Star	  Forma)on	
  Newsle0er	
  	
  #259	
  29-­‐33本目	
麻生 有佑	

Debris	  disc	  forma)on	
  induced	
  by	
  planetary	
  growth	
  H.	
  Kobayashi	
  and	  T.	
  Lohne	  (2014)	

Ø デブリ円盤進化モデルでG型星デブリ円盤のSpitzer観測を説明。	
  Ø 1	
  µm以下はblow	
  out、ガスやradial	
  driFのないデブリ円盤進化モデルを使う。	
  Ø まずモデル毎の進化の特徴を述べる。	
  Ø 初期微惑星の大きさs0,	
  微惑星が存在する半径rin-­‐rout,	
  面密度分布x,	
  pをパラメーターとして、観測されたデブリ円盤の年齢-­‐フラックス関係ををフィット。	
  Ø 30	
  AU付近に幅2	
  AUのnarrowな微惑星円盤が良さそう。	
  ß	  A型星でもnarrow	
  diskが良いという研究がある。	
  Debris Disc Formation Induced by Planetary Growth 9Ø gasは入れなかったが、ﬂuxの増大がgas入りの方が早い、collisional	
  cascadeの効率が悪くなる、など特に100	
  Myr以前で重要で、rgas	
  (snow	
  line)とrinの関係にも依る。	
  eters to observational data: For each initial planetesimal radius s0 , the inner and outer radii of the discy scaling factor x, the surface density radial slope −p, and the total mass Mtot of the initial planetesimalx and p are discussed in the main text.
s0 [km]rin [AU]

0.1
1
10
100
1000

70.6+1.3−0.04
39.6+0.7−0.8
34.3+0.1−0.8
30.5+0.7−1.3
26.3+0.4−1.2←初期微惑星半径s0毎のベストモデル	  半径はフラックスから推定されたものとお13.5+0.03
0.23
1.1
5.7+0.5−5.1−0.2
1.47+1.33
0.40
0.56
14+0.01
よそ合う。	
  
−0.77
−1.5
+1.53
+2.9
2.23−0.12
1.34
0.04
33−1.8質量はフラックスから推定された値~0.01	
  1.75+1.48
2.6
0.0
45+49
−0.07
−13
1.16+1.29
79
1.9
122+50
MEより3桁大きい(赤外フラックスは小さい
−0.43
−71
粒子しか見えない)。	
  Kobayashi, Ormel, & Ida 2012).	
After gas depletion, colli-rout − rin [AU]

24µm
10km
1000kmxp

Mtot [M⊕ ]sional cascades can produce smaller bodies and then debris
disc fluxes increase. If planet formation occurs inside a radius rgas prior to gas depletion, planets are subsequently
formed beyond rgas in a gas-free disc. If rgas corresponds

7

10 yr

6

0

]

8

10

10

−2

10

−3

10

−4

10

−5

Embryo Mass [M ]

10

−6

−1

10

10

−1

10

−2

10

−3

6

10

7

10

8

10

9

10

10

1000km

0

10

−1

10

−2

10

−3

100km
0.1km

1km

10km

10

Time [yr]Figure 5. Same as the bottom panel of Fig. 4, but optical depth τ and time t are divided by (Σ/0.95 g cm−2 ) and(Σ/0.95 g cm−2 )−1 (r/10 AU)3/2 , respectively.

It should be noted that the temporal evolution of τ
depends on the initial planetesimal radius s0 , as shown in−1
10 Fig. 6. For smaller s0 , runaway growth occurs earlier andthus τ increases earlier. Once active dust production occurs,−2 more frequent collisions of more fragile planetesimals (lower
10 Q∗ ) for smaller s lead to higher dust production: Smaller0
D−3 s0 results in higher τ , whereas τ decays earlier for smaller s0 .
10 For s0 ! 10 km, τ increases along with runaway growth ofplanetesimals, while τ increases prior to runaway growth for−4
10 larger planetesimals. When the runaway√ growth starts, planetesimals have random velocities vr = e2 + i2 vk as large as−5
10 the surface escape velocity, vesc , of the planetesimals, where
vk is the Keplerian velocity. Since their specific impact en789ergies at6 the beginningof runaway
growthare10much smaller
10
10
10
10
10
than Q∗D of planetesimals with s0 ! 10 km, τ is very low
before runaway growth and suddenly increases at the onsetof runaway growth. For s0 " 100 km, the specific impact
energy is slightly smaller than or comparable to Q∗D of iniFigure 4. Evolution of planetary embryo mass (top panel),tial planetesimals at the beginning of runaway growth. Due
eccentricity (black) and inclination (gray) of 10 km-radius bodto collisional erosion of planetesimals, collisional cascadesies (middle panel), and optical depth τ (bottom panel), starting
increaseτ prior to forrunaway
growth,from 10 km-radiusplanetesimals
Σ = 2.7g cm−2 ,resultingr = 5 AUin the small
peak
value
of
τ
.
Therefore,
thedependence
τ evolution on−2(dotted curves), Σ = 0.95 g cm , r = 10 AU (solid curves),ofand
becausefragmentationeﬃciencyof plan0 isΣ = 0.34 g cms−2, rcomplicated,= 20 AU (dashedcurves),where Σ is the
solid
etesimals determined by Q∗D depends on s0 . Although we
surface density.
cannot derive a formula for s0 dependence, the scaling forΣ and r is valid for each value of s0 .
The rapid increase in τ is caused by embryo formation

Time [yr], inclinations Ø 線は左から右へr=5,	
  10,	  20	  AU。	  rface density
bodies larger Ø 暴走的成長àfragment、寡占成長。	
  of planetesirface density Ø τの成長タイムスケール∝ΣΩ。	

vr / vesc

yr

10

−4

10

10

4

10

2

10

0

0.1km
1km

10

Optical Depth, τ

6

10

−2

Optical Depth, τ1 x 10 yr

Optical Depth, τ Eccentricity, Inclination Embryo Mass [M ]

8

10km
100km

1000km

−2

0.1km

10

0

10

−1

10

−2

10

−3

10

−4

1km
10km
100km
1000km

10

5

10

6

10

7

10

8

10

9

10

10

Time [yr]Ø 初期微惑星半径s を変化させる。	
  Ø s が大きいと暴走的成長以前からcollisional	
  cascadeが起きる。	
  50 AU withàτの増加が緩やか。	
x = 1 and p = 1.5, initially composed of 10 km-

Figure 6. Temporal evolution of embryo mass (top), the ratio of random velocity vr of bodies with initial0radii s0 to theirsurface escape velocity vesc (middle), and optical depth (bottom) for diﬀerent
0 initial planetesimal radii s0 = 0.1–1000 km with
Σ = 0.95 g cm−2 at 10 AU.

radius planetesimals (s0 = 10 km). The fluxes increase ataround 106 years for the wide disc, but 10 times later for the

p=
2

−1

0

10

0

10

100km

−1

10

p=

70µm

0

10

Fdisk,ν / F*,νFdisk,ν / F*,νFdisk,ν / F*,ν

2

70µm

0

2
p=

10

1000km

10

−1

10

24µm

10km

0.1km

p=0

0

10

10

Fdisk,ν / F*,ν

10

1

10

p=1

1

Fdisk,ν / F*,νFdisk,ν / F*,ν

1

24µm

m
1k

24µm

0.1kmp=1
1k

2

10

2

10

0

0

70µm

100km

m

1000km
10

10

10km
0

2

10

10

4

0

10

10

Figure 7. Temporal evolution of flux ratios at 24 µm (top) and
0

in

in

out

out

p. After the rapid rise of flux ratios, growth propagation in
the disc determines the flux ratio evolution. For 70 µm, theflux ratios decrease for p ! 1, while the ratio increases for
p = 0.
Since the flux ratios from discs with x = 1 are muchlarger than those obtained from observations, we further in-

