1. Molecular Cloud Formation and Evolution. Scenario and Simulations
Enrique Vázquez-Semadeni
Centro de Radioastronomía y Astrofísica, UNAM, México

2. Collaborators: CRyA UNAM: Javier Ballesteros-Paredes Pedro Colín
Adriana Gazol
Gilberto Gómez
Jonathan Heiner
ABROAD:
Robi Banerjee (Heidelberg)
Patrick Hennebelle (ENS, Paris)
Katharina Jappsen
Jongsoo Kim (KASI, Korea)
Ralf Klessen (Heidelberg)
Thierry Passot (Obs. Nice)
Dongsu Ryu (Chungnam U., Korea)

3. I. INTRODUCTION

4. GMCs seem to form from the HI gas

5. Color image: HI distribution
Engargiola et al. 2003: Study of M33
Color image: HI distribution
Circles: GMCs
GMCs seem to be the “tip of the iceberg” of the gas density distribution.
They conclude that GMCs form out of the HI. (See also Blitz+07, PPV; Molinari+13, PPVI)

6. This talk addresses: The general evolutionary scenario,
atomic cloud formation: how do the clouds acquire their
mass?
turbulence (at what level)?
GMC formation:
need for self-gravity and global contraction
filamentary structure from gravitational contraction.
destruction:
through stellar feedback.
The numerical tools and database.
Caveat: no time for discussion of magnetic effects.

7. II. THE EVOLUTIONARY SCENARIO

8. II.1 Formation of CNM Clouds

9. When a dense cloud forms out of a compression in the WNM, it “automatically”
cools down
acquires mass
acquires turbulence (through TI, NTSI, KHI – Vishniac 1994; Walder & Folini 1998, 2000; Koyama & Inutsuka 2002, 2004; Audit & Hennebelle 2005; Heitsch et al. 2005, 2006; Vázquez-Semadeni et al. 2006).
The compression may be driven by global turbulence, but mostly by large-scale gravitational instabilities:
HI superclouds: <n> ~ 10 cm-3, M ~ x107 Msun, gravitationally bound (Elmegreen & Elmegreen 1987; Molinari+13).
WNM
n, T, P, -v1
n, T, P, v1

10. The system’s structure:
~ cooling length.
Adiabatic or
phase-transition front.
WNM
CNM
Unstable
Vázquez-Semadeni et al. (2006 ApJ, 643, 245).

11. For stronger compressions and later times, the compressed layer becomes denser, turbulent, and thick, and continuously grows in mass.
Adiabatic shocks
Phase-transition fronts
Thermally unstable,
transient gas
Ms ~ 2
Audit & Hennebelle 2005

12. For moderate compressions, the process may be responsible for the formation of thin CNM sheets (Heiles & Troland 2003) at its early stages.
Ms = 1.2, tfin ~ 40 Myr
Vázquez-Semadeni et al. (2006 ApJ, 643, 245).

13. The warm-cold transition

14. Dense clump structure (Banerjee+09, MNRAS, 398, 1082).
In a B0 = 1 mG supercritical simulation, with no AD:
log n [cm-3]
log T [K]
log P [K cm-3]
B [mG]
Cuts through densest point in clump.
Gas flows from diffuse medium into dense clumps.
The boundaries are “phase transition fronts”, not rigid walls. 
Clumps accrete.

15. II.2 Formation of Molecular Clouds

16. When a CNM cloud forms from a large-scale compression it may involve enough mass to be strongly self-gravitating in this state.
Upon transition to the cold phase, n increases by 100x, T decreases by 100x,
 The Jeans mass, MJ ~ n-1/2T3/2, decreases by ~ 104.

17. 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
Dtinflow
5.2 Myr
12.2 Myr
Minflow
1.1x104 Msun
2.6x104 Msun
Converging inflow setup
Lbox
Linflow
Rinf
Mbox
6.6 x 104 Msun
5.2 x 105 Msun

18. Run with Lbox = 256 pc; 2.6x107 SPH particles:
(Gómez & Vázquez-Semadeni 2013, ApJ, subm., arXiv: )
WNM in box is initially Jeans-stable. (Mbox ~ 0.01 MJ)
Compression cools and compresses the gas.
Dense, cold gas soon becomes turbulent and Jeans-unstable.
Note: Local fluctuations collapse earlier than whole cloud.
Face-on view.

