星形成ゼミ 2014/ 7/ 3 Newsletter #257の4–8本目!
1. ”Temperaments of young stars: rapid mass-accretion rate changes in T Tauri and Herbig
Ae stars” Grainne Costigan et al.!
!
!
http://mnras.oxfordjournals.org/content/440/4/3444.full.pdf+html!
!
!
http://ads.nao.ac.jp/abs/2014MNRAS.440.3444C!
目的；YSOsのHα輝線を観測して、accretion processについて調べたい。この論文ではHα輝線の等価幅やプロファイルの変化のタイムスケールの短い側に着目している（カバーしているのは数分から年）。変動のタイムスケールを求めることでaccretion processに対して制限を与えたい。!
サンプル；Table 1, 15個のT Tauri star and Herbig Ae stars ( K7-B2 )!
結果；

accretion rateの変化；!

!

!

一時間以内；0.01-0.07 dex!

!

!

数日；!

0.04-0.4 dex!

!

!

年；! !

0.13-0.52 dex!

数日での変動がサンプルにわたってみられ、これは中心星の回転周期に依存した質量降着流が変動の起源として考えられる(asymmetric accretion flow, rotational modulation of theaccretion-related emission)。今回のサンプルで、T tauri starsだけでなくHerbig Ae starsも含み、これらでも同様の変動が見られた。従って、この質量範囲で同じaccretion processがあると考えられる。!
サンプルの中には早い強度変動(<2.4hとか)がありdiskでの不安定性による降着起因。!
3446

G. Costigan et al.

Table 1. Target list. Magnitudes are given in the V band. Variations in V band are given where found in the literature. The T
Tauri type is taken from Herbig & Bell (1988), where an SU Aur type is given as ‘A star like SU Aur: type late F to K, weakemission at Hα and Ca II, very broad absorption lines (v sin i >50 km s−1 ), and relatively high luminosity’. Exposures are given
as number of exposures times the exposure time in seconds. References: (1) Mora et al. (2001), (2) Høg et al. (2000), (3) Cohen& Kuhi (1979), (4) Rydgren, Strom & Strom (1976), (5) Jaschek, Jaschek & Andrillat (1988), (6) Herbig & Bell (1988), (7) Basri& Bertout (1989), (8) Grankin et al. (2008), (9) Cody et al. (2013), (10) de Winter et al. (2001), (11) Rydgren & Vrba (1983),(12) Davies et al. (1990).
Name

Magnitude"Magnitude

SpT

Reference

RY Tau10.1

9.55–11.56

K1

3, 8

AB Aur

7.1

± 0.7

A0

3, 9

T Tau

10.3

9.75–10.18

K1

3, 8

CTTS

SU Aur

9.0

8.92–10.02

G2

3, 8

SU AURDR Tau11.43

10.76–12.78

K52, 1, 8CTTS

RW Aur A

10.36

9.32–11.75

K12, 7, 8CTTS

GW Ori
V773 TauUX Tau A
BP Tau

11.1
10.35
11.3
12.1

9.74–10.53
10.82–11.03
10.64–12.77
11.67–12.99

G5
K2
K2
K7

3, 8
4, 11
3, 8
3

CTTS
CTTS
WTTS
CTTS

BF Ori
LkHα 215
MWC 480

12.2
10.8
7.6

9.82–11.67
10.36–10.47
–

A0
B1
A3

3, 10
3, 12
5

HAe
HAe
HAe

CO Ori

9.83

9.81–12.73

F8

6, 8

SU AUR

ページ 1/8

Type

Date

Exposures

Total
(h)

CTTS

2001-12-26
2003-12-10
2003-12-12
2003-12-13
2001-12-27
2003-12-10
2003-12-11
2003-12-12
2003-12-13
2001-12-12
2003-12-12
2001-12-27
2003-12-10
2003-12-11
2003-12-13
2001-12-27
2003-12-12
2001-12-26
2003-12-10
2003-12-13
2003-12-11
2003-12-13
2003-12-13
2003-12-12
2003-12-13
2001-12-27
2001-12-12
2001-12-26
2001-12-27
2001-12-27
2001-12-24

4×120, 12×180
8×120, 20×240
8×90, 12×180
8×120, 12×180
20×30, 16×30, 16×30
12×90
20×60
20×60
4×120, 12×90
8×45, 16×120
4×60, 18×150
12×1808×90,16×150
4×90, 5×240
12×120
16×1804×60, 20×180
11×180
12×1504×60, 20×150
4×60, 20×240
4×60, 16×240
1×120, 24×240
4×90
4×30, 24×300
16×180
16×12016×75, 16×30
16×45, 8×45, 16×60
8×120, 8×180
8×12, 8×180

4.0

1.83

1.37
2.30

1.87
1.40

1.40
1.13
1.63
2.13
0.80
0.53
1.03

1.09

Downloaded from http://mnras.oxfordjournals.org/ at National Astronomical Observatory

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3448

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G. Costigan et al.

2. “A First-Look Atmospheric Modeling Study of the Young Directly-Imaged Planet-Mass
Companion, ROXs 42Bb” Thayne Currie et al.!
http://iopscience.iop.org/0004-637X/787/2/104/pdf/apj_787_2_104.pdf!
http://ads.nao.ac.jp/abs/2014ApJ...787..104C!

3. “Molecular Gas Clumps from the Destruction of Icy Bodies in the β Pictoris Debris Disk”
W.R.F. Dent et al.!
http://www.sciencemag.org/content/343/6178/1490.full.pdf!
http://ads.nao.ac.jp/abs/2014Sci...343.1490D!

!
!

REPORTSimplies that C+ is being removed on a time scaleof 3 × 103 to 104 years; because this is several
orbital time scales at 85 AU, the braking gas canbe spread throughout the disk.
If the gas is on circular Keplerian orbits, eachpoint in the PV diagram corresponds to one oftwo points in the disk. Figure 3 shows possible
deprojections of the data to form the face-on gas
distribution (8). A compact clump of CO is foundat a radius of 85 AU, which contains ~30% of theflux, along with an extended “tail” of emission.
The radial distribution of the millimeter-sized

dust can also be derived (8, 12) and shows excess
around this radius in the southwest (Fig. 3C). The
millimeter-sized dust shows an abrupt drop in density around a radius of 130 AU, coincident with achange in slope in the radial distribution of scattered light. This was interpreted as a transition
from a dust-producing planetesimal belt to a region dominated by submicrometer-sized grains
blown out by radiation pressure (9, 24).
What is the origin of the CO clumps and corresponding mid-infrared and continuum features?
There are two possible interpretations, both re-quiring planet-mass objects in the outer disk, butwith different predictions for the deprojected gas
distribution. In the first (Fig. 3A), outward migration of a planet traps planetesimals into both the
2:1 and 3:2 mean motion resonances, resulting
in a distribution with two clumps of asymmetricbrightness on opposite sides of the star that orbit
with the planet (25). Planetesimal collisions would
occur most frequently in the clumps that would
then be the most vigorous production sites of both
CO and the short-lived micrometer-sized grains
seen in mid-infrared images (12). The morphology

