The effect of photoionising feedback onstar formation in colliding clouds

Kazuhiro Shima (Hokkaido)
Elizabeth J. Tasker (ISAS/JAXA)
Christoph Federrath (ANU)
Asao Habe (Hokkaido)

INTRODUCTION

Star formation is importantsupernova

UV radiation
massive star

giant molecular cloud(GMC)

return gas
into ISM

Massive stars have important roles.
-> How do massive stars form?

Cloud-Cloud Collision (CCC) scenario(Habe+Ohta 1992, Klein+Woods 1998, Anathpindika 2010,Inoue+Fukui 2013, Takahira+ 2014, Balfour+ 2015, Wu+ 2015,1016)

GMCcollisionmassive starmassive coreGas is compressed at the collision interface.
Massive cores will form.

The Astrophysical Journal, 792:63 (15pp), 2014 September 1

Takahira, Tasker, & Habe

Previous simulations
Figure 3. Density slice of the two clouds after one complete free-fall timeof Cloud 1, 5.31 Myr, for static (non-colliding) simulations. The left panel
shows the clouds where no initial turbulence has been applied while the rightpanel shows the outcome of adding an initial turbulent spectrum to both clouds.
Without turbulence, the clouds collapse with Cloud 1 forming a dense point at
x = −7 pc. When turbulence is included, the two clouds remain supported.
(A color version of this figure is available in the online journal.)

The Astrophysical Journal, 792:63 (15pp), 2014 September 1
Figure 2. Surface density of the initial conditions. Both spheres have aBonnor–Ebert density profile and constant temperature. When turbulence isincluded, the velocity field is perturbed as described in Section 3.
(A color version of this figure is available in the online journal.)(Heyer & Brunt 2004; Brunt & Mac Low 2004; Brunt et al.
2009). However, in our case, we want the focus of the results
to be on the impact of the cloud collision, so our choice ofturbulent modes is dominated by those that would stabilize thecloud, preventing collapse prior to collisional contact from gascooling. For our smaller cloud, Cloud 1, we selected 6 < k < 12
while the larger cloud, Cloud 2, was given 10 < k < 25. The
amplitude of the turbulence was dictated by the Mach number,M ≡ σ/cs , where σ is the velocity dispersion inside the cloudand cs is the sound speed. Prior to the cloud being given a bulkvelocity, M = 1. The effect of the turbulence on the clouds’
stability is discussed further in Section 3.2.
When turbulence is applied, the clouds remain in their staticpositions for 0.5 Myr. This allows the clouds to reach a new
equilibrium stage with turbulent support, as measured by theirvolume density distribution which evolves to the expected
log-normal profile for super-sonic isothermal turbulent gas(Vazquez-Semadeni 1994; Scalo et al. 1998; Ostriker et al.
1999; note that the cloud can be considered isothermal prior
to collision since this time for static evolution is approximately
50 times as long as the cloud’s cooling time, causing the clouds
to reach 10 K within 0.1 Myr). After this time, Cloud 1 is given
a bulk velocity in the direction of Cloud 2. Where no turbulence
is included, the motion begins immediately.

Table 1
Initial Cloud Parameters

TBE (K)tff (Myr)rc (pc)Mc (M⊙ )σv (km s−1 )n̄ (cm−3 )k modeCloud 1Cloud 2

120
5.31
3.5
417
1.25
47.4
6–12240
7.29
7.2
1635
1.7125.310–25(Takahira+ Takahira,2014) Tasker, & H

Note. From top to bottom: temperature, free-fall time,
radius, mass, velocity dispersion, average density,and initial k mode used when turbulence is included.

However, molecular clouds have also been observed to show
a Bonner–Ebert density profile in the work of Alves et al.
(2001). Other clouds, meanwhile, have a higher mass than their
Bonner–Ebert mass, but despite this are not in free-fall collapse
due to additional support from internal turbulent motions. This
allows cs in the above equation to be switched for the effective
sound speed which also includes a contribution from the velocity
dispersion.
Compared to observed GMCs, the cloud mass we haveselected is small. Typical clouds within the Milky Way havemasses ∼104 –105 M⊙ (Heyer et al. 2009), a factor of 10 above
our chosen sizes. The results from collisions between larger
clouds will be explored in subsequent papers, but selecting asmaller cloud at this stage allows a simpler study of the shock
front evolution at high resolutions.