19. Apparent virialization:
These clouds are never in true virial equilibrium, but appear virialized because of gravitational contraction.
SF starts (17.2 Myr)
Collapse starts
(~11 Myr)
|Eg|
Apparent virialization:
|Eg| ~ 2 Ek Ek
Plots for the dense gas
(n > 50 cm-3)
Eth
(Vázquez-Semadeni et al )

20. Ekin driven first by inflow, then by gravitational contraction.
Lbox = 256 pc , Linf = 112 pc
4.1
Inflow weakens, collapse starts (12.2 Myr)
SF starts (17.2 Myr)
Turbulence driven by compression, through NTSI, TI and KHI (Walder & Folini1998; Koyama & Inutsuka 2002; Audit & Hennebelle 2005; Heitsch et al. 2005, 2006; Vázquez-Semadeni et al 2006)
2.7
1.4
~ 0.5 km s-1
(Vázquez-Semadeni et al )

21. This scenario implies that
At least the densest, star-forming MCs might be undergoing global gravitational contraction, not be in equilibrium.
Consistent with various recent observational studies (e.g., Hartmann & Burkert 2007; Peretto+2007; Galván-Madrid+09; Schneider+10).
Hartmann & Burkert 2007

22. A more realistic simulation:
No colliding-flow setup.
Avoid the converging-flow “stigma”.
Decaying random turbulence in n=3 cm-3.
Clouds form at local shock sites, grow by gravitational accretion.
See J. Heiner’s talk for synthetic HI and CO observations.

24. Filament formation by gravitational contraction

25. Because the cloud contains many Jeans masses, its collapse is nearly pressureless.
Collapse proceeds fastest along shortest dimension (Lin+65):
Spheroids  Sheets  Filaments
Because collapse of filaments is slower than that of spheres (Toalá+12; Pon+12), spheroidal fluctuations within a filament collapse earlier than rest of the filament.
 Start over?
 Rest of filament “rains down” onto star-forming clump

26. Gómez & VS 2013, (arXiv:1308.6298) 2.6 x 107 SPH particles.

27. Properties of filaments formed in simulation:
Filaments are flow features (not equilibrium objects) where accretion changes from being ~2D to ~1D:
cm-2
Gómez & VS 2013, submitted (arXiv: ).
2 km s-1

28. Properties of filaments formed by this mechanism:
Accretion flow along filament develops hierarchy of collapse centers and velocity jumps.
Gómez & VS 2013, submitted (arXiv: ).

29. Properties of filaments formed by this mechanism:
Plummer-like radial column density profile:
Simulation:
Rc ~ 0.3 pc
p ~ 2.4
L ~ 15 pc
Nc ~ 1022 cm-2
l ~ 40 Msun pc-1
Arzoumanian+11:
0.01 < Rc < 0.08 pc
1.3 < p < 2.4
L ~ pc
Nc ~ 1022 cm-2
lrms ~ 30 Msun pc-1
Gómez & VS 2013, submitted (arXiv: ).

30. Position-velocity diagram:
Asymmetric radial velocity profile at each position.
2-component Gaussian fit:
Two-filament appearance due to asymmetry of radial velocity profile.
Compare to Hacar+13.
Gómez & VS 2013, submitted (arXiv: ).

31. II.3 Molecular Cloud Destruction

32. If clouds are free-falling, one must confront the Zuckerman-Palmer (1974) conundrum:
Free-fall estimate of SFR:
Observed rate is SFRobs ~ 2—3 Msun yr-1; i.e., ~100x lower.
I.e., need to reduce SFR from free-fall value to observed one (~1/100).