beta pic の debris diskのCO ガス(と連続波)の分布/mass から、まさに微惑星衝突が活発に起きている現場であると考えられる。!
Fig. 1. Images of b Pic using ALMA in continuum and line emission. Both have been rotated by +29°, the position angle of the main dust
disk. The beam size (0.56 × 0.71 arc sec) is shown at
the lower left, and the locations of the star andplanet on the date of observations are indicated by
the star and the cross, respectively. (A) Continuum
emission at 870 mm from the millimeter-sized dust;
root mean squarenoise level is 61
per beam. mass andof thetheclumps
constrains
themJy planet’s(B) Total 3-2 CO line emission (rest frequency =–20 W m–2.
migration
parameters
Notably,
the planet
345.796 GHz);
the noise level (25).
is 0.02 × 10
The planes of the main and secondary dust disks (9)must arebeshown>10byMtheEarthto have captured material into
dashed lines.

;ALMAの12CO(J=3-2)と870um
dust continumm!

REPORTSits 2:1 resonance, and it would currently be close
to the inner edge of the gas-dust belt, ~90° in
front of the southwest clump. The CO clump’s
tail would point in the opposite direction to therotation, and its length is given by the ratio of CO
photodissociation lifetime to the synodic period.
The alternative interpretation (Fig. 3B) is that
the CO and micrometer-sized dust originate in asingle recent collision (12, 26). Because the clump
also contributes ~10% of the flux in our submillimeter continuum image, the parent body musthave a mass approximately equal to that of Mars,
as giant impacts typically release ~10% of the progenitor’s mass as debris (27). Whereas collisional
debrisFig.
persists
indistribution
a clumpalongfor onlyyears
2. Velocity
the disk~100
major axis.
This afterimageevent,shows theitobserved
velocityof the CO
emissionsuch anis morelikelythat
therelative
collisionto the velocity measured toward the star (which has a centroid
occurred~0.5
ago,
withframe).
theGasasymof +20.3± 0.1 million
km/s, in theyears
barycentricreference
the brighter southwest side is approaching us; the two dashedmetryonarisingbecausetheweorbitsof allfrom
collisional
whitelines represent
the velocity
would measuregas atinner andouter radii of
the CO
belt. The solid
red linesashow
debristhepass
throughthecollision
point,
regionthe true orbital velocity, the maximum observed velocity fromthat woulda point,
highasdensity
andcollision
gas at theretain
tangential
a function of
distancefrom the ratestar, assuming a stellar mass of 1.75 times the mass of the Sun.
(26). Contours
Such area clumpstationary,and10, 20, 30,would40, 60, andbe
80%of the peak (0.06
Jy theper beam).
Theliespectral/spatial
resolution isdirection,
illustrated at the
CO tailwouldin the rotation
with alower left.
length given by the ratio of photodissociation time
to sidereal period (Fig. 3B).
www.sciencemag.org!

Tentative evidence has been published for theclump’s motion (28), which, if confirmed, would
favor the resonance interpretation. Either way,these observations provide a valuable opportunity to ascertain the prevalence of planet-sized objects at large orbital distances in this disk.
The CO gas detected in b Pic is unusual
among debris disks. So far, two others have been
detected in CO [49 Cet and HD21997 (16)] andone in O I [HD172555 (29)]. Most debris disks
are presumed to contain icy grains, so we would
expect all such systems to host CO and its photodissociation products. The high collision rates
found in clumps may substantially enhance thegas abundance. If CO is formed in collisions, its
brightness will scale as the collision rate, which is
proportional to vrnd2, where vr is the collisionvelocity and nd is the number of dust grains. Bothnd and vr are enhanced in clumps due to resonances and giant impacts, increasing collision rates
by factors of up to 10 to 100 (7, 26). The presenceof these clumps can increase the overall collision
rate and CO flux from a disk by one order ofmagnitude. The CO and compact clump in the b
Pic disk indicate that this system is undergoing aperiod of intense activity driven by planets orplanet collisions.

SCIENCEVOL 343!

References and Notes

dust mass(870um); 6.4 Mmoon!
CO mass; 0.0023 Mmoon!

1. F. van Leeuwen, Astron. Astrophys. 474, 653–664 (2007).
2. A. S. Binks, R. D. Jeffries, Mon. Not. R. Astron. Soc. 438,
L11–L15 (2014).
3. B. A. Smith, R. J. Terrile, Science 226, 1421–1424 (1984).
4. A. Vidal-Madjar et al., Astron. Astrophys. 290, 245–258(1994).
5. A.-M. Lagrange et al., Science 329, 57–59 (2010).
6. A. Brandeker, R. Liseau, G. Olofsson, M. Fridlund,
Astron. Astrophys. 413, 681–691 (2004).
7. M. C. Wyatt, Astrophys. J. 639, 1153–1165 (2006).
8. Materials and methods are available as supplementarymaterials on Science Online.
9. D. A. Golimowski et al., Astron. J. 131, 3109–3130(2006).
10. W. R. F. Dent, H. J. Walker, W. S. Holland, J. S. Greaves,
Mon. Not. R. Astron. Soc. 314, 702–712 (2000).
11. G. Chauvin et al., Astron. Astrophys. 542, A41 (2012).
12. C. M. Telesco et al., Nature 433, 133–136 (2005).
13. A. Roberge et al., Astrophys. J. 538, 904–910 (2000).
14. I. Kamp, F. Bertoldi, Astron. Astrophys. 353, 276–286(2000).
15. R. Visser, E. F. van Dishoeck, J. H. Black, Astron. Astrophys.
503, 323–343 (2009).
16. B. Zuckerman, I. Song, Astrophys. J. 758, 77 (2012).
17. K. I. Oberg et al., Astrophys. J. 740, 109 (2011).
18. M. P. Collings, J. W. Dever, H. J. Fraser,
M. R. S. McCoustra, D. A. Williams, Astrophys. J. 583,
1058–1062 (2003).
19. A. Grigorieva, Ph. Thebault, P. Artymowicz, A. Brandeker,
Astron. Astrophys. 475, 755–764 (2007).
20. A. G. G. M. Tielens, C. F. McKee, C. G. Seab, D. J. Hollenbach,Astrophys. J. 431, 321–340 (1994).
21. A. Roberge, P. D. Feldman, A. J. Weinberger, M. Deleuil,J.-C. Bouret, Nature 441, 724–726 (2006).
22. J.-W. Xie, A. Brandeker, Y. Wu, Astrophys. J. 762, 114 (2013).
1491
23. R. Fernandez, A. Brandeker, Y. Wu, Astrophys. J. 643,
509–522 (2006).
24. J. C. Augereau, R. P. Nelson, A. M. Lagrange, J. C. B. Papaloizou,
D. Mouillet, Astron. Astrophys. 370, 447–455 (2001).
25. M. C. Wyatt, Astrophys. J. 598, 1321–1340 (2003).
26. A. P. Jackson, M. C. Wyatt, Mon. Not. R. Astron. Soc. 425,
657–679 (2012).
27. S. T. Stewart, Z. M. Leinhardt, Astrophys. J. 751, 32 (2012).
28. D. Li, C. M. Telesco, C. M. Wright, Astrophys. J. 759, L81(2012).
29. P. Riviere-Marichalar et al., Astron. Astrophys. 546, L8 (2012).

