1 Enrique Vázquez-Semadeni Centro de Radioastronomía y Astrofísica, UNAM, México

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Enrique Vázquez-SemadeniCentro de Radioastronomía y Astrofísica, UNAM, México

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Collaborators:

CRyA UNAM:

Javier Ballesteros-Paredes

Gilberto Gómez

ABROAD:

Robi Banerjee (ITA, Heidelberg)Dennis Duffin (McMaster,

Canada)Patrick Hennebelle (ENS, Paris)Jongsoo Kim (KASI, Korea)Ralf Klessen (ITA, Heidelberg)

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I. INTRODUCTION

• The interstellar medium (ISM) is turbulent, magnetized (e.g., Heiles & Troland 2003, 2005), and self-gravitating.

• Turbulence and gravity in the ISM lead to the formation of density enhancements that constitute clouds, and clumps and cores within them (Sasao 1973; Elmegreen 1993;

Ballesteros-Paredes et al. 1999).

• This talk:

– Outline of underlying physical processes.

– Results from cloud-formation simulations including MHD and ambipolar diffusion (AD).

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II. BASIC PHYSICAL PROCESSES

1. Fundamental fact:

A density enhancement requires an accumulation of initially distant material into a more compact region.

i.e., need to movemove the material from the surroundings into the region.

udtd

5

2. ISM thermodynamics.

– A key property of the atomic ISM is that it is thermally bistable.

• The balance between the various heating and cooling processes affecting the atomic ISM…

Heating Cooling

Wolfire et al. 1995

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… causes its atomic component to be thermally bistablethermally bistable.

– A warm, diffuse phase (WNM, T ~ 8000 K, n ~ 0.4 cm-3) can be in a stablestable pressure equilibrium with a cold, dense (CNM, T ~ 80 K, n ~ 40 cm-3) phase (Field et al 1969; Wolfire et al 1995, 2003).

Wolfire et al. 1995

WNM(stable)

CNM(stable)Mean ISM

thermal pressure

Peq, at which heating equals cooling n

Thermally unstable range

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– This is the famous two-phase modeltwo-phase model of the ISM (Field et al 1969).

• Mean ISM density in the unstable range.

• Predicts spontaneous fragmentation of ISM into cloudlets immersed in warm phase.

• Cloud-warm medium interface usually considered a contact discontinuity.

Wolfire et al. 1995

WNM(stable)

CNM(clumps)Mean ISM

thermal pressure

Thermally unstable range

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– The presence of turbulence and magnetic fields complicates the problem.

• Transonic compressions in the linearly stable WNM can nonlinearly trigger a transition to the CNM… (Hennebelle & Pérault 1999).

• … and, aided by gravity, an overshoot to molecular cloud conditions (Vázquez-Semadeni et al 2007; Heitsch & Hartmann 2008).

• This constitutes a fundamental process for molecular cloud formationmolecular cloud formation out of the WNM.

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3. Compressions and the mass-to-flux ratio in ideal MHD.

• The ratio of gravitational to kinetic energy

implies the existence of a critical mass-to-flux ratio (; M2FR) for a cloud to be supported against self-gravity by the magnetic field:

– A cloud with • M/ > (M/)crit is magnetically supercritical: collapses.

• M/ < (M/)crit is magnetically subcritical: cannot collapse.

;5

185

185

18 2222

42

2

GMGRB

GME

E

m

g

2/1

2crit 185

G

2BR

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• Ambipolar Diffusion (or “ion-neutral slip”): in a partially ionized medium, neutrals can slip through the ions.

• Ionized fraction typically lower at higher densities.– This process increases the M2FR (breaks flux-freezing condition).– The innermost parts of a subcritical cloud can then become supercritical

and collapse.

Ion

Neutral

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• Standard SF model (Shu+87; Mouschovias 1991):

– Most clouds are subcritical.

– Slow, low-efficiency star formation through AD.

– Only massive stars form in supercritical clouds.

• However, recent realizations:

– Most clouds are nearly critical or supercritical (Bourke+01; Crutcher+10).

– Most stars form in regions of high-mass star formation (Lada & Lada 03).

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supercritical diffuse

v vBB

subcritical diffuse


subcritical dense


v v

supercritical dense

Assumption: the background medium extends out to a sufficiently long distances to be supercritical.

Example: for B=3 G and n=1 cm-3, a length L > 230 pc is supercritical.

In ideal MHD, if a cloud is formed by a phase-transition induced by a compression along the field lines, the cloud’s observed mass and mass-to-flux ratio increase together (Mestel 1985; Hennebelle & Pérault 2000; Hartmann et al. 2001; Shu et al. 2007; VS et al. 2011).