2

3

2
10 10

10 104410

Age [Myr]Age [Myr]Age [Myr]µm (bottom) for s = 10Akm,
x = 1, and p =d1.5
in a wide discØ70 solidが5-­‐100	
  Uのwide	  isk。	
  (r = 5 AU and r= 100 AU; solid curves) and a narrow discØ(r do0edが10-­‐50	
  AUのnarrow	
  disk。	  = 10 AU and r= 50 AU;
dotted curves). Circles
indicate
the observational data shown in Fig. 1.
Ø τの増加(惑星形成)が外へ伝わる。	
  →特に70	
  µmでは数10	
  AUの放射が効
distributions of surface density. Since the surface densities at
くので、フラックスが持続する。	
the inner edge are diﬀerent, the flux ratios rise later for large

1

10

Kobayashisional cascdisc fluxes
dius rgas p
formed beto the inn
assume insimilar: Th
lated to thother handclean up a
the format

Planetbecause raof dust inplanetesim(Okuzumi
in a cluste
ing their ecounter tru
expected iedge of pl2001) andobjects (Ketesimal fo
explain the

11. Temporal
evolutionusing best-fit
Figure 8. Figure
Dependenceof flux evolution
onofp thefor flux
s0 =ratios
10 km,
Table 1 for initial planetesimal radii of
x = 1, rin =parameter
5 AU and0sets
rout listed= 100 inAU.
0.1, 1, 10, 100, 1000 km.

Ø s 毎のベストフィットと観測の比較。	
   In thebefore theØ s0=0.1	
  kmが最も良いが、データの少and Neptu
Planet form
then start decreasing at 10 –10 years: These model fluxesない30-­‐90	
  Myrに引っ張られていて、
eﬀects
of
gas
even
in
early
times.
Even
startingwithsimilaryond 10–2
are much larger than observational ones before 10 years. On
initialplanetesimals,
the
time
when
disc
fluxesincreaseistion of thethe other hand, theそこを除くとsfluxes increase later forlarger planetes=100	  kmが最適。	
  earlierfor
oursimulation.
This
means
that
gas
drag
plays
0
yield theimals and the fluxes remain high even after 10 years: Theanimportant
role
in
flux
evolution
before100
millionyears.
50 AU (Komodel fluxes Øsignificantly
exceeds
observational もごく限られた範ones after
ssince
=0.1	
  
kmではM
0
tot
Indeed,collisionalcascadescannoteﬀectively
produceplanetesim
10 years. Therefore, the smooth discs seem unlikely to ex1µm-sizedbodiesinagaseous
disc(Kobayashietal.
2010),
囲でしか合わず不適。	
100km) thplain the observational data even for a wide range of initialdisc fluxes may not rise before gas depletion occurs.
8

9

9

9

8

planetesimal sizes (0.1–1000 km).
If gas depletion is taken into account, the inner edgeof a disc may also be naturally explained. If discs still
have asDisc
much gas as the minimum-mass solar nebula, col4.3 A Typicallisional fragmentation between bodies smaller than aboutsimilar todepletion,
dress in fu

TOWARD	  COMPLETE	  STATISTICS	
  OF	
  MASSIVE	
  BINARY	  STARS:	  
PENULTIMATE	
  RESULTS	
  FROM	  THE	
  CYGNUS	  OB2	
  RADIAL	  VELOCITY	
  SUVEY	
  Hernry	  A.	
  Kobulnicky	
  et	
  al.	  (2014)	

Ø Cybnus	
  OB2	  Associa)onにある48個の大質量連星系で軌道解析を行った。	
  Ø そのうち23個は新しい大質量二重連星である。	
  Ø Cyg	  OB2の大質量星は35%が連星系。	
  Ø 質量比は0.2-­‐1.0でおよそ一様に分布。	
  Ø 離心率は0.1-­‐0.6に一様分布と、e=0	
  (真円軌道)に別の分布がある。	
  Ø P<45	
  dには概ね一様に分布している(累積分布が線形)。	
  Ø P=1.4-­‐2000	
  dをsingle	
  powerでフィットすると冪は–0.22	
  (累積は0.78)。	
  Ø Galac)c	
  open	
  clusterなどの他の系と比べても分布が似ている(尤度91%)。	
  àP<25	
  dの二重連星の性質はdisk/clump	
  fragmenta)onの局所的物理で決まり、
環境や進化の影響が少ない。	
  Ø Cyg	  OB2には6d,	
  14d,	
  45	
  dつまり~0.2,	
  0.4,	
  1	
  AUに特徴的なスケール	  ←進化の影響？	
  – 94 –

←離心率の分布	  e~0とe=0.1-­‐0.6の2成分。	
  	
  →質量比の分布	  q=0.2-­‐1.0に一様分布。	
	Fig. 28.— Observed distribution of eccentricity for the sample of Cyg OB2 binaries. The
left-hand y-axis shows the cumulative probability, corresponding to the plotted points. The
right-hand y-axis provides the number of objects in each histogram bin. The distribution isapproximately uniform between e = 0 and e ≃0.6.

Ø Cyg	  OB2とその他のO型連星の軌道周期分布。	
  Ø 領域に依らず概ね似ている。	

ig. 30.— Observed cumulative distribution of orbital periods for the Cyg OB2 sample (filledrcles), the Sana et al. (2012) sample of O stars in Galactic open clusters (pluses), and O
tars from Garmany et al. (1980) (open squares).

– 95 –

Fig. 29.— A statistical distribution of mass ratios for 48 known massive binaries in Cygnus
OB2, based on Monte Carlo realizations over allowed inclination angles.

(上図)	
  
7個ずつ見て分布が一様(線形)である確率。6,	
  14,	  45	  dの折れを示唆。	
  
(下図)	
  
軌道周期分布のベストフィット。	
  Fig. 31.— (Lower panel) Observed cumulative distribution of orbital periods in the unbiased
Cyg OB2 sample as a fraction of the entire sample (filled circles) and the the inferred true
distribution of orbital periods (open circles) using the completeness corrections shown in
Figure 26 and assumptions for the underlying distribution of eccentricities and mass ratios,
as described in the text. The solid curve is a power law with slope β = −0.22. (Upper panel)
Probability that the observed distribution is consistent with uniform in a moving window ofwidth seven observed systems. Probable changes in slope near 6 days, 14 days, and 45 days
appear as dips in the probability curve.