!

UV photon でCOは壊され、そのtime scaleは600yr 程度。!
観測されたCOが定常的に存在するためには、COを供給しないと行けない。!

10^-5 Mmoon/yr!
collisionなどでdustから解放される
還元率0.1と考えると10^-4
Mmoon/yr.でこれは、彗星サイズ
が5分おきに破壊されていることに
なる。!

!
!

28 MARCH 2014edge-on diskなのでCOの観測結果
から円盤での分布には二通りの解釈が可能である。!
二つのピークをもつか一つのピークを持つか。!
いずれも理由付け一応出来る。!

Fig. 3. Deprojected distributions of gas anddust around b Pic (8). (A and B) Two possible
face-on distributions of the CO, assuming circular orbital motion. The dashed circles denotethe inner and outer radii of the gas disk, thecurved arrows indicate the direction of rotation,and the asterisks represent the location of thestar. The distance along the line of sight (l.o.s.)
is relative to the stellar position and is positivefor gas on the far side of the star. (A) The twoclump distribution, interpreted as mean motion
resonances with an inner planet. In this case, thebright southwest clump lies on the far side of
the star and is approaching us. (B) Single-clump
distribution, interpreted as a collision of objects
with mass approximately equal to that of Mars. In
this case, the southwest clump is stationary, andthe tail of CO points in the direction of rotation. (C) Radial distribution of millimeter-sized dust in thesouthwest (blue line) and northeast (red line) sectors of the disk, obtained by fitting consecutive annuli tothe continuum
ページ distribution
4/8 on the two sides (12). The dashed line is an axisymmetric model for the parentbody distribution, predicted from scattered light images of the submicrometer-sized grains (24). Surface
density units are cross-sectional area per unit disk area, in AU2/AU2.

1492

28 MARCH 2014

VOL 343SCIENCE

Acknowledgments: This paper makes use of the following
ALMA data: ADS/JAO.ALMA#2011.0.00087.S. ALMA is apartnership of ESO (representing its member states), NSF(USA), and National Institute of Natural Sciences ( Japan),
together with National Research Council (Canada) andNational Science Council and Academia Sinica Institute of
Astronomy and Astrophysics (Taiwan), in cooperation with theRepublic of Chile. The Joint ALMA Observatory is operated by
ESO, Associated Universities, Inc./National Radio Astronomy
Observatory and National Astronomical Observatory of Japan.
Partial financial support for S. Casassus, M.C.W. and A.H. wasprovided by Millenium Nucleus P10-022-F (Chilean Ministry of
Economy). A.R. acknowledges support by the Goddard Center
for Astrobiology, part of the NASA Astrobiology Institute.
M.C.W. was supported by the European Union throughEuropean Research Council grant number 279973, I.d.G.-M.
acknowledges support from Ministerio de Ciencia e Innovación(Spain) grant number AYA2011-30228-C03 (including
European Funds for Economic and Regional Development),
A.P.J. was supported by a Science and Technology Facilities
Council postgraduate studentship, and J.-C.A. acknowledges
the French National Research Agency (ANR) for support
through contract number ANR-2010 BLAN-0505-01(EXOZODI).

二つのピークは共鳴(resonance,

惑星による)。!

シングルピークはそこで最近衝突イベントが起きた。!
いずれにせよこの系で微惑星衝突が活発に起きていると考えられる。

!
!

Supplementary Materials
www.sciencemag.org/content/343/6178/1490/suppl/DC1
Materials and Methods
References
19 November 2013; accepted 20 February 2014
Published online 6 March 2014;10.1126/science.1248726

www.sciencemag.org

4. “GG Tau: the fifth element” E. Di Folco et al.!
http://www.aanda.org/articles/aa/pdf/2014/05/aa23675-14.pdf!
http://ads.nao.ac.jp/abs/2014Sci...343.1490D!
!

!

E. Di Folco et al.: GG Tau: the fifth ele

VLTI/PIONIERでGG tau Abにさらにもう一個、伴星/惑星を

Around G
at 1.65 µm
cal of prot
GG Tau A
tion of ⇠5dial extent
Ab2 (Rout <⇠vides a sim
mm contin
3. With five c
becomes a
provided tphysical p

見っけた。!

!

GG tauは階層的な４重星(hierarchical quadruple). GG tau自体が二つの低質量連星系で、GG tau Aも連星系(0.26arcsec,
36au, GG tau Ab)。GG tau A周りの周連星系円盤(Circumbinarydisk)はRin=180au.!

Fig. 3. Sketch of the new triple system GG Tau Aa (M0V), Ab1 (M2V),
and Ab2 (M3V) in their 2012 orbital configuration.

E. Di Folco et al.: GG Tau: the fifth element

Ab attested by PdBI (Piétu et al. 2011) and ALMA observations

Acknowledgemen
Stellaire” and thefor financial supp
Center SearchCal

References(Dutrey et al. 2014). The Ab1 and Ab2 components are indeed Akeson, R. L., W
Table 1. Relative astrometric position and flux contrast for the main binary Aa–Ab (photo-center of Ab1–Ab2),
and for the close binary Ab1–Ab2,
surrounded by Roche lobes of radius ⇠2 au. Tidal truncation ef- Artymowicz, P., &M. R., & Bo
A&A
565,
L2
(2014)
as derived from our best-fit of the closure phases measured by VLT/NaCo-SAM and VLTI/PIONIER. fects naturally prevent the existence of stable disk(s) larger than Bate,
Beck, T. L., Bary,


Ab1
PIONIERH (2012-10-30)
best-fit.

∆ Dec [mas]⇢ [mas] Aa–Ab
PA [deg] Aa–Ab
Aa
F(Aa) / ïF(Ab)⇢ [mas] ï
Ab1–Ab2
31.7
PA [deg] Ab1–Ab2
219.6
aF(Ab1) ï
/ F(Ab2)
4.3




ï
.