3.2. Static Evolution of Clouds
Before considering the cloud–cloud collision, the durationof the clouds’ stability is tested while in situ over the free-falltime of Cloud 1 (see Table 1). This time is longer than thecollision duration (as measured by the shock crossing time) for
the two faster collision speeds we consider in Section 4.2 andapproximately 70% of the collision duration for our slowest
collision speed.
This run was performed to differentiate between structural
evolution from the collision process and independent changes
within the cloud. Figure 3 images the density for the case whenturbulence is not included (left) and when it is added to the initialconditions as described in Section 3.1. Without turbulence, theclouds collapse as they cool within the expected free-fall time.
After 5.3 Myr, one free-fall time for Cloud 1 has passed and its
radius has contracted to the dense point shown at x = −7 pc in
Figure 3. When turbulence is included, the cloud is supported
against cooling over the same duration.
In the left-hand panel of Figure 3, four dense lines are seen
like compass points on Cloud 2 as it collapses. These have theFigure 13. Surface density evolution for the high-resolution 5CCHR simulation. Images, times, and properties match those of the middle panel in Figure 6.
evolution mirrors the 5CC run, with the characteristic arc of shocked gas fragmenting to form cores.
3.1. Turbulence(A colorIn simulations
versionwhereof thethisfigure is available in the online journal.)
gas is given an initial turbulence,
we impose a velocity field with a power spectrum of vk2 ∝ k −4 ,corresponding to the expected spectrum given by Larson forGMCs (Mac Low et al. 1998; Larson 1981). To ensure theturbulence modes were adequately resolved, we selected amaximum k mode value of one-tenth of the number of cells
across the cloud. In addition, we removed the lower-ordermodes since these larger-scale perturbations disrupted the cloud
structure, causing it to fragment prior to collision. In previous
work designed to model turbulence in GMCs, driving on larger
scales was found to produce a closer match to observations

MJ,ef f /(c2s +23/2)
turbp⇢

4Jeans mass increase byturbulence in the shock.

Motivation

collision
massive star formation-> What happens to the cloud next?
Massive stars emit larger quantities of UV photons.
The energy will change the physical state of the cloud.
-> (Next) star formation is affected.

Star formation and feedback

giant molecular cloud (GMC)
Star formation is controlled
by the GMC’s state- self-gravity- turbulence- (magnetic fields)
and feedback
from other massive stars.
Stars- massive stars emit large energy

Photoionisation feedback

Ionization front
3QH 1/3
Rs = ()
24⇡nH ↵B
1trec =nH ↵ B
ph = kph (EphHII region (ionised gas)
~ 10000 [K]>>molecular clouds gas~ 10 [K]HII regions expand by high pressure.

Eph )Photoionisation feedback(test simulation)
density slice plot
Questions:enhance star formation?
orsurpress star formation?
expanding hot shell
MJ,ef f /massive star(c2s +23/2)
turbp

⇢

NUMERICAL MODEL & METHODSGMC model

GMC
dense core

~ 0.1 pc
(1015 m)~100 pc(1018 m)The dynamic range is very large.

simulation code

AMR:

ADAPTIVE-MESH REFINEMENT
createand code
destroy grid
Enzo; a •3D
AMR
patches dynamically (block(Adaptivestructured)
Mesh Refinement)(Bryan et al.•2014)

grids at multiple resolutions• multiple refinement criteria:

Hydrodynamics is calculated• density (gas or dark matter)on the meshes.
• gradients, shocks• cooling time

Meshes areadded adaptively• Jeans length
over regions
thatrequire• refineregions
around particles
higher resolutions.
• easy to create new criteria(Enzo Workshop)

Star formation model

GMC
dense core~ 0.1 pc(1015 m)~100 pc(1018 m)stars~ 109 m

It is hard to resolve Individual stars.
-> sink particle model.