n(s)=C·s ,
ch larger
than theWhile
blow-outsize
in Fomalhaut’s
main belt andinmodellingthe Herschel acolddebrissystems.
theslopeofissize.
thefragment
sizeofdistribution
and
ing
from
grain
collisions
essential
range
ofdisks.
ten atdust
some
small
fragment
To the whenbest
our knowledge,

size ofthe
thelargestfragment
wellrelevantcharacterized
andcan with 3 < ↵ < 4, and C
nt – thengs
interplanetarymedium– minorplanets,areasteroids:
general–forsolidthestate:
refractory
however,regimeoffragment
sizes
analysisA	
  dof
earth	  of	
  small	
  pmodels,ar)cles	  in	
  debris	  disks	  beusedconfidently
inthesmallest
fragment
size is lesspee sizethelargestfragment
arewellknown,
the behaviour
the is dominated by
below has not yet been probed by available experimental
dataof masswell
and isBasedusually
tofragment	  bewe
constantallcol- fragment
nt
An	
  
eunderstoodnergy-­‐constrained	
  mallest	
  
sfor
ize	
  
thus the surface
energyonexperiments,
adopt
the
standard
size
norpoorly
described
theoreticallyinsassumed
anastrophysicalcontext.
ntallyunderstood.
This
leads
debris
disk
codes
to
generallyWe
provideaframeworkforself-consistently
calculating
ra lisions.
S.	
  Krijt	
  
and	
  M.	
  Kama	  (2014)	
distribution
Assuming
spherical
fragments with sizes between smin and As the creation of infi
a
range
of
astrophysicalthesmallest
fragmentsize
as a functionof material
and arecollision infinite amount of ene
as s ( s ), the total fragment
↵
mass
and
surface
area
max
min
n(s)
Csize
· s distribution,its implications(1)
werboundaryofthefragment
forfora rangeof collider
ent size
distributionand2),
parameters(Sect.
and =discussmodellingreavailable in a collisionØ ダストサイズ分布の小さい端が未だ不明でblow-­‐out	
  sizeが仮定される。	
  ll characterizedandcan 3).
we
apply
the
methoddebris4⇡⇢Cdebrisdisks(Sect.
with3 < disks.
↵ < 4,4⇡C
and C 3a coefficient
we express below.
While
thesmall fragm
4to↵
↵
on
some
Mfrag
= size is lesssmax ,Afrag =
smin ·(2) ten atØ
質量は大きい粒子が決め、表面積(表面エネルギー)は小さい粒子が決める。	
  lest
fragment
ments isNumerous
founddependoniscollisionvelocity,materialparameters,
mass
dominatedbythe largest
particles,
the surface area andstudies
at thefragment
3(4 toexperimental↵)↵have
3 lookedns
however, the regime of
to beØ
constant
for all col- thus the surface energy is dominated by the smallest
無限小の粒子を作るには無限大のエネルギーがいるので必ず分布に端がある。	
  fragments.
size
distribution
destructive
collisions,focussingon
the slope
motivatedforof
thecalculationof ofthesizesmallest
fragment,
which
ebelow
has annot yet bee-consistently
calculating
Forγは単位面積辺りの表面エネルギーで物質に依る。	
  a recipe
collision
betweentwobodies
s
and
mass
M
=
Ø
0
0
As
the
creationofinfinitely
small
fragments
wouldrequire
of
the
power
law(s),
and
on
the
size
of
the
largestfragment3arystems.
Forparameters,implies
our results
the described theoreticof material
andplausible
collisionnor(4⇡/3)⇢s, mass conservation
Mfrag =are
2Mconsistentandamountthus withØ
ηは表面エネルギーに変換される運動エネルギーの割合。	
  
0 ,theinfiniteamountofenergy,whileofkinetic
energy0&modelling
Ryan 1990;
Ryan
etal.in1991;
Nakamuracold& Fujiwara
ysize(Davisin
Fomalhaut’s
main
belt
and
the
Herscheldebrisdisks.
plicationsfor
AssumingØ 等質量、等サイズの衝突を考える。	
  available in a collision is finite, the power law must stopor flat- spherica
3↵4Ryan↵)s2000).
The smaller end of the size distribution has s ( s ), the total f
ed 1991;
C = 2(40 smax . ten at some small fragment size. To the best(3)of ourmax
knowledge,minØ 初期サイズが小さいと運動エネルギーも小さく、粉砕して表面積を作ることができ
me– minor
planets,
asteroids:
general–solidstate:
refractory
receivedconsiderably
lessattention;
thesmallest
fragmentsaree lookedat thefragment
2 for the analysis
however,the regimeof fragment
relevantないàsThekinetic
energyis simply
UKhigh=sizes(1/2)µv,
4⇡⇢C 4 ↵max~smin~2^(–1/3)s0と分裂(split)する。	
  s, focussing
on
the
slope
hard
topre-collisioncountexperimentally,andrequireavery
resolution
rel
below
has
not
yet
been
probedbyavailable
experimental
dataM=smax ,fragØ
それが分布の小さい方の端である(分布形成を段階を追って考えている？)。	
  
where
µ
=
M
/2
denotesthereducedmass.
The
di↵erence0of thelargestfragment3(4 ↵)
to be captured in numericalsimulations.
Fragment
distributionscontext.
nor describedtheoreticallyin an astrophysical
Ø
このs
とs
の関係が計算できて、いくつかの観測(s
>10	
  
s
)が説明できる。	
  insurfaceenergybefore
and
after
the
collisionequalsU=
Basedonexperiments,
adopt
fragment; Nakamura&
Fujiwara
min
blow
min
S blowaretherefore
incomplete
belowwesizes
of 100theµm,standard
or masses
beAssuming
spherical
fragments
with
sizes
betweenssize
and betwee
min
For
a
collision
2
3
the size
distribution
has
(A
8⇡s
),
where
equalsthesurfaceenergyperunit
surfrag
distribution
0low
10 gr (Fujiwara
et A&Aal.
Takagial. 1984).
Molecularsmax( 1977;smin), thetotal etfragmentmass
and surface area
are 3 , mass conser(4⇡/3)⇢s566,
L2(2014)
fragments
are0
le smallest
face ofthematerial.
Assumingthat
onlyora smooth
fractionparticle⌘ of thehykidynamics(e.g.
Dominik& Tielens
1997)
4⇡⇢C
4⇡C
↵
4 surface,↵3 ↵re a very3 ↵ 4
netichighis usednewwecan combinen(s)=energy
Cresolution· s(Geretshauser, Mfor(1)(2)=et al. 2010)
s
,
A
=
s
·
dhe
fragcreating
fragdrodynamics
simulations
have
limited
C
=
2(4
↵)s
.
max
min silicate
Table
1.
Material
properties
for
and
ice
used
in
this
work.
0 smax3(4↵)↵
3s. Fragment
distributions
Eqs. (2) andto obtain
a lower
for the smallest
fragment
and(3)
tend
to focuson thelimit
fragmentationthresholdvenf1ir100resolutionµm,
ormassesbewith
3
<
↵
<
4,
and
C
a
coefficientwe
express
below.
While
the
The
pre-collisionkine
Forbetweentwo bodies
mass
M0 =
size. Forthethanspecificcasea collisionof ↵fragments.
= 3.5,
this reduces
to of size s0 and.
locityratherthesmallest
321984). Molecular (4⇡/3)⇢s3 , mass conservationMaterial
sgi et al.
⇢ (g cm ) , and thus
(Jµm =) M /2 den
impliesMsurfacefrag = 2M0where
0
1
0
mass
is
dominated
by
the
the
area
and
0 largest particles,2
7)orsmoothparticlehyBC
24s
Silicate
2.6
0.05-simulations
BBB surface0 energy
CCC 1is dominatedin surface energy befo
3 ↵ 4
thus
by
the
smallest
fragments.
s,(4)smin =the
have
C
=
2(4
↵)s
s
.
(3) 2
A
@ limited
max
Ice
1.0
0.748⇡s
0 max
2(A), where⌘⇢sv+
24
ggmentation
frag
0 rel
thresholdve- of infinitely
Aggregate would⇠10 1require⇠10 4an
102 3 0AsMinimumthecreationsmall
fragments
2.
fragmentsize
inasinglecollision
The pre-collision kinetic energy is simply UK face
= (1/2)µv,of therelmaterial.
As.