.

.



E 9/71D&Rï6$0
1.66 µm

this limit, and thus not massive enough to be strong mm emitters, in contrast to Aa. The 10 µm silicate
36.4 emission probably
arises from warm grains located within 2 au (i.e., well inside the(c) VLTI/PIONIER
26.6
disturbance may also
1.66Rocheµm lobes). The resulting gravitationala↵ect the supply of0 material from the outerregions through dust
19.4
and gass streamers, as it breaks the symmetry of the Aa–Ab system. The close binary GG Tau Ab also strengthens
the impact of
14.2
tidal truncation onto the circumbinary ring. However, the loca10.3 more distant thantion of its inner rim (180 au), which is much.
the apparent .separationof the Aa and Ab(1+2)
components, re7.55
mains aAb1
puzzling characteristics of the system.



.


NACO-SAM
NACO-SAM
NACO-SAM
NACO-SAM
Ab2


H (2012-12-06/07) Ks (2012-12-06)
H+K
L (2012-12-07)




best-fit
best-fitmean
best-fit


256.1
1.5
255.8
3.5
256.1
1.3
256.3 3.3




329.6
0.3
329.3
0.8
329.5
0.4
328.9
0.8 5.51
Aa


ï
2.36
0.04
1.99
0.04
1.88 0.234.03


5. Conclusioní 31.7

2.94
emblematic, 31.4
young binary
GG Tau A
0.2N
4.1
31.6 N 5.8
31.6 The 3.3
fixedsystemNï(0.2600 separation) has
observed with inAb2been successfully


2.15
219.9 7.3
227.6E
10.3 222.6
6.0
219.9
fixed
terferometricandAO/
sparse-aperture-masking
techniques
E 0.3
UV planeE+0.6(SAM) at the Very Large
Telescope.
We 1.57
found that: í
2.3a ï  ï
1.6
2.3ï ï0.2
2.8
0.2
0.2 
ï



ï



í
í


.



.

∆ Dec [mas]D 9/71D&Rï6$0
1.66 µm∆ Dec [mas]



.



.

+7

.



.

.

.

.

.

í

.



∆ RA [mas]Notes. The formal errors on NaCo-SAM PA do not include uncertainties due the detector orientation.
text), the related uncertainty dominates.

Aa

Square Visibility

0.8
0.6
0.4
0.2

í

1. The secondary GG Tau Ab is itself a close binary, with a pro∆ RA [mas]jected separation of 0.03200 (or 4.5 au) and PA = 220 (end2012). It is consistent with a M3V (Ab2) and M2V (Ab1)
Fig. 1. Chi2 maps for NACO-SAM H-band closure-phase data (6+7 Dec. 2012): location of GG Tau Ab1 (a))
and Ab2
the primary
low-massbinary.(b))
This aroundfinding solves
the discrepancy between
dynamicalinstellarderived from CO gas kinestar GG Tau Aa, and for PIONIER (c)) H-band closure-phase data for Ab2 location around Ab1, with VLTI (u,v) thesamplingthemass
inset.
matics (Guilloteau et al. 1999) and the most recent spectraltype estimate of Aa and Ab (Hartigan & Kenyon 2003).
Based on a tentative a posteriori identification in archival
VLT/NACO
orbital periodthan
is estimated to
the gravitationally unstablezone
is not empty of dust. Indirect high-contrast companions and (2003)
provedto be images,
moreitsefficient
1.0
Ab
PAb1 Ab2 ⇠ 16 yr, a value consistent with the period derived
evidence for gas flow from the ring towards the inner system(s) classical AO-imaging within ⇠20300mas
and Ks -bands
from thebinarymassatandH
separation.
2. All stars in this triple system present significant IR ex0.8
has been found from 12 CO
J = 2–1 gas image (Guilloteau & (Lacour et al. 2011). We used
a 27 mas/pixel plate scale andcesses, confirming the presence of circumstellar material.
∆ RA [mas]

1.0

+7



!
!

(a)

Bessell, M. S., Br
Brandner, W., Zin
Cieza, L. A., Laco
Cutri, R. M., Skru
of point source
Delorme, P., Gagn
Doyle, L. R., Cart
Dutrey, A., Guillo
Dutrey, A., Di Fo
Guilloteau, S., &H. Zinnecker,
Guilloteau, S., Du
Hartigan, P., & Ke
Huélamo, N., Lac
Köhler, R. 2011,
Köhler, R., Kaspe
Lacour, S., Tuthil
Le Bouquin, J.-B.
Leggett, S. K. 199
Lenzen, R., Hartu
M. Iye, & A. F
Mathis, J. S. 1990
Monnier, J. D., B
Olofsson, J., Beni
Piétu, V., Gueth, F
A81
Pinte, C., Ménard
L63
Roddier, C., Rod463, 326
Silber, J., Gledhil
Skemer, A. J., Clo
Tallon-Bosc, I., T
Tuthill, P. G., Mo
P. Léna, & A.
Udry, S., & Santo
Welsh, W. F., Oro
White, R. J., Ghez

After correction for FOV attenuation (seein H band. To properly account for the resulting flux attenuation,
we oversampled the Fourier plane by a factor of 3. The derived
NaCo-SAM
flux
ratiosare thenmode,
1.6±0.4
and 2.4±0.3
at H and Ks
Dutrey 2001) and from near-IR
H
transitions
(Beck
et
al.
2012).
high-cadence
frame
acquisitionthesciencetarget itself
GG
tau Abには0,032arcsec(4.5au,2
0.6
values
wereOnused
The warm H2 gas may be heated by shocks, as material from the bands,
being respectively.
used for the IRThese
wavefront
sensing.
Dec.to6,estimate
data werethe spec0.4
Page
6 isAb1/Ab2
available inwhile
the H-band
electronicof the journal a
recordedtheat
H 2012end)のばbinaryがある。!
and Ks bandsthe(2.0–2.1µm)
filters,
H edition
circumbinary ring is accreted
onto material close to the stars. tral
PA=220deg
type
ofwithAb2.
Surprisingly,
inferredflux
The existence of inner CS0.2disks is independently attested by mm ratio
and appears
L0 filters were
used
on
Dec.
7.
Atmosphericconditions
were
to be lower than our PIONIER estimate (4.3 ± 2.3).
excess emission on GG Tau Aa (Piétu et al. 2011), strong H↵ これがあることにより、これまでgasstable (✓0 ⇠ 0.5 0.800 , ⌧0 ⇠ 3 6 ms). The same two calibratorThis
discrepancy
is discussed in Appendix A. から求
0.0
accretion signature separately detected around Aa and Ab, [OI] sources as for PIONIER were selected, with a fast-switch pointPA = 220 deg

