との関係(Kennicutt-Schmidt則)がいろいろな対象，スケールで議論。

【対象】以下を満たす12領域。距離は1.0-5.4kpc。
(a) they contain an IRAS source with characteristics of an ultra-compact
HII region (Wood & Churchwell 1989),(b) the IRAS sources are associated with the dense cores detected by
CS(2–1) line emission (Bronfman et al. 1996),(c) the line of sight (LOS) for each cloud is devoid of any otherforeground molecular component associated to other MCs as inferredby the 13CO (J = 1-0) spectra(d) they have GLIMPSE (Churchwell et al. 2009) and 24 μm-MIPSGAL(Rieke et al. 2004) Spitzer public data.
The Astrophysical Journal, 839:113 (20pp), 2017 April 20

Retes-Romero et al.

【Σgasの決定】• Normal Spirals中のCO+HIでトレースされる領域は N=1.4±0.15 (Kennicutt 1998)，• IR luminous galaxiesのHCNでトレースされる領域(n(H2)>3×104cc-1)だとN≈1 (Gao &Solomon 2004)• 近年では，系内分子雲に対しても調べられている（混沌としている？）。

• Galactic Ring Surveyのアー
カイブ13CO(J=1-0)データを使い，N(H) ≈ 1021 cm-2以上の領域を対象とする。
• CS(J=2-1)と同じ視線速度をもつ成分のみを抽出。

【本研究の内容】
sub-pcからpcスケールでの12個の巨大分子雲について調べた。一応，本研究の売りとしては，
1. サンプルに光学同定された散乱星雲がなく，分子雲は星形成時の状態をよく保っている。

【YSOsの同定】• MIPSGAL 24μmとGLIMPSEで候補天体選出。
• MIPSGAL 24μm天体については

2. 最低1個のHigh-mass YSOを含む。

AGBやMain Sequenceを注意深く

3. Extinction mapではなく，13CO(J=1-0)で柱密度を求めた。

除去。
• GLIMPSEを使いSED Class決定。
Figure 1. Color composite RGB image of our sample of molecular clouds using Spitzer 24 μm (R), 8 μm (G),and 3.6 μm (B) bands. The velocity-integrated 13CO
column densities are given in contours, with the lowest level corresponding to N(H2)=1×1021 cm−2 (AV≈1.0 mag) and successive levels increasing in steps of5×1021 cm−2. The IRAS source position is marked with the cross symbol. The scale bar corresponding to 5′ is shown as a horizontal bar.

【YSO質量分布の導出】【KS則に関わる議論】

The Astrophysical Journal, 839:113 (20pp), 2017 April 20

Retes-Romero et al.

Table 7
Parameters of the Broken Power-law Model Fit• GLIMPSEデータのみの検出：0.5M⦿を平均とする対数正規分布• 各クラウド中でのΣSFR vs. Σgas (Fig. 10): 折れ曲り，低ΣgasでΣSFR一定。

(Chabrier 2003)のIMFと仮定。

• Σgas の閾値 or 折れ曲り： (150-360) M⦿
MC2• MIPSGAL検出されてClassわけもなされたものについては，近傍の星形成領域で求められているSp. Classごとのβ=L24μm/Lbolのデータをもと

MC9

MC12

MC20
MC21
MC23

MC75

• 24μmのみの検出天体(Class 0/I)は，適当なスケーリングでLbolを推定。
• Classごとで適当な年齢を仮定し，質量への換算。

α
(2)

A
(3)

0.49
2.34
0.80
3.05
0.54
2.80
0.25
1.31
0.73
1.54
0.26
1.94
0.28
2.68
0.23
3.01
1.01

−1.01
−5.33
−1.65
−6.76
−1.18
−6.68
−0.56
−3.14
−1.19
−2.96
0.63
−3.02
0.29
−5.39
0.01
−7.04
−2.01

0.10
0.14
0.10
0.05
0.07
0.35
0.13
0.10
0.12
0.04
0.03
0.17
0.06
0.14
0.06
0.19
0.47

0.61
2.69
0.55
3.35

−1.38
−6.09
−1.70
−8.96

0.15
0.33
0.36
1.18

χ2
(6)

σA
(5)

σα
(4)

R
(7)

Σth
(8)

MC76
MC78
Total YSOs

Retes-Romero et al.

Class I YSOs

y(Σth)
(9)

xi
(10)

0.69
0.71
226.0
1.6
(1–4)
-2
0.19
0.90
K
K
(3–6)
pc . 以前の研究結果と近い。

0.82
2.32
0.50
4.06
0.44
3.50
0.31
1.05
0.59
1.71
Retes-Romero et al.
0.43
2.17
0.33
6.29
0.63
7.75
0.27

0.30
0.10
0.15
0.90
0.91
0.27
0.20
0.10
0.10
0.26
0.14
0.18
0.22
0.34
2.71

0.59
0.92
0.92
0.64
0.82
0.98
0.66
0.94
0.83
0.61
0.93
0.91
0.97
0.95
0.98

211.0
K
285.0
K
255.0
K
180.0
K
150.0
K
237.0
K
360.0
K
K

1.0
K
1.6
K
1.0
K
3.2
K
15.9
K
7.1
K
3.1
K
K

(1–3)
(3–5)
(1–4)
(3–6)
(1–5)
(3–9)
(1–3)
(2–5)
(1–3)
(2–4)
(1–4)
(3–6)
(1-5)
(4–8)
(1–18)