the true
⌘. We
that
valid ,foryieldsonsmin⌧ value
sblow offor⌘566,=stressandour theory= 0.1isJ/m
but3 >sminand'⌘ = energy,
A&A
L20.1
(2014)
10 2 for this com
f , an3 not apply to models that use shallower power
↵for
>
4,
and
does
6
µm
⌘
=
10
.
Thus,
the
di↵erence
betweenour
results
and1
3 1
1
Table 1. Material properties for silicate and ice used in this work. on smin /sblow.15Qpr (L? /L )(M? /M )laws,(⇢/gforcmexample) (s/µm)
Sect. 4.2 ofKrivov et al. (2013).
K type stars. Krivov efragmentsizes
ofKrivov
et
al.
may
be
substantial,
depending
the radiation andthe
gravitational
force.
Particles
give our calcu
The importance of the limit given by
Eq. (4)⇢dependson(JtheMaterial(g cm )m ) with a collisional castrue byvalue⌘.presWe per
stressthat Silicate
our
theorydepending
is valid0.05on
for 3 > and ⌘ = 10 2
are removed fromon
thethesystemradiation
parameters,
andofcanvary
individual
collision,
2.6
proposed that the largvely, Gáspár et al.↵ (2012)
calculatea notcollision> 4,
doesvelocity
apply
to modelsuserestshallower
Icethat1.0
theandcollisionand choice
for smax. In theof this 0.74
sec-power
unstirred material. Ou
Aggregate⇠10⇠10 10from mass conservation,
not studythewedo
explorein which
this limit
relevant.
laws, tion,
forbutexampleSect.
4.2casesof Krivov
etisal.most(2013).
explainedasthe stars
outco
K
type
Notes.
The
valuesforthetypicalaggregateareexplainedinInadebrisdisk,aparticle
of
size
s
is
most
likelyformed0 Eq. (4) depends on model
highlydegen
TheEq.
importance
of
the
limit
given
by
the iswith
AppendixA.
a collis, for any relevant collision(4)
predictss>minin a collision between only slightly larger particles. In addition, belt properties( f ) areandcanper individual
collision,
dependingon proposedting the fragmentparameters,
size distribution
down
tovarythesebetweenth
we focus oncollisions
equal-sizedparticles,asthesemaximum fragment that carries half of the initial collider
mass.
impactons.
min
ified. For example,thestarting
from
Eq.
(2)
of
Krivovcollision
velocity at
andchoiceforsfragments
Inbodies
therest
max . for
Gravity
is importantlarger ofthanthis
100 msec(see below).
formingsmall(AppendixB).
unstirredma
In Fig.
2, we assu
⇤are most efficient
6
m-sized bodies have
Q
'
5
⇥
10
erg/g.
In
the
Smallerbodiesareweaker,andcanproducefragments
down
totion, we
exploreweinuse
which
cases
limit isformost
relevant.
Therefore,
Eq. (6)asanthisindication
the lower
limit
explainedasparticles.
In re
the smin indicated by the solid curve. For example,for
SiOall2 fragamework, a collision between
twosuch
bodiesatparticle
sizea distribution.
Quantitative
comparisons
reInofa thedebrisdisk,
particle
ofsmaller
sizethans0a micron
is mostformedments
can, atlikely
this velocity,
only
be eccentricities
formedthesmmodel isofhig
en result in fragmentation,asthekinetic
energyby collisionsof bodieslargerthan a fewbodies
centimetres. The shadedquire
relative
collision
velocities,
which
for
the
largest3 a collision between only slightly larger particles. In addition,eccentricity
can
be wr
ng ⇢ = 2.35 g/cmin) slightly
exceeds
theincriticalregion, top left, is forbidden, as there Mfrag > 2M0 and massbelt
isproperti
areoften
written
terms
of
the
Keplerianorbitalvelocityatthe⇤itynon-linearof such a radiationconserved.
Close to sminparticles,⇠ s0 , the solid curvesare
we focusequal-sized
asthese' 10 J), and fragments
willonbe collisions
createdfrombetween
afromnotthe
impacton sEmcorresponding
distance
centralobject.
For
bodiesonvB).
/ s 1 , while
Fig.the1. Top:minimum fragment
size sof in
a 20 m/s etcollision(Eq. (4)) as the pre- and post-collision surface areas become comparable.
rel /
e to
impactor(Eq.
(21)
Krivov
al.
2006)
are
most
efficientatformingsmall
fragments(Appendix
Ø three
物質毎の式sの関係。	
  interesting
compareEq.
(6) withcan
the traditional
form Informaterials, as a functionofcollidersize sidentical. We have assumed
withsemi-major
the torelative
Fig.
0とsorbits
min
Fig.It2.isaxes,
Predicted
smin/sblowvelocity
in debrisdisks,
asa function
rad2
scalesas vrelof/disks0 1/2.
ow-out
size.
For
this
particularcollision,
Eq.
(4)
of
the
catastrophic
fragmentationthresholdvelocityinequal⌘ = 10 and s=Therefore,
2 s . The grey weshadeduseareas areexcluded
Eq.
(6)
as
an
indication
for
the
lower
limit
Ø
上図垂直点線は分裂する半径。	
  
