THE STAR FORMATIONNEWSLETTER
No. 296 (#1-5)
塚越崇(茨城大)29 Sep. 2017

1. A Statistical Spectropolarimetric Study of Herbig Ae/Be Stars
2. Improved torque formula for low and intermediate mass planetary
migration
3. The shapes of column density PDFs - The importance of the lastclosed contour
4. Destruction of Refractory Carbon in Protoplanetary Disks
5. How do binary clusters form?

A Statistical Spectropolarimetric Study of Herbig Ae/Be Stars
K.M. Ababakr et al.

• 最もサンプル数の多いHa spectro-polarimetryデータ• 既存のデータ+新規17天体=>56天体のHAeBeサンプル• Ha polarization: 中心星近傍の円盤の証左• 3つのpolarization機構
Spectropolarimetry of Herbig Ae/Be Stars 3• Depolarization• 強い連続波- polarized• 再結合線-unpolarized• HBeで多い• Line Polarization• 内側で生じたHαがdiskで散乱•

acc. shockなど• HAeやTTSで見られる• McLean効果

Figure 1. Schematic showing spectropolarimetry expectations across the Hα line in triplots (top) and (Q, U) diagrams (bottom). In the triplot, the Stokes
intensity (I) is shown in the bottom panel, polarisation (%) in the centre, while the position angle (PA) is shown in the upper panel. The first column showswhere the geometry of the circumstellar environment on the sky is circular and hence no line effect is detected. The other three columns show where thegeometry on the sky is not circular and a line effect is seen. The second column shows a depolarisation line effect, note that the depolarisation across Hα line
is as broad as Stokes I. This depolarisation line effect translates into (Q, U) diagram as a linear excursion from continuum knot towards the central line. The
arrows in the (Q, U) diagrams indicate the polarisation moves in and out of the line effect from blue to red wavelengths. Intrinsic line polarisation is shown inthird column, where Hα line from the accretion compact region is scattered in a rotating disk. In this case the polarisation across Hα is narrower that the widthof Stokes I and a flip is seen in PA caused by a rotating disk. This flip is seen as a loop in (Q, U) diagram. Finally column four shows a different polarisation
signature across the absorption component of Hα which is commonly known as the McLean effect. The figure is adapted from Vink et al. (2002).

• 中心星からの無偏光Hαが星周物質で吸収->再放射した一部が散乱偏光• 非対称成分があると偏光として見える• early Bは低検出率• B7-B8で偏光メカニズムが切り替わる• 後期側->磁気降着優勢• 早期側->Boundary Layer model?

• Line effectと相関なし• 上記は天体幾何にのみ依存

Figure 3. The figure shows the observed line effect across Hα line in each sub group of spectral type of the whole sample of HAeBe stars that have been
observed spectropolarimetrically. Please note that spectral types such as A4, A6 and A9 are not always defined in spectral type classification schemes, and willthus be missing in a graph such as this (Jaschek & Jaschek 1990).

Spectropolarimetry of Herbig Ae/Be Stars

flip in polarisation across the line. This flip appears as a loop when
it is mapped on the (Q, U) diagram. MWC 863 shows two different line effects, a McLean line effect is seen across the absorptive
component while the emission line displays a narrow polarization
which is identified with intrinsic polarisation (in the following sections, the classificaiton criteria are outlined). Fig. 2 also shows theintrinsic polarisation angle which is measured from the slope of theline effect in the (Q, U) diagram. For the depolarisation line effect,
the angle is measured from the (unpolarized) line to the (polarized)
continuum while for the intrinsic polarisation and McLean effect it
is measured from continuum to (polarized) line (see the discussionin Ababakr et al. 2016). Although the direction for both the depolarization (HD 240010) and intrinsic polarization (HD 163296) are
the same in the respective QU graphs, the intrinsic polarization angles differ, as this angle is measured from the line center to thecontinuum in the case of the depolarization, it is measured in the
opposite direction for the intrinsic polarization.

7

21 HBe and 21 HAe stars. 14 objects (25 ± 6%) do not show any
signs of a line effect. The detection rate for Herbig stars of spectral
type B0-B7 is 66 ± 9% while that of the later type (i.e. all other)
objects is 85 ± 7%, a difference that is close to 3σ .

