Star Forma)on Newsle0er#275 46-50本目
麻生 有佑

The VLT/NaCo large program to probe the occurrence of
exoplanets and brown dwarfs at wide orbits⋆

arXiv:1510.08453v1 [astro-ph.EP] 28 Oct 2015

III. The frequency of brown dwarfs and giant planets as companions tosolar-type stars

M. Reggiani1, 2 , M. R. Meyer1 , G. Chauvin3 , A. Vigan4 , S. P. Quanz1 , B. Biller5 , M. Bonavita5, 6 , S. Desidera6 , P.
A&A p
3 , frequency
1 , dwarfs
11 toReggiani
et al.: Theof brown
and giant10
planets
companions
solar-type stars
Delorme3 , J. Hagelberg7, 17 , A.-L. Maire6 , A. Boccaletti8 M.
, J.-L.
BeuzitE. Buenzli
J. Carson, E. asCovino, M.
14 , G. Montagnier4 ,Feldt9 , J. Girard12 , R. Gratton6 , T. Henning9 , M.
Kasper13 , A.-M. Lagrange3 , D. Mesa6 , S. Messina
disk fragmentation) can actually form objects down to a few
1. Introduction
15
3
16
17
1
18,
Jupiter
Star19and planet formation
mechanisms thereplanet-formation
scenarios”
and gave
C. Mordasini , D. Mouillet , J. E. Schlieder, D. Segransan , C. Thalmann “standard, and
A. masses.
Zurlo
Binary systems have been observed and characterized for almost
fore overlap in the planetary-mass regime. Companions in this100 years (see e.g. Aitken 1935). Since the seminal works by mass range could be the lower mass tail of the stellar CMRD
Duquennoy&
Mayor(1991)
andFischer&Marcy(1992),
the1
as well as the higher mass end of the planet CMF, but theyInstitute for Astronomy (IfA), ETH, Zuriche-mail:reggiani@phys.ethz.ch
propertiesof stellar binaries have also been widely studied. One have usually been excluded by the statistical analyses of direct
2
Département d’Astrophysique, Géophysique etofOcéanographie,
Université
17 AlléedumassSix Août,4000 Liège, Belgium
the most interesting
parametersdeof aLiège,
binary systemis theimaging surveys. Diﬀerent features in the frequency of BD com3
ratio q = et
M2d’Astrophysique/M1 , defined as the ratioof the secondaryUJF-Grenoble1/CNRS-INSU, Institut de Planétologie
de Grenoble
UMR(M
5274,
38041
Grenoble,
France2 ) overpanions
and planetsas a function of mass and semi-major axis
4
the primary
mass (M1 ). The dedistributionof q UMR
values fora sample
Aix-Marseille Université, CNRS, LAM (Laboratoired’AstrophysiqueMarseille)
7326,
13388could
Marseille,
France diﬀerent formation mechanisms (see also
help distinguishofbinariesisthecompanion
mass-ratio
distribution(CMRD).
5
Brandt et al. 2014b). Although spectroscopy may help in invesInstitute for Astronomy, University of Edinburgh,Blackford Hill, Edinburgh EH9 3HJ, UK
Several surveys in the past decades focused on the detection of tigating whether a given detected object formed by one process
6
INAF – Osservatorio Astronomico di Padova, Vicolodell
Osservatorio
5,35122
Padova,Italystellar binaries with the purpose of characterizing the occurrence or another, large surveys could contribute in assessing whether a7Institute for Astronomy, University of Hawaii, 2680
Woodlawn
Drive,
Honolulu,
96822
of companions
and their
mass
distributionHI
bothin theUSA
field (e.g. stellar-like or planet-like formation process dominates the CMF
8
al. 2010;
Janson etFrance
al. 2012)
and in star forming re- in a given companion mass range.
LESIA, Observatoire de Paris Meudon, 5 Pl. J. Raghavan
Janssen, et92195
Meudon,
Italy
9
gions
Patience
et al. 2002).
Reggiani & Meyer (2013), as an
Max-Planck Institute for Astronomy, Königstuhl
17,(e.g.
69117
Heidelberg,
Germany
As a project within the VLT/NaCo large program (hearupdate of Reggiani & Meyer (2011), have shown that in the field after NaCo-LP, P.I. J. Beuzit, Desidera et al. 2015; Chauvin et al.
10
Department of Physics and Astronomy, Collegethe
ofCMRD
Charleston,Charleston,SC universal,
29424 , USAisconsistent
with
being
independentof
11
INAF Osservatorio Astronomico di Capodimonte
via Moiarello
16, 80131
Napoli,
Italy by the obser- 2015), the work presented in this paper represents the first atprimary
mass and separationin therange covered
tempt to place some constraints on the full CMF in the substellar
12European Southern Observatory, Casilla 19001,vations,
Santiago
19, beChileand canfit by a single power-law slope dN/dq ∝ qβ , regime. It takes into account both BDs and planets and makes use
13with β =± 0.29. Garching,
In addition, Germany
N-body simulations suggest of the results of most of the direct imaging surveys of solar-type
European Southern Observatory, Karl Schwarzschild
St,0.252, 85748
the CMRD
is onlyCatania,
modestly
by dynamics,
evenin planets
M.
Reggiani etaﬀectedal.: The frequencyof brown dwarfs
and giantas companions to solar-type stars
14
INAF – Catania Astrophysical Observatory, viathat
S. So
a 78, 95123
Italy
primaries
currently available. In Sections 2 and 3 we present ourdense clusters, as opposed to the semi-major axis (SMA) distri- model for the mass distribution of substellar companions and the15
Physikalisches Institut, University of Bern, Sidlerstrasse
5,CH-3012Bern,
Switzerland
obtained by using the COND evolutionary models. Dupuy et al.
bution(Parker&
Reggiani2013).
The
CMRD
therefore
seems
Monte
Carlo
tool that
we developed
to test it. Then,
16(2014) present
evidencefor simulationa substellar luminosity
probleminNASA Ames Research Center, Moﬀett Field, CA,2
to beUSAa good diagnostic for diﬀerent star formation mechanisms.
the predictions
from evolutionarymodels. The
lumi- (logcBD )we describe
the datasets
thatpredicted
we adopted
fora−log
the aanalysis(Sec17
which we estimate planet and BD masses could−in
While
distributions
massesand orbitalparametersnositiesare2 from
Geneva Observatory, University of Geneva, Chemin
destheMailettes
51, of
1290
Versoix,
Switzerland
2
α
2
σ
tion
4)
and
the
results
of
the
Monte
Carlo
simulations
based onBD
fact
be underestimated (Dupuy et al. 2014), which would make
BD
18
quite
well
establishedforstellarcompanions,
the
shape
of
the
BD dataBD 5).
Núcleo de Astronomía, Facultad de Ingeniería, Universidad Diego Portales, Av. Ejercito 441, Santiago,
Chile
Finally,
discuss
our surveytheseresults
more (Section
constraining
regardlessthe wefrequencyof the results in Section 6
companion mass(CMF) Universidad
and of the SMA
19
mass
objects.
Although
the COND
models2thecloudless,α pl 7.
β pland36-D,summarize
conclusions
in Section
Millennium Nucleus “Protoplanetary Disk”, Departamento
defunction
Astronomía,de distribution
Chile,planetary
CasillaSantiago,
Chile
show
the
smallest
discrepancy
withtheobserved
luminosities
in the substellar and planetary mass regime is still poorly underpl
plcompared
to
the
DUSTY
models(Chabrier
et
al.
2000)
and
the
stood. The over 500 extrasolar planets discovered with theSaumon
ra- &Table
Planetandmodels.
BD distributions:
Marley1.(2008)
hybridThe DUSTY model
models values.
—
dial velocity (RV) method allowed astronomers to fit power-law
might be more appropriate for some of the higher mass (and presumably hotter) browndwarfs that we simulate. Howevertheslopes to the mass and semi-major axis distributions for planets
Parameter
Valueswith both families of evolutionary models lead toa
with masses between 0.3-10 M Jupiter and within ∼3 AU (seesimulations
e.g.
αBD
1.25
consistent results.
ABSTRACT
Fischer & Valenti 2005; Cumming et al. 2008). However, nothα pl-0.31bing guarantees that the same behavior holds at larger separa-BD,placBD pl50 AUc
4. Dataset
tions ortohigher
masses. Direct
imaging is aanddetection
methodContext. In recent years there have been many attempts
characterize
the occurrence
distributionof stellar, σbrowndwarf (BD) 1.68c
BDallowsto characterizelarge-separation
exoplanets.
InThethedatasetthat weusedtest the modelfor the substellar
β pl tovelocity
0.39b
and planetary-mass companions to solar-type stars,that
withtheusaimof constraining
formationmechanisms.
FromradialobserCMF
of thefortargetsof the NaCo-& all separationsc
past decade many direct imaging surveys (e.g. Lowrance etal.described in Section
fBD2 consisted
0.61[q=0.08-1]
vations a dearth of companions with masses between
10-40
M
has
been
noticedatclose
separations,suggestingthepossibility
BD
Jupiter
LP al.
(Chauvin et al. 2015; Desidera et al. 2015), a large observing
2005; Biller et al. 2007; Lafrenière et al. 2007; Chauvin et
f pl in the context
0.0329forVLT/SPHERE[1-13 M J ] & [0.3-2.5 AU]dprogram (ESO: 184.C-0157)
of theof a distinct formation mechanism for objects above
andHeinze
below
range.
2010;
etthisal. 2010;
Vigan
et discontinuity
al. 2012;at Biller
al. 2013;
scientific preparation.mThis
Fig. 1. Combined
substellar
CMF. Thelog M/Met
5 survey
M Jupiter⊙ =-2.3
minBDprogram is a direct imaging
Aims. We present a model for the substellar companion(CMF).
consistsof theofmtheplanet andBDstudy
providing a homogeneous
statisticallysignificant
is duethe opacityWahhaj
limit
for fragmentationthat seta minimum
Rameaumass
etal.tofunction
2013a;
et al.It2013;
Chauvinetmassal.superposition
2015;
80ofMthemaxBD
Jupiterfor objects formed through core fragmentation. The minimum mass is occurrence of giant planets
and BDs in wide (5-500 AU) orbits
Brandtetal.
2014a;
Bowler
et
al.
2015)
have
been
carriedcompanion mass distributions, assuming that we can extrapolate
velocity measured companion
massnearby
functionfor planets to 0.1 AU
aminassumed to thebe 5 Mradial
Jupiter in our model.
around young,stars.
BD It focused on a carefully selected◦outtoevaluatetheoccurrenceofgiant
planets
inwideorwith adeclinations
δ ≤ both
25 , agest ≤ 200
Myr,AU
10000
larger separations and the stellar companion mass-ratio distribution over all separations into the BDsample,
massregime.
ByBD usingthemaxplchosendistancesR-band brightnesses R ≤ 9.5 and with—exbits (10-500 AU). Besides a few planets (e.g. Kuzuhara etal. d ≤100 pc, mminpl theresults of the VLT/NaCo large program (NaCo-LP, 2013;
P.I. J. Rameau
L.interested
Beuzit)andcomplementaryarchivethat probe
occurrence
clusionbinariesandvisual binaries with separawe
run
Nthe
simulations
the survey,
in whichevery datasets
etin,al.
2013b)and ofbrowndwarfs(BDs)(e.g. of spectroscopic
BD,pl
m
0.1
x
M star
max
tion
<6”.
The
samplewas
initially
comprisedof84
targets,none
targetstar
israndomly
assignedanumberofplanets
andanumpl
of planets and BDs on wide orbits around solar-typestars,ber
place
some
constraintsonthe planet
andBD distributions.
Chauvinetweal.
2005b;
et al.
2010;
etPal.
2010;of which had been observedof BDs,based Biller
on Poisson
statistics
withMugrauer
mean P pl andBDamin plbefore in a planet survey. These stars—
werethen observed with
VLT/NaCoin theof
H bandforal.
planets
and Carson
BDs,
In caseprobability
Methods. We developed a Monte Carlo simulation
tool etto
predict
therespectively.
outcomeofthe
aPoissongiven
survey,dependingon
the shapethebetween
Wahhaj2011;
et al. 2013)detected,
many
surveyse
amax
rcutoend
ff
plof 16.5 nights. A complete descripa number
smaller than 0.5,
the nullnumberof planetsor BDsbe 2009
foundeccentricity
no returns
planetarycompanions.
The
results
cannotusedand 2013, for a totalthe
orbital parameter distributions (mass, semi-major axis,
andinclination).
the predictions
resultsof thetion of the samplewith
and its properties(distance,
age, mass) canfor the given staris zero.
However, if theComparing
star turns out to haveto fit are
power-laws
tothecanplanetary
distributions
beyondAU.
found inNotes.
Desidera(a)et Reggianial. (2015). The
summary(2013),
of the programone
or moreplanets(orBDs),
the mass
and semi-major
axis for10 be& Meyer
measured for stellar companobservations, we calculate how likely diﬀerent models
and
which
be ruled
out.
observations
is provided in Chauvinal. (2015).
As a (b) Heinze et al. (2010),
onesuggestof them is arandomly
selectedof
fromthe planet
input planet(or and of the ionsHowevereachtheytruncation
thesemi-major
but extrapolated
to theet BD
regime.