Sink particle modelsink formation conditions(Federrath et al. 2010)+ the finest level of refinement+ over density ⇢gas > ⇢crit+ converging flowr = 0.07 pc
1
r=2
J = 5Jx⇡c2s⇢crit =G 2J+ gravitational potential minimum
center  (i, j, k)+ Jeans instability check|Egrav | > 2 Eth+ bound state check
Egrav + Eth + Ekin < 0Feedback model

GMC
dense coresinksfeedback
UV radiationfrom massive stars

Radiation is treated with ray-tracing method.

Adaptive ray tracing

Adaptive Ray Tracing(Wise(Enzo+Moray)& Abel 2011)

Abel & Wandelt (2002)
Wise & Abel (2011)• Ray directions and splitting basedon HEALPix (Gorski et al. 2005)

The radiative transfer equation• Coupledwith rays.
(magneto-)
is solved
alonghydrodynamics of Enzo

• Rays are split into 4 child rays
Ionisation
ofhydrogenandthewhen the solid angle is large
UV heatingrate
is cell
calculated.
comparedto theface area
• Well-suited for AMR

Rays• Canare calculate
split intorays
the childphoto-ionization
when rates
the sosolidis largethat angle
the method
is photonconserving.
comparedto the cell face area.
• MPI/OpenMP hybrid parallelized.

Saturday, 19 October 13(Enzo Workshop)

Initial conditions

Surface density
Isolated cloud

5.5 ⇥ 104 Msun

Colliding clouds
with 10, 20 km/s

1.1 ⇥ 104 Msun
4.4 ⇥ 104 Msun

Box size:
90 pc
Maximum refinement level: 5Resolution:
0.03 pc

RESULTS

Isolated cloud (NoFeedback)Surface Density

SFE v.s. Time

Turbulence decays and the cloud begins to collapse.
The SFE reaches ~ 2% at 6 Myr.

Colliding cloud at 10 km/s (NoFeedback)Surface Density

SFE v.s. Time

The colliding clouds begin star formation earlier.
The SFE reaches 12 % at 6 Myr.

Colliding cloud at 20 km/s (NoFeedback)Surface Density

SFE v.s. TimeThe faster collision produces stars more rapidly.
The SFE reaches 17 % at 6 Myr.

Probability Distribution Function (PDF) of density

turbulence-> log-normal PDF

collapse -> tailGas is compressed by collision.

Collision effect on star formation

cumulative mass function
isolated10 km s−1
20 km s−1

MJ,ef f /(c2s +100dN/d log10 M

103N(< M)

101

10223/2)
turb

p⇢fragment into smallspecies
10−210−1

101
10−3
100

10−210−1100
M (M⊙)

101

more small & massive sinks(c2s +10−4MJ,ef
10f−3/ 10−223/2)
turb

p−1
10100
⇢ M (M⊙)

more massive sinks

1Feedback effect on star formation (colliding cloud)Surface Density

SFE v.s. TimeThe effect is positive in the colliding clouds.
The SFE reaches 23 % at 6 Myr.

Feedback effect on star formation (colliding cloud)Surface Density

SFE v.s. TimeThe effect is positive in the colliding clouds.
The SFE reaches 24 % at 6 Myr.

DISCUSSION

40

Why feedback is positive ?

20HPBW
348.3
348.2
Galactic Longitude [degree]he12

CO and1pc
348.1△ 13CO J=1–00180

900-90-180

Angle [theta]

13Density slice

CO emission taken with NANTEN2. The

HII Density slice

azimuthal distributions of the CO integrated intensities

by a fit with ellipse to the 8 µm image, and the outer ringg, resulting a major axis of 1.6 pc and 2.4 pc, respectively,

enter of the ellipses is (l, b) = (348.◦ 257, 0.◦ 483), and thehe position of the O star. (c) Azimuthal distributions ofensity at the inside of the ring, where the origin of thehere the distance from the O star to the ring is smallest.

compressedlayer2high-mass star3

HII region

HII regions formed in the interface.
8μm emission

Why feedback is positive ?

mass function

less small sinks & more massive sinks-> fragmentation is suppressedCONCLUSIONSWe made numerical simulations to study star formation in colliding
cloud considering feedback.

The colliding clouds promote star formation efficiency by a factor of
10 higher than the isolated cloud.

The photoionising feedback increases the SFE in the colliding
clouds.
-> feedback is positive in colliding clouds!