3.2.1

Line effect signatures

The decision on whether to classify a line effect as depolarization
or intrinsic polarization can sometimes be subjective. To avoid suchbiases, we aim to differentiate between the depolarisation and theline polarisation effect in a quantitative manner. To this end, thewidth of the line effect can be used as proxy (see Table 2). The
method was first used by Vink et al. (2002, 2005) to categorize theline effects. They statistically classified stars according to the fractional width [∆λ (pol)/∆λ (I)] at which the polarisation changes
across the line. This quantity measures the width of the polarization over the line divided by the width of the line itself. Generally awide fractional width is associated with depolarisation line effect,
whereas the width of line polarisation effect is often narrower than
3.2 Statistical Results
the depolarisation. Both ∆λ (I) and ∆λ (pol) are measured at Full
We present here Hα spectropolarimetric results from a sample ofWidth at Zero Intensity (FWZI). If the line effect is detected across
56 HAeBe stars combined from this work and the literature. We
the absorption component of the emission line then it is considered
as a McLean line effect. The line effect across the emission line is
begin with discussing the observed line effect and its type, before
classified based on two criteria; the value of the fractional width
we focus on the magnitude and width of the line effect.
and whether there is a flip in the polarisation and PA spectra or not.
The Hα spectropolarimetric results of each target are listed in
Figure4. Thefigure 3
representsof the observed
line effect acrossa functionof spectralof atosampleof the51 0.7
HAeBe
T Taurifractional
width istype
equal
or larger
than
and andthere
is noTable 2.
Columns& 6 listthe
thetype
spectroscopic
characterizationof Hα lineIfasthe
objects
exhibita linespectrum.
effect acrossthelinepolarization.
Noteproperties
that the B4ofand B5 spectral
typepolarisationbins which are
in PA
the spectra
previous acrossfigure areunpopulated,asflip in theandthenowemissionline thenStokesthatI, theintensity
The
polarimetric
their (only) members do not show a line-effect.
the line effect is consistent with depolarisation. On the other hand,each target are tabulated in columns 7-12 & 15. Finally, the con-

Improved torque formula for low and intermediate mass planetary migration
ed 2017 July 27; in original form 2017 April 25
M.A. Jimenez and F.S. Masset
ABSTRACTThe migration of planets on nearly circular, non-inclined orbits in protoplanetary discs
is entirely described by the disc’s torque. This torque is a complex function of thedisc parameters, and essentially amounts to the sum of two components: the Lindblad
torque and the corotation torque. Known torque formulae do not reproduce accurately
the torque actually experienced in numerical simulations by low- and intermediatemass planets in radiative discs. One of the main reasons for this inaccuracy is that theseformulae have been worked out in two-dimensional analyses. Here we revisit the torqueformula and update many of its dimensionless coefficients by means of tailored, threedimensional numerical simulations. In particular, we derive the dependence of the
Lindblad torque on the temperature gradient, the dependence of the corotation torqueon the radial entropy gradient (and work out a suitable expression of this gradient ina three-dimensional disc). We also work out the dependence of the corotation torqueon the radial temperature gradient, overlooked so far. Corotation torques are known
to scale very steeply with the width of the horseshoe region. We extend the expressionof this width to the domain of intermediate mass planets, so that our updated torqueformula remains valid for planets up to typically several tens of Earth masses, provided
these relatively massive planets do not significantly deplete their coorbital region. Our
torque expression can be applied to low- and intermediate-mass planets in opticallythick protoplanetary discs, as well as protomoons embedded in circumplanetary discs.
Key words: Planetary systems: formation – Planetary systems: protoplanetary discs

The shapes of column density PDFs - The importance of the last closed contour
J. Alves et al.

• log-normalなPDF形状はcompletenessによるものであり、より自然な定義を用いることでlog-normalピークは無くなりpower-law分布João Alves, Marco Lombardi, Charles J. Lada: Completeness limit of PDFs

のみを示す。

Oph streamers

Oph North

Polaris• ‘last closed

contour’を定義とするのが良い全質量(全領域)を正しくカバーしていないslope=-4.4

slope=-2.5

slope=-2.0

104

Number of pixels• open contourはHerschel,Planck,2MASS[Lombardi+2015]

105

103

102

101

100

2

1

0

Log10(AK ) [mag]

1

2

1

0

Log10(AK ) [mag]

1

2

1

0

1

Log10(AK ) [mag]Fig. 2. Column density map and respective PDF for a diﬀuse cloud (Polaris), a star formation poor cloud (Oph North), and astar forming rich cloud (Oph streamers). The red line on the map and on the PDF corresponds to the last closed contour while
the gray line corresponds to the peak of the PDF. The blue line represents the slope of the distribution above the completenesslimit. All maps cover about the same physical area of about 200 pc2 .