measured CMF but extrapolated to larger separatof course some caveats to these assumptions. ForØ binaryの伴星主星質量比q=M1/M2はM1に依らずstellar massではdN/
not take into account how gravitational instabilidq∝q^(0.25±0.29)。
cretion diﬀer in the distributions of orbital parame
The fact that there are multiple binary formatioØ VLT/NaCo large programなど観測感度の向上により、substellar側がわかってきた。
and that both planets and BDs migrate makes ev
complicated. In this paper we propose a simple,
and test whether it works.
Ø “stellar-like mechanism”でできるものをBD, “standard planet-forma)on
Instead of tryingscenarios”ででto fit the substellar CMF withlaw distribution (see e.g., Brandt et al. 2014b),
きるものを惑星と呼ぶ。
overall frequency of substellar companions to beØ Companion Mass func)onをsingle powerではなくBDと惑星の和と考える。
contributions:Ø モンテカルロで擬似サーベイ。

d N

Ø 検出感度は星からの距離で決まる
contrast curve (距離や年齢も考慮)。
Ø 観測は主にVLT/NaCo LP (δ<25°,
t<200 Myr, d<100 pc, R-band輝度<9.5, sepera)on<6”)で、substellarは47天体中無検出。過去のサーベイも追加して１99天体中3天体検出。

1 Moのとき。

=Cq d log q e
d log a,d N = C m d log m a d log afor BDs and planets, indicated with the “BD ”
scripts, respectively. q is the mass ratio, as defineαand β are the exponents of the power-law
major axis distributions (c.f. Cumming et al. 2008
and σ are the mean and the standard deviation
aration distribution, assuming it is log-normallyfor solar type primaries (see e.g. Raghavan et al.
C are normalization constants that can be obtai
surements of the BD and planet frequency fmasses and semi-major axes.
In this paper we assume values for the para
think are appropriate for solar-type primaries,

Results. Current observations are consistent with the proposedmodelthe2).CMF,
as longas a suﬃciently
smallno outerresult of the campaign,
substellartruncationcompanions were detectedBD) distributions(seeforSectionThe eccentricity
is randomly

The VLT/NaCo large program to probe the occurrence ofの続き
et al.: The frequency of brown dwarfs and giant planets as companions to solar-type stars
exoplanets and brown dwarfs at wide orbitsM.M.⋆Reggiani
Reggiani et al.: The frequency of brown dwarfs and giant planets as companions to solar-type stars

arXiv:1510.08453v1 [astro-ph.EP] 28 Oct 2015

III. The frequency of brown dwarfs and giant planets as companions tosolar-type stars
Ø 惑星のaの最大値を決めるr
cutoﬀを変え
1, 2
1
3
4
1
5
5, 6
6

て、3000回実行。NaCo-LPで無検出の確率は100, 30, 20 AUで、9, 45, 53%。

M. Reggiani , M. R. Meyer , G. Chauvin , A. Vigan , S. P. Quanz , B. Biller , M. Bonavita , S. Desidera , P.
Delorme3 , J. Hagelberg7, 17 , A.-L. Maire6 , A. Boccaletti8 , J.-L. Beuzit3 , E. Buenzli1 , J. Carson10 , E. Covino11 , M.
Feldt9 , J. Girard12 , R. Gratton6 , T. Henning9 , M. Kasper13 , A.-M. Lagrange3 , D. Mesa6 , S. Messina14 , G. Montagnier4 ,C. Mordasini15 , D. Mouillet3 , J. E. Schlieder16 , D. Segransan17 , C. Thalmann1 , and A. Zurlo18, 19
1

Institute for Astronomy (IfA), ETH, Zuriche-mail: reggiani@phys.ethz.ch

Département d’Astrophysique, Géophysique et sampleで3天体
Océanographie, Université de Liège, 17 Allée du Six Août, 4000 Liège, BelgiumØ その他も合わせたfull
UJF-Grenoble1/CNRS-INSU, Institut de Planétologie et d’Astrophysique de Grenoble UMR 5274, 38041 Grenoble, France
Aix-Marseille Université, CNRS, LAM (Laboratoire d’Astrophysique de Marseille) UMR 7326, 13388 Marseille, France
検出の確率は、2,
19, 25%。
Institute for Astronomy, University of Edinburgh,Blackford Hill, Edinburgh EH9 3HJ, UK
2

Fig. 2. Detection probability for the NaCo-LP observed sample for rcuto f f =100, 30, 20 AU (from left to right).
Fig. 2. Detection probability for the NaCo-LP observed sample for rcuto f f =100, 30, 20 AU (from left to right).

3

4

5

6

INAF – Osservatorio Astronomico di Padova, Vicolo dell Osservatorio 5, 35122 Padova, Italy
Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822 USALESIA, Observatoire de Paris Meudon, 5 Pl. J. Janssen, 92195 Meudon, France Italy
9
Max-Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
10
Departmentof Physics and Astronomy, College of Charleston, Charleston, SC 29424 , USA
pl
cutoﬀ
11
INAF Osservatorio Astronomico di Capodimonte via Moiarello 16, 80131 Napoli, Italy
12European Southern Observatory, Casilla 19001, Santiago 19, Chile
13
European Southern Observatory, Karl Schwarzschild St, 2, 85748 Garching, Germany
14
M. ReggianiAstrophysicalet al.: The frequencyof brown dwarfs via
and giantplanets
as companions
to solar-typeItaly
stars
INAF – Catania
Observatory,
S. So
a 78,
95123 Catania,
Fig. 3. Detection probability for the full sample for rcuto f f =100, 30, 20 AU (from left to right).
Fig. 3. Detection probability for the full sample for rcuto f f =100, 30, 20 AU (from left to right).
15
plPhysikalisches Institut, University of Bern, Sidlerstrasse
5,CH-3012Bern,
Switzerland(2014b), that some of the so-far directly imaged exoplanets could
16
NASA Ames Research Center, Moﬀett Field,haveCA,formed
USAby either core or disk fragmentation and constitute17
the low-massof the brown
mass
distribution.
Geneva Observatory, University of Geneva, Chemin
destail
Mailettes
51,dwarf
1290
Versoix,
Switzerland
18
In the next few years,
newPortales,
instruments,
likeEjercito
the VLT SpectroNúcleo de Astronomía, Facultad de Ingeniería,
Universidad
Diego
Av.
441, Santiago, Chile
Polarimetric High-contrast Exoplanet REsearch (VLT/SPHERE)
19
Millennium Nucleus “Protoplanetary Disk”, Departamento
deImager
Astronomía,
denew
Chile, Casilla 36-D, Santiago, Chileor the Gemini Planet(GPI), willUniversidad
enable us to find78

Ø β とrを変えて、検出が3個以下になる確率が0.3%以下の範囲を調べた。
(Cumming et al. 2008ではβ =0.39)

Ø Sahlmann et al. (2011)はCompanion MFが25-43 MJupに極小値を持つことを見つけた。
à惑星のhigh mass tail、つまりBDと惑星は質量で分かれると主張。
Ø しかし、極小値は今回のモデルのように重ね合わせでも現れる。
of a distinct formation mechanism for objects above and below this range.
Aims. We present a model for the substellar companion mass function (CMF). It consists of the superposition of the planet and BDØ 観測的にも、惑星質量の伴星がac)ve accre)onやmassive diskを
companion mass distributions, assuming that we can extrapolate the radial velocity measured companion mass function for planets tolarger separations and the stellar companion mass-ratio distribution over all separations into the BD mass regime. By using both the示すà質量では分けられないだろう。
results of the VLT/NaCo large program (NaCo-LP, P.I. J. L. Beuzit)
and the complementary archive datasets that probe the occurrence
planetary-mass companions. To what extent large surveys withthese new instruments will help us constrain the distributions oforbital parameters still remains to be seen. With the next generation of extremely large telescopes instead (e.g. the European
Extremely Large Telescope, E-ELT), our understanding of planet
ABSTRACT
statistics will makea huge step forward. It will be possible to directly measure the shape of the substellar CMF and locate withhigher precision
the minimum evenwide companions.
In thisContext. In recent years there have been many attempts
to characterize
the foroccurrence
and distributionof stellar, brown dwarf (BD)context, it will be interesting to study how the distribution ofand planetary-mass companions to solar-type stars,
with the aim of constraining formation mechanisms. From radial velocity obsercompanion masses in the substellar regime varies not only withvations a dearth of companions with masses between
MJupiterhasas been
noticedat closerespect 10-40
to separation
but also
a functionof primary
mass. separations, suggesting the possibility—

7. Conclusions

In this paper we propose a simple model for the substellar mass
spectrum, as a combination of the planet CMF and an extrapolation of the stellar CMRD into the BD mass regime. Taking
advantage
the placelargest sample
to date of solar-type
ob- and BD distributions.
of planets and BDs on wide orbits around solar-typestars,of wesome constraints
on thestars
planetserved with direct imaging, we ran Monte Carlo simulations to
Methods. We developed a Monte Carlo simulation
tool
to predict
outcomeof a given
survey,depending on the shape of thecomparepredictionsof ourthemodelwith the observations
fromtheand archival data.
conclude that: Comparing the predictions with the results of theorbital parameter distributions (mass, semi-majorNaCo-LP
axis, eccentricity
andWeinclination).

observations, we calculate how likely diﬀerent models are and which can be ruled out.