0.0


20

40

60

80



20

40

60

80

2EVí0RGHO σline detection around Ab (White et al. 1999; Hartigan & Kenyon めたAa,Abの質量と、スペクトルタイプの食ing sequence. The observations were reduced using the Paris
2003), and 10 µm silicate0 feature from hot grains in both Aa SAMP pipeline as described in Lacour et al. (2011).
Discussion
and Ab environments (Skemer et al. 2011). We have recently 4.
い違いの問題が解決するらしい。!
ïï
undertaken
resolution
programof
20
40 observing
60
80
20
40
60a very high-spatial
80
3. Results
Spatial frequency [10 λ]Spatial frequency [10 λ]GG
Tau A, from UV to mm
wavelengths.
In this Letter, we report 4.1. Nature of the detected component


Ab
near-IR VLT interferometric observations of the inner region of 周連星系円盤の非対称性の説明もできるら
Aa
The PIONIER measurement for GG Tau Aa is consistent withzero closure-phaseindicates
a non
the GG Tau A system, where
we detect a new component and Aanon
marginallyresolved, symmetricemission,as axisymmetricattested by the bright2
ness
distribution,
which
may
eitherbeinterpreted
as 2.the pres circumstellar dust emission.

direct evidence for resolved
fringe visibility (V ) and CP functions displayed in Fig.
しい。!
ence
of
a
stellarcompanion,orasabrightness
asymmetry
Aroundthedimmer
GG
Tau
Ab,
we
reportthedetectionofa
CP in the00signalas large asSimilar
30 deg, which
revealswith
an asymmetricbrightnesshave redisk
emission.
detections
SAM
techniquesï
2. Observations andïdata analysis
distribution.
We attributeto a third
companion
centlybeen reported
forthisa feature
few
other
young
sources(Ab2)with known
5重連星系であるGG
tauは連星系を調べるのïï
in the main binary system GG Tau A. Square visibilities also
We observed the GG Tau
A system on 2012 October 30 with protoplanetarydisks(e.g.,
T
Cha,
Huélamoetal.
2011). Forshow oscillation-like structures, but we chose to rely on the CPïに良いターゲットになる。!
the VLTI, using the fourï5840m Unit
Telescopes(UTs)80 on base5 40
thesetransitional
disks,
ithas
been
demonstrated
thatstarlight
50
60
70
90
50
60
70
80
90
line lengths between 32 and 140 m, and the PIONIER instru- values to derive the binary characteristics, because they are lessscattered
o↵
the
inner
edge
of
the
outer
disk
(typicallyat R ⇠a↵ectedbyatmosphericphasefluctuations
and
known
telescope
00ment (Le Bouquin et al. 2011)
operating in the H band (1.5–1
We usedwell
the LITPRO
software(Tallon-Bosc
et al.
au) can equally
reproduce
the detected
closure-phaseas a1.80 µm, three spectral channels). Thanks to the combination of 10vibrations.
ïï2008) to extract
the Ab1–Ab2
binary etflux
andCieza
astrometric(sub)stellar
companion(Olofssonal.ratio2013;
et al. 2013).
the60MACAO
adaptive
opticsand60 the tinyinterferomet40 system
50
70
80
90
40
50
70
80
90
position bythe
independently
fittingin
thethese
PIONIERand NaCo-SAM
MaOPQRa a Q  Q λMax. Spatial frequency [10 λ]ric field of view (FOV) of VLTI /UTs
(FWHM ⇠ 41 mas in However,
CP amplitudes
systems
are much smaller00
data(Table1).
A
simple
model
with
two
unresolvedstars yields
Hband),
we
were
able
to
separately
point
at
the
0.26
binary
than
for
GG
Tau
Ab
(.1
deg,
implyingmuchhigherIR contrasts
Fig. 2. VLTI/PIONIER square visibilities (squares, top panels) and cloa good fit to the CP values ( 2red = 1.5 vs 7.1 for a single star),
GG Tau Aa (M0V) and Ab (M2V) with PIONIER. Seeing condi- mag
⇠
5).
It
also
requires
the
disk
to
have
a
high
inclination(atsure phases (triangles, bottom panels) separately measured for GG Tau
tions were stable, with optical seeing values ✓0 ⇠ 0.6 0.900 , and with a raw flux ratio of 8.1 ± 2.1 (H band). We derive a separaAa (left, blue)andAb1+Ab2(right,
red).
Solid
lines
or
cross
markers
least
60
deg)
for
forward-scatteringbyµm-sizedgrainstobeeftion
of
31.7
±
0.2
mas
and
a
position
angle
PA=
219.6
±
0.3
deg
a coherence time in the range ⌧0 ⇠ 3–5 ms. We performed interrepresent best-fit
models:unresolved
halo ofandknownring forAa ficient(Fig. 1)
Becausethe IRedge.
photo-centerof Ab1–Ab2
is closer
at2 .thegap outer
We judgea disk-origin
to tobe highly
leavedobservationsof twophotosphere,calibrator sources
diameterH
Ab1
andtheir separation
represents
about
30%
of
the
instrumen(model-2 in Table
3),
and
two
unresolved
photospheres
and
a
halo
for
unlikely,
since
wedetect
a
CP
as
large
as
30
deg.
(HD
28462,
K1V,
⇥
=
0.169
±
0.012
mas,
and
HD
285720,UD
ページ
5/8
FOV (i.e., an 8 m telescope Airy disk), we applied a correcAb (model-4).
Below
H each plot we display the fit residuals.
K4V,⇥UD= 0.148 ± 0.011 mas). Four independent series of cal- talWe
calculated the probability P for the CP to be caused bytion for the FOV attenuation. The correction factor (based on
ibrated observations were acquired, with interferometric fringes contaminationfroma backgroundsource.
is evaluateda Gaussian-profile
attenuationof FWHM= 41 Pmas,centered fromsimultaneously recorded on six baselines, and reduced with the thesurfacedensity⇢(m)ofsourcesbrighterthanmuncer= H+ H =
on
the
K
-band
centroid)amounts
to
f
=
0.53.
(The
s
corr
pndrs package (Le Bouquin et al. 2011).
taintyon f=depends
on thecase)
AO andtip-tiltGG
stabilizer
perfor9.1+ 2.5(worstaroundTau A:
P(⇥, m) =corr 11.6
0!

6

Closure Phase [deg]6

2EVí0RGHO σ

!

6



!
!
!
!
!
!