then
be
writteninterms
oforbitaleccentricity
andinclinationØs/sの理論線と観測。	
  Arrowsindicate
how
the
ratio
changeswithstellarluminosity,
surf
2
⇤
⇤
2
min
0
for
all
particbecause(right).
The dotsizedcollisions: v f = 8Q . The criticalenergy, Qsmallest, has unitsparticles incr
sblow
forof ⌘mass= conservation
0.1 and (left),= and
0.1self-gravity
J/m , butsmin
' 2 energy,
2 1/2 f , and ⌘.
1/2 indicate
Colouredregions
observational
constratedlines
indicate
the
limit
of
Eq.
(6).
Bottom:criticalenergies
versus
as
f
⌘
v
/v
=
(1.25e
+
i
)
,
with
v
=
(GM
/a)
the
of
the
particle
size
distribution.
Quantitative
comparisons
rerel
K
K
?
Ø
矢印は各パラメーターの依存性。	
  oferg/g,
andvarieswithparticle
mass.
For
small
bodies,the3Ø. Thus,
下図実線は粉砕に必要なエネルギー。	
  fragmentation.
As a rtheeccentric
0 sizethedi↵erence
betweenour
results
andfor equal-sized collisions. The energy needed to split a particle on
smin&/sforvarioussystems(seetext),
the diagonal solid li
strength
isDentdominatedby cohesion,and forlarge
onesandby gravity
blow
Keplerianorbitalvelocity(Wyatt2002).
Inadebrisdisk,
quire
relative
collision
velocities,
which
for
the
largestbodiesEq.
(6)) is shown⌘ =be10(dotted) and ⌘depending= 1 (dashed).
Øofdo0edはη=1e–3,	
  dsubstantial,
ashedはη=1の分裂に
Ø 1999).
sblowfor並みに小さいダストが観測
2
sizesoccurs
thisregime.
zes(e.g.
Krivov
et al. formay
eccentricity(Benz& AsphaugFor
solid
thisWetransition
give
ourcalculations
each⇤bodies,system.
fix=in0.1Jm, f = Pa10
a rangefragmentationof eccentricities
inclinations
will
bepresent.
Fora
The solid curves correspond to catastrophicof aggregatesand
72around
100
m
in
size.
Values
of
Q
⇠
10
erg/g
are
often
taken
on
a
short
timescale.
ue(Beitzof ⌘.
stressthat
ouris valid
forshowing
3 >of andarewrittenin1999),terms
the⌘Keplerian
orbitalvelocityat the ity of such Fa
必要なエネルギー。	
  = 10
for されていないことを説明できる。	
thiscomparison.
et We
al. 2011),
and iceandoftenbasalttheory(Benz& Asphaugroughcomparison,
weuse
averagequantities
hei
and
hii
to
obas typical for asteroids, and experimentally obtained
values for for each parstrength-dominated(smallself-gravity dominatedevaluated
es bothnottheapply
to models
thatsizes)
useandshallower
power
corresponding
distancefrom
thecentralobject.
For
bodiesonØ
一般に粉砕の方がエネルギーを使うこと
small
grains(mm
tocm
sizes)
canbeseveralordersofmagnitude
tain
typicalcollision
velocities.
In
reality,
hei
and
hii
are
poorly/material/ saertiesofvrelthethese
pleregimes
Sect.(large
4.2sizes).
of Krivov et al. (2013).
smaller
(Blum
&
Münch
1993;
Beitz
et
al.
2011).
Figure
1
shows
3
1
K
type
stars.
Krivov
et
al.
were
not
able
to
model
syste
orbitsconstrained.
with identicalsemi-major
axes,velocity
Estimates
rangethefrom
hei ⇠thehii relative⇠ 10 10, de- canA dearthがわかる。	  critical energy for splitting predicted by Eq. (6) as a function
of as
small
v
ance ofthe limit given by Eq. (4) depends on the withacollisionalcascadereaching
downto⌘ =sscales3
min = 3 µm,rea
and gives the size of thesmallest
fragments
createdina collisionpending
on
the
level
of
stirring(Matthewsetal.
2014).
of
size
for
the
materials
in
Table
1
assuming
⌘
=
10
and
1.
then
be
writteninterms
oforbitaleccentricity
andinclination
dictedbyThébault&d canper ↵individual
collision,on proposed
smallestparat vrelvary, assuming= 3.5 and smax
sminratio. dependingthat
the criticallargegrains
inand
these
are
primord
The
indicate
fragmentationenergies
for basalt
2 smallest
2 solid
1/2 lines
1/2 systems
The
between
the
grain
size
from
Eq.
(6)
as
fsmax⌘. Invdistribution,/vresti )ice (Benz, withvK Our=1999)(GM
thesminInsteadforminga fragment
we (1.25e
imaginethe +unstirredlocityand ofchoice
for
the
this
secon
.fragmentatio
In
their
rel
K =of
? /a) aggregatesand& Asphaugand silicate(Beitzmaterial.
calculations
suggestthat
theycanscenaalso
theblow-outsize
thenbecomes
limiting
case
in
which
the
kinetic
energyjust
suffices
to
split
et
al.
2011).
The
criticalfragmentationenergies
exceedthesplite in which cases this
limit
is
most
relevant.
ofthesmallest
grains
Keplerian orbital
velocity&
Inofa adebris
disk,cascade.
explainedas the2002).
outcomecollisional
However,!(Wyatt! 2Dent
both colliders in half1 , i.e. ⌘UK = 2⇡s20 . Solvingfors0 , we1 ting energy,
sizes
in isthis
✓
◆
✓
◆
✓
◆
indicatingthat
substantiallymoreenergyisrequired1
disk,
ss0minisofmost
likelydestruction
rate
a formed
L? andmodelf⌘obtaina particle ofishighlydegenerate,asmaterial
properties(⌘and det)aa sizerange
eccentricities
inclinations
will
bepresent.
Fora
to destroy – rather than split – colliders. ,Thevalues plotted for
=
2.4
(7)
on
a
short
1 stirring. Wh
etweenonly
slightlylargerparticles.
In
addition,
fected
by
2
2
2
ice
and
basalt10
were(obtainedat Jcollisionvelocitiesof 3 kmands , all have a tim
3
belt
propertiesf)areusually
poorlyknown,
la
s
5
AU
L
10
0.1
m
split
blow
rough
comparison,
weuse
averagequantities
hei
and
hii
to
ob⇤
s0 = between,(5) substantially higher than the velocities considered here,andQollisionsequal-sizedparticles,
as
these
2
of blow-out
size, theirevaluatedfo⌘⇢vrelimpact on smin .
3

1

2

4

3

min

2

max

1/3

0

0

3

is known to depend on velocity (Leinhardt & Stewart 2012).

Inves)ga)on	
  of	
  the	
  stellar	
  content	
  in	
  the	
  western	  part	  of	
  the	  Carina	
  nebula	
  Brajesh	
  Kumar	
  et	
  al.	  (2014)	

Ø Carinaは、200個のOB	
  star,	
  compact	
  HII	
  region,	
  数個の
embedded	  IR	
  source,	
  PDR,	
  proplyds-­‐likeなどを含み、massive	  starが低質量星形成に与える影響を調べられる理想的な領域である。(←左下のpillarsは大質量星のフィードバック)	
  Ø 西側のCrW	
  (d=2.9	
  kpc)について、U,	
  B,	
  V,	
  R,	
  I,	
  Hαの測光とChandra,	
  XMM-­‐Newton,	
  2MASSのサーベイを使って、PMSのパラメーターを決めてカタログを作った。	
  Ø 分光から星のtypeを決めたところlate	
  typeが多いとわかった。	
  Ø Hαや赤外超過からPMSと主系列星を区別。	
  Ø 数Myrを超えるWTTSでは赤外超過がなくなるので、X-­‐ray	
  sourceで可視に対応天体があるか調べた。	

B. Kumar et al.: Stellar content in the Carina west region

1. Color composite image of the large (2.7◦ × 2.7◦ ) area containing the Carina Nebula and centered at α(J2000) = 10h 41m 17.s 5
δ(J2000) = −59◦ 40′ 36.′′ 9. This RGB image was made using
the WISE
4.6 Stellarµm (red),2MASS(green),DSS R
B. Kumar
et al.:
content
in K
theCarinawest andregions bandd (blue) images. Approximate locations of diﬀerent star clusters (Tr 14, 15, 16; Bo 9, 10; Cr 228, 232, and NGC 3324) areoted by white boxes. η Carinae is marked by an arrow and in the lower left part of the image, south
0 pillars (Smith et al. 2000)
shown. The region covered in 0the present study is shown by the green box. Part of the selected field region can be seen in theeme western part of the image. North is up and east is to the left.
1

4

2
low- and intermediate-mass star formation. Very recently, an isolated neutron star candidate discovered
3 in the neighborhood of η
Carinae suggests there are at least two episodes of massive starformation (Hamaguchi et al. 2007; Pireset al. 2009).
4
V-J

V-I

1 that star formation is still
ces, Smith et al. (2000) showed
g on in this region. Later, Brooks et al. (2001) also identitwo compact Hii regions possibly linked with very young
pe stars. Rathborne et al. (2002) traced the photodissocia2 to be present in the masregions (PDRs) that are expected
star-forming regions. They conclude that the star formawithin the Carina region has certainly not been completely
ed despite prevailing unfavorable conditions imposed by the3
hot massive stars (see for moredetails Claeskens et al.
1). Detection of proplyds-like objects in these regions (seeour et al. 1998; Smith et al. 2003) proves the ongoing active