• 距離(分解能)に対しては不変, 空間構造(分布)には感度=>空間構造を調査するツールとして、まだPDFは使用可能

120 pc240 pc
480 pc960 pc1920 pc

120 pc240 pc
480 pc960 pc1920 pc

4.

103

102

5.

101

10

• 正しくcompletenessを定義

Radomized pixels

104

Number of pixels

を持つ

Original

105

0

1

0

1

Log10(AK ) [mag]

2

1

0

1

Log10(AK ) [mag]2Fig. 3. Left: Eﬀect of distance on the Oph Streamers PDF.
Right: Same, but with randomized pixel positions. The powerlaw PDF is invariant to distance (resolution), but not to thearrangement of cloud material.

したPDFはlog-normalでは•expected. We then computed the PDF of the two maps,
the original and the randomized one, for diﬀerent distances
なくpower-law分布(resolutions). Remarkably, as the distance (resolution) increases (decreases), the power-law slope of the PDF of theoriginal cloud remains essentially invariant to distance (res=>観測だけでなく理論研究もこの定義を用いるべき
olution), while the PDF of the randomized cloud changes
dramatically. This implies that the column density PDF is
PDFの新しい物理解釈が必要 invariant to distance, but not to the spatial arrangement ofcloud material, and as such it may ultimately prove to bea useful tool for investigating cloud structure.

Ack
He
dir
res
res
Str
log
use
tro
use
dat

Re

Ab
H
Alv
Ast
A
Ba
M
Bea

Destruction of Refractory Carbon in Protoplanetary Disks
C grainのアバンダンス分布
D.E. Anderson et al.
6• 原始惑星系円盤中におけるrefractorycarbonのdepletionメカニズムの調査• 円盤表層による酸化or光分解• 表層のC grainとPAH• 円盤モデルを使った1+1D化学計算• T Tauri star, power-law disk
• >600 chemical species,~7000 reaction• ダストサイズ 0.01~10µm, (+10µm porous)• 光分解の方が外側まで有効, ダストサイズには弱く依存• 円盤寿命より早くdeplete

99• midplaneのCは残る

Fig. 2.— Vertical cross-sections of the protoplanetary disk above the midplane demonstrating the refractory carbon abundance relative
to total hydrogen at 106 years for carbon grains with grain radii equal to 0.01 µm (a,b), 0.1 µm (c,d), and 10 µm with 96% porosity (e,f)
including oxidation (a,c,e) and UV photolysis (b,d,f).