33. Ionization feedback to the rescue
But not by providing support for the clouds.
... but rather by cloud destruction.
Colín+13 (MNRAS, 435, 1701): simulations of MC formation and evolution using:
AMR code ART + HD (Kravtsov+1997; Kravtsov 2003)
Stellar feedback with
Imposed Salpeter-like stellar IMF.
Crude radiative transfer.

35. Qualitatively consistent with observations of gas dispersal around clusters
Leisawitz+1989:
Clusters older than ~ 10 Myr do not have more than a few x103 Msun of dense gas within a 25-pc radius.
Surrounding molecular gas receding at ~ 10 km s-1.

36. - Mayya+2012:
- CO, HI and Spitzer study of environment of Westerlund 1:
- Region of radius 25 pc contains only a few x103 Msun. Much less than cluster.
- Surrounding molecular gas exhibits velocity difference ~ 15 km s-1.

37. Virial parameter a evolves:
towards unity while driven by gravity.
away from unity when feedback starts.
 unbinds clouds.
Feedback starts
: Density weighted
: Volume weighted

38. III. THE NUMERICAL DATABASE

39. 4 types of simulations: All with: 1. Gadget2 SPH simulations:
Cooling
Self-gravity
Resolution: 3.5 orders of magnitude (~250  0.1 pc).
1. Gadget2 SPH simulations:
Lagrangian method
Sink particles
Current manageable resolutions: up to 5x107 particles.
2. ART (AMR) simulations:
Sink particles.
Ionization (and soon SN) feedback.
A realistic stellar IMF.

40. 4. Fixed grid simulations (Adriana Gazol & Jongsoo Kim):
3. FLASH simulations
Sink Particles
Include magnetic field and ambipolar diffusion.
Ionization feedback.
4. Fixed grid simulations (Adriana Gazol & Jongsoo Kim):
No sink particles.
Manageable resolution up to
Uniform resolution useful for medium- and low-density gas studies.

41. Volume Density PDF Density Spectrum
Gazol & Kim 2013, ApJ, 765, 413
Density Spectrum
Gazol & Kim 2013, ApJ, 723, 482
MODEL
3D, (100pc)3, periodic boundary conditions, the PDFs in the figure result from simulations with 512^3
Code based in a MUSCL type scheme (Monotone Upstream-Centered Scheme for Conservation Laws)
Hydrodynamic equations with cooling (Sánchez Salcedo et al. 2002)
Forcing : in Fourier space at a fixed wave number (kfor=2) and random amplitude with constant energy injection rate. Solenoidal.
Initial conditions: v=0, uniform density (1cm^-3) and temperature (2400K): thermal equilibrium and thermal instability.
VOLUME DENSITY PDF
The distribution of the diffuse gas is well described by a log normal.
The distribution of the dense gas is described by a log normal only for M large enough.
For low M the dense gas PDF is well described by a power law
The power law is stepper than predicted by Passot & Vázquez-Semadeni (-4.4 for <M>=0.28,-2.4 for <M>=0.73)
The different behavior for different Mach numbers can be explained by considering the amount of dense gas in thermal equilibrium. In the low M case the distribution is dominated by gas in thermal equilibrium (polytropic behavior), whereas in the high M case the distribution is domineted by gas where there is not a clear correlation between density and pressure.
DENSITY SPECTRUM
For thermally bistable flows, the density spectrum flattens as the Mach number is increased.
This is the same behavior as previously reported for isothermal turbulence (e.g. Kim & Ryu 2005), but in the present case the spectral slopes are shallower.
We interpret this fact and the behavior with M as a consequence of a combined effect of the presence of strong density fluctuations produced by TI and turbulence with the fact that the larger the M, the weaker the pressure forces in diffuse gas produced by the interaction of turbulence and TI.
Resolution effects, in particular for large M simulations, can probably change the spectral slopes but the trend is not modified by these effects.
Comparison with isothermal simulations (with the same model and Mach number), confirm that with TI spectra are shallower.
<M>: mean value of the local Mach number 41