0.26
0.35
0.96
0.98

445.0
K
380.0
K

1.8
K
0.5
K

(1–30)(20–48)(1–20)(16–37)• 傾きは，N=1 やN=1.4とは比べるとかなり急（高Σgas で）
The Astrophysical Journal, 839:113 (20pp), 2017 April 20に，24μmの測光データからLbolを推定する。

The Astrophysical Journal, 839:113 (20pp), 2017 April 20

GMC
(1)

0.07
0.44
0.47
3.85

5.11
3.65
6.68
8.45

• 雲全体で見たKS則(Fig. 12)：Kennicutt
1998とWu+ 2005のNote. Brief explanation of columns: the ﬁrst row lists the ﬁt parameters for the low-density range, while in the next row are shown the ﬁt parameters for the highdensity range; (1) GMC name; (2) slope for the linear ﬁt; (3) Y-intercept value of the linear ﬁt; (4) slope error; (5) Y-intercept error; (6) chi-square value for the ﬁt;(7) regression coefﬁcient; (8) gas surface density intersection value (Σth) in Me pc−2units; (9) ΣSFR-value corresponding to the Σth in Me Myr−1 pc−2 units; (10)range of data points used for each linear ﬁt.

中間に分布。

• 各領域について，YSOsのMFがもとまった。
• Lbol < 10L⦿の個数が合う
ようにChabrier (2003)のField stars’ MFをプ
Figure 12. Globally averaged Schmidt law for the clouds. The Kennicutt(1998) relation is plotted with asolid line, while the linear relation of Wu et al.
(2005) is plotted with adashed line. The data of previous studies for galactic
star-forming regions are taken from c2d+GB surveys (square symbol;
Heiderman et al. 2010) and dense massive clumps (diamond symbol, Wu
et al. 2010; cross symbol from Heyer et al. 2016). The ﬁlled symbols showthevalues for the clouds.

ロットしたのが点線。
• 大質量側でそこからのexcessあり。Salpeter
的なIMF（ベキ関数）で
フィットできる。
Figure 6. Mass function (MF) of the HLYSOs (shaded histogram) compared to a log-normal Chabrier (2003) IMF (dotted curve) that is normalized for each MC so as
to contain the same number of sources as the observed number of LLYSOs in that MC. The contribution of Class I and Class 0/I sources to the histograms is shown by
the shaded part. The error bar for each bin of the histogram corresponds to N statistical uncertainties. The arrows marked with mCI, mCII, gCI, and gCII correspond to
the detection limit for ClassI and ClassII YSOs in MIPSGAL and GLIMPSE surveys, respectively. These values were obtained with the procedure described in
Section 3.0. There is clearly an excess number of HLYSOs over the Chabrier (2003) IMF. This excess is well represented by a Salpeter-like IMF (dashed line).

values of Σgas are increased by a value of 0.6 (in log scale) and
our distribution follows the distributions for dense clumps
Figure 10. Broken power-law ﬁts in the ΣSFR–Σgasplane for each sample MC. The power-law indices for the ﬁt in the low (α1) and high gas density ranges (α2) reported
areby Heyer et al. (2016) andWu et al. (2010) well.The
given in the top-left of the plot. The dashed vertical line indicates the density at the break in ΣSFR. The Kennicutt–Schmidt law with N = 1.4 (thin solid line) and thecorrected
values of our clouds lie on the KS relationship.
Figure 11. ΣSFR–Σgasrelation for (a) the total ofall Classes and (b) Class I
Wu et al. (2005) relation (dashed line) are shown for reference.
YSOs in the clouds that presents the BPL trend. The power-law indices for
It can be noted in the ﬁgure that the average gas densities of
and
α
)
are
given
in
the
top-left
of
the
plot.
The
each
gas
density
range
(α
1
2
the KS relation by a factor of up to 17. They found the factors
In recent work by Heiderman et al. (2010), it has been foundseveral MCs from our sample are clustered around log
dashed vertical line indicates the density
at the break in ΣSFR. The Kennicutt–
to be as high as 54 for regions containing the youngest
sourcesthat the use of 13COin the calculation of mass of a molecular(Sgas)=2.6±0.3, compared to clouds from Heiderman
Schmidt law (thin solid line) and the Wu et al. (2005) relation (dotted line) are(Class I and Class Flat). This latter value overlaps with values
cloud results in an underestimation of the mass compared toetif al. (2010) clustered around log(Σ )=2.0. On the othershown for reference.
gas
for the high-density massive clumps of Wu et al. (2010) andHeyer et al. (2016). Our clouds lie between the linear relationof Wu et al. (2005) and the canonical Kennicutt relation, andmostly related to the lower SFR dense clumps from Heyer et al.
(2016) and Wu et al. (2010).

visual extinction is used, which is considered abetter tracer ofthe mass of the cloud. According to their results, the mass ofthe cloud is underestimated by a factor of four to ﬁve.18
If thiscorrection factor is applied in calculating the mass of oursample of clouds plotted in Figure 12, the result is that the