5

Figure 1 shows a three-color composite image, using the5
WISE 4.6 µm, 2MASS K s band and DSS R band images, ofthe large region of the Carina nebula.
6 The prominent V-shapedlane is associated with the nebular complex and consists of dust
and molecular gas (Dickel 1974). Trumpler(Tr) 16 is located7
near the central portion of this lane and thought to be ∼3 Myrold. This cluster also hosts one of the
8 most massive stars in our
9

0.5

1.0

1.5
B-V

2.0

2.5

3.0

0

0

1

1

2

2

3

3

4

4

V-K

V-H

0.0

5

0.5

1.0

0.0

0.5

1.0

1.5
B-V

2.0

2.5

3.0

1.5

2.0

2.5

3.0

5

6

6

7

7

8

8

9

0.0

9
0.0

0.5

1.0

1.5
B-V

2.0

2.5

3.0

B-V

←two	
  color	
  diagrams	
  Ø 2成分あって、赤はnormal	
  galac)c	
  valueで
空間的に一様分布。	
  Ø 黒は赤よりsteepで、分子雲のobscuredな部分から離れて分布à背景星	
  Ø 分子雲を通して見える背景光(黒)の傾き
からCrWではRv=Av/E(B-­‐V)=3.7と大きく、ダストサイズがISMより大きいことを示唆。	
  B. Kumar et al.: Stellar content in the Carina west region

11

60←color-­‐color	
  diagram	  Fは主系列星,	
  giants,	
  Class	
  III。	
  
TはCTTS。	
  Fig. 13. Histograms showing the distribution of YSOs ages (leftand red histograms are for the estimated√ ages and masses of YS
error bars along ordinates represent ± N Poisson errors.
PはClass	
  0/I。	
40

45

20

3

40

0

0

Cumulative number

35

2

12

30
25

1

2

4

5

6

7

8

B. Kumar et al.: Stellar content in the Carina west region
6

8

10

0

3

20

!
" 2 #$−rc5
Φ(d ≤ rc ) = A 1 − exp
2 σ2
%
&
0
+ (N − A) 1 − exp(−π B 0rc2) .

02

Age (Myr)of cataloged sources as a function of the cross-correlation radius
15
rc is given by