– The outcome of the direct imaging surveys is consistent with
Fig. 4. Probability of our surveys detecting 3 substellar companions, asResults.
are consistent
proposed ofmodel
forderived
the CMF,
long as a suﬃciently small outer truncationa superposition
the CMF
by RV asmeasurements
a functionof theCurrent
power-law observations
slope of the semi-major
axis distributionwith the(α pl = −0.31
and β pl = 0.39)Some
and of thestellar CMRD
down
β pl ,radius
and the outerradiuscutoﬀ
ofthesemimajor
axis
distribution.
The(!100 AU) is introduced for the planet separation
distribution.
regionsof parameter
space can be excluded by theoverall probability is normalized to be 1 within the figure. The region
to 5 M Jupiter , as long as rcuto f f ! 100 AU (99.7% confidence).
observations.
above
the line can be ruled out at 99.7% confidence.
– When all the other parameters are fixed, some combinations

Conclusions. We conclude that the results of the directsurveyssearchingfor substellarof β pl -rimaging
ruled outby the observations
with a companions around Sun-like stars
cuto f f can be
99.7% confidence.
are consistent with a combined substellar mass spectrumof planets and BDs. This mass distribution has a minimum between 10 and

BDs in close orbit (period ≤ 5 yrs) around nearby sun-like

The Young Stellar Population of the Cygnus-X DR15 Region–6–

arXiv:1510.02835v1 [astro-ph.SR] 9 Oct 2015

S. Rivera-Gálvez1 , C. G. Román-Zúñiga2,5 , E. Jiménez-Bailón2 , J. E. Ybarra2 , J. F.
Alves3,5 and Elizabeth A. Lada4

Ø Cygnus-Xは数個のOB associa)ons, 数十の星団、数百のHII領域、ABSTRACT40以上の大質量星を含む。その中の南にあるDR15 (d~1.4 kpc)は、
We present a multi-wavelength study of the young stellar population in the
B star, HII領域、PDRを含む。IRDCの先端は可視で見える段階、そCygnus-X DR15 region. We studied young stars forming or recently formed atの隣により若いスポット。
and around the tip of a prominent molecular pillar and an infrared dark cloud.
Using a combination of ground based near-infrared, space based infrared and
X-ray Altodata, weconstructeda point source Spitzer
catalog fromwhich we identified 226
Ø 観測：スペイン Calar
3.5m
JHK seeing~1”,
IRAC&MIPS,
young stellar sources, which we13classified into evolutionary classes. We studied
Chandra ACIS-I X線0.2-7.0
kev, FCRAO CO (1-0)
their spatial distribution across the molecular gas structures and identified several
groups possibly belonging to distinct young star clusters. We obtained samples ofthese groups and constructed K-band luminosity functions that we compared withthose of artificial clusters, allowing us to make first order estimates of the meanages
and age spreads of the groups.
We used a 13
CO(1-0) map to investigate theØ YSOの同定。24µmで受かればClass
I/0。Class
IIはgas kinematics at the prominent gaseous envelope of the central cluster in DR15,
Ybarra et al (2013)に従う。X線源が赤外線源と一致す
and we infer that the removal of this envelope is relatively slow compared to other
るものでJ-H>0,cluster>1.97(K-[4.5]),[3.6]regions, in which[4.5]-[5.8]>0.5,
gas dispersal timescale
could be similar or shorter thanthe circumstellar
disk dissipation timescale. The presence of other groups with
[4.5]>0.7はClass
III。
slightly older ages, associated with much less prominent gaseous structures may
à26 Class 0/I, 155
Class II, 45 Class IIIで、Kryukova et al.
imply that the evolution of young clusters in this part of the complex proceeds(2014)と大体合う。
in periods that last 3 to 5 Myr, perhaps after a slow dissipation of their dense
molecular cloud birthplaces.

Fig. 2.— False RGB (Spitzer MIPS 24 µm, IRAC [8.0], IRAC [4.5]) image of the DR15
region. Images are log-scaled. The DR15 pillar is located at the center. Bright PAH
emission and reflections saturated the pixels at the center of the DR15 cluster shell in the
IRAC [8.0] and MIPS 24 µm channels, thus the cyan-colored region. Other fainter, molecularpillar structures are visible at both flanks of the main pillar. The dark infrared cloud at thenorth shows recent star formation activity and extends westward towards the LBV source– 14 –
G79.29+0.46, located at the center of a bright red shell.

24:00.043

22:00.040

40:20:00.0

36

33

18:00.029

16:00.026

12:00.0

14:00.022Ø 柱密度(Av)が大きいところにClass Iが多い。
Facultad de Ciencias, Universidad Autónoma deØ あるAv以上にいるClass
Iの柱密度は、Avとpower law
Baja California, Ensenada, México(~2.9)にある(Schmidt
type rela)on)。
Instituto de Astronomı́a,
Unidad Académica en Ensenada,
1

2

Universidad Nacional Autónoma de México, Ensenada 22860, México
3

Astronomy Department, University of Vienna, Austria

19

15

1.0 pc12

10.0

20:33:00.0

50.0

40.0

30.0

20.0

10.0

32:00.0
8.4

Fig. 5.— Spatial distribution of the identified YSOs in DR15 plotted on the extinction map.
The grayscale indicate visual extinction, AV , in magnitudes, with contours highlighting levels
from 15.0 to 30.0 in s.pdf of 2.5. The red circles indicate the Class I objects, the green circles
the Class II objects and the blue circles the Class III objects.

The Young Stellar Population of the Cygnus-X DR15 Regionの続き

S. Rivera-Gálvez1 , C. G. Román-Zúñiga2,5 , E. Jiménez-Bailón2 , J. E. Ybarra2 , J. F.
Alves3,5 and Elizabeth A. Lada4

Ø Gather algorithm (n番目への距離と等価な円から密度を決める)より、Class IIのクラスターを同定。
ABSTRACT
Ø クラスターごとにK-band luminosity Func)onをモ
デルと比べる。
We –present
a multi-wavelength study of the young stellar population in the
20 –Cygnus-X DR15 region. We studied young stars forming or recently formed
at From left to right: Color scaled surface density maps, in units of sources per
Fig. 7.—
Ø モデルは、IMFは固定で年齢と年齢の分散を振る。
sq. arcmin, for Class I, II and III candidate YSOs in DR15, constructed with the Gather
and around the tip of a prominent molecular pillar and an infrared dark algorithm.
cloud. Extinction contours are similar to Figures 3 and 5. Yellow circles indicate theàembeddedなC,
Wの方がそうでないSE,
SWより
location
Using a –combinationof ground based near-infrared, space based infraredandand selected sample extension for clusters and groups identified in the Class II map.
20 –若い。Cは3Myrなのにエンベロープが多い。
X-ray data, we constructeda point source catalog from which we identified 226– 29 –

75895

L2

young stellar sources, which we classified into evolutionary classes. We studied Table 1. Main Parameters and Age Estimates for Cluster Samples in the DR15 Region
Cluster
Mean Age Age Spread No. CI No. CII No. CIII
their spatial distribution across the molecular gas structures and identified several[Myr]Ø
Cを通るPV図の楕円(expanding
groups possibly belonging to distinct young star clusters. We obtained samples ofenvelope)はMdot~360
Mo
Myr–1with
で、 DR15-C 3.0[2.5,3.5] 4.5[3.5,5.0] 1 8
these groups and constructed K-band
luminosity functions that wecompared4
DR15-W
3.5[2.5,4.5] 4.5[1.0,5.0]
2
16
5those of artificial clusters, allowing
us to makefirst order estimates of themean
DR15-SE 3.5[3.0,4.5] 3.0[1.0,5.0]0
50
Cの1023
Moを飛ばすのに~3
MyrとDR15-SW 4.5[4.0,5.0] 3.0[1.0,5.0]0
112
ages and age spreads of the groups. We used a 13 CO(1-0) map to investigate theDR15-N–– – 16 – 15
21
6
長い。
DR15-NE––0113
gas kinematics at the prominent gaseous envelope of the central cluster in DR15,
and we infer that the removal
this envelope
is relatively slow compared to otherØ ofCはClass
Iが1個、IIが8個、IIIが4個とThe number pairs inside the brackets indicate the range of model
ages within the 2-sigma (68%) confidence level. The number listed
cluster regions, in which gas dispersal
timescale
couldbesimilaror
shorterthan
少ないので、「星形成の終わりを迎え、 before the bracket is the central value, which we list as the best estimate
for the age/age spread of the cluster
the circumstellar disk dissipation timescale. The presence of other groups with
母体はゆっくり散逸している」。
Estimated as number of sources of indicated class falling within theslightly older ages, associated with much less prominent gaseous structures may
circle used for the KLF sample analysis
imply that the evolution Øof young
clusters in this part of the complex proceeds
普通は中大質量星団のガス散逸は
in periods that last 3 to 5 Myr, perhaps after a slow dissipation of their dense
縦速いので、DR15の細さが原因かも。
molecular cloud birthplaces.
Fig. 6.— Left: Distribution of Class 0/I candidate sources mass estimates from SED model(細い光蒸発で~100 Mo Myr–1,
38077

a

19084

a

b

b

b

75895

L2

9482

24:00.038077

40:20:00.0

19084

4724

9482

L4

2335

16:00.0

4724

1126

L4

2335

12:00.0

1126

528

528

225

08:00.0

225

0.0

a

75

75

30.0 20:33:00.0

20:33:00.0

30.0 30.0

32:00.0
32:00.0

0

0

b

1

Westmoque0e et al. 2013)

Facultad de Ciencias, Universidad Autónoma deBaja California, Ensenada, México

横2

Instituto de Astronomı́a, Unidad Académica en Ensenada,

Zero moment (integrated intensity) 13 CO(1-0) map of the DR15 region,
Universidad
Nacional
Autónomade México,
Ensenada
22860, México
thesurvey of Schneider
et al. (2006),
the grayscale
is indicatedin unitss indicate
visual extinction, similar to Figure 5. The two red arrow lines
3
Astronomy Department, University of Vienna, Austria
L4 indicate cuts along which position-velocity (P-V) plots were obtained

fits. Right: Distribution of Class 0/I candidate sources disk accretion rate estimates from
SED model fits.

arXiv:1510.05641v1 [astro-ph.GA] 18 Oct 2015

Complex molecules in W51 North region
6 Rong et al.
Jialei Rong1⋆ , Sheng-Li Qin1⋆, Luis A. Zapata2, Yuefang Wu3 ,Tie
Liu4, Chengpeng Zhang3, Yaping Peng1, Li Zhang1 and Ying Liu5
1

Department of Astronomy, Yunnan University, and Key Laboratory of Astroparticle Physics of Yunnan Province,
Kunming, 650091, China
2 Centro de Radiostronomı́a y Astrofı́sica, Universidad Nacional Autónoma de México, 58089 Morelia, Michoacán, México
3 Department of Astronomy, Peking University, Beijing, 100871, China
4 Korea Astronomy and Space Science Institute 776, Daedeokdaero, Yuseong-gu, Daejeon, Republic of Korea 305-348
5 Department of Physics and Hebei Advanced film Laboratory, Hebei Normal University, Shijiazhuang 050024, China

