1	

磁化した星間媒質における分子雲形成・進化・破壊と分子雲衝突に誘起された星形成
Star Formation Induced by Cloud-Cloud Collisions and Galactic
Giant Molecular Cloud Evolution in the Magnetized ISM( Kobayashi+ 2017 in ApJ, 2018 in revision in PASJ, 2018 in progress.)

Masato I.N. KOBAYASHI
BISTRO workshop 2017, Dec. 20th 2017 at Kagoshima U

SKA-JP Collaborators; Shu-ichiro Inutsuka, Hiroshi Kobayashi,
Square Kilometre Array
Japanese Consortium

Team BISTRO-J

Yasuo Fukui, Kenji Hasegawa,
Tsuyoshi Inoue (Nagoya U)

2	Outline
ü Backgroundw Multiple Episodes of Compression in magnetized ISM

ü Time Evolution of GMCs on Galactic Scalesw Network of expanding shells
w Formulation of GMC MF evolution with Cloud-Cloud Collisions(CCC)ü CCC-driven (Massive) Star Formationw Rapid dispersal of GMCs

ü Towards Galactic-Scale Studiesw Shock propagation in the multiphase ISMü Summary

3	

Backgroundsü Observed GMC MF
ü Multiphase Simulationsü Multiple Episodes of Compressions

4	

IRAM: GMC Distribution in M51
Sub-division in the galactic disk (Colombo+ 2014a)
1) Face-on view of identified GMCs1507 GMCs

2) Cumulative mass function of GMCs
2DEC (J2000)

1IRAM 30mRA (J2000)
IRAM PdBIlog n(>M) [/kpc2]

0-1
21InterArm

ArmInterArm

0-1
2
1

Power-law slope variation:
shallower (<-2) in arm regions,steeper (>-2) in inter-arm regions

Arm0-1
56

7

56

7

5

6

Larger GMCs tend to reside along spirals. log GMC mass [Msun](Consistent trend from Koda+ 2009)7

ISM Simulations

Similar results (e.g., Heitsch+ 2009,
Körtgen & Banerjee 2015, Valdivia+ 2016)

Magnetic fields retard cloud formation
Inoue & Inutsuka, 2012

Inoue & Inutsuka, 2008
Without B-fieldection
riddleif
B

With B-field (2µG)

I flow
Supersonic H2 pc

Supersonic HI flow

02 pc

12log # [/cc]3log # [/cc]

4.0
3.2
2.1
1.0
0.2

Cloud formation take place
after supersonic compression with multiple times.

5	

6	

ISM Simulations
Typical time scale for GMC formation
Multiple episodes of compression is essential
to form molecular clouds from magnetized WNM,
which occupy most of the volume in galactic disks.

GMC

HI cloudA few 10 Myrs	e.g., Inoue and Inutsuka, 2012
Inutsuka+ 2015

Goal: determine how this multiple compression governs: the observed variation in GMC mass functions. 	

7	Time Evolution of GMCs
on Galactic Scalesü Network of expanding shellsü Formulation of GMC MF evolution

GMC Formation & Evolution
Network of expanding shells
on galactic scales(Inutsuka+ 2015 A&A)

HII region / SNR

8	Cloud-Cloud Collisions(CCCs)
Fukui+ 2014
Nakamura+ 2012
Torii+2015

Formulation

9	(c.f., Levinson & Roberts 1981, Kwan 1979,
Scoville & Hersch 1979, Cowie 1980, Tomisaka 1984): differential number density of GMCs with mass m

GMC self-dispersal
due to radiation by massive stars(Td ~ 14 Myr; c.f. radiation hydrodynamics
simulation: Inutsuka 2015)

GMC formation/growththrough compressions(Tf ~ 10 Myr;c.f. Inoue &Inutsuka 2012)

Gas Resurrection
Cloud-Cloud
Collisions (CCCs)(coagulation)(Replenishment of minimummass population)
DispersedCompressions

GMC

Kernel Function (Collision Rate)

10	Kernel = cross section x relative velocity

Column Density:(Onishi+ 1999, Tachihara+ 2000)