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4. Combining compressions, MHD and thermodynamics:• Magnetic criticality condition (Nakano & Nakamura 1978):

• This is very similar to the column density threshold for transition from atomic to molecular gas, N ~ 1021 cm-2 ~ 8 Msun pc-2 (Franco & Cox 1986; van Dishoek & Black 1988; van Dishoek &

Blake 1998; Hartmann et al. 2001; Bergin et al. 2004; Blitz 2007).

• When taking into account the magnetic criticality of the dense gas only, expect the clouds to be:– subcritical while they are atomic (consistent with observations of

atomic gas, e.g., Heiles & Troland 2005)

– supercritical when they become molecular (consistent with observations of molecular gas; Bourke et al. 2001; Crutcher, Heiles & Troland 2003).

• A consequence of mass accretion and a phase transition from WNM to CNM and H2, not AD (Vázquez-Semadeni et al. 2011).

2

22

4B

GN 221

crit cmG5

105.1

B

N

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5. When a dense cloud forms out of a compression in the WNM, it “automatically”• acquires mass.

• self-consistently acquires turbulence (through TI, NTSI, KHI – Hunter+86; Vishniac 1994; Walder & Folini 1998, 2000; Koyama & Inutsuka 2002, 2004; Audit & Hennebelle 2005; Heitsch+2005, 2006; Vázquez-Semadeni+2006).

– The compression may be driven by global turbulence, large-scale instabilities, etc.

WNMn, T, P, -v1

WNMn, T, P, v1

15Vázquez-Semadeni et al. (2006 ApJ, 643, 245).

Ms = 1.2, tfin ~ 40 Myr

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Audit & Hennebelle 2005

2D, 10242

Ms ~ 2

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III. MAGNETIC MOLECULAR CLOUD FORMATION• Numerical simulations of molecular cloud formation with

magnetic fields, self-gravity and sink particles (Banerjee et al. 2009, MNRAS, 398, 1082; Vázquez-Semadeni et al. 2011, MNRAS, 414, 2511).

– Use FLASH code (AMR, MHD, self-gravity, sink particles, AD by Duffin & Pudritz 2008).

• 11 refinement levels.

– Same initial conditions as non-magnetic simulations with GADGET.

– Low-amplitude initial fluctuations allow global cloud collapse.

– Add uniform field in the x-direction.Converging flow setup

Lbox

Linflow

Rinf

BSee also Inoue & Inutsuka (2008) for configuration with B perpendicular to compression.

Lbox = 256 pcLinflow = 112 pcxmin = 0.03 pcmax res = 81923

Ms,inf = 1.2, 2.4

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• Dense clump structure (Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398, 1082).

– In a B0 = 1 G supercritical simulation, with no AD:

log

n [c

m-3]

log

T [

K]

log

P [

K c

m-3]

B [G

]

Cuts through densest point in clump.

Sharp boundaries between WNM and CNM…

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log

n [c

m-3]

log

T [

K]

log

P [

K c

m-3]

B [G

]


… but also there are intermediate-n, thermally unstable regions.

More abundant towards periphery of cloud.

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log

n [c

m-3]

log

T [

K]

log

P [

K c

m-3]

B [G

]


Gas flows from Gas flows from diffuse medium into diffuse medium into dense clumps.dense clumps.

There is a net mass flux through clump boundaries.

The boundaries are “phase transition “phase transition fronts”fronts”.

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log

n [c

m-3]

log

T [

K]

log

P [

K c

m-3]

B [G

]


There exist warm, low-pressure, diffuse “holes” in the dense gas.

Clouds are porous.

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log

n [c

m-3]

log

T [

K]

log

P [

K c

m-3]

B [G

]


Magnetic field strength exhibits correlation with high-density gas...

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log

n [c

m-3]

log

T [

K]

log

P [

K c

m-3]

B [G

]


Magnetic field strength exhibits correlation with high-density gas...

… but almost none with low-density gas.

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B-n correlation

n1/2

B-v correlation

B-histogram in dense gas (n > 100 cm-3)

(Banerjee et al. 2009, MNRAS, 398, 1082)

(See also Hennebelle et al. 2008, A&A)

Large B scatter in dense clumps.

B and v tend to be aligned, even though B is weak (~ 1 G).

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Three simulations with = 1.3, 0.9, and 0.7, including

AD.

Face-on view of column density.

Dots are sink particles.

= 1.3B=2G

= 0.9B=3G

= 0.7B=4G

Vázquez-Semadeni et al. 2011, MNRAS, 414, 2511.

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Evolution of the mean and 3 values of M/.

Whole cloud High-N gas

= 0.9

= 0.7

Mass-to-flux ratio is highly fluctuating through the cloud, and evolving.