Ø 大質量星は周囲に化学的なインパクトをもたらすß化学種から条件や段階がわかる。
Ø W51 NorthにはH2O, OHメーザー、ダスト連続波、分子流、インフォールが見られ、実際に大質量星を形成している。また、cm波がないので、早期段階。
Ø 観測：SMA, 216.5-218.5 GHz, Δν=0.8
MHz (~1 kms–1), θ~3”, σcont~0.01 Jyb–1, σline~0.1 Jyb–1
ABSTRACT3
We present Submillimeter Array (SMA) molecular line observations in two 2 GHz-widebands centered at 217.5 and 227.5 GHz, toward the massive star forming region W51
North. We identified 84 molecular line transitions from 17 species and their isotopologues. The molecular gas distribution of these lines mainly peaks in the continuum
IRS2d–3and has a small tail extending to the west, probably associposition of W51 North,ated with W51 d2. In addition to the commonly detected nitrogen and oxygen-bearing
species, we detected a large amount of transitions of the Acetone (CH3 COCH3 ) andKJD3
W51d2
Methyl Formate (CH3 OCHO),
which may suggest that these molecules are present in W51 N
H2
an early evolutionary stage of the massive stars. We also found that W51 North is anethanol-rich source. There is no obvious diﬀerence in the molecular gas distributions
between the oxygen-bearing and nitrogen-bearing molecules. Under the assumptionof Local Thermodynamic Equilibrium (LTE), with the XCLASS tool, the molecuFigure 2. The are
LSB andUSB spectraWe
extracted
at thecontinuum
lar column densities, and rotation temperatures
estimated.
found
that
the peak position. The black curve is th
indicates simulated spectra using the XCLASS program. U marks the unidentified transitions.
oxygen-bearing molecules have considerable
higher column densities and fractional
abundances than the nitrogen-bearing molecules. The rotation temperatures range
2. The PhysicalParametersfrom 100 to 200 K, suggesting that the Table
molecularemission
could be originated froma warm environment. Finally, based on the gas distributions, fractional abundances
Molecule
N
Trot
fH 2
and the rotation temperatures, we conclude that CH3 OH, C2 H5 OH, CH3 COCH3 and(cm−2 )
(K)
CH3 CH2 CN might be synthesized on the grain surface, while gas phase chemistry is 18
CH3 OH
2.3 × 10138
3.6 × 10−7
responsible for the production of CH3 OCH3 , CH3 OCHO and CH2 CHCN.
3 CH OH
1.1 × 1017
138
1.7 × 10−8
3CH3OH
217.886 GHz

CH2CHCN
227.907 GHz

H2S
216.710 GHz

CH3COCH 3
227.939 GHz

CH3CH2CN
218.389 GHz

SO2
216.643 GHz

7
CH3OCHO
216.966 GHz

Intensity ()Ø 連続波から、粒子半径0.1µm, 密度3 gr cm (=0.2g/cc?), g/
d=100, 温度はCH3OHの回転温度138 KでM ~1348 Mo。

Ø 輝線は17種84遷移を検出。
Ø O, N系は中心が連続波に一致、LTE温度(XCLass, 右表)も似ている。
Ø à混ざり合い、同じ起源。OrionKL,KeyG19.61-0.23とは異なる。
words: ISM:abundances — ISM:individual (W51 North) — ISM:molecules —radio lines: ISM — stars:formation
Ø S系は連続波からずれ、高温なのでou|low。
building block to understand massive star formation, since
1 INTRODUCTION
these molecules can provide information on the physical conØhotcoreが発達してO-richからNThere are three promising theoretical models to explain the
ditions and evolutionary phases of massive star formation
formation of the massive stars: monolithic collapse, com(Herbst& van Dishoeck 2009).
richになる(Rodgers& Charnley
petitive accretion, and mergers of low mass stars (see forThe
W51 North is one of well-studied massive stara review, Zinnecker & Yorke 2007). However, their relative
2001)ので、W51は早期。
forming regions within the luminous cluster W51-IRS2 (Zalarge distances (a few parsecs),
the clustered formation en-

Figure 1. The continuum image at 227 GHz, shown in both contours and grey. The contour levels are 5%, 10%, 20%, 30%, 40%, 50%,
60%, 70%,80%, 90%, 100% of the maximum intensity of ∼3.0 Jy beam−1 . The color scale on the right shows the intensity ranging from0 to 3.5 Jy beam−1 . The synthesized beam is shown in the bottom right corner.

DCN
217.240 GHz

image the corresponding molecular names are labelled,
including oxygen-bearing molecules of CH3 OH, H2 CO,C2 H5 OH, CH3 OCHO, CH3 OCH3 , CH3 COCH3 , nitrogenbearing molecules of CN, CH3 CH2 CN, HC3 N, CH2 CHCN,
sulfur-bearing molecules of SO2 , H2 S, SiS, and deuterated
molecules of DCN and CH3 CCD. The quantum numbers,
frequency, Sij µ2 and Eu of each transition are summarizedin Table 1. Column (1) lists the species and column (2) lists
quantum number, column (3), (4) and (5) give frequency,
Sij µ2 and Eu . The source size θa ×θb , ∆V and I are given
in column (6), (7) and (8), respectively.

C2 H5 OH
7.4 × 1017
140
1.2 × 10−7
CH3 OCH3
1.8 × 1017
140
2.8 × 10−8
Figure 3 presents a sample of images from the oxygenCH3 COCH
1.4pro-× 10417DATA ANALYSIS
140
2.2 × 10−8
, nitrogen-, and sulfur-bearing
molecules,3which canvide spatial distribution of specific molecules. In genTherotation
temperaturesand fractional −9abundances of
16
4.3 × 10complex
110can reflect6.7
× 10
2 CO
eral, all molecular H
imagesshow a compact structure.
molecules
immediateenvironments close
The peak emission of the oxygen-bearing molecules of
to17
the stars or star-forming cores, but also canprovide key
3.0 × 10clues in understanding
138 formation
4.7mechanism× 10−8
3 OCHOCH OH, CH COCHCH
and CHOCHO, and nitrogen-bearingof the specific3.3

SiS217.818 GHz3

Gas distribution

3

3

3

molecules of CH2 CHCN, CH3 CH2 CN and DCN are coincident with the continuum peak position. The oxygenand nitrogen-bearing molecules are probably well mixed in

Figure 3. The sample images of specific molecules. In each pannel, the synthesized beam is shown in the bottom right corner, the crosssymbol marks the continuum peak position. The contour levels are 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%,80%, 90%, 100% of thepeak value. The peak values of CH3 OH, CH3 COCH3 , C2 H5 OH, CH2 CHCN, CH3 CH2 CN, DCN, H2 S, SO2 and SiS are 24.7, 14.9, 78.6,
15.7, 14.1, 24.3, 45.4, 85.6 and 95.2 Jy beam−1 , respectively.

the column densities of the nitrogen-bearing molecules range
from 2.8 × 1015 to 2.6 × 1016 cm−2 .
4.2

Abundance and isotopic ratio

vironments, and their short timescales have made extremely
diﬃcult to discard any of these models (Zapata et al. 2015).
Massive stars have a substantial impact on their sur-al. 2010). The chemical model proposed by Rodgers &Charnley (2001) suggested that hot-core composition (Orich or N-rich) depends on core temperature and the ammonia/methanol ratio of the evaporated ices, and the timescale

space, which imply that they may have same chemical origin (Remijan et al. 2004). While the emission peak of thesulfur-bearing molecules of H2 S, and SO2 are located east of
the continuum peak. Probably the sulfur-bearing molecules
have diﬀerent chemical routes and form in diﬀerent environments when compared with the oxygen- and nitrogenbearing molecules. In addition to the compact source structure, there is an obvious gas extension to the west of thecontinuum traced by the DCN, H2 S, and SiS is observed.

molecules. In order to obtain reasonable parameters, we use
the XCLASS to estimate the column densities and rotation

CH2 CHCN
CH3 CH2 CN
HC3 N
HCC13 CNof the molecules.
15
9.2 × 10temperatures
140
1.4 × 10−9
2.6 × 1016
140
4.1 × 10−9
2.8 × 1015
105
4.4 × 10−10
1.2×1014
105
1.9×10−11

SO2
33 SO
H2 S
SiS

9.4 × 1017
3.4 × 1015
4.4 × 1016
1.9 × 1015

180
170
143
130

1.5 × 10−7
5.3 × 10−10
6.9 × 10−9
3.0 × 10−10

16

130
138

1.0 × 10−8
1.1 × 10−11

CH3 CCD
6.6 × 10
pata, Tang & Leurini 2010). The distance from
W51 North
DCN
6.8 × 1014
to the Sun is approximately 7 kpc (Imai et al. 2002). However, a more recent and accurate estimation from Xu et al.

Complex molecules in W51 North regionの続き

arXiv:1510.05641v1 [astro-ph.GA] 18 Oct 2015

Jialei Rong1⋆ , Sheng-Li Qin1⋆, Luis A. Zapata2, Yuefang Wu3 ,–7。gas-phaseでは~10–11なので、より多く
4
3
1
1
5
Ø メタノールCH
OH・・・abundaceが最も多く、3.6x10
Tie
Liu
,
Chengpeng
Zhang,
Yaping
Peng
,
Li
Zhang
and
Ying
Liu
3
1
Department of Astronomy, Yunnan University, and Key Laboratory of Astroparticle Physics of Yunnan Province,
生産できるgrainsurfaceの方が合う。
Kunming, 650091, China

2 Centro de Radiostronomı́a y Astrofı́sica, Universidad Nacional Autónoma de México, 58089 Morelia, Michoacán, México

3 Department of Astronomy, Peking University, Beijing, 100871, China
4 Korea Astronomy and Space Science Institute 776, Daedeokdaero, Yuseong-gu, Daejeon, Republic of Korea 305-348–8 Hebei Normal University, Shijiazhuang–11
Department of Physics
and Hebei Advanced film Laboratory,
050024,China
Ø アセトンCH。Orion-KLではhotcoreに集中して3COCH3・・・X~2.0x10 。gas phaseでは~10
いるが、W51 Nでは未発達なのでgrain surface。すぐに壊れるので早期を示唆。
5

ABSTRACT–7)とメタノールに対する比が他の領域より大きØ エタノールCH3CH2OH・・・存在量(X~1.2x10
We present Submillimeter Array (SMA) molecularline observations in two 2 GHz-widebands centered at 217.5 and 227.5 GHz, toward the massive star forming region W51
North. We identified
84 molecular line transitions from 17 species and their isotopoい。上2つと同じ理由でgrainsurface。
logues. The molecular gas distribution of these lines mainly peaks in the continuum
position of W51 North, and has a small tail extending to the west, probably associated with W51 d2. In addition to the commonly detected nitrogen and oxygen-bearing
species,a large amount of transitionsof the Acetone (CH3 COCH3 ) and3 we detected3
3Methyl Formate (CH3 OCHO), which may suggest that these molecules are present inan early evolutionary stage of the massive stars. We also found that W51 North is anethanol-rich source. There is no obvious diﬀerence in the molecular gas distributions–8
between the oxygen-bearing and nitrogen-bearing molecules. Under the assumptionof Local Thermodynamic Equilibrium (LTE), with the XCLASS tool, the molecular column densities, and rotation temperatures are estimated. We found that theoxygen-bearing molecules have considerable higher column densities and fractionalThe
2abundances than the nitrogen-bearing molecules.
3
2 rotation temperatures range
from 100 to 200 K, suggesting that the molecular emission could be originated froma warm environment. Finally, based on the gas distributions, fractional abundances3
and the rotation temperatures, we conclude that CH3 OH, C2 H5 OH, CH3 COCH3 andCH3 CH2 CN might be synthesized on the grain surface, while gas phase chemistry is
responsible for the production of CH3 OCH3 , CH3 OCHO and CH2 CHCN.