Cross Section:~ 7.52 pc2 for collisions
between 104 Msun GMCs

Relative Velocity:(Stark & Lee, 2005, 2006)

11	

Fate of Dispersed Gas
Dispersed gas may resurrect to replenish theminimum-mass population.
CO-dark
H2

Total gas dispersal rate
due to stellar feedback

Minimum-massin the system

CO-dark
H2
Optically
thick HI
Furthercompressions

GMC

Resurrecting factor (0.01-1)
The rate to generate new generation
minimum-mass GMCs out of the total dispersed gas.
N.B.: In a steady state,
can be understood as a rateto accrete onto pre-existing GMCs out of the total dispersed gas.

Self-growth Timescale Tf
Maximum GMC created in the bubble paradigm:
10/cc

SNR

If swept up up to 100pc
and pile them up into
one gigantic cloud…

= 10 Myr

12	

13	Resultsü Slope of GMC MF
ü Gas Resurrection

14	

Steady State with different Tf

f ,fidd-2-2

Observed shallow slope	-3-3Time [Myr]-4-4-5-5-6-6
44

20
40
60
80
120
160
200

55

66log(GMC Mass [M ])log GMC mass [Msun]

77

Kobayashi+ 2017a11T= 22.4 [Myr]Tf: 22.4Myr
T = 14.0 [Myr]f ,fiddlog(ncl [/kpc /M ])T= 4.2 [Myr]Tf: 4.2Myr
T = 14.0 [Myr]log dn/dM [ / kpc3 3 / Msun]

Kobayashi+ 2017a-1-1log(ncl [/kpc /M ])3 / Msun]log dn/dM [ / kpc
3CCC affects only the massive-end evolution…

-1-1

Observed steep slope	Time [Myr]

-3-3

20
40
60
80
120
160
200

-5-5
4

45566log(GMC Mass [M ])7log GMC mass [Msun]

Arm regions: short Tf due to many massive stars/supernovae.
Large surveys may put unique constraints on GMC formation/dispersal timescales on galactic scales by measuring slopes.

15	

Optimal Steady State Resurrection
Coagulation equation for mass evolution

Net mass flux(in case of)Outgoing flux
Incoming flux

Define the resurrecting factor
mResurrecting factor depends on α

16	

Optimal Steady State Resurrection

Log (Resurrectinglog("res ) factor)

Relation between resurrection and GMCMF slope
Kobayashi+ 2017a00

Inter-arm regions
CCC mode-1-1
Decay mode

-2-2

Arm regions"res,stdminmax

1.2 1.4
1.4 1.6
2.2 2.4
2.0 2.2
2.6
1.2
2.4 2.61.8 2.0
1.6 1.8
GMCMF↵Slope

Resurrecting factor: Arm ~ 1%, inter-arm ~30%

Resurrection in arm regions

17	cllog dn/dM[/kpc3 3 / Msun]
log(n [/kpc /M ])Little resurrection (~1%)
Kobayashi+ 2017a-1-1

Tf ,fid = 4.2 [Myr]Td = 14.0 [Myr]"res = 0.0123-2-2

Observed shallow slope	

-3-3Time [Myr]

2040
60
80
120
160
200-4-4-5-5
445665loglog(GMCGMC mass
Mass[Msun][M ])Only 1% is required in arm regions (because abundantmassive GMCs capture dispersed gas).

Resurrection in inter-arm regions

18	Kobayashi+ 2017a11Tf ,fid = 22.4 [Myr]Td = 14.0 [Myr]"res = 0.45

-1-1Time [Myr]20406080120160200-3-3cllog dn/dM[/kpc
3 3 / Msun]log(n [/kpc /M ])Substantial resurrection (~45%)-5-544

Observed steep slope	

6655loglog(GMCGMC mass
Mass[Msun][M ])About 45% is required in inter-arm regions (lack ofmassive GMCs let dispersed gas easily resurrect).