1

1

10

1

2

3

3
4
5
Cross correlation radius 12

6

7

H-K

In this equation N, A, σ,Fig.
and 10.
B represent
the total
numberofofcorrelations between the X-ray
Cumulative
numbers
14
cross-correlated X-ray sources (N = 43), the number of true cordetectedsourcesandthe
WFI
Fig. 9. (J − H)/(H − K) color-color diagramsourcesde- in the X-ray source position, and thecatalog. The thick curve reprerelations,ofthe
uncertainty
sents
the
observednumbers,
thedashedcurve
shows the best fit,tected in the JHK s bands in the CrW region.
The sequences
surface densityof the catalog of photometric sources, respecG9andthetheintegrated
dot-dashedline (magenta)(red) curves corre16
tively. In
the courseof fitting
numberof corre- and dottedof dwarfs (solid curve) and giants (thick dashedcurve)
are from
K1.5
spond tothe numbersof reallations withthe
thelocus
CrW ofphotometriccatalog
as a functionof andthe spurious sources, respectively.
Bessell & Brett (1988). The dotted line represents
K4
verticalindicates
the looptimal correlation radius rc .
(where 43
X-rayThe
sourceshaveline
an opticalsourceT Tauri stars (Meyer et al. 1997). Parallelseparation
dashed straightlines
18
closerThe
thancrosses
8 arcsec), we derived the fitting parameters as
represent the reddening vectors (Cohen etcatedal. 1981).
K5.5
M0
−2
−2
M5
33.78,
σ = 0.9on the dashed lines are separated by AV =A5=mag.
YSOs
arearcsec,
also and B = 2.3 × 10 arcsec (see Fig.
012310). The optimal correlation radius was chosen to be rc = 2.7 ′′ ,shown. Open magenta squares = Spitzer;which
filled implies
magentacircles (seemore
Briceño
et al.
2007).associaAt an age of ∼3 Myr, only ∼50% J-H
that there is nothan onespurious= Hα; filled squares = X-ray emitting WTTSs(green=XMMof thestarscounterparts
still show ofNIR excesses, and by ∼5 Myrtion among the 34 correlations;
i.e.,young
the optical
Newton, blue = Chandra); open red triangles
and open sources
this fraction
is reduced
to ∼15%et al.−2011c).
79%=ofCTTSs
the XMM-Newton
in the CrW
field should
thus (PreibischFig. 11. J/(JH) CMDSince
for the stars in the CrW region. The
green circles = probable NIR-excess sources
(see
text
for
the
be reliably identified.
= 0.02)the expected ages of most young isochronestars in ofthe2 Myr
CNC(Zaresev-by Marigo et al. (2008) and PMS Fig. 12. V/(V − I) CMD for all the detected YSOs (symbols asclassification scheme).
isochronesof age2, 5 and 10 Myr taken from Siess et al. in Fig. 9, see Sect. 4.2.2 for details). The isochrone for 2 Myr by
Claeskens et al. (2011) eralalso Myr,cross-correlated
these X-ray YSO
any IR-excess-selected
samplewill0.1,be1,highly(2000)
a distancesources (N = 43), but theyincomplete.
searched theTooptical
tacklecounterparts
this problem,
we corrected
used the for
X-ray
emit-of 2.9 kpc and a reddening E(B −Marigo et al. (2008) (continuous line) and PMS isochrones forV)identify
are also
shown. The symbols are the same as in 1, 2, 5, and 10 Myr by Siess et al. (2000) (dashed lines) are alsousing the Guide Star Catalog(GSC2.2).
Theirfit- tomin = 0.25YSO
tingversion
point 2.2
sourcesintheregioncandidates.
−2
Fig. 9 (seetoSect.
4.3.1stars
for theclassification scheme). The shown shown. All the isochrones are corrected for a distance of 2.9 kpc
tingparametersA = 35.4,
B = 2detection
× 10−3 arcsec, and
The X-raymethods
are sensitive
young
that
dening lines and are considered to be either
fieldstars (MSarestars,
masses and spectral types have been taken from the 1 Myr PMS and reddening E(B − V) = 0.25. The horizontal line with arrowσ = 1.8 arcsec. The numberof alreadytrue correlations(A)theirof bothntent in the Carina
west
region15
have
dispersed
circumstellar
disks,
thus
avoiding
giants)or Class
III and Class II sources with
small
NIR-excess.
studies are very much consistent. The surface density (B) of isochrone of Siess et al. (2000).
is the completeness limit of the observations.
the bias introduced when selecting samples only based on IR‘T’ sources are located between the middle
and lower
reddenthe catalog
of opticalsources in the present study is an order
3.0
excess(Preibischetal.
2011c).
ing lines. These sources are considered toofbemagnitude
mostly CTTSs(orhigher than in Claeskens et al. (2011), while ourClass II objects) with large NIR-excess. Theremayisbean thatoverlap
σ value
halfof these authors. The results of the cross- Classification of X-ray emitters based on NIR TCD
The age and mass of the YSOs have been derived usingof Herbig Ae/Be stars in the ‘T’ region (Hillenbrandet areal. 1992).
identification
listed in Table 2. When several optical counthe V/(V − I) CMD. The Siess et al. (2000) isochrones have
XMM-Newton
observations
We
haveidentified
WTTSs
based
on
their
X-ray
emission,asareofpresent,
only the closest one is given. The first col‘P’ sources are those located in the regionterparts
redwardthe lower
well as on their respective position in NIR TCD (Fig. 9) through2.5
umn
is the (protostellarID of the X-ray sourcesfrom Claeskenssatellite
et al. (2011).
reddening line and are most likely Class 0/I
objects
The XMM-Newton
has observed the CrW region in the
Columns
2
and
3
are
their
and Dec in degree (from Chandra and XMM-Newton observations. The sources having Xlike objects; Ojha et al. (2004)). It is worthwhile also mention- respective
course RAof thestudy of the massiveray
binaryWRand
22.lying
Theincorreemission
the ‘F’ region above the extension ofphotometriccatalog). In the next columns the V magnitude,
ing that Robitaille et al. (2006) show thatour
there
is a significant
sponding
results
have beenpresented
in separate(see
the intrinsic
CTTSspapers
locus, aswell as sources having (J−H) ≥ 0.6
colors
(V
−
I),
(V
−
R),
(B
−
V)
and
(U
−
B)
are
reported.
Sourcesoverlap between protostars and CTTSs. The NIR TCD of the Gosset et al. 2009; Claeskens et al.mag
and lying
to theleft of wethe first (leftmost) reddening vector2011).
In thissectionwith a spectral classification are mentioned in the next-to-last
2.0
observed region (Fig. 9) indicates that a column.
significant number of cross-correlated the sources detected(shownFig. 9) are assigned
in ourinphotometricdata ofas WTTSs/Class III sources (see,JoseX-ray
et al. 2008;
Pandeysources that have previously been identified as probable NIR- the CrW region with the positionse.g.,of 43sources
fromet al. 2008; Sharma et al. 2012).
Hereofit isworthwhile
to mention
excess stars lie in the ‘T’ region. Forty-one sources have been Claeskens et al. (2011). The positions
the
X-ray sources
as that some of the X-ray sourcesclassified
as WTTSs/Class
III sources, lying near the middle
ChandraX-raythatobservations
designated as CTTSs in our study with thecondition
they given by Claeskens et al. (2011, columns
8 and
9 of their table
vector, could be CTTSs/ Class II sources. Out of 34
fall in the ‘T’ region of the NIR TCD (Fig. 9) and are redward of 2) refer2 to the astrometric frame as reddening
1.5
determined fromthe XMMRecently, a wide area (1.42 deg ) of the Carina complex (XMM-Newton)
and 469 (Chandra) sources, 7 and 119, respecthe dashed blue cut-oﬀ line in the dereddened
CMD (Fig. 8). We NewtonX-ray
on-board
Attitude(CCCP,
and Orbittively,
ControlThe
has been mapped by the Chandra
Observatory
wereSystem.
identified
as crossWTTSs, with 4 in common. These arealso have plotted probable NIR excess sourcesthataredetectedcorrelation
withobtained
the GSC withand theopticalcatalogsuggests
Townsley et al. 2011). These
images were
thepresent
identified
in Table3 (bynumbers 4-5 in the last column and filledin ‘J’ band (10 out of 60). Most of these Advanced
sources arelocatedinmaking a small
correction.
decreasing the
CCD Imaging Spectrometer(ACIS;
GarmireWeet al.therefore
squaressuggest
in Fig. 9).
the ‘P’ region in Fig. 9, which means thatthey Thisare most2003).
CCCPlikely
study mainly
includes thedata from ettheal. (2011) by 0.′′ 25 and increas1.0
right ascensionof Claeskens′′
Class 0/I objects.
ACIS-I array, although ACIS-S
CCDs S2 andalsorotation was detected. We adopt
ingarraythe declination
byS3
0.were96. No4.3. Age and mass of YSOs
operational during the observations.
Butpositions
most of thethese newforsources
the 43 on
X-ray sources.
S2 and S3 are crowded and dominated by the background in the 4.3.1. Using NIR CMD
We
definedanoptimalcross-correlation
radius to find a com-0.8 4.2.3.-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
On the basis of X-ray emission CCCP data (Townsley et al. 2011). In this survey, 14369 X-ray
promisecorrelations
missedto astrometricerrorsLog MO•
sources were detected over thewhole between
CCCP survey
region. Out
ThedueCMDs
are useful tools
for studying the nature of the stellar
The NIR-excess-selected YSO candidate
and spurious
associationsin thefield. To
derivethe opti- regions. In Fig. 11, we plottedof samples
these, the are
CrWgenerregion contains
1465 sources.
Since theon- CrW
population
withinstar-forming′′ mal correlation radius, we applied the technique of Jeﬀries et al.
allyconsidered
incomplete
becausethe
NIR-excess
emission
axisCrW
Chandraregion.
PSF is 0.5Logand Φ
because it degrades at large oﬀ- the J/(J − H) CMD for all the YSOs identified in the previous
Fig. 14. Plot of the mass function in the
Log Φ

→	
  
赤外と可視のcolor	
  magnitude	
  diagram	  年齢と中心星質量を決定。	
  ←Mass	  Func)on	  Ø 環境の影響はIMFのlow	
  mass	  endに見られるはず。	
  Ø IMFについて、l1	
  Moより軽い側でSalpeter	
  (Γ=–1.35)より浅くなって折れる、大質量形成領域では軽い側は
ﬁeld	
  IMFより少ない、などの予想がある。	
  Ø しかし、CrWでは軽い側で折れていない(Γ=-­‐1.13)。	
  àgalac)c	
  ﬁeld	  star	  popula)onは主にOB	
  associa)onsや大質量星団が決めているのではないか。	

A	
  search	
  for	
  ﬂares	
  and	
  mass	  ejec)ons	
  on	
  young	
  late-­‐type	
  stars	
  in	
  the	
  open	
  cluster	
  Blanco-­‐1	
  M.	
  Leitzinger	
  et	
  al.	  (2014)	
Ø coronal	
  mass	  ejec)on	  (CME)は星の最も高エネルギーな現象で、惑星大気などにも影響。	
  Ø 太陽では良く調べられているが他の星では点源なので難しい。	
  Ø 太陽ではCMEとフレアが相関しているので他の星でもそうだろう。	
  Ø Blanco-­‐1はメンバーが多い(メンバーである確率が高いものが多い)。	
  Ø 12個のM型星のうち7個でHα輝線、4個でHα吸収線	
  Ø 14個のK型星のうち1個で輝線、13個で吸収線	
  Ø 彩層が活発だと吸収線で、不活発だと輝線になる。	
  Ø フレアは4天体で検出。	
  Ø フレアのある天体で、CMEによるHαの時間変動を調べるも4天体とも3σレベルで検出できず、à検出限界を検証。	
  Ø フラックスの感度から、必要なCMEの質量が決まり、その質量のCMEが観測条件において検出される回数が決まるà1	
  イベント以下。	
  Ø FS1とFS4ではフレアの前にdipを検出(FS3は解析による人工物)	
  Ø FS1,	
  4ともにblue	
  wingが減っている.	
  ←太陽ではフィラメントやプロミネンスのような噴出現象がHαの吸収を起こすことが知られている。	
  ←フレアが検出された4天体。	
  3.3.3 Flare rates
FS1とFS4にはフレアの直前にdipがある。	
  To give a parameter on the flare frequency of the stars
FS3にもあるが解析による人工物と判明。	
we computed flare rates and flare duty cycles. For ourOB−3_ID

OB−10/11_ID
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

1.5
1.8

1.4

normalized flux

1.3
normalized flux

tion, and therefore the background emission has no influenceon the detected flares.

