Enrique Vázquez-Semadeni
Centro de Radioastronomía y Astrofísica, UNAM, México
1
Collaborators:
CRyA UNAM:
ABROAD:
Javier Ballesteros-Paredes
Gilberto Gómez
Robi Banerjee (ITA, Heidelberg)
Dennis Duffin (McMaster, Canada)
Patrick Hennebelle (ENS, Paris)
Jongsoo Kim (KASI, Korea)
Ralf Klessen (ITA, Heidelberg)
2
I. INTRODUCTION
• The interstellar medium (ISM) is turbulent, magnetized
& Troland 2003, 2005), and self-gravitating.
(e.g., Heiles
• 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).
3
II. BASIC PHYSICAL PROCESSES
1.
Fundamental fact:
A density enhancement requires an accumulation of initially distant
material into a more compact region.
d
    u
dt
i.e., need to move the material from the surroundings into the
region.
4
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
5
… causes its atomic component to be thermally bistable.
– A warm, diffuse phase (WNM, T ~ 8000 K, n ~ 0.4 cm-3) can be
in a stable pressure equilibrium with a cold, dense (CNM, T ~ 80
K, n ~ 40 cm-3) phase (Field et al 1969; Wolfire et al 1995, 2003).
WNM
(stable)
Mean ISM
thermal
pressure
Peq, at which
heating G equals
cooling nL.
CNM
(stable)
Wolfire et al. 1995
Thermally
unstable range
6
– This is the famous two-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.
WNM
(stable)
Mean ISM
thermal
pressure
CNM
(clumps)
Wolfire et al. 1995
Thermally
unstable range
7
– 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
formation out of the WNM.
8
3.
Compressions and the mass-to-flux ratio in ideal MHD.
•
The ratio of gravitational to kinetic energy
18 GM 2 18 2G  M  18 2G 2


m ;
  
2 4
Em
5 B R
5 F
5
2
Eg
F  BR2
implies the existence of a critical mass-to-flux ratio (m; M2FR) for a
cloud to be supported against self-gravity by the magnetic field:
1/ 2



2
 18 G 
mcrit  
–
5
A cloud with
•
•
M/F > (M/F)crit is magnetically supercritical:
M/F < (M/F)crit is magnetically subcritical:
collapses.
cannot collapse.
9
•
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.
Neutral
Ion
10
•
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
–
Most stars form in regions of high-mass star formation (Lada & Lada
Crutcher+10).
are
nearly
critical
or
supercritical
(Bourke+01;
03).
11
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).
B
B
v
v
subcritical dense
subcritical diffuse
supercritical diffuse
supercritical diffuse
v
v
supercritical dense
supercritical diffuse
Assumption: the background medium extends out to a sufficiently long
distances to be supercritical.
Example: for B=3 mG and n=1 cm-3, a length L > 230 pc is supercritical.
12
4.
Combining compressions, MHD and thermodynamics:
•
Magnetic criticality condition (Nakano & Nakamura 1978):
2
B
GN 
4 2
2
•