Resurrection in inter-arm regions

19	N.B.

log dn/dM[/kpc
3 3 / Msun]
log(n [/kpc /M ])Substantial resurrection (~45%)
Kobayashi+ 2017a

11Tf ,fid = 22.4 [Myr]Td = 14.0 [Myr]"res = 0.45

-1-1

cl

Time [Myr] factor properly reproduces observations.)(We suggest what resurrecting
Observed steep slope	
20-3-340
Resurrecting processesof optically thick HI and

60
80
120
160
200

CO-dark H2 should be confirmed/understood in the-5-5
context of physics
by massive simulations.	
446655loglog(GMCGMC massMass[Msun][M ])About 45% is required in inter-arm regions (lack ofmassive GMCs let dispersed gas easily resurrect).

20	

Exponential self-growth
GMC mass grows exponentially by compression
12log T [Myr]1086Growth Suppressed

Exponential Growth42023456789log GMC mass [Msun]

Massive GMCs are long-lived;
Typical “Age” and typical “Lifetime” is different!

21	CCC-driven
Star Formationü Rapid Massive Star Formation
ü Star Formation Rateü Collision Frequency

Star Formation at CCC sites22	O(B) stars and YSOs are often observed.
Ex.) RCW38 (Fukui+ 2016)

O(B) star candidates form at the intersection.

CO velocity	

1) Complementary distribution on the sky and2) bridging feature in CO position-velocity diagram
indicate a recent CCC event ~0.1 Myr ago.

Star Formation at CCC sites

23	O(B) star formation possibly triggered by CCC.
Ex.) NGC3603
12CO contour + JHK image
Fukui+ 2014

Probability of stellar ages
(with assumed isochrones).
Kudryavtseva+ 2012

10 pc	

Multiple O stars might form ~0.5pc scale within 1Myr!
Similar trends observed in different sites (Westerlund2, W51, M17, NGC6334, NGC6357, M16,W33, M42, RCW166, S116, S117, S118, M43, RCW36, M20, RCW120, NGC2024, RCW34, … etc.)

24	

Two GMC Populations
Short Td for GMCs undergoing CCC
1) Normal Population

2) CCC Population
Dispersed Gas

Dispersed Gas

Normal GMCs

CCC / Normal GMCs

Normal GMCs

Normal GMCs

CCC GMCs

CCC GMCs

CCC / Normal GMCs

Growth through HI accretion

CCC

CCC GMCs

CCC GMCs

CCC GMCs

Dispersal due to massive starsü GMCs join the CCC population once they experience CCC.
ü CCC population has a short Td ~ 5Myr
representing observed rapid massive-star formation.

Two GMC Populations

25	

Time evolution equation and star formation rate (SFR)
nacc: normal
population
ncol: CCC
population
Td = 14 Myr
Td,col = 5Myr

εSFE = 1%
CCC-driven star formation

26	

Two GMC Populations
GMCMF and CCC-driven star formation rate
Tf ,fid = 10.0 [Myr]Td = 14.0 [Myr]εres = 0.15

Typical power-law ~ -1.7	-1-1-2-2-3-3Time [Myr]-4-420406080-5-54455

Mass[Msun][M⊙ ])
loglog(GMCGMC mass

66SFR(>m) m)[ Msun/ kpc33/Myr]/ Myr]
SFR(>[M /kpc

3 / Msun]
3log
dn/dM
[ / kpclog(ncl [/kpc /M⊙ ])

00

x10 5
⇥105

Kobayashi+ 2018 in revision

5544

Kobayashi+ 2018 in revision= 10.0 [Myr]Solid: total TTf ,fid= 14.0
[Myr]d"res = 0.15 alone
Dotted: CCC-driven
Time [Myr]33020406080221100

4455log(GMC
Mass[Msun]
[M ])
log
GMC mass6610kpc x 10kpc x 100pc disk (like Milky Way), this SFR = a few Msun per year.

CCC-driven star formation may amount to a few 10 percent of thetotal star formation in the Milky Way and nearby galaxies,
which is mostly driven by GMCs > 105 Msun.

Which GMC mass is important?

27	

e-folding timescales for GMCs of mass m(with pure coagulation assumed)
Growth terms from the evolution equation

Number change by collision with populationof mass m2 with a bin width of e x m2.
1) “Number” e-folding timescale due to collision with GMCs with mass m2 alone.