⃝
C 2014. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

CHARACTERIZING THE STRUCTURE OF DIFFUSE EMISSION IN Hi-

D. Elia1 , F. Strafella2 , N. Schneider3 , R. Paladini5 , R. Vavrek6 , Y. Maruccia2 , S. Molina
S. Pezzuto4,5 , K. L. J. Rygl1,7 , A. M. Di Giorgio1 , A. Traficante8 , E. Schisano4 , L. Calzo
9,10,11,12
13
14
15, M. Huang, P. etMartinJ. Liu1 , P. Natoli
5. ”Characterizing the structure of diffuseS.emissionin Hi-GAL maps”
D. Eliaal.! , Y. Fukui , and T. Ha!

1 INAF-IAPS, Via Fosso del Cavaliere 100, I-00133 Roma, Italy; davide.elia@iaps.inaf.i

2 Dipartimento di Matematica e Fisica E. De Giorgi, Università del Salento, CP 193, I-73100 Lec
http://iopscience.iop.org/0004-637X/788/1/3/pdf/apj_788_1_3.pdf!
3 Univ. Bordeaux, LAB, CNRS, UMR 5804, 33270, Floirac, France
http://ads.nao.ac.jp/abs/2014ApJ...788....3E!
4 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218!

(よくわかりませんでした）!

5 Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 911
6 Herschel Science Centre, European Space Astronomy Centre, Villafranca del Castillo, Apartado de Correos 78,

7 Research and Scientific Support Department, European Space Agency (ESA-ESTEC), P.O. Box 299, 2200-AG N

8 Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Manch

9 Agenzia
Herschel 70,160,250,350,500umのデータ；Hi
GalSpaziale
program;の2degx2degの4領域に対しItaliana Science
Data Center, c/o ESRIN, via Galileo Galilei, I-00044 Frasca

10 Dipartimento di Fisica e Science della Terra, Università di Ferrara Via Saragat, 1, I-44100 Ferr

11 INFN, Sezione di Ferrara, via Saragat 1, I-44100 Ferrara, Italyて、Δ-varianceという手法を用いて、ISMの定量的な解析。!

!

12 INAF-IASF Bologna, Via P. Gobetti 101, I-40129 Bologna, Italy
13 National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, Ch

14 Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON

15 Department of Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Jap
ISMでのfractal次元は乱流長や乱流の散逸スケールに関わるらしい。!
Elia et al.

The Astrophysical Journal, 788:3 (14pp), 2014 June 10

Received 2014 January 17; accepted 2014 April 4; published 2014 May 16

4. ∆-VARIANCE ANALYSIS(a) β = 2.0(b) β = 2.4(c) β = 2.8 dimension を多波長で解析するツール。!
Δ-varianceというのはfractal!

The ∆-variance method is a generalization of the Allan
ABSTRACT
variance (Allan 1966), elaborated and characterized in detailbyStutzkietal.
(1998).
Fora
two-dimensional
observablefield
We present a study of the structure of the Galactic interstellar medium (ISM) through the ∆y), the ∆-variance at the scale L is definedas the variancerelatedA(x,powerofspectrum
the !
fractalproperties of infrared/submillimeter maps. T
ofto
the theconvolution
A with a filterandfunction,L:
it is possible to provide quantitative
parameters,
which are useful for characterizing differe"#$ %2 &
1
physical conditions,andthe theoreticalmodels. In this respect, the HerscA ∗constrainingσ∆2 (L)= better
,
(4)
2π
x,y
L

結果として、ISM fractal dimensionとstar formation efficiency にanti-correlationが見られた。!
(d) β = 3.2

!
ーーーー!