42. Column Density PDF σ2ln(Σ/Σ0)= AΣ ln(1 + bΣ2M2)
Gazol & Kim 2013, ApJ, 765, 413
Lognormal widths as a function of Mrms
Isothermal
(Buckhart & Lazarian 2012)
COLUMN DENSITY PDF
At high densities, the column density PDF can be described by a lognormal for all of the Mach numbers we consider.
As M increases, the density range where the lognormal fit is adapted expands and the lognormal becomes wider.
The width of the column density distribution is systematically larger than the width obtained in the isothermal case.
This is a natural consequence of the large density dynamical range produced by the presence of TI.
The resulting relationship between the lognormal width and the Mach number has to include the fact that when TI is present, the density contrast is large even for low Mach numbers.
The relationship between the width of the column density distribution and the rms Mach number at the mean temperature has the same
form as the one reported in the literature for the isothermal case, but the parameters resulting from our fit are very different.
σ2ln(Σ/Σ0)= AΣ ln(1 + bΣ2M2)
Red : AΣ =0.084, bΣ =12.5
Blue: AΣ =0.081 bΣ =14.29
Mrms: rms Mach number at mean temperature.
<M>: mean value of the local Mach number 42

43. IV. CONCLUSIONS

44. The scenario: The simulations: GMCs form by convergence of atomic gas.
 GMCs and their clumps accrete in general.
Early stages form:
First thin sheets...
... then cold HI clump complexes.
Ensemble of CNM clumps is gravitationally unstable and begins contracting.
Contraction needed for both molecule and star formation.
Nearly pressureless contraction naturally proceeds via
sheets  filaments  clumps.
SFR increases in time, until sufficient to destroy clouds.
The simulations:
Available for synthetic observations.

45. THE END

46. The magnetic case

47. If a cloud (i.e., a dense region) is formed by a compression with a component along the field lines, the cloud’s mass-to-flux ratio increases together with its mass (Mestel 1985; Hennebelle & Pérault 2000; Hartmann et al. 2001; Shu et al. 2007; Vázquez-Semadeni et al. 2011).
supercritical dense rv B
subcritical diffuse
supercritical diffuse
subcritical dense
Conclude: the cloud evolves from a subcritical to a supercritical regime.
Example: for B=3 mG and n=1 cm-3, a length L > 230 pc is supercritical.

48.  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 mass of the dense gas only, the clouds evolve so that they are:
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+03, +10).
Conclusion: even in ideal MHD, the M/f of a cloud is a continuously evolving quantity. 

49. Converging inflow setup
Numerical simulations of molecular cloud formation with magnetic fields, self-gravity and sink particles (Vázquez-Semadeni et al. 2011, MNRAS, 414, 2511).
Use FLASH code (AMR, MHD, self-gravity, sink particles).
AD by Duffin & Pudritz (2009).
Similar initial conditions as non-magnetic simulations with GADGET.
Add uniform field in the x-direction.
Optionally add fluctuating field.
Maximum resolution equivalent to
Converging inflow setup
Lbox
Linflow
Rinf B
See also Inoue & Inutsuka (2008) for configuration with B perpendicular to compression.

50. Evolution of the mean and 3s values of M/f = m.
Whole cloud
High-N gas
m = 1.3
Mass-to-flux ratio is highly fluctuating through the cloud, and evolving.
m = 0.9
m = 0.7

51. What is the effect of the newly formed stars on their parent cloud?
Community currently divided into two main camps:
Stellar feedback provides energy source for clouds’ turbulence and virial equilibrium (e.g., Norman & Silk 1980; McKee 1989; Matzner & McKee 2000; Matzner 2002; Krumholz, Matzner & McKee 2006; Nakamura & Li 2007; Wang et al. 2010).
Low SFE due to large Dt and low SFR.
Stellar feedback disperses cloud (at least locally) (e.g., Whitworth 1979; Larson, 1987; Franco+94; Hartmann+01; Ballesteros-Paredes & Hartmann 2007; Vazquez-Semadeni+10; Colin+13).
Low SFE due to short Dt and large-ish SFR.