Ø ジメチルエーテルCH OCH とギ酸メチルCH OCHO・・・ジメチルエーテルはエタノールの異性体だが、存在量が相関せず、親が違う。ギ酸メチルとは温度、柱密度、分布が似ている。gas phaseでX~4.8x10 を作れる。
Ø シアン化ビニルCH CHCNとシアン化エチルCH CH CN・・・2つの存在量比は他の領域と同じくらい。CH3CH2CN/HC Nに対する比~10はgrain surfaceに合う。
Ø 重水素系・・・DCNは早期を示唆。CH
3CCDは大質量星形成領域では報告が少なく、dark
Key words: ISM:abundances— ISM:individual (W51 North) — ISM:molecules —–8
radiolines:
ISM—
stars:formation
cloudと比較するために重要。X~1x10 はgrain surfaceを支持。
building block to understandmassive star formation,since
1 INTRODUCTIONØ S系・・・H
surfaceでできて、SOàSO
2S/SO2比~0.05は他の領域と同じくらい。H
2Sがgrain2。
these molecules can provide
information on the physical conThere are three promising theoretical models to explain theformation of the massive stars: monolithic collapse, competitive accretion, and mergers of low mass stars (see forditions and evolutionary phases of massive star formation(Herbst & van Dishoeck 2009).

.1 AU, and we fix

1510.04258v1 [astro-ph.EP] 14 Oct 2015

ion of the mixing
ion; indeed someexceeds the soundcg = (kT /µ)1/2 ⇠between wind andcomponent of thece balances the gas(11)

ABSTRACTing a non-vanishing flux generates a torque that is about 10

Here a small imbalance in the amplitude of the applied radialØ hot Jupiterを説明する原始惑星系円盤内のgas ﬂow modelを決定した
on protoplanetary disks (PPDs), which are exposed during their later evolution to an intense,
Star magnetized wind
⌃
⇠
⇢
h
=
1
⇥
10
g
cm
(17)
い。
from the central star. A radial magnetic field is mixed into a thin surface layer, is wound up by the disk
Disk
shear,and iswind
pusheddownward
a dependence
combinationforthe adopted
parameters,with a by
weak
on of turbulent mixing and ambipolar and Ohmic drift. TheØ <1 AUで重要なMRIに基づいたモデルを提案する。
Radially
Protoplanetary Disk:R.
The highvalueof the coolingcompared
withthe seed vertical field that is usually
toroidalfield
reachesmuch density
greater(16)strengths
thaninvokedMagnetizedin PPD models,

ocity and the diskf the disk. The soal profile of P and
ect the upper disk
y uniform temperhich Equation (11)5temperature due to the steep increase in H electronic transiRADIALLYMAGNETIZEDDISK: VERTICAL PROFILE
tions at higher temperatures.
A rapidtransition at thePROTOPLANETARY
base ofthe atomic layer to lower temperatures and higher densities
M ATTHEW RUSSO
is driven by molecularcooling, of
notably
COUniversity
roto-vibrational
Department
Physics,of Toronto, 60 St. George St., Toronto, ON M5S 1A7, Canada.
emission (Glassgold et al. 2004).
We now balance the wind energy flux with the radiative
2
Russo &
emission from the corresponding volume of the mixed layer,
C
HRISTOPHER T HOMPSON
thereby defining a characteristic mass density
CanadiansInstitute for Theoretical Astrophysics, 60 St. George St., Toronto, ON M5S 3H8, Canada.
Astrophysical Journal 2015, in press
B 3
Radially Magnetized Protoplanetary Disk: Vertical ProfileṀwVw23⇢cool (R) ⇡ µg
⇠
10
⇢
.
(16)
w
and on the stratification of the disk. In the largest simuThe change of sign of Br across the disk plane is mirrored
8⇡R3 ⇤
lations performed to date, an imposed vertical field carryby the toroidal magnetic field that is wound up inside the disk.
Here µg is the mean molecular weight. The corresponding
than a toroidal field of equal strength (Baifield between the two hemispheres has a marked effect on theThis paper studies the response of a thin accretion disk totimes
anstronger
external
radialmagnetic
Our
focus
isThe region near the midplane is2internalstructureof the disk.
& Stone2011),
as comparedwith ⇠ 10times stronger field.
inatomic H column isvery weakly ionized, leading to rapid reconnection of toroidal
the older unstratified simulations of (Hawley et al. 1995).
cool

cool g

-3

-2

-1/2
fields of opposing signs. The current sheet sits at the midplane
The scaling hB2 i / 0 is obtained in the ideal MHD limit
in the case of perfect reflection symmetry, but otherwise iswhen the plasma parameter of the seed magnetic field isdisplaced to one side.
2
1.
0 = 8⇡P/B0
Now consider now a geometrically thin disk in which a visTo estimate the torque that results when a radial magnetic
cosity given by the second half of Equation (4) is excited. We
field Br0 is imposed at the top of the disk, we write3
move
to cylindrical(Rstar' r, interactingz ' ✓r). ThewithmagnetiF IG . 1.— Poloidal magnetic
fieldcoordinatesof a T-Tauri
the up!
cally active gasthincolumnassumedto be regulated
a characper layers of a geometrically
andisweakly
conducting
PPD.to The
kinetic
B2 0
c2g
teristic
value⌃
byexternal
ionization,
with
a
slow
inward⌫MRI = ↵eMRI.
pressure(2)of the wind exceeds theactpressureofanyverticalfieldremaining
from
-k⌃
8⇡P
⌦
growth
⌃
(R)
/
R
due
to
the
increasing
ionization
rate
act
the first stages of infall from a natal molecular cloud.
and angle of attack of X-rays on the disk near the protostar. In
Here B 0 is the toroidal field that is generated by linear windthe inner disk, where the flaring of the dust absorption layer
2 /R)/d ln R . R /2R, the temperature ofing of the imposed radial field over the vertical diffusion
smaller thanspeedtime
cg and isviscosity
↵cd(h
p
?
g /⌦),
through the disk. The numerical simulations of weakly maga
passively
irradiateddisk scales as T ⇠ R-3/4 . Combining
netized disks ( 01) just described suggest-4 = 1/2.
-2 In the-22Equation
cgVw (4) and (5) with these radial profiles of ⌃act and T ,⇢wstrongVwcalculations performed laterr in this paper, we encounterthe local rate of mass transfer scales as
magnetization (. 1) and use the alternative scaling = 1⇠ ✏w ↵⇢eventhat thesuperthermal.
type of boundary
outflow
envisagedbyw implies
becoming
Linearstability
analysisindicates that the disk experiences the magnetorotational
Matsuyama et al. (2009) has a small effect on the instantaandon the magnetizedstratification
the bothdisk.the In
the oflargest
simuinstability
(MRI)
at
a
highermagnetization
thanaverticallydiskofwhen
effects
ambipolar
neous disk structure.

The chaØ PPDがT-Tauridate,andan magnetic
imposedfieldverticalfield
carryby the toroand Hallwindと星からのX線と相互作用する状況で、放射状drift are taken into account. Steadylations
verticalperformed
profiles of todensityare obtainedat(12)
動圧>ガス圧でingtoaa non-vanishing
fluxBgenerates
a torquethat G.
is Careful
about 10Here a sm
3.2. Temperatureseveral radii between
0.06 andProfile
1 AU in responsewind magnetic field⇠ (10 –10)(r/AU)(radial)の磁場を入れたときのケプラー回転、軸対称円盤の鉛直分布P(⌦r)
飛ばされる。
attention
is
given
to
the
radialandverticalionization
structure
resultingfromirradiationbystellar
X-rays.
The
TABLE
1
times
strongerthanatoroidal
field
of
equal
strength
(Bai
field
betw
We employ an analytic temperature profile in each hemie base of the mixed
✓
◆ ✓
◆⇣
⌘
D
M
P
2
sphere
of
the
disk.
This
consistsoftwoisothermal
layers
that
T
V
r
disk
is
more
stronglymagnetizedcloser
to
the
star,
where
it
can
supportahigherrate
ofmass
transfer.
Asare matches
the fullinternalを計算する。windとdiskのshearの乱流とMRI乱流。Hall
dri~は無視。
& Stone 2011), as comparedwith ⇠ 10 ⇠ 0.003✏
times ↵stronger in. st
are separated by a sharp transition at a freely adjustable height
200 K
400 km s
AU
EFAULT

2

0

ODEL

disk
(Equation 49).
Consider the simplest configuration with Br0 uniform withheight between the top of the disk and a reconnection layer
near the midplane. Such a configuration emerges in the vertical profiles to be presented in Section 6. Taking

ARAMETERSṀMRI ⇠ 3⇡⌫MRI ⌃act ⇠ R(6-8k⌃ -(5+8k⌃ ) )/8(1+2 ) .
1/2

w

(6)

