1 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 1.Fundamental fact: A density enhancement requires an accumulation of initially distant material into a more compact region. move 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 thermally bistable … causes its atomic component to be thermally bistable. stable –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). Wolfire et al WNM (stable) CNM (stable) Mean ISM thermal pressure P eq, at which heating  equals cooling n  Thermally unstable range

7 two-phase model –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. Wolfire et al WNM (stable) CNM (clumps) Mean ISM thermal pressure Thermally unstable range

8 –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). molecular cloud formationThis constitutes a fundamental process for molecular cloud formation out of the WNM.

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 (  ; 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.

10 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

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 supercritical diffuse vv vvBB subcritical diffuse supercritical diffuse subcritical dense supercritical diffuse vv 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).

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 ~ cm -2 ~ 8 M sun 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 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. WNM n, T, P, -v 1 WNM n, T, P, v 1

15 Vázquez-Semadeni et al. (2006 ApJ, 643, 245). M s = 1.2, t fin ~ 40 Myr

16 Audit & Hennebelle D, M s ~ 2

17 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 L box L inflow R inf B See also Inoue & Inutsuka (2008) for configuration with B perpendicular to compression. L box = 256 pc L inflow = 112 pc  x min = 0.03 pc max res = M s,inf = 1.2, 2.4

18

19 Dense clump structure (Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398, 1082). –In a B 0 = 1  G supercritical simulation, with no AD: log n [cm -3 ] log T [K] log P [K cm -3 ] B [  G] Cuts through densest point in clump. Sharp boundaries between WNM and CNM…

20 Dense clump structure (Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398, 1082). –In a B 0 = 1  G supercritical simulation, with no AD: log n [cm -3 ] log T [K] log P [K cm -3 ] B [  G] Cuts through densest point in clump. … but also there are intermediate-n, thermally unstable regions. More abundant towards periphery of cloud.

21 Dense clump structure (Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398, 1082). –In a B 0 = 1  G supercritical simulation, with no AD: log n [cm -3 ] log T [K] log P [K cm -3 ] B [  G] Cuts through densest point in clump. Gas flows from diffuse medium into dense clumps. There is a net mass flux through clump boundaries. “phase transition fronts” The boundaries are “phase transition fronts”.

22 Dense clump structure (Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398, 1082). –In a B 0 = 1  G supercritical simulation, with no AD: log n [cm -3 ] log T [K] log P [K cm -3 ] B [  G] Cuts through densest point in clump. There exist warm, low-pressure, diffuse “holes” in the dense gas. Clouds are porous.

23 Dense clump structure (Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398, 1082). –In a B 0 = 1  G supercritical simulation, with no AD: log n [cm -3 ] log T [K] log P [K cm -3 ] B [  G] Cuts through densest point in clump. Magnetic field strength exhibits correlation with high- density gas...

24 Dense clump structure (Banerjee, VS, Hennebelle & Klessen, 2009, MNRAS, 398, 1082). –In a B 0 = 1  G supercritical simulation, with no AD: log n [cm -3 ] log T [K] log P [K cm -3 ] B [  G] Cuts through densest point in clump. Magnetic field strength exhibits correlation with high- density gas... … but almost none with low-density gas.

25 B-n correlation n 1/2 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).

26 Three simulations with  = 1.3, 0.9, and 0.7, including AD. Face-on view of column density. Dots are sink particles.  = 1.3 B=2  G  = 0.9 B=3  G  = 0.7 B=4  G Vázquez-Semadeni et al. 2011, MNRAS, 414, 2511.

27 Evolution of the mean and 3  values of  M/ . Whole cloudHigh-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

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

29 Low-  gas develops buoyancy Run with B=3  G (  = 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. phase transition frontsCloud 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 time-dependent quantities.Thus, the mass, mass-to-flux ratio (M2FR), and SFE of a cloud are time-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 ), ~ n 1/2, 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 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 (v inf = 9.2 km s -1 ) –1% velocity fluctuations. Run 1Run 2 L box 128 pc256 pc L inflow 48 pc112 pc  t inflow 5.2 Myr12.2 Myr M inflow 1.1x10 4 M sun 2.6x10 4 M sun M box 6.6 x 10 4 M sun 5.2 x 10 5 M sun Converging inflow setup L box L inflow R inf

35 (Vázquez-Semadeni et al. 2007, ApJ 657, 870) Edge-on view of a molecular cloud formation simulation using GADGET. Start: colliding streams of WNM. End: turbulent, collapsing dense cloud.

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

37 idealfixed cloud mass 3.1.Under ideal MHD conditions, and for a fixed 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). mass = M size = R flux =  size = r mass = (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:

38 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

39 Crutcher et al The core has lower  than the envelope. core envelope

40 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  ff 10 n 0 40 n n 0 J ~ 1.3  ~ 1.7 J ~ 0.5  ~ 0.9 each J ~ 1.45  ~ 2.0 J ~ 1.5  ~ pc 1.0 pc