FS2_2MASS J00031154−2958103

FS1_2MASS J00032088−3004472

1.2
1.1
1.0

1.6

Stellar activity in Blanco-1

1.4

1.2

7

multi-object observations the flare rate is defined as
Nflares /(Nobjects ⇥ t). The flare rate for every flaring starof the study is 0.2 flares per hour (fph). If we do not distinguish between likely (membership probability>5%), possible (0%<membership probability<5%), and non-members(membership probability=0%) the flare rate for all stars is
0.03 fph. If we take a look at the flare rates for the di↵erent member states of the stars then we get 0.03 fph for the
likely members (12 stars), 0.1 fph for the possible members(2 stars) and 0.01 fph for the non-members (14 stars). If weconsider mid-M type (dM3-5) dwarf stars only (6 stars), we
get a flare rate of 0.1 fph.
An alternative parameter for the flare frequency is the flare
duty cycle which is the ratio of flaring time to total observing time (given in %) and is defined as flare / t. tflare is
the number of flare spectra times the duration of one spectrum and t is the total observing time times the numberof stars. For FS1 we get 13%, for FS2 2%, for FS3 4%, andfor FS4 we get 2%. This gives for all stars 0.7%. For the
likely members we get a duty cycle of 0.2%, for the possible
members 3.9%, and for the non-members we get 0.17%. For
the 6 mid-M-type stars of the sample we calculate 3%.
H↵ flare rates are rarely reported in the literature. Lee et al.
(2010) studied H↵ variability of M dwarfs and found of 0.1
events per hour with a factor of 2 increase in EW and < 0.05
Figure 4. Spectral sequence of H↵ of FS1 (upper left panel), FS2 (upper right panel), FS3 (lower left panel), and FS4 (lower rightper
hpanelwith
Hiltonetblueal.
foundpanel).
In eachwe plota
the factor
spectral time 10
series increase.
of the flare events from
Fig. 3. The
solid (2010)
line corresponds
to the average
spectrum of the whole OB, whereas the red dotted line corresponds to the respective individual spectra. Grey areas denote parts of thefromtime-resolved
Sloan
DigitalSurveyspecspectrum
which arecovered by both average andsingle spectrum,blue areasSky
correspondto the average(SDSS)
spectrum only andred areas to
the respective individual spectra. This makes it easily visible where the respective spectrum is lower than the average spectrum (blue)
and where
respective spectrum
is enhancedwith respect
averageduty
spectrum. cycle
In the right(percentage
part of each panel we showtrathe(coveringH↵,
H (red)) thattheto theflaredi↵erence plots of the individual spectra minus the average one.
of time during which flares occur) increases from 0.02% forearly M dwarfs to 3% for late M dwarfs. If we compare ourresults to the findings of Hilton et al. (2010) we see that theflare
duty000,cyclesof our mid-M-type stars fit well to the 3%
c 2002
RAS, MNRAS
1–??
for late-type M dwarfs.
FS1_2MASS J00032088−3004472

FS2_2MASS J00031154−2958103

average spectrum
single spectrum

0.9

1.0

0.8
08:20

average spectrum
single spectrum

11_9
11_8
11_7

08:40

09:00
09:20
time UTC

09:40

09:10

09:20

09:30
09:40
time UTC

09:50

11_6

3_9

11_5
11_4

OB−2_ID

OB−1_ID

1

2

3

4

5

6

7

8

1

9

2

3

4

5

6

7

8

9

1.4

1.20

3_8

11_3

spectrum number

FS4_2MASS J00032273−2953505

spectrum number

FS3_2MASS J00024051−3001598

11_2
11_1
10_9
10_8

10_6

1.3

3_4

10_5

3_3

10_4

normalized flux

normalized flux

1.10
1.05
1.00

3_6
3_5

10_7

1.15

3_7

10_3

3_2

10_2

1.2

10_1

−1000

1.1

3_1

−800

−600
−400
−200
velocity [km s−1]

0

200

−800

−600

−400
−200
velocity [km s−1]

0

−1000

200

−800

09:40
09:50
time UTC

10:00

0.9
08:10

08:20

08:30
08:40
time UTC

08:50

maximum expected Hα flux [erg cm−2 s−1]

Stellarofactivity
in detected
Blanco-1
Figure 3. Light-curves
the flareson the11stars
2MASS J00032088-3004472, 2MASS J00031154-2958103, 2MASS
10−13
J000240513001598,
and 2MASS J000322732953505. The labelling
OD = 2ODx-axis=5of the upperofeach plot corresponds to the spectrum num10−14
bers ofFig. 4. The flux is normalized to the first spectrum of thetime series.
10−15

200

−800

−600

−400
−200
velocity [km s−1]

0

200

0

200

average spectrum
single spectrum

2_8

1_9

2_7

1_8

2_6

1_7

spectrum number

09:30

spectrum number

0.90
09:20

0

FS4_2MASS J00032273−2953505

2_9

1.0

0.95

−600
−400
−200
velocity [km s−1]

FS3_2MASS J00024051−3001598

average spectrum
single spectrum

2_5

2_4

1_6

1_5

2_3

1_4

2_2

1_3

2_1

1_2

←フレアのあった4天体のHαの時間変動。	
  青は平均、赤は個々、黒は共通部分。	
  左は(個々–平均)。	
  
速度ごとに時間変動がわかるので、dipの詳細がわかる。	

1_1

−1000

−800

−600
−400
−200
velocity [km s−1]

0

200

−800

−600

−400
−200
velocity [km s−1]

0

200

−1000

−800

−600
−400
−200
velocity [km s−1]

0

200

−800

−600

−400
−200
velocity [km s−1]←	  (上図) ODはプラズマを抜けてくる輻射の割合(の逆数)。	
  (下図) 点線と実線はdN/dEの冪の違い。赤と青はLXの違い。	
  	
  3.3.2 Flares
3.3.4 Flare energies
To identify flares we calculated the H↵ line fluxes with 上図でフラックスの検出感度からわかる必要なCMEの質量afixed 20Å window centered on H↵. We found four stars
To maximize the net observing time per OB we did not reに対して、下図でそのイベント数を見ると、諸々補正した右軸
showing distinct flaring activity (see Table 1). In Fig. 3
quest standard star observations for flux calibration. Therewe show the H↵ flare light-curves constructed from thefore we need a di↵erent method to obtain flare energies. To
で1イベント以下。	
spectra. Three additional stars show possible “fragments”
estimate the total energy output of the flares in H↵ we cal10−16

−17

−18

α = 2.3
log(LX) = 28.4 erg/slog(LX) = 30 erg/s

100.00

10.00

10.00

1.00

1.00

0.10

0.10

0.01

0.01
16

number of CMEs during tobs with vproj>135 km s−1

number of CMEs (M>MC) per day

to inactive dM star thereby filling the intrinsic absorption
profile10 due to an increased number of H↵ active regions.
Another possibility is that these dM stars have no chromo10
spheres.
100.00α = 1.8

17
18
19
20
of flares, either increasinglog(Mline) [g] fluxes at the end of anCculate the continuum flux using the relations (Eqs. 2 and 3)