=>vertical mixingが必要

than compact 1 µm grains can be lofted into the photodestructive layers and within a limited distance from thestar of ⇠15 au.
PAHs in the gas phase would remain coupled to thegas, similar to the small carbon grains, and are not subject to settling. However, given that hydrocarbons havea sublimation temperature of ⇠400 K (B15), in dense regions of the disk where the chance of interaction withgrains is high, PAHs will likely freeze out and remain on
grain surfaces. We would expect these PAHs to attach
mainly to the smallest grains because they represent thelargest surface area. Therefore, in the limit where all of
the PAHs are frozen out, the results would be similar to
those of the 0.01 µm grains. PAHs that evade interaction
with grains would be destroyed at the rates presented
in Section 3.1 at the disk surface where conditions areappropriate for oxidation, but would remain largely una↵ected in deeper layers of the disk.
Even if grains are able to reach the heights where destruction occurs within the disk, the amount of time
grains spend at those heights is equally important toensure their destruction. Where the stirring timescaleis short compared to the disk lifetime, grains will cycle
through the vertical column multiple times. In lower ↵disks with longer stirring timescales, grains tend to experience longer excursions through a smaller number ofdi↵erent environments. Alternatively, in higher ↵ diskswith shorter stirring timescales, grains rapidly change environments spending brief intervals of time in each one(Ciesla2010). The average time spent in a particular12
region over multiple stirring cycles ends up being only
weakly dependent on ↵, however, and related primarily
to the density structure of the disk. Here the fractionof the disk lifetime that an average grain spends above
a height z is taken to be approximately the ratio of theintegrated gas density above height z to the total gas
density of the vertical column above the midplane.
Figure 7 compares the time spent at heights above themidplane for a disk lifetime on the order of 106 years
to the time required to deplete the 0.1 µm grains by one
order of magnitude. Although carbon grain destruction
occurs rapidly, grains would only be exposed to destructive conditions several scale heights above the midplanefor ⇠1–10 years for oxidation or ⇠100–1000 years forphotolysis. Where the depletion timescale, represented
by the filled contours in Fig. 7, is longer than the exposure timescale and therefore a filled contour crosses
over solid contour lines corresponding to comparable or
shorter amounts of time, depletion of refractory carbon
in 0.1 µm grains can occur within the disk lifetime. For
UV photolysis in panel (a), the crossover occurs around
10 au, where the depletion and exposure times are on
the order of 10 years. In comparison, this crossover occurs at ⇠0.5 au for oxidation. These numbers represent
upper estimates because they assume that the particles
spend all of their time behaving aerodynamically as small• 円盤表層でCがdepleteする時間v.s.乱流でダストが表層に留まる時間=>円盤内側でdepleteが可能• 光分解~10au, 酸化<1au• 外側ではCは残る

for 0.1µm C• 10-4 depletionを満たすのは、turbulent
disk(α=10-2)でも<1µmダストのケース=>小ダストでないとC depletionを説明できない• 他考えるべき事項=>future work
• dust growth, fragmentation,
radial transport…

• dust composition (e.g., ice
coating)• 角運動量輸送

Fig. 7.— Comparison of the time grains are exposed to the conditions above heights outlined in contours to the time required todeplete the abundance of 0.1 µm carbon grains by an order of magnitude via UV photolysis (a) and oxidation (b) represented by thefilled contours. The dotted line represents the radius beyond which
the depletion time is less than the exposure time and the 0.1 µm
carbon grains will mostly survive. As discussed in the text, the exposure time does not strongly depend on the choice of ↵ regarding
the disk turbulence.

0.01 µm grains, the maximum is about 3–5 au for depletion levels similar to the carbonaceous chondrites via
oxidation. However, UV photolysis will clear out thesegrains throughout the planet-forming region. Larger,
from compact 0.1 to porous 1 µm, grains are depleted out
to less than 1 au via oxidation but 3–10 au via photolysis.
Once carbon has been incorporated into grains of 10 µm
or larger (or compact 1 µm grains), it will likely survivethese processes and remain in refractory form with the
exception of porous grains in very turbulent disks within
1 au. For a constant-↵ disk, depletion requires sufficientturbulence to allow for lofting of the grains into the surface layers within the disk lifetime. Values of ↵ ⇠10 2
are needed to deplete carbon from 1 µm grains out to evena few au. For lower turbulence disks, depletion is limited
to submicron grain sizes out to a few au (↵=10 3 ) or4

n Goodnerated
centre.
d’ stars
gridlikebecometed unoduced.
ox, andin. Wendard’.
he fracroughly

How do binary clusters form?
B. Arnold et al.
• バイナリクラスター生成のN体計算
2.0

1.5

1.0

• クラスターはペアでしばしば見つかる• 単一クラスターより若いものが多い• 生成についてはよく分かっていない
1.0

0.5
x ( 0.0
pc)

−0.5

1.0

0.5 )
y (pc

0.0

−0.5

z (pc)

0.5

0.0

−1.0
−1.5
−2.0
−2.5

0 Myr

0.4 Myr

0.8 Myr

1.2 Myr

1.6 Myr

2.0 Myr−0.5

KIRA integrator/STARLAB•
rom theparam= 2.3.
.4. TheM . Thehabrier−1.0

1.5

N=1000,t=20Myr• turein a regionR=2pc,
with 100 stars
and a radius of 1 pc. The red dots
indicate the positions of stars, and their velocity vectors are deNO bygas/stellar• notedblack arrows. evolution/external tidal field• IMFとconsistentな質量分布
Figure 1. A set of initial conditions demonstrating velocity struc-• 速度構造•velocity
as from) strucappear
es et al.