Firstw,-1
let us-1consider how this result depends on the rela-tion (2)betweenaroundstress and the linearly ampligreen 1978). This
result, the inner ⇠ 1 AU of a PPD is found to theevolvetowardlower surface
density. Masstransfer
rates
older
unstratified
simulationsof (Hawley
etal.MRI-generated
1995).
fied toroidal
magnetic
field. We take k⌃ = 1/4very
from the weak
dezbl , -8
-1
irst, the Disk
windParameterscartailedmodel
developed
later
in
the
paper. Equation (6) gives(1)B=-(3/2)⌦t
B
,
(3)
0
diff
r0
10
M
yr
are
obtainedunderconservative
assumptions
about
the
MRI-generated
stress.
Theevolution
of
-1/2
-2
1/32
fields
✓
◆
✓
◆
2
⌃
200
g
cm
Ṁ
/
R
in
a
weaklymagnetized
disk
with
=
1/2;
and
g,tot
MRI
o overturn deeper-1 obtained
The scalinghB/ intimeis⌫MRI
in
the
ideal
MHD
limit the disk must haveofa oAnypoloidalmagnetic
field
threadingwith idiffusion
tdiff ⇠
h2g across the thermal
scale
Tblthe- Tcimplications forz planet
Tbl + Tmigration,c
0theṀMRI / R-1/8 ina strongly magnetized disk, for which we
the
disk,
and
are
investigatedaccompanying
paper.
T
5000
K
2
bl
in Thenthethecas
T
(z)
=
tanh
a
ln
+
.
(18)
height hg = cg /⌦, one finds
ayer cannot radiatepressure
largerthan= 1.
⇢wVw , orit will be
swept back.
cool
adopt
when
the plasma
parameterof◆1/(1+2theseedmagnetic
field
is
2
zbl
2disks —1.27 mug,bl✓◆2/(1+2and)
magnetic
geometrydiffersfromthat
postulated
byBlandford) ✓ 2 satellites:
2
Subject
magnetic
fields—planetsformation—
protoandµstellar
X-rays.
6 headings: accretion, accretion
Russo & Thompson
B 0
3
Br0
displaced
2µg,c2.32 mu=; & Payne (1982) and Pudritz & Norman (1986), and any mag8⇡P/B
1.
ed thetemperature
8⇡P
2e
↵MRI
8⇡P
planetarydisksdensity— turbulence
The transition is matchedto the cooling
(16),
⇢gthe
(z0tradial)== optical
0 of stellar
pared withdepth ⌧opt,rphotons byacool
5
netocentrifugal
wind
from
the
disk
surface
(Bai
&
Stone
2013;coNow✓◆ /(1+2 ) 2-2⇤1/(1+2 ) B2r0
local balance becwhen
a factor ⇠ (IR /we ⇥simply2
opt )(cestimateg /⌦R) ⇠ 10 . ThereforegTotheradial⇢cool (R).
Lesur
2013)
will bemagnetic
quenched. Instead, the T-Tauri wind
⌫MRItorque= (3/2) ↵eMRIthat results. et(4)al. atakeStellar Parameters
8⇡P
⌦
giv
al to density)
and3 surface of the disk, andcosity
interacts
directly
with theits magnetic
Sample temperature profiles for an unmagnetized disk
are B Tc =is
field
at(22)the top of the disk,wewrite
r0 Teff imposed
M⇤did notM set aThis demonstrates that a radial seed field can leadto a issubfield
entrainedbyathinboundarylayer(Figure
1).
they
move
to
c
shown in Figure
3.
TheparameterainEquation(18)
in the denser molecular layer.
viscousstress compared with an equiva1. INTRODUCTION cool
thestantiallysignenhancedof thischange.
R⇤
2R
This paper is devoted to understanding how the magnetic
t reflects
a balance!
lent toroidal seed when B20 . 8⇡P.
sets
themagnitudeofthetemperature
gradient,
with
a
⇠
5
cool
3.3. Ionization Model
activ
field thatin this ofboundarylayercallywill diffuse
RX cooling.
10R
The MRI-driven torqueongivenoutpatch
the disk
2 is ashearedng andB2 acting
Understanding
the similar
formation
andobtained
migrationofSeveralplanets
giving profiles
to those
by Glassgold
et al.ofin
2.2. Mass Transfer
Windcg into the disk, and the equilibrium structure that resources
ionization operate in protostellar
disks. Induced by a Split-monopolar
0 downwardL⇤L
teristicva
Magnetic
Field
dependsonthemagnetic
flux
threadingit(Hawley
et
al.
1995;
We focus ongas
X-rayscorona, whose⌫absorption= ↵mixed layer iscircumstellar
obeMRI. care must be taken(2)The transition
and molecularisfromsults. Particularwith regard to the radial
MRI
presentsbetween
severalatomic
challenges,
firstofofthefreestellarL2 ⇥ 1030 erg s-1(2004).disks
is thethe dominantsourceelectrons inThethemagnetized
innerdisk atwind that is emitted by
a T-Tauri star may-2
8⇡P⌦
dentk Xoveraheightof the ionizationin the disk,
well as the ⌃Sano
et al.
Pessahet bedependenceal.launched2007).This
flux israteusually
as-asgrowth⌃g . 50 g cm below thesurface(Glassgold
et2004;al. internal
by varying
the mean molecularµflow
be sourced
by thestar’sdynamo; or may
g = (1.27–
1 keV
which is handled
to develop
a deterministic
model weightof thecolumns
of gasB TX
1997,
and references
therein).
from the inner regions of the disk itself (Pudritz depletion& Norman of dust in the active layer by the settling of partineeded to overturn2.32)mu in parallel with Equation (18). The turbulent
diffutobeoriented
verticallywithrespecttothedisk
plane.
Radioactive
decay could supplysumed
an ionization
rate⇠iThroughout most of this paper, we approximate
the an outer gas reservoir that feeds the accretion
and angle
cles fromflow
and dust sivity
withindisk.Thefor tackling
this zfirstdominate X-ray 1986).
Wind Parameters
10-19heights-1 that would
photo-absorptionwind
flow near theat disk
plane (✓
= ⇡/2 isin sphericalcoorin thethe mixing
layermotivation
is cut off sharply
below
bl B 0 isOur
Herethetoroidalfield
thatgeneratedby linearwind-be dis- the inner-9 M yr-1
poorhow
verticalflux would
through-2
Ṁw
10step⌃many(Umebayashi & Nakano2009).
isunderstanding
sup-and spherical, with an ofdinates)as Itsteadyembedded
split-the inner ⇠ AU.
g & 50 g cmhas
been
strengthenedwiththediscoveryofplan(Section 4.5.2).
Not surprisingly,
strong magnetizationin our disk
pressed if the abundance of refractory elements
is reduced
byfield,monopole
magnetic
Vw
400 km s-1
tributed
acrossthe disk
has presented
somethingof sustained
ingin ofthegasimposedradialfield
oversurface
theverticaldiffusion
time emerges
φ0particle settling
the outer
reservoir, r0
and is neglected
✓ ◆2
ets
of
a
substantial
mass
in
close
orbitsaroundnearbysun-like
solutions within the active layer (where it is is
as
The
upper
atomiclayer
hasatemperaturesmallerw-2R
R(2⇡R).
(13) 1AU) GBR✏B (R/0.1
here.
?
aroadblocktowardbuilding
globaldisk
modBwr = numericalB(Rsgn(⇡/2- ✓). thedeterministic(5) of aof
resultbalancebetweenverticaldiffusionandlinear?)through
the
disk.
The
simulations
weaklymagCosmic
rays
dominate
X-raysasasourceofionization
onlyrstars . In most models of suchprotoplanetary
disks(PPDs)–✏B
0.01-1
Tbl (R)= 5000 K,
winding),of
as geometricallyatscaling
the oftop
inthe rate
wind-disk
passivelat larger radii (19)
(R & 5 AU), and would
in anycase be heavily
Fwell. 2.—asRadialthe masstransferdriven bya
MRIboundary
turbulence,els.
Globalnumerical
simulations
thin
disks
Becausekineticpressuredescribedof the windis much suggest
less than
netized
disks
1)
just
1/2.
In
the
shielded fromthe disk by the
impacting(solar
windtheconsidan =imposedradialmagnetic
fieldwith a profile -2 >ofd ln(Bln R >
variantsofthe‘minimal-mass
Solarnebula’(Hayashi
1981)
0
layer
(where given
it reflects
thestrongmagnetizationthe)/dT-Tauri
Turbulence
Parameters
onverted
to kinetic
theinternalhydrostaticpressure of the disk, theprincipal-2.5. A profile slightly steeper than monopolar near the midplane
could reered here (Cleeves et al. 2013). Finally,
weneglect
thermalEquation(h/r. of0.03)
that
resolve
non-ideal
effects
cannotpresently
which is taken
to be independentofincreases
R. This representsthewind).
In contrast
withthestronglymagnetized
Shakurasult from collimation
towardthe rotation
axis.
Black curves label
different
quantity
the magnetic
flux thatpaper,
threads
it. Weperformed
in
this
we
encounterstrongionization, calculations
which
is only relevant at temperatures&interest
1000 Kislater
densityofthedisk
inward.
Em↵
eMRI,0 0.1– the surface massdependencesofT
driven
by
the
MRI
on
seed
toroidalmagneticpressure,g determine
F . 3.— Vertical temperature profile in an unmagnetized disk at R = 0.1, 1
considerradial fields
to ⇠ 1 G at 0.1 AU fromSunyaev
the proto- type disk solutions derived by Pariev et al. (2003)(Fromang
et al. 2002). We find thatsuchtemperatures
are upcombinedof X-rayand
UV(18).absorption,
the damplocalrtheevolutionofverticalmagnetic
AU. Topeffectpanel: temperature
versus height,
Equation
The upper atomic and⌫/ (B /8⇡P)flux.
. The vertical disk models constructedthein this paperuse↵mix,0
1 bedded planets
star,
corresponding
to a surface
dipolemagnetic⇠alternative
102discussed
G atreached only
inside⇠ 0.1 AU, due to a combinationofmodarepredicted
drift
rapidlythestarmagnetization
(
.
1)
and
use
the
scaling=disk1decreases
hydrogenlayer
is fixed to T = 5000 K,toand thelower temperature
T is set by toward
andBegelman&thePringle(2007),
a significant= by
1. Thesurface density of
innerwith time
between the0
ingofwind-disk
turbulence;
turbulentheating
dominates
in
R⇠
2R(Valenti&
Johns-Krull
2004;
Daou
et
al.
2006). property
radiative equilibrium of dust. Vertical dotted line: transition height z given?
est accretion rate and (partial) dust depletion.
two horizontalof
red lines.
Results plotted here depend
mildly on the radial
Amcrit 10
Here
we
are
guidedbyabasic
protostars:
they
part of the magnetic
pressure support is provided .by a laminarby Equation (16) with a1980;= 5. BottomLin
panel: temperature
as a function of(Goldreich
Tremaine& Papaloizou1986),
on
Details of the
X-ray aionization model
are given in Appendix
profile of the X-ray irradiated active column, ⌃ / R
49).
the &
present
context.
scale
column density
below disk The
surface. upper layer has a large enough(Equation
Throughout
the paper we use ↵e to denote the viscosity coefficient
withmagnetic field. Johansen & Levin (2008) have de⇤O,crit100(14)
toroidal
A and are summarized here. The rate
ofstrongly
photo-absorption
ithearemagnetizedandṀM
dependence on backgroundmagnetic pressure factored
out. are sources of intense winds durtimescaleheightthat isthantemperature
theobserved
disk lifetimes.
Alperof disk
gas is calculatedthe
as a functionof ⌃g at configuration
thatshorterthe thewind-diskboundary,as flowing
definedbynucleon
Equationvelopeda shearing
box model thatis initialized with a strong
disk
surface,effectiveof the radiation
Considersimplest
with
Br0 uniform
with

初期にB とB をone zone
ideal MHD diskに加えたときのΣ が減るδの範囲。

IG

IG

R

MRI

bl

c

2

r

0

bl

cool

3

each radius using a simplified numerical integration of the

act

-1/4

RADIALLY MAGNETIZED PROTOPLANETARY DISK: VERTICAL PROFILEM ATTHEW RUSSO

b.l.はwind disk boundary layer
Radially Magnetized Protoplanetary Disk: Vertical Profile

16

の続き

Russo & Thompson

15

Department of Physics, University of Toronto, 60 St. George St., Toronto, ON M5S 1A7, Canada.