2) “Mass” e-folding timescale due to collision with GMCs with mass m2 alone.

Note: Number e-folding timescale can be intuitively/easily understood,
but it does not necessarily mean how fast GMCs can movein the GMC mass-coordinate! (Indeed, that is what mass e-folding timescale tells you.)

Which GMC mass is important?

28	

e-folding timescales for GMCs of mass m(with pure coagulation assumed)log (Number e-folding timescale [Myr])log
GMC masslog(GMCMass [Msun][M⊙ ])Kobayashi+ 2018 in revision
66.0(now -α = -1.7)

3.2
2.8

5.5
5.5

2.4
2.0

5
5.0

1.6

i.e., Smaller cloud population
outnumbers larger one.

1.2

4.5
4.5

0.8
4
4.0
4.0
4

4.5
5.0
5.5
6.0
65
4.5
log(GMCMass [M⊙ ])log
GMC mass[Msun]

i.e., Larger clouds have larger surface area.

Clouds are often bombarded by smaller clouds(smaller cloud population outnumbers, and larger clouds have larger surface area.)

29	

Which GMC mass is important?
e-folding timescales for GMCs of mass m
Kobayashi+ 2018 in revision

Kobayashi+ 2018 in revision

66.0

3.2
2.8

5.5
5.5

2.4
2.05
5.0

1.6
1.2

4.5
4.5

0.8
4
4.0
4.0
4

4.5
5.0
5.5
6.0
65
4.5
log(GMC
Mass [M⊙ ])log
GMC mass[Msun]

log
GMC masslog(GMC
Mass[Msun][M⊙ ])log (Mass e-folding timescale [Myr])log
GMC masslog(GMC
Mass [Msun][M⊙ ])log (Number e-folding timescale [Myr])

6.0
6

3.30
3.15

5.5
5.5

3.00
2.85

5.0
5

2.70
2.55

4.54.5

2.40
4.0
4
4.0
4

Less than one order(with pure coagulation assumed)

4.5
5.0
5.5
6.0
65.5
5
4.5
log(GMCMass [M⊙ ])log
GMC mass[Msun]

GMCMF growth due to CCC is still dominated by small-large GMC collision,but equal-mass CCC also contributes to GMC mass-growth!

Which mass pair can we observe?

30	

Observability: Duration over which CCC
can be identified as CCC: Survey volume	Let us optimistically assume= 1Myr, and survey the entire MW disk.

log
GMC masslog(GMCMass[Msun][M⊙ ])

Kobayashi+ 2018 in revision
6.0
6 log (# of possibly

observable events)

2.4
1.6
0.8

5.5
5.5

0.0
−0.8

5.0
5

−1.6

4.5
4.5
4
4.0
4.0
4

−2.4
−3.2

4.5
5.0
5.5
6.0
6
5.5
5
4.5
log(GMCMass [M⊙ ])log
GMC mass[Msun]

Mof the CCC pairs that current observations can probe must consistof GMCs ~104 Msun; it is desired to push observations further topairs of >105 Msun, which are important for galactic star formation!

31	SummaryüBackgrounds: Multiple Episodes of Compressionw Variation of GMC MF on galactic scalesw Magnetic fields retard molecular cloud formation

üFormulation: Coagulation Equation with CCCw GMC MF slope is characterized by Tf/Td

whereas its massive end is governed by CCCw CCC-driven SF may amount to a few 10 per centof total SF in the Milky Way galaxy.

üFuture Prospects:

0Tf ,fid = 10.0 [Myr]Td = 14.0 [Myr]log(ncl [/kpc3/M ])log(ncl [/kpc3/M ])w The column density ofstar formation rate (SFR)w Transition from arm regions
to inter-arm regions

With CCC

Without CCC
0-2
Time [Myr]-420406080120
160200-6-8456log(GMC Mass [M ])7

Tf ,fid = 10.0 [Myr]Td = 14.0 [Myr]-2Time [Myr]-420406080
120
160200-6-8456log(GMC Mass [M ])7