 B  2
Ncrit  1.5 1021 
cm
5
m
G


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,
–
supercritical when they become molecular (consistent with observations of
e.g., Heiles & Troland 2005)
molecular gas; Bourke et al. 2001; Crutcher, Heiles & Troland 2003).
A consequence of mass accretion and a phase transition from WNM
13
to CNM and H2, not AD (Vázquez-Semadeni et al. 2011).
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).
WNM
n, T, P, v1
WNM
n, T, P, -v1
– The compression may be driven by global turbulence, largescale instabilities, etc.
14
Vázquez-Semadeni et al.
(2006 ApJ, 643, 245).
Ms = 1.2, tfin ~ 40 Myr
15
2D, 10242
Ms ~ 2
Audit & Hennebelle
2005
16
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
Rinf
Linflow
B
Lbox = 256 pc
Linflow = 112 pc
Dxmin = 0.03 pc
max res = 81923
Ms,inf = 1.2, 2.4
See also Inoue & Inutsuka
(2008) for configuration with B
perpendicular to compression.
17
18
•
Dense clump structure
(Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398,
1082).
log T [K]
Cuts through densest
point in clump.
Sharp
boundaries
between WNM and
CNM…
B [mG]
log n [cm-3]
In a B0 = 1 mG supercritical simulation, with no AD:
log P [K cm-3]
–
19
•
Dense clump structure
(Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398,
1082).
log T [K]
B [mG]
log n [cm-3]
In a B0 = 1 mG supercritical simulation, with no AD:
log P [K cm-3]
–
Cuts through densest
point in clump.
… but also there are
intermediate-n,
thermally unstable
regions.
More abundant
towards periphery of
cloud.
20
•
Dense clump structure
(Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398,
1082).
log T [K]
Cuts through densest
point in clump.
Gas flows from
diffuse medium into
dense clumps.
B [mG]
log n [cm-3]
In a B0 = 1 mG supercritical simulation, with no AD:
log P [K cm-3]
–
There is a net mass
flux through clump
boundaries.
The boundaries are
“phase transition
fronts”.
21
•
Dense clump structure
(Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398,
1082).
log T [K]
Cuts through densest
point in clump.
There exist warm,
low-pressure, diffuse
“holes” in the dense
gas.
Clouds are porous.
B [mG]
log n [cm-3]
In a B0 = 1 mG supercritical simulation, with no AD:
log P [K cm-3]
–
22
•
Dense clump structure
(Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398,
1082).
log T [K]
Cuts through densest
point in clump.
Magnetic field
strength exhibits
correlation with highdensity gas...
B [mG]
log n [cm-3]
In a B0 = 1 mG supercritical simulation, with no AD:
log P [K cm-3]
–
23
•
Dense clump structure
(Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398,
1082).
log T [K]
Cuts through densest
point in clump.
Magnetic field
strength exhibits
correlation with highdensity gas...
B [mG]
log n [cm-3]
In a B0 = 1 mG supercritical simulation, with no AD:
log P [K cm-3]
–
… but almost none
with low-density gas.
24
B-n correlation
B-v correlation
n1/2
(See also Hennebelle et
al. 2008, A&A)
B-histogram in dense gas (n > 100 cm-3)
B and v tend to be
aligned, even though
B is weak (~ 1 mG).
(Banerjee et al. 2009,
MNRAS, 398, 1082)
Large B scatter in
dense clumps.
25
Three simulations
with m = 1.3, 0.9,
and 0.7, including
AD.
Face-on view of
column density.
Dots are sink
particles.
m = 1.3
B=2mG
Vázquez-Semadeni et al.
2011, MNRAS, 414, 2511.
m = 0.7
B=4mG
m = 0.9
B=3mG
26
Evolution of the mean and 3s values of m  M/f.
Whole cloud
High-N gas
m = 1.3
m = 0.9
m = 0.7
Mass-to-flux
ratio is highly
fluctuating
through the
cloud, and
evolving.
Vázquez-Semadeni
et al. 2011,
MNRAS, 414, 2511
27
Evolution of gaseous and stellar masses, and of the SFR.
• Cloud mass
nearly same in all
cases.
• SFR of m=0.7
case nearly shuts
off.
• SFE of m=0.9 and
m=1.3 cases not too
different.
• Upon inclusion of
stellar feedback,
expect further SFE
reduction, so favor
higher-m cases.
Vázquez-Semadeni et al. 2011, MNRAS, 414, 2511
28
Low-m gas develops buoyancy
Run with B=3 mG
(m = 0.9).
Like a
macroscopic
analogue of AD.
Vázquez-Semadeni et al.
2011, MNRAS, 414, 2511
29
V.
CONCLUSIONS
–
Forming clouds and cores involves moving material from
surroundings into a small region
Implies:
•
•
•
–
d
    u
dt
Significant component of inward motions into clouds and cores.
Cloud and core boundaries are phase 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
•
The M2FR of a cloud that accretes from the WNM generally
increases in time.
time-dependent quantities.
–
Not an AD effect, but a result of increasing mass.
30
–
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.
31
–
Moderately supercritical simulations of global cloud collapse with
AD produce
•
•
–
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.
•
–
SFEs somewhat larger than canonical observed value for average
clouds,
but need to take into account SF feedback.
Marginal difference with ideal MHD simulations.
Subcritical regions exhibit buoyancy; tend to float away from
gravitational potential well.
32
THE END
33
•
Simulations of MC formation and turbulence generation
including thermal instability AND self-gravity (VázquezSemadeni 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
Dtinflow
5.2 Myr
12.2 Myr
Minflow
1.1x104 Msun
2.6x104 Msun
Converging inflow setup
Lbox
Rinf
Linflow
Mbox
6.6 x 104 Msun 5.2 x 105 Msun
34
Edge-on view of a
molecular cloud
formation
simulation
using GADGET.
Start: colliding
streams of WNM.
End: turbulent,
collapsing dense
cloud.
(Vázquez-Semadeni et
al. 2007, ApJ 657, 870)
35
Face-on
view.
Note: Local
fluctuations
collapse
earlier than
whole
cloud.
36
3.1. Under ideal MHD conditions, and for a fixed cloud mass, the
mass-to-flux ratio m of a clump of size r within an initially uniform
cloud of size R is expected to range within:
r
m0  m  m0
R
where m0 is the mass-to-flux ratio of the parent cloud (VázquezSemadeni, Kim et al. 2005, ApJ 618, 344).
Consider two limiting cases under ideal MHD:
a) A subregion of a uniform cloud with a uniform field:
mass = M
size = R
flux = f
size = r
mass = (r/R)3 M
flux = (r/R)2 f
mblob = (r/R) m0
37
b) A full compression of the region into a smaller volume:
mass = M,
f=f0, mm0
mass = M,
f=f0,
mblob = m0
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.
38
• Crutcher et al. 2009
envelope
core
The core has lower
m than the envelope.
39
Clumps in a subregion of an ideal-MHD simulation of a 4-pc box with
global mass-to-flux ratio m=2.8 by Vázquez-Semadeni, Kim et al. 2005, ApJ,
618, 344 (see also Luttmila et al. 2009).
t = 0.24 tff
1.28 pc
t = 0.32 tff
10 n0
40 n0
100 n0
1.0 pc
J ~ 1.3
m ~ 1.7
J ~ 0.5
m~ 0.9
each
J ~ 1.5
m ~ 2.0
J ~ 1.45
m~ 2.0
Numerical dissipation has started
to act, increasing m in the densest
40
regions.