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【背景】ALMAにより初めて原始惑星系円盤からCH3OH輝線を検出（Walsh et al. 2016; 下図)。

The Astrophysical Journal Letters, 823:L10 (7pp), 2016 May 20
Table 1
Methanol Transitions
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-phase methanol in a nearby protoplanetary disk (TW Hya,
54 pc), the results for which are reported here.
2. OBSERVATIONS

triggered by energetic photons or particles or by energy
released during exothermic chemical reactions (reactive
desorption, e.g., Garrod et al. 2006). The rates for suchprocesses remain relatively unconstrained except for a small setof molecules and reaction systems (e.g., Westley et al. 1995;Öberg et al. 2009b; Fayolle et al. 2011; Bertin et al. 2013;
Fillion et al. 2014; Cruz-Díaz et al. 2016; Minissale
et al. 2016). It also remains a possibility that gas-phasechemistry contributes to the gas-phase abundance (e.g.,Charnley et al. 1992; Garrod et al. 2006). For example, therate coefﬁcient for the OH + CH3OH gas-phase reaction was
only recently determined to be rapid at low temperatures (<100K, Shannon et al. 2013; Acharyya et al. 2015).

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, P. I. C. Walsh). The quasars J1256-0547 andJ1037-2934 were used for bandpass and phase calibration,
respectively, and Titan was used for amplitude calibration. The
Band 7 (B7) methanol transitions listed in Table 1 weretargeted using a channel width of 122 kHz (corresponding to0.12 km s−1). A continuum-only spectral window at 317 GHz
Because the methanol chemistry applicable to disks remains
relatively unconstrained, we adopt a parametric approach to (with a total bandwidth of 2 GHz) was also covered. The total
constraining the location and abundance of gas-phase methanol on-source observation time was 43 minutes. All data were selfin 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 theverticallayers:0.2 - z r - 0.3, where z and r are the disk height and radius,
continuum band at 317 GHz, and using a timescale of 20 s (≈3
respectively (dashed lines in Figure 3). A small grid of models
was run in which the inner and outer radii of the emission were times the integration step). This increased the dynamic range ofvaried (in steps of 10 au), in addition to the fractional
the continuum data by a factor of »30 . Self-calibration using
abundance of methanol (relative to H2). Ray-tracing calculations were performed using LIME (LIne Modelling Engine, the continuum around the methanol lines between »304 andBrinch & Hogerheijde 2010) assuming LTE, a disk inclinationand position angle appropriate for TW Hya (Hughes 307 GHz gave almost indistinguishable results. The rms noiselevel achieved for the 317 GHz continuum following imaging
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

Walsh 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 signiﬁcant 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
domain). This resulted in a synthesized beam of 1 4 × 0 73(-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.
3. RESULTS
3.1. Detection of Gas-phase Methanol
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 red dashedlines in left panel) within the 3s contour of the continuum,
which is marked by the gray contour in Figure 1. The peak ﬂux
density for the stacked line proﬁle is 33 mJy and the rms noiseis 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
density (33 mJy) in the spectrum of W16. Thus, we assume theaveraging can safely be neglected.
W16 considered the Band 7 21 − 20 A−+ (304.208 GHz),(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) transidiﬀ
bintions (hereafter,
B6 lines). The difference in the maximum specific intensity of the synthetic images for these lines between the‘Ediff /Eb = 0.77’ and ‘Ediff /Eb = 0.4’ models does not exceed
45 per cent. The spatial distribution of the CH3 OH emission, however, is significantly different, primarily caused by the difference inthe methanol column densities NM between the models (see Sec-【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

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.

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).

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• TW Hyaに合わせた円盤モデルではガス(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

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

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に含まれる星々分布(Σ)を，質量(m)の関数として表のデータから，Qによる構造解析や星質量によるsegregationの有無，星す。

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. These4341

【IC348の結果】【N体計算との比較】• 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• 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

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).

the orange line. The surface density ratio for the most massive starsis " LDR = 1.77, but a KS test between the two populations gives
D = 0.25 and a p-value of 0.49 so that the two populations sharethe 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.
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,
which suggests that the brown dwarfs reside in areas of lower than
average surface density. However, the KS test between the two
distributions has D = 0.33 and the p-value is 0.20, again suggestingthat the two populations share the same underlying distribution.
Previous studies have suggested that the most massive objects in
IC 348 have significantly higher surface densities than the lowest
mass objects (Kirk & Myers 2012), and this gradient is also visuallyapparent in our data set. The conclusion in Kirk & Myers (2012)
was drawn from analysing a sample of 232 objects, which was split
into two bins (high and low mass). This may introduce an inherent
bias if one of the subsets in question (e.g. the most massive stars)
contains stars in regions of higher or lower density, because one isthen 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 thecentre, and as for the full sample, the difference between the surface
densities of the most massive stars compared to the whole region
is not significant. We find similar conclusions when comparing thesurface densities of the substellar objects to the whole region.

【NGC1333の結果】• Q=0.89，N(r) ∝ r•Λ

and s̄ = 0.64. This is a less centrally concentrated spatial profile
than is measured for the full data set, and corresponds to a uniform
distribution. Again, this is unsurprising as we are pruning the moredistant objects from our determination of Q.

の中心集中した球対称分布で説明。

4.2.2 Mass segregation ratio, !
Σ-m：mass segregation や分布の違いの兆候なし。
In Fig. 4(a), we show the evolution of !
as a function of the N
MSR

MSR

MST

most massive stars in the subset, which is compared to the MSTsof objects randomly drawn from the spatial distribution shown in
Fig. 2. !MSR = 1.2+0.4−0.3 for the NMST = 10 most massive stars, andalso does not deviate from unity if we consider fewer (e.g. NMST = 4)
or more stars.
We then show the !MSR ratio for the NMST least massive objects(brown dwarfs) in Fig. 4(b). !MSR = 0.9+0.2−0.3 for the NMST = 10
least massive brown dwarfs and this plot suggests that these objects
are not more or less spatially concentrated than the stars in IC 348.
!MSR ∼ 1 for the ACIS-I completeness field, suggesting that our
results are not influenced by the inclusion or otherwise of outlying
objects.

4.2.3 Local surface density ratio, " LDR
The local surface density as a function of mass is shown for all of
the stars in our sample in Fig. 4(c). The median surface density for
the whole cluster is shown by the blue dashed line, the median for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
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。

【13CO, C18O(J=2-1)】※ 分子雲成分の混入で，vlsr = 2.7-4.05km/sでは放射がよく捉えられていない。

【ダスト詳細構造の解析】= 1.4• 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，
a circle
Visibilityの実部を使って円盤構造を（イメージングdeconvolutionに依存しない形で）議論できる。具体的には…

【結果】• 似たようなフィットのあい具合。

【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
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。
• 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）。

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】• 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⦿ pc-2. 以前の研究結果と近い。

• 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• 傾きは，N=1 やN=1.4とは比べるとかなり急（高Σgas で）成領域で求められているSp. Classごとのβ=L24μm/Lbolのデータをもとに，24μmの測光データからLbolを推定する。
• 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。
The Astrophysical Journal, 839:113 (20pp), 2017 April 20

Retes-Romero et al.

• 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).

the KS relation by a factor of up to 17. They found the factors
to be as high as 54 for regions containing the youngest sources(Class I and Class Flat). This latter value overlaps with values
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).

In recent work by Heiderman et al. (2010), it has been foundthat the use of 13CO in the calculation of mass of a molecular
cloud results in an underestimation of the mass compared to if
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. If thiscorrection factor is applied in calculating the mass of oursample of clouds plotted in Figure 12, the result is that the