•Table 1. Letters are used to describe the initial conditions ineach set of simulations. Two parameters are varied: the fractal
dimension D, and the virial ratio (i.e. the ratio of kinetic to poinherited velocity (親;ランダム, 子;ランダム
tential energy) ↵vir . Highly-substructured simulations (D = 1.6)
aredenoted[Goodwin&Whitworth(2004)]
by the letter ‘H’, moderate substructure (D = 2.2) is+相続)
denoted by the letter ‘M’, and smooth structure (D = 2.9) by ‘S’.
Simulationsof coolregions field(↵vir =(パワースペクトルより)0.3) are denoted by ‘C’, viriturbulent
velocityalised regions (↵vir = 0.5) are denoted by ‘V’, andregionset al.
4 warmBecky Arnold(↵vir = 0.7) by ‘W’.

• 二つの初期状態パラメータ

hat theh otherof twot as the, or byvelocity

↵vir

ビリアル比

0.3
0.5
0.7

バイナリクラスターとなっフラクタル次元 D
1.6
2.2

2.9

HC
HV
HW

SC
SV
SW

MC
MV
MW

Figure 3. Snapshots at 0 Myr, 0.4 Myr, 0.8 Myr, 1.2 Myr, 1.6 Myr and 2 Myr of simulation (c) from Fig. 2. Stars are represented
by arrows plotted in 3 pc-by-3 pc-by-3 pc boxes. The arrow’s positions indicates star’s positions in space, and the arrow’s directions
indicates the star’s velocities. The arrows are colour coded: blue if the star is in the left hand cluster after the region finishes dividing,
red if it is in the right cluster after division, and black means the star is unbound.

たケースの時間変化例

MNRAS 000, 1–10 (2017)

Outcomes of H simulations

Microclusters

1.0
SingleMergerBinary0.8• 速度分布の違いによる影響
20=>速度コーヒーレンスの有無がバイナリ形成
z (pc)

Probability
Fraction

10

0.6

0

−10

0.4

にとても重要
−20

0.2
0.0

0.3

0.5
Virial ratio αvir

0.7

Outcomes of M simulations
1.0
SingleMergerBinary0.6• 初期状態との関係
20

20

10

−10

0
x (pc)−20• 最終分布に対し3つの構造を機械的に抽出• ビリアル比⤴でbinary fraction⤴

Figure 7. A highly-substructured, dynamically warm region thathas been evolved for 20 Myr. The star’s positions are indicatedby dots in a 40 pc-by-40 pc-by-40 pc box. The simulation has
developed numerous long lived overdensities. We call these overdensities ‘microclusters’, and they are highlighted by red arrows.

=>warmな領域の方が生成されやすい
Elongated cluster

10

0.4

0.3

0.5
Virial ratio αvir

0.7

−4

SingleMergerBinary

0.6
0.4
0.2

0.3

0.5
Virial ratio αvir

00.8

H mass ratios
M mass ratios
S mass ratios

A
A

W
o

−2

1.0

0.0

2

元で明確な違いがある

Outcomes of S simulations

0.8

1.0
z (pc)

0.0

CDF of mass ratios

4• 質量比はフラクタル次

0.2

Probability
Fraction

Becky Arnold et al.

0.7• 高フラクタル次元では構造
4

2

−2
0 c)
y (p

−4

0.6

CDF

Probability
Fraction

0.8

−20
−10
y( 0
pc
) 10

0.4

がないので速度構造のみで0.2決まるため、これが標準とFigure 8. An initially smooth, virialised region after evolving for
3 Myr.
It has developed an elongated shape which collapses backなるはず。フラクタル次元
0.0
into a sphere within the next few Myr.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
の変化に伴い、構造+速度
Mass ratio
ACKNOWLEDGEMENTS
構造のカップルによって分 Figure 9. Cumulative distribution functions of the cluster mass
The CDF for highly-substructured (H) simulations is plotBA acknowledges PhD funding from the University ratios.
of
布も異なる
ted by a black line, the moderately-substructured (M) simulations
Sheffield, and DWG from the STFC. RJP acknowledges0x (pc)

−2

−4

4

2

by a magenta line and the smooth (S) simulations by a red line.
support from the Royal Society in the form of a Dorothy
Hodgkin Fellowship. Thanks also to Søren Larsen for useful

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