C HRISTOPHER T HOMPSON

Canadian Institute for Theoretical Astrophysics, 60 St. George St., Toronto, ON M5S 3H8, Canada.
Astrophysical Journal 2015, in press

ABSTRACTThis paper studies the response of a thin accretion disk to an external radial magnetic field. Our focus ison protoplanetary disks (PPDs), which are exposed during their later evolution to an intense, magnetized windfrom the central star. A radial magnetic field is mixed into a thin surface layer, is wound up by the disk
Magnetized Protoplanetary
Vertical Profile
17
shear, and is pushedRadially
downward
by Disk:a combinationof turbulent
mixing and ambipolar and Ohmic drift. The
toroidal fieldreachesmuchthan forthe
verticalthat is usually invoked in PPD models,
and the temperaturefrom Equation(19).greater strengths
ary. The equations@ B seedand @arethen integratedfield
upward from the lower boundary, where= 0.
5.2. Hybrid Numerical Method
We start analysis
with the a small valueof the imposedmagneticeven becoming superthermal.
Linear stability
indicatesthatthe disk experiences the magnetorotational
field, typically ✏ = 10 in Equation (74). The entire process
obtain vertical profiles of the gas variables, ionizationis repeatedseveraltimes at each radius until
well converged
instabilityrate,We(MRI)
atmagnetic
a highermagnetization
thana verticallymagnetizeddisk when both the effects of ambipolarand horizontal
field in three
separate stages,
solutions to both the hydrostatic and induction equations arewhich are iterated until convergence.
obtained. Finally✏ is gradually raised
to unity, resulting
in a
The first step
involves
solving theequationsof hydrostaticand Hall equilibrium
drift
are
taken
into
account.
Steadyverticalprofilesofdensityand magnetic field are obtained atsequence of disk profiles for a range of imposed radial mag(Equation 29) and of continuity. To obtain the
neticfields.
boundariesz/z
self-consistently,
weemploytherelaxation
several radii
between 0.06 and 1 AU in response to a wind magnetic field Br ⇠ (10-4 –10-2 )(r/AU)-2 G. Carefulmethod described in London & Flannery (1982), which treats
dependent variable
at theradial
cost of introducing
newattention zODEs.
isas agiven
to theandtwovertical
ionization6. structure resulting from irradiation by stellar X-rays. The
The expanded system is written as a finite difference
6.1. Magnetic Field and Density Structure
equation and solved on a fixed grid by iteratively improving
disk is morestrongly
the verticalstar,profiles
whereituniformly
can spaced
support a higher rate of mass transfer. As a
We obtained
at six radii,on an initial
trial solution. magnetized closer tosolving for hydrostatic equilibrium, the dependence
in logarithmic radius between R = 10
AU and 1 AU, usresult, theof When
inner
⇠
1
AU
of
a
PPD
is
found
to
evolvetowardlower
density. Mass transfer rates around(B , B ) on ⌃ is held fixed. We first guess the midplane
ing the numerical method described in Section 5. Results surfacearemass-1density ⇢ (0), and then integrate both upward and downshown in Figures 9-11. The magnetic field profiles are qual-8
10 M ward
yr until are
obtainedunderassumptions
aboutis thethe pressure
boundary condition(11) is conservative
reached.
itatively similar
at all radii, but the magnetizationmuch MRI-generated stress. The evolution of
We then improve the consistency of the temperature profile
higher in the inner disk.
The fields remain fairly
constant
throughout the wind-disk
the disk, byandthe implications
forz planet
migration,areinvestigatedin the accompanying paper.
re-calculating
the base of the boundary layerin eachboundary layer, where the diffusion time is comparable to thehemisphere by matching the density to the transition valueof (B , B ) moves toward z = 0, but only in the case of premagnetized, especially in the innermost disk, which is conorbital period. The shear-driven diffusivity ⌫drops dra(16)betweenatomicandmolecular
gas.
Given
the
densitycise symmetry
does itsatellites:
remain in the midplane layer
where thesistent—
with theestimate in Equation (59). (It is worth reSubject headings:
accretion, accretion disks— magnetic fields — planets
andformation
protomatically at the base of the boundary layer, resulting in strong
structure, we then obtain the ionization rate at each column
Ohmic timescale is shorter than the orbital period. The heightemphasizing that this strong magnetization in the upper disk
downward pumping of the toroidal magnetic field. The equiintegrated torque is less dependent on this detail, and more
results from the interaction with the magnetized T-Tauri wind,density, as described in Appendix A, using a simple Riemannplanetary disks — turbulence
rapidly approaches symmetry between the two hemisphere as
not from the buoyant expulsion of MRI-amplified magneticØMRI tur-abstractによると・・・
librium B also increases to higher densities, where
sum. These last two steps involve strong nonlinear changes
F IG . 10.— Left panel: vertical magnetization profile in the more strongly magnetized disk hemisphere (with ✏B = 1) at radii R = 0.1, 10-0.5 and 1 AU. Column
density increases toward the midplane. Dashed lines: imposed boundary magnetic field reduced by factor 0.1. Left vertical dotted lines: base of the active layer(⇤O = 102 ). Right vertical dotted lines: base zbl of wind-disk boundary layer. Right panel: same as top panel, but in the more weakly magnetized hemisphere(z < 0).

F IG . 9.— Vertical profiles of background toroidal and radial magnetic field at R = 0.1, 1 AU. Solid, dashed, and dotted lines: boundary field strength ✏B =1, 0.1, 0.01 in Equations (74)-(77), respectively. Dashed vertical lines mark base zbl of wind-disk boundary layer.
z

z

R

R

-2

B

B

w

+
w

RESULTS

-1.25

R

g

g

±
F IG . 12.— Vertical profiles of density and column density (below disk surface),
bl showing the effect of magnetic inflation at R = 0.1 AU (left panel) and 1
AU (right panel). Density is normalized to the midplane value ⇢0 ⇡ 3 ⇥ 10-9 g cm-3 at 0.1 AU and ⇢0 ' 2.3 ⇥ 10-10 g cm-3 at 1 AU. Solid and dashed lines
correspond to the imposed magnetic field ✏B = 1 and 0.1. Dotted line: unmagnetized hydrostatic structure.

in the disk structure if first performed for a finite value of theimposed radial magnetic field, but convergence is obtained bystarting with a purely hydrostatic disk, and then slowly increasing BR (z±w ) from a small value.
Having obtained a self-consistent hydrostatic profile, the total column through the disk generally differs from the fixedcolumn ⌃g,tot (Equation (9)), and so we repeat this series ofsteps with different values of ⇢g (0) until ⌃g = ⌃g,tot .
The next step is to recalculate the profiles of BR and B
using a shooting method based on a fifth order Runge-Kutta
algorithm. Starting at the top of the disk, where the radial andtoroidal fields are given by Equations (74)-(77), we integrate@z Br downward across the entire disk. This step is repeated
while adjusting @z Br |- (the constant C- in Equation (72)) until
the desired radial field BR (z-w ) is achieved at the lower bound-

1. INTRODUCTION

F IG . 11.— Left panel: toroidal (blue) and radial (green) magnetization vs. height at R = 0.1 AU in the more strongly magnetized hemisphere. Solid, dashedand dotted lines: boundary field strength ✏B = 1, 0.1, 0.01 in Equations (74)-(77). Right panel: same as top panel but at R = 1 AU.

mixbulence dominates, which is in agreement with the analytic
arguments of Section 4.6.
The disk is fully turbulent from the wind-disk interface tothe base of the active layer, which we define as the surface⇤O = 102 . The range of the active layer is marked by verticaldotted lines in Figures 10 and 11.
Because the imposed magnetic field has a bipolar symmetry, the background field (BR , B ) must switch sign at somedepth in the disk. The examples shown here start with a relatively strong asymmetry in the applied field, with BwR (z-w ) =-0.5BwR (z+w ). We see that the stronger magnetic field in the upper hemisphere diffuses through the weakly conducting midplane layer into the lower hemisphere. BR and B switch signnear the base of the active layer in the lower hemisphere.
As the imposed field is made more symmetric, the zeroR

|BwR (z-w )| approaches |BwR (z+w )|.
The magnetization (shown as a function of ⌃g in Figure 10, and of coordinate height in Figure 11) directly influences the MRI diffusivity, as well as the strength of the density gradient. The wind-disk boundary layer is very strongly

fields that is seen in vertically stratified shearing box calculations; e.g. Miller & Stone 2000; Flaig et al. 2010.)
The magnetization shows a local maximum at a column. 10-2 g cm-2 . This results in some inflation of the disk,
although it is limited to a 20 - 30% increase in scale height

BRが円盤のシアで曲がり、乱流とambipolar &the sign of this change.
dri~で内側へ流れ、troidal
TheOhmic
MRI-driven
torque acting on a given patch of ﬁeldがseed
the disk
dependsonthemagnetic
flux
threadingit(Hawley
et
al.
1995;
ver)cal ﬁeldより強くなり、superthermalまで強くな
Sano et al. 2004; Pessah et al. 2007).This flux is usually asる。星に近いほど強く支えるので、<1
AUではΣがsumed
to be oriented vertically with respect to the disk plane.
Our poor
understanding of how vertical flux would be dis減る。

standing the formation and migration of planets inellar disks presents several challenges, the first of
to develop a deterministic model of the flow of gas
within the disk.The motivation for tackling this firstbeen strengthened with the discovery of many plantributed across the disk surface has presented something of
ubstantial mass in close orbits around nearby sun-likea roadblock toward building deterministic global disk modmost models of such protoplanetary disks (PPDs) –els. Global numerical simulations of geometrically thin disks
given our imposition of marginal Parker stability. Moving inmarginal Parker stability is not imposed on the density profile.
of the ‘minimal-mass Solar nebula’ (Hayashi 1981)
F IG . 13.— Vertical profiles of various transport coefficients in the disk model obtained in Section 6, shown at R = 0.1, 1 AU. Ohmic diffusivity ⌘0 (cyan), MRI
turbulent diffusivity ⌫MRI (green), ambipolar diffusivity ⌘a (red), and turbulent diffusivity ⌫mix in the wind-disk boundary layer (blue) are shown. Magenta dottedline shows viscosity that would drive the same steady radial mass transfer as the laminar Maxwell stress, corresponding to TR = BR B /4⇡ = 32 ⌫⇢⌦. Applied
radial magnetic field has full strength (✏B = 1) in the upper hemisphere (z > 0); -0.5 this value in lower hemisphere.

Herschel HIFI observations of the Sgr A +50 km s−1 Cloud ⋆Deep searches for O2 in emission and foreground absorption
Aa. Sandqvist1 , B. Larsson1 , Å. Hjalmarson2 , P. Encrenaz3 , M. Gerin4 , P. F. Goldsmith5 , D. C. Lis3,6 , R. Liseau2 ,L. Pagani3 , E. Roueﬀ7 , and S. Viti8
Stockholm Observatory, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden–7
Ø SWASとOdin衛生によって、Oe-mail: aage@astro.su.se 2分子は予想より100倍少ないとわかった(<1.2x10 @Sgr A)。
Department of Earth and Space Sciences, Chalmers –1
University of Technology, Onsala Space Observatory, SE-429 92 Onsala,Ø Herschel Oxygen
CloudのO2 487と774 GHzを観測(dv~0.5 kms–1)。
SwedenProjectでSgr A +50kms
LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universits, UPMC Univ. Paris 06, F-75014, Paris,
FranceØ 結果、O2輝線はnondetec)on。487 GHzがTmb,3σ<1.06 mK、774 GHzが<2.0 mK。
LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universits, UPMC Univ. Paris 06, cole normale su4 cm–3, ΔV=17.1 kms–1àX(O )<5x10–8, OdinやPDFモデルより小さい。
F-75005,
Paris,
FranceØ RADEXでT=80prieure,
K,
n
=10
H2
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove2 Drive, Pasadena CA 91109, USA

arXiv:1510.06620v1 [astro-ph.GA] 22 Oct 2015

1

2
3

4

schel observations of the Sgr A +50 km s−1 Clouded in CO,ance withmodelling992; Aalto
ng results
bservations
Lundgrenof the Sgr A +50 km s−1 Cloud
predicted
e.g. NGCng absorbside of theding at the5

Aa. Sandqvist et al.: Herschel observations of the Sgr A +50 km s−1 Cloud

6

California Institute of Technology, Cahill Center for Astronomy and Astrophysics 301-17, Pasadena,
CAdensities
91125,
Table 3. Column
and USAabundances for O2 . (T k = 30 K, nH = 1000 cm−3 )LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universits, UPMC Univ. Paris 06, F-92190, Meudon,
FeatureOriginN(O2 )
N(H2 )
X(O2 )
X(OH) aX(H2 O) a
France( km s−1 ](cm−2 )
(cm−2 )
(×10−6 ) (×10−6 )(×10−9 )8−1
16
23
Department of Physics and Astronomy, University College London, London WC1E 6BT, UK+45.2+50 km s Cloud ≤ 1.4 × 10
2.4 × 10
≤ 0.05840
7

