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

1. Molecular Cloud Structure and Evolution with Magnetic Fields and Ambipolar Diffusion Enrique Vázquez-Semadeni Centro de Radioastronomía y Astrofísica, UNAM, México

2. 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)

3. 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).

4. II. BASIC PHYSICAL PROCESSES • Fundamental fact: A density enhancement requires an accumulation of initially distant material into a more compact region. i.e., need to move the material from the surroundings into the region.

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

6. WNM (stable) CNM (stable) Mean ISM thermal pressure … 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). Peq, at which heating G equals cooling nL. Wolfire et al. 1995 Thermally unstable range

7. WNM (stable) CNM (clumps) Mean ISM thermal pressure Wolfire et al. 1995 Thermally unstable range • 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.

8. … 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 formationout of the WNM. • 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).

9. 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 (m; M2FR) for a cloud to be supported against self-gravity by the magnetic field: • A cloud with • M/F > (M/F)crit is magnetically supercritical: collapses. • M/F < (M/F)crit ismagnetically subcritical: cannot collapse.

10. Neutral Ion • 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.

11. 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).

12. B B rv rv subcritical dense subcritical diffuse supercritical diffuse supercritical diffuse rv rv supercritical dense 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). 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.

13. 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). 

14. WNM n, T, P, -v1 WNM n, T, P, v1 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.

15. Ms = 1.2, tfin ~ 40 Myr Vázquez-Semadeni et al. (2006 ApJ, 643, 245).

16. 2D, 10242 Ms ~ 2 Audit & Hennebelle 2005

17. Converging flow setup Lbox B Rinf Linflow 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. 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.

19. log n [cm-3] log T [K] log P [K cm-3] B [mG] • Dense clump structure (Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398, 1082). • In a B0 = 1 mG supercritical simulation, with no AD: Cuts through densest point in clump. Sharp boundaries between WNM and CNM…

20. log n [cm-3] log T [K] log P [K cm-3] B [mG] • Dense clump structure (Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398, 1082). • In a B0 = 1 mG supercritical simulation, with no AD: Cuts through densest point in clump. … but also there are intermediate-n, thermally unstable regions. More abundant towards periphery of cloud.

21. log n [cm-3] log T [K] Gas flows from diffuse medium into dense clumps. log P [K cm-3] B [mG] • Dense clump structure (Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398, 1082). • In a B0 = 1 mG supercritical simulation, with no AD: Cuts through densest point in clump. There is a net mass flux through clump boundaries. The boundaries are “phase transition fronts”.

22. log n [cm-3] log T [K] log P [K cm-3] B [mG] • Dense clump structure (Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398, 1082). • In a B0 = 1 mG supercritical simulation, with no AD: Cuts through densest point in clump. There exist warm, low-pressure, diffuse “holes” in the dense gas. Clouds are porous.

23. log n [cm-3] log T [K] Magnetic field strength exhibits correlation with high-density gas... log P [K cm-3] B [mG] • Dense clump structure (Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398, 1082). • In a B0 = 1 mG supercritical simulation, with no AD: Cuts through densest point in clump.

24. log n [cm-3] log T [K] … but almost none with low-density gas. log P [K cm-3] B [mG] • Dense clump structure (Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398, 1082). • In a B0 = 1 mG supercritical simulation, with no AD: Cuts through densest point in clump. Magnetic field strength exhibits correlation with high-density gas...

25. B-v correlation B-n 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). Large B scatter in dense clumps. (Banerjee et al. 2009, MNRAS, 398, 1082)

26. 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 m = 0.7 B=4mG m = 0.9 B=3mG Vázquez-Semadeni et al. 2011, MNRAS, 414, 2511.

27. Whole cloud High-N gas Mass-to-flux ratio is highly fluctuating through the cloud, and evolving. Evolution of the mean and 3s values of m = M/f. m = 1.3 m = 0.9 m = 0.7 Vázquez-Semadeni et al. 2011, MNRAS, 414, 2511

28. 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

29. 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

30. 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 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 aretime-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 cold gas increases steadily.

31. 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.

32. 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.

33. THE END

34. Converging inflow setup Lbox Rinf Linflow • 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.

35. 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)

36. Face-on view. Note: Local fluctuations collapse earlier than whole cloud.

37. mass = M size = R flux = f size = r mass = (r/R)3M flux = (r/R)2 f mblob = (r/R) m0 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: where m0 is the mass-to-flux ratio of the parent cloud (Vázquez-Semadeni, Kim et al. 2005, ApJ 618, 344). Consider two limiting cases under ideal MHD: • A subregion of a uniform cloud with a uniform field:

38. mass = M, f=f0, mblob = m0 mass = M, f=f0, m=m0 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.

39. envelope • Crutcher et al. 2009 core The core has lower m than the envelope.

40. t = 0.24 tff t = 0.32 tff 10 n0 40 n0 100 n0 1.28 pc 1.0 pc • J ~ 0.5 • ~ 0.9 each • J ~ 1.45 • ~ 2.0 J ~ 1.3 m ~ 1.7 J ~ 1.5 m ~ 2.0 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). Numerical dissipation has started to act, increasing m in the densest regions.