= 1.3

Vázquez-Semadeni et al. 2011, MNRAS, 414, 2511

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Evolution of gaseous and stellar masses, and of the SFR.

• Cloud mass nearly same in all cases.

• SFR of =0.7 case nearly shuts off.

• SFE of =0.9 and =1.3 cases not too different.

• Upon inclusion of stellar feedback, expect further SFE reduction, so favor higher- cases.


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Low- gas develops buoyancy

Run with B=3 G ( = 0.9).

Like a macroscopic analogue of AD.


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V. CONCLUSIONS

– Forming clouds and cores involves moving material from surroundings into a small region

Implies:• Significant component of inward motions into clouds and cores.• Cloud and core boundaries are phase transition frontsphase transition fronts, not contact

discontinuities.• Masses of clouds and cores evolve (generally increasing) with time.

– Cold cloud assembly by WNM compression with a component along the magnetic field lines implies that

• Thus, the mass, mass-to-flux ratio (M2FR), and SFE of a cloud are time-time-dependent quantities.dependent quantities.

• The M2FR of a cloud that accretes from the WNM generally increases in time.– Not an AD effect, but a result of increasing mass.

the mass-to-flux ratio of the the mass-to-flux ratio of the coldcold gas increases steadily. gas increases steadily.

udtd

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– B and v tend to be aligned, even for weak fields (B dragged by v).

– At high densities (n > 100 cm-3), <B> ~ n1/2, but with large scatter around mean trend.

• Should expect large core-to-core fluctuations of B.

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– Moderately supercritical simulations of global cloud collapse with AD produce

• SFEs somewhat larger than canonical observed value for average clouds,

• but need to take into account SF feedback.

– Moderately subcritical simulations• Produce initially realistic SFEs for average clouds, but• Have SF that shuts off after ~ 15 Myr, even with AD, due to

cloud rebound.

– At the scale of the present simulations, AD is at the level of numerical diffusion.

• Marginal difference with ideal MHD simulations.

– Subcritical regions exhibit buoyancy; tend to float away from gravitational potential well.

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THE END

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• Simulations of MC formation and turbulence generation including thermal instability AND self-gravity (Vázquez-Semadeni et al 2007, ApJ 657, 870; see also Heitsch et al. 2008, 2009).

– SPH (Gadget) code with sink particles and heating and cooling.

– WNM inflow: – n = 1 cm-3

– T = 5000 K

– Inflow Mach number in WNM: M = 1.25 (vinf = 9.2 km s-1)

– 1% velocity fluctuations.Run 1 Run 2

Lbox 128 pc 256 pc

Linflow 48 pc 112 pc

tinflow 5.2 Myr 12.2 Myr

Minflow 1.1x104 Msun 2.6x104 Msun

Mbox6.6 x 104

Msun

5.2 x 105

Msun

Converging inflow setup

Lbox

Linflow

Rinf

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(Vázquez-Semadeni et al. 2007, ApJ 657, 870)

Edge-on view of a molecular cloud formation simulationusing GADGET.

Start: colliding streams of WNM.

End: turbulent, collapsing dense cloud.

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Face-on view.

Note:Note: Local fluctuations collapse earlier than whole cloud.

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3.1. Under idealideal MHD conditions, and for a fixed cloud massfixed cloud mass, the mass-to-flux ratio of a clump of size r within an initially uniform cloud of size R is expected to range within:

where 0 is the mass-to-flux ratio of the parent cloud (Vázquez-

Semadeni, Kim et al. 2005, ApJ 618, 344).

00 Rr

mass = Msize = Rflux =

size = rmass = (r/R)3 M

flux = (r/R)2 blob = (r/R) 0

Consider two limiting cases under ideal MHD:a) A subregion of a uniform cloud with a uniform field:

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b) A full compression of the region into a smaller volume:

Thus, under ideal MHD conditions, the mass-to flux ratio of a fragment of a cloud must be smaller or equal than that of the whole cloud.

mass = M, =0, 0

mass = M, =0,blob = 0

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• Crutcher et al. 2009

The core has lower than the envelope.

core

envelope

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Numerical dissipation has started to act, increasing in the densest regions.

Clumps in a subregion of an ideal-MHD simulation of a 4-pc box with global mass-to-flux ratio =2.8 by Vázquez-Semadeni, Kim et al. 2005, ApJ, 618, 344 (see also Luttmila et al. 2009).

t = 0.24 ff t = 0.32 ff10 n0

40 n0

100 n0

J ~ 1.3 ~ 1.7

J ~ 0.5~ 0.9each

J ~ 1.45~ 2.0

J ~ 1.5 ~ 2.0

1.28 pc

1.0 pc

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1 Enrique Vázquez-Semadeni Centro de Radioastronomía y Astrofísica, UNAM, México