(e) β = 3.6(f) β = 4.0

Plane Survey, carried out at five photometric bands from 70 to 500 µm, constitutes a uniquestatistical
wheretools to a variety of regions across the Milky Way. In this paper, we derive a robust e
◦
◦
⎧
#
%
The Astrophysical Journal, 788:3 (14pp), 2014 June 10
Elia etal. located in the thlaw portion of the power
tiles
1spectrum of Lfour contiguous 2 × 2 Hi-GAL
⎪
◦
◦ ⎪
◦
◦
r
!
⎪
⎪
2 ! 0 ). The(217 ! ℓ ! 225 , −2
!
b
low
level
of
confusion
along
the
line
of sight, testified
⎪
π
(L/2)
2
⎪
⎪
#
%
$ an⎨ideal case.
makes this regionWe
L find very
1
3L different values for the power spectrum slope fr<r!
(r) = −
(5)⎪
Figure 2. Synthetically generated fBm 300 × 300 pixels images, generated with
8π (L/2)2 (2 2! β ! 3),
2 with similarities between fields attributable to cfrom wavelength
to wavelength
⎪
L
⎪
#
%
⎪
increasing power spectrum slope, β, and starting from the same random phase⎪
3L⎪
the same distance. Thanks
to comparisonswith models of turbulence, an explanation of the⎪
distribution. Map units are arbitrary.
r>⎩0
2(A color version of this figure is available in the online journal.)
terms of the fractal geometry is also provided,and possible relations with the underlying phy
In particular,
an anti-correlation
fractalis the+ down-up-downcylinder (or between
French hat)ISM
functionand dimension and star formation efficienc
most relevant ones, which will prove to be useful in the analogy
2 . The two non-zero terms of the above definition
we make with ISM maps in the following sections. First, theyr = x 2 + ycomponents
main distanceobserved in these fields. A possible link between the fractal pro
are characterized by having a power-law power spectrum withrepresent the core and the annulus component of the filter,emissionand the resulting clump mass function is discussed.
exponent β = E+2H , where E is the Euclidean dimension of therespectively.
considered space (for cloud maps, E = 2) and H is the so-called
Ossenkopf
et al. (2008)
recommended
a possible
alterna- structure – methods: data analysis – m
Key words:
infrared:
ISM– ISM: asclouds– ISM:
Hurst exponent, ranging from zero to one. Therefore, β can taketive to the French hat function to obtain a more reliable estimate
statisticalstars: index,
formation
values from two to four. Second, the phases of their Fourierof the–spectralβ, is to use the smoother Mexican hat,transforms are random. Based on these two constraints, it isdefined as
Online-onlymaterial:color
figuresquite easy to obtain fBm images once β is assigned and a random$r2r2 , r2 2
4
4phase distribution is generated.17 In Figure 2, six 300×300 pixele (vL/2) − e (L/2)2 , (6)(r) =e (L/2)2 −2
22
Figure5.
Grayscale
map
of
the
Mach
numberfor
distancecomponents
IandII(identified
withpurpleandorangecontours,
respectively) of Paper I, calculated acrossπL
π L (v − 1)
fBm images are shown. They have the same phase distribution
LentireNANTENavailable
data fromcube asthe text. Contours range from 5 to 30 in steps of 5. The gray dotted squares enclose the four areas investigated
and thedifferonly
by β, whichranges
2.0described
to 4.0 inin steps
ranges is generally considered ain thispaper.
where themain terms in the right side of the equation repreof 0.4.
It canbe seen that the phase distribution determines
1.two
INTRODUCTION
sent the core and the annulus components, respectively, and v is
(A colorappearance
version of thisfigureis available
online journal.)
the overallof the“cloud,”but asin βtheincreases
the
The Astrophysical Journal, 788:3 (14pp), 2014 June 10an estimate of the turbulence inthe diameter ratio between them. To speed up calculations, thestructure becomes smoother and smoother due to theOne
transfer
An extensive and detailed review
ofofthe mostintriguingtasks in the observational study
same authors suggest to perform the operation in Equation (4)power from high to low spatial frequencies. We recall that the
β =Fourier
2.0 is domain,
β = 2.4(c)theβ = 2.8
ofpresence of turbulence inmedium (a)(ISM)
to extract(b)information
as a multiplicationinthecase β = 0 would correspond to white noise. of the interstellar
to be concomitantthen surpassedby thatinof shaping
other physicalin Section 5.1) and (2) the significant
differences
between the/$̃the/2 andtheir structure in a
about
the
clouds,starting. . of
In terms of the fractal description, it has been shownthat
the three-dimensional structure/
1 (e.g., //Rosas-Guevarafactors
et al. 2010).
Theand∆-v
structureobservedin the westernand easterntiles.
fractaldimensionof an E-dimensionalfBm imageis givenby:/ objects,σ∆2 (L)=P/
dkx dky , generally(7)
Vázquez-Semadeni(1999)
Sfromthetwo-dimensional
maps
of
these
/
To
this aspect in our data, we derived the three2πinvestigate
In the three tiles showing fractal behavior (ℓ220, ℓ222, andvariance(
L
D = E + 1 − H,(1)
It
is noteworthy
that the ISM
taken
different
and withturbulent
different
techniques
dimensional
Machnumbers
fromthe
NANTENdataℓ224), all the values we derived range
from atD=
2.61 (500wavelengthsµm
Stutzkiw
˜self-similarity
as stochasticby
fractals,andAlthoughacube
certaindegreeof!
so thatdirectcolumn
relation between
β is: towhereis the power
spectrumofA, andfor thevelocity
components
I and II, ascategory
the ratio betweenof theℓ222
densityDofandℓ224)
D resolutions.
= 2.94 (160µmP of
L is the Fourier
A(x,y), thetransform
filtersimilar,but rathersof themaps
overrangevaluesof spatial
can be+ 2 are− β compatible
thefunction.
localof the scales
deconvolved
CO(1–0)perfectly
line widthself⟨σCO⟩ℓ220), and most of 3E
them
withISMthe typicalrangeofathegiven
of
the
conv
D=
.
(2)
The fundamental relation that relates the slopes of ∆-variance
and
the
sound
speed
c
:
set
and
a
part
of
it
do
not
have
visually
perceivedinmanycases,
therearenumerous,
moreof variability found throughstatisticaltechniques(Rowles&2sand of the power spectrum (β) was shown by Stutzki et al.
Schneider
et al.images
2011,
references
therein),AnFroebrich
important 2011;
propertyof the fBm
isand
that
the
they have the same statistical prsolid,
argumentssuggesting that this may be the case, √starting(1998):⟨σCO ⟩
2power
spectrum
of
the
(E
−
1)-dimensional
projectiononanbut also mostly with the 2.6 ! D ! 2.8
foundbySánchez
et al. (1990).
(L) ∝ Lβ−2 .
possible
from
the
work
of
Scalo
(d) β σ=∆3.2(e)
β== 3.63 (8) .
(f) β = 4.0 to useM(9)a fractal descripti
E-dimensionalfBm throughset is again
power law with the
same
cfor
(2007, 2009)
theaperimeter–area
relation.
s
Given theabove, one mainly
can derive thepower spectrum
There are many observational
Inout
this
theexpression
phenomenon
responsible
spectral index (Stutzki et al. 1998). This result turns
to be respect,
Instead, the values we obtained are significantly
largerthanslope byperforming a linear fit over the range of spatial scales forimportant for establishing a link between the observed
two- morphologies
1/2 a largely recObservationsof the lo
self-similar
is turbulence.
This
cs = manifests
(kT
/µ)is
= 0.188(T/10 K)1/2 scenario.
km s−1 , whereT
the logarithmHere,of ∆-variancea linearbehavior. In
the average
found
on real
IRAS
100 µm maps bywhich
Mivilledimensional
columnvalue
densityand thethree-dimensional
where molines
inseveralstar-forming
ognizedfact
inmolecular
clouds,beingatypical,scale-free
this
work,
we
adoptedthis
procedure
followingtheprescriptions
is
taken
from
the
dust
temperaturemaps
obtainedin
Paper
I
Deschênes
etal.
(2007;
β
=
2.9,
which
is
D
=
2.55
in
the
fBm
cloud density field for clouds that can be considered isotropic, as
18of Ossenkopf
et al. simultaneously(2008),(see,i.e., usinga Mexican
filteret
with
Falgarone& Phillips 1996; Schnphenomenon
inducing
fractality
e.g.,with
Sreenivasanal.
the Hatcolumndensitymaps.
The amountsuggestedthrough theoreticalarguments those(Brunt etal. 2010)
and µm,approximation),in particularfound
at 160which
isFurthermore,
v
=
1.5.
we
do not adopt any strategy based
empirical
evidences(Federrathal. 2009;
Gazol
&one.
Kim 2010).
ofCO
spectrasuitablefor
thisanalysisislimitedbyfew the measured lin
1999)
show
that
Turbulenceisindeedcharacterized
by
the
lack
of
a
spethe closest
band
to theetIRAS
100µm1989).
on assigning different weights to the pixels involved in theThus, invoking Equation (2), it is found that
onlydistribution
lineswith a ofreasonable
signal-to-noisecannotbe produced in clouds ofscale,
it canconstraints.
producefractal
In any case, the values we findcificare length
far awayfromthenthe calculation,∆-variancewhich isaFirst,
recommended
by Ossenkopf$
3 dimension of interstellar
ratioofconsideredin Paper I);density.
second, This
the line
et al.
(2008)
in overcasemapscharacterized
bydetails
a variable
first estimates DofE−1thefractalcloudssuggests that thematter in(3)a molecular
cloud
aare
wide
range of(seescales.
There=DE − ,data
reliability.
The
portionsofthe
Hi-GALmaps
wechose,
2
full
width
at
half
maximummust
belargerthanthespectral(D = 2.3; Falgarone et al. 1991; Elmegreen& determination
Falgarone 1996;
fromgenerated
being withhomogeneous, inste
fore, theof far
the2.
starting
endingFigureSyntheticallygenerated
fBm
300of
× these300−1pixels images,
indeed, beingfrom
the tile andboundaries,
arepointscharacterized
resolution
element(∆v
km sby) to theallow
deconvolution;i.e., Elmegreen
the fractal dimensionof an fBm
objectchanges a
under
1997a), which
initially
described
quite constantandincreasing
power
spectrumslope,
β,=and1
startingfromsame
random phase
quite
uniform
coverage(see
also
Traficante
et
al.
2011)
and,
projection
by 1.5,not by 1 astheunits
locationof CO spectra must lie within one of the four
universal
behavior
ofone
thecould
ISMerroneously
structure, expect.
and were foundalso distribution.
to by a third,
Map
are arbitrary.
consequently,
stablerms
noise.