Ø 未確認の吸収線があり、O2と仮定
するとSgr Aの連続波を受けた手
前のspiral arms内の50”-70”サイズの吸収、またはOFF beam
(spiral armのみ)にexcessがあった
せいかもしれない。

Received <date>; accepted <date>−7.1

Scutum Arm

7.9 × 1017
≤ 4.9 × 1016
2.7 × 1016
9.0 × 1017
≤ 7.8 × 1016
3.1 × 1016

5.5 × 1021

140 b
≤9 c
4.9 d
280 b
≤ 20 c10 d−32.6−30 km s−1 Arm
3.2 × 1021
O2 tentaABSTRACT−1.6 km s ,4) we finda
ing a preKarlsson et al. (2013)
Context. The Herschel Oxygen Project (HOP) is an Open Time Key Program, awarded 140b fromhours
of observing time to search forat least 20
Herschel“ON-absorption”
cthe Milky
Odin
limit
molecular oxygen (O2 ) in a number of interstellar sources. To date O2 has definitely been detected
in only two sources, namely ρ Ophdsity wave,
Herschel “diﬀerential OFF-ON emission”
e6, foundA and Orion, reflecting the extremely low abundance of O2 in the interstellar medium.
may be a blend of the Local, Sagittarius, and Scutum Arms
moderately−1
Aims. One of the sources in the HOP program is the +50 km s Cloud in the Sgr A Complex in the centre of the Milky Way. Its
ave shock
Of course,
environment is unique in the Galaxy and this property is investigated to see if it is conducive to the presence of O2 .
are made
5. Conclusions+
Methods. The Herschel Heterodyne Instrument for the Far Infrared (HIFI) is used to search for the 487 and 774 GHz emission lines
he geomeFig. 8. Upper profile: Herschel H35
2 Cl absorption profile, raised
We have searched for O2 in the Sgr A +50 km s−1 molecular
by 0.01 K for clarity. Middle profile: Herschel Unidentified, orction canof
Oab2A. +50 km s−1
absorption
profile.
6 cmtheH2SgrCO
10. 487line
GHz
O2 Lower
spectraprofile:towards
cloud in the Galactic centre, using the HIFI system aboard thestage HDCO?,
and Fig.
sorptionCloud.
profile (6arcmin resolution,1970);
thispro- V) polarisaHorizontal(middle Sandqvist
H) and Vertical(lowerHerschel
Space Observatory.
We obtain a 3σ
upperlimit for the
Results.
No O emission is detected towards the Sgr A +50 km s−1 Cloud, but a number of strong
emissionlines of methanol
(CH
3 OH)
file has tions.
been scaleda factor(upperof 0.02.H+V) of these two profiles is also 2
The byaverage
O2 abundance relative to H2 of X(O2 ) ≤ 5 × 10−8 in that cloud.
and absorption lines of chloronium (H2 Cl+ ) are observed.
shown.
From an analysis of the CH3 OH-A and CH3 OH-E emission linestion−1

ln[C_l x W]

6

3 e
30

Conclusions. A 3σ upper limit for the fractional abundance ratio of [O2 ]/[H2 ] in the Sgr A +50 km s Cloud is found to be X(O )≤ 5 × 10−8 . However, since we can find no other realistic molecular candidate than O itself, we very tentatively suggest that twoØ メタノールCH3OH-Aと-Eも受かっていて、popula)on diagram
からそれぞれTrot=64, 79 Kと+50 kms–1 Cloudの力学温度80
Kに近かった。RADEXよりX(CH3OH)~5x10–7で、銀河系中心–7-10–9より少し多く、このCloudとSgr
Key words. Galaxy: centre –の10
ISM: individual
objects:
Sgr A – ISM: molecules – ISM: clouds
A East shellのinterac)onによるものと思われる。

visual extinction). We estimate an uncertainty in the H2 valuesof 40%, of which
30% is duein the300CO-H2
0
100 to the uncertainty
200
400
[K]
conversion factor in the Milky Way disk E_u(Bolatto
et al. 2013).
The corresponding main beam brightness temperature of the
487 GHz O2 emission from the uniform, extended spiral arm
GoldsmithFig. 11.in the
Population
diagramfor CHby(squares) and3 OH-Acloud assumed
current analysis,
as predicted
RADEX,-E lines(circles).
Eu islimit
the reachedenergy inofour
theearlier
upper level, Cl a
is in
0.2 K.CH
However,
5σ intensity
3 OH-E the, possibly
Odin observations
at the487 line
GHz,andusing
a dis-beam line inconstant of
Wposition-switchingis the integratedtomain
shownin emission-freetant,tensity. region is as low as 0.02 K in the 2.′ 4 antenna
beam (Sandqvist et al. 2008). This leads us to conclude that ouration temprevious
assumption of an exactly uniform cloud covering the
H3 OH-E,−1
Herschel ON and OFF beams must be incorrect. It is unlikely
Cloud.
that the O2 absorption comes from the cold neutral medium, but

1. Introduction

The core of the Milky Way Galaxy is a region of great complex-

35Adler, D. S., Lo, K. Y., Wright, M. C. H., et al. 19
Bolatto, A. D., Wolfire, M., & Leroy, A. K. 2013,
Chen, J.-H., Goldsmith, P. F., Viti, S., et al. 2014,
Corbel, S. & Eikenberry, S. S. 2004, A&A, 419, 1
Ekers, R. D., van Gorkom, J. H., Schwarz, U. J.
122, 143
Ferrière, K., 2012, A&A, 540, A50
Gerin, M., Ruaud, M., Goicoechea, J. R., et al. 20
we obtain a rotation temperature range of approximately
2 64 to 79 Goldsmith, P. F. & Langer, W. F. 1999, ApJ, 517,
Goldsmith, P.F., Liseau, R., Bell, T.A., et al. 2011
K and a CH3 OH abundance of 5 × 10−7 .
G. C. & Cox, D. P. 2004a, ApJ, 615, 744
If two Herschel weak apparent absorption lines in the 487 Gomez,
Gomez, G. C. & Cox, D. P. 2004b, ApJ, 615, 758
GHz
2 spectrum are due to O2 , we estimate the O2 abundance with Hollenbach, D., Kaufman, M.J., Bergin, E.A. &respect to H2 in two inner Galactic spiral arms (the−6
Scutum Arm
1497
2 the −30 km s−1 Arm) to be
Karlsson, R., Sandqvist, Aa., Hjalmarson, Å., et aand−4Larsson,B., Liseau, R., Pagani, L., et al. 2007, A(i) 1.4 − 2.8 × 10 , assuming absorption by foreground
Lindblad, P. A. B., Lindblad, P. O., & Athanassou
clouds,
Lindqvist,
M., Sandqvist, Aa., Winnberg, A., Jo(ii) ≤ (1 − 2) × 10−5 , assuming weak excess emission in theL.-Å. 1995, A&ASS, 113, 257
2 average and using Odin non-detection lim- Lique, F., Kalugina, Y., Chefdeville, S., et al. 201
Herschel OFF-beamLis, D. C. & Carlstrom, J. E. 1994, ApJ, 511, 235
its,
R., Goldsmith, P.F., Larsson, B. et al. 201(iii) ≈ (5 − 10) × 10−6 , assumingthat the apparent absorp- Liseau,−1Lundgren, A. A., Wiklind, T., Olofsson, H., & R
tion lines are due to a diﬀerential emission between the Herschel505−7
OFF and ON beams and using Herschel intensities.
Lundgren, A. A., Olofsson, H., Wiklind, T., & R
865
A simple model study suggests that shocks caused by a
Galactic spiral density wave may produce O2 in a 30 K and 1000 Martos, M. A. & Cox, D. P. 1998, ApJ, 509, 703
McGary, R.S., Coil, A.L. & Ho, P.T.P. 2001, ApJ−3
cm medium located in the giant Scutum spiral Arm.
Melnick, G. J., Stauﬀer, J. R., Ashby, M. L., N. e
Melnick, G. J., Tolls, V., Goldsmith, P., et al. 201
Acknowledgements. We wish to thank Per Olof Lindblad for useful discussions
Mezger, P. G., Duschl, W. J., & Zylka, R. 1996, A
and comments concerning Galactic density waves and resulting shock interacMorris, M. & Serabyn, E. 1996, ARA&A, 34, 64
tion with Galactic spiral arms. We are very grateful to our anonymous refereeMüller, H. S. P., Schlöder, F., Stutzki, J., & Winnew
whose thorough report significantly improved this paper. 4We also wish 5
to thank
742, 215
the Swedish National Space Board (SNSB) for its continued financial support.⊙ Mueller, M., Jellema, W., Olberg, M., Moreno, R.
Furthermore we express our appreciation to the individuals making, updating
Release Note for Astronomers, HIFI-ICC-RP
and maintaining the Splatalogue, CDMS and JPL molecular spectroscopy data
Neufeld, D.A., Roueﬀ, E., Snell, R.L., et al. 2012
bases for their unselfish demanding work. HIFI has been designed and built
Nordh, H. L., von Schéele, F., Frisk, U., et al. 200

2
conclude that the hydrogen density in these regions is closer toce of these1000 cm−3 rather
than an order of magnitude lower. weak absorption lines at 487.261 and 487.302 GHz may be caused by the 487 GHz line of O in two foreground spiral arm clouds.
xists with
27
energy ofIf we now again apply RADEX to the above absorption O2
Byof 1000
considering that the absorption may only be apparent, the estimated upper limit to the O abundance of ≤ (10 − 20) × 10 inoptical depths using a temperature of 30 K and density
nergy con26
cm−3 we get column densites of 7.9 × 1017 cm−2 and 9.0 × 1017
t detected
these
foreground clouds is very high, as opposed to the upper limit in the Sgr A +50 km s−1 Cloud itself, but similar to what has been
−2
cm
for
the
two
features.
The
H
columndensities
of
these
2
fication of
two features towards
the +50 km s−1 Cloud are 5.5 ×
1021 and25
reachedin recent chemical shock models for Orion. This abundance limit was determined also using Odin non-detection limits, andon is only
3.2 × 1021 cm−2 (Sandqvist et al. 2003). Thus we arrive at O2
ons, whereabundances with respect to H2 of X(O2 ) = 1.4 ×assumes
10−4 andthat O2 fills the beam. If the absorption is due to a diﬀerential Herschel OFF-ON emission, the O fractional abundance may
24.201 GHz−4−1
2.8 × 10 in the −7.1 and −32.6 km s features, respectively,
onger than
beformofofthe order of ≈ (5 − 10) × 10−6 . With the assumption of pure absorption by foreground clouds, the unreasonably high abundance
implying that practically all available oxygen is in theons areOnot
2 . However,23we note that the estimated strikingly high abunof (1.4
− 2.8) × 10−4 was obtained. The rotation temperatures for CH3 OH-A and CH3 OH-E lines in the +50 km s Cloud are foundﬃcientsof of O2 partly is a result of the low H2 column densities
danceof
ntification
the spiral arm clouds (corresponding to only 3-6 magnitudes
to beof≈ 64 and 79 K, respectively, and the fractional abundance of CH OH is approximately 5 × 10 .
22

2 e

X(NH3 ) a(×10−9 )Nuclear Disk (CND). The CND has a mass of 10 to 10 M
and a gas temperature of several hundred degrees. Beyond this,
there exists a large molecular belt, consisting predominantly of