!
!
!
!
!
!
!
!
!
!
!
!

!

fields we investigate in this paper. These are shown in Figure 5
be in good agreement with the predictions of the Kolmogorov(A color version of this figure is available in the online1journal.)

17 The fBm images generated in such a way are periodic, i.e., it is possible to18 The IDL package for calculating the ∆-variance can be found atplace the image and its exact copy side by side and to connect with continuity(left panel), overlaid to the distribution of the Mach number
incompressible
turbulence(β of=real3.6
the density field,then
http://hera.ph1.uni-koeln.de/∼ossk/Myself/deltavariance.html.
the imageto itself. Clearly, thiscannot be the case
ISMformaps.

across theentireNANTEN
data set.
most relevant
ones,
which
will prove
to be useful in the analogy
D = 2.2; Falgarone et al. 1994). Instead, the values found here,
We
note
that
we
can
derivemeaningfulsections.
statistical information
as well as the others obtained through the ∆-variance5 (Schneider
we make with ISM maps in the following
First, they
only for thebybrightest
while theobservations
notet al. 2011, and references therein), are more compatible withare characterized
havingregions,a power-law
power
spectrumarewith
sensitive enough to trace the cirrus component, which is the one
the power spectra slopes of compressible turbulence, (e.g.,
exponent
β = E+2H, where Ebehavior
is the Euclidean
dimensionof theshowing
the self-similarthat justifies
such a test.
For
Federrath et al. 2009), and in particular for the case of solenoidal
considered
space (for
cloud
maps,
E = 2) andH betteris the so-called
thisreason,westressthat
observations
withsensitivity
driving of turbulence (β = 2.89, D = 2.55).
Hurst exponent,
rangingfromto one.
β cantakeand spectral
resolution
arezerorequired
for Therefore,
confirming thisresult.
ページ
6/also8 compare with the theoretical predictions of Gazol
We canvalues
from
two
to
four.
Second,thephasesoftheirFourierWe
recall
that
in
Paper
I
the
distancecomponents
IandII& Kim (2010) on the power spectrum of both three-dimensional
have arebeenrandom.
found to differ
in starby a factor
transforms
Basedon formationthese twoefficiency
constraints,
it isand column density in turbulent thermally bistable flows.20 Theirof two(0.008 fBm
against0.004,once
respectively).
Interestingly,
a directquite easy
to obtain
imagesβ is assigned
and a random
slope (calculated between 7 and 25 pc, i.e., a range of scales
correspondence
between a17
largerfractal2,dimensionand a higher
larger than ours) gets shallower as the Mach number increases:
phase distribution
is generated.
In Figuresix 300×300
pixel

is the+ dow
r = x2 +represent t
respectivel
Ossenkotive to the Fof the spec
defined as$(r) =The Astrophysical Journal, 788:3 (14pp), 2014 June 10

Elia et al.
-1.5

β = 2.58

log(σ∆2(L))

-2.0

(i)

!

!

-3.0
-3.5
-4.0
-4.5
0.5

log(σ∆2(L))

(ii)

1.0

1.5 2.0 2.5
log(L[arcsec])

3.0

3.5

3.0

3.5

2.0 2.5 3.0
log(L[arcsec])

3.5

β = 2.77

-2.5
-3.0
-3.5
-4.0
-4.5
-5.0
0.5

log(σ∆2(L))

(iii)

1.0

1.5

2.0 2.5
log(L[arcsec])

β = 2.88

-3.0
-3.5
-4.0
-4.5
-5.0
-5.5
0.5

1.0

1.5

β = 2.51

-2.5
-3.0

(iv)

log(σ∆2(L))

!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!

-2.5

-3.5
-4.0
-4.5
-5.0
0.5

1.0

1.5 2.0 2.5
log(L[arcsec])

3.0

3.5

Figure 3. Simulation of a Hi-GAL image in four main steps (left panels) and corresponding ∆-variance plots (right panels). Step (1): an 1800 × 1800 pixel fBm image
is generated as a background. Step (2): the brightness of a few limited regions is enhanced. Step (3): the characteristic shape of the Galactic plane is introduced througha Gaussian profile. Step (4): 500 Gaussian compact sources are spread across the map and a low-level white noise is finally added. The ∆-variance curves are plottedin the right panels. The x-axis variable is the decimal logarithm of the spatial lag, L, (expressed in arcseconds) and the range is the same for all panels. The range on
the y-axis is different for each panel but its width has been kept the same in all panels to allow a visual comparison of the slopes. The ∆-variance is represented as a
black solid line, while the linear fit over the inertial range (i.e., the range where the curve has a power-law behavior, here highlighted with a gray area) is plotted as a
blue dashed line. In the top right panel, the ∆-variance of the larger original fBm set is also plotted as a green solid line. In the same panel, the error bars associatedwith the ∆-variance values are shown by way of example.
(A color versionof this figure
is available
the online
The AstrophysicalJournal,788:3(14pp),in2014
Junejournal.)
10

and the white noise (β = 0) borderline case for the power spec2.2 kpc
trum slope. 0.1 L[pc] at
1.0
10.0
For the remaining wavebands and for the column densityomaps, only one
linear range has been identified for eachl = common
220tile. Note
-4 that scales shorter than 100′′ have not been considered

about 40′′ and 25′′ , respectively. At larger spatial scales, in all
L[pc] at 2.2 kpc
cases, the 70 µm curves appear as0.1
slopes smaller
1.0 than those
10.0of the larger wavelengths and are even negative in three casesoout of four. This behavior -4
is expected
l = 217in the presence of low
signal-to-noise ratio in the maps, keeping in mind Equation (8)

-5

7

-6

-6

-7

-7

-8
β = 1.02 1.45 1.65 1.90 2.15

10100
L[arcsec]
L[pc] at 1.1 kpc
0.1
1.0

1000

10.0

-2
-3
-4
-5
-6
-7
10

ページ 7/8-5100
L[arcsec]

1000

-8

β = 2.12 2.21 2.25 2.35 2.35

10100
L[arcsec]

1000

Elia et al.

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