1. 1 Enrique Vázquez-Semadeni Adriana Gazol CRyA UNAM, México Collaborators: Thierry Passot (OCA) Jongsoo Kim (KASI) Dongsu Ryu (Chungnam U.) Ricardo González (CRyA UNAM)

2. 2 Contents 1.Introduction –“Classical” ISM models vs. turbulence: Equilibrium vs. out-of-equilibrium 2.Turbulence in thermally bistable media –Effects of net cooling Effective thermodynamic behavior Dependence of probability distributions on turbulent parameters 3.Magnetic field correlations with density and pressure 4.Thin CNM sheet formation 5.Small-scale structures in simulations

3. 3 I. INTRODUCTION Classic theories of ISM: Based on pressure balance and equilibrium states. –ISM theories: multiphase: Field, Goldsmith & Habing (1969): “two-phase” model: dense, cool (100 K) clouds in thermal-pressure equilibrium with surrounding warm (10 4 K), diffuse medium. McKee & Ostriker (1977): “three-phase model”: supernova-dominated ISM, with shell fragmentation into cold clouds and warm medium. Hot gas in interiors of SN remnants. All 3 phases in rough pressure equilibrium.

4. 4 –Caveat: left out advection (transport by gas motions), self-gravity, magnetic fields, rotation,... (see Elmegreen 1991, 1994 for linear instability analysis). E turb, E mag, E cr > E th in ISM (Boulares & Cox 1990) E turb  advection (transport) and inertia (not just an additional pressure) (Ballesteros-Paredes, Vázquez- Semadeni & Scalo 1999). –The ISM is turbulent: WNM is transonic (Kulkarni & Heiles 1987) CNM (e.g., Heiles & Troland 2003) and molecular gas (e.g., Zuckerman & Palmer 1974) are supersonic.

5. 5 Turbulent flows are characterized by strong nonlinear fluctuations of the physical variables about their mean values. The fluctuations (tails of the probability distributions) –are transient and locally out of equilibrium. –are responsible for important phenomena. E.g.: Star formation TSAS?

6. 6 II. TURBULENCE IN THERMALLY BISTABLE MEDIA 1.Effects of net cooling (heating  + cooling  ): 1.1Net cooling determines the compressibility of the gas (Tohline et al. 1987). If heating and cooling laws are power laws, the gas response to compressions can be described by a polytropic law P ~   eff and effective polytropic exponent  eff (Elmegreen 1991; Vázquez-Semadeni et al 1996, 2003) :  eff Thermal-equilibrium (TE,  =n  ) value  TE for  cool <<  cros Adiabatic value  for  cool >>  cros

7. 7 log n (cm -3 ) adiabatic (fast) isobaric TE (slow)

8. 8   ~0.7   ~ -0.7   ~0   ~0.7  P instab 1.2.In the presence of externally-driven velocity fluctuations, density field is expected to include a roughly stationary population of zones at “unstable” values, made up of fluid parcels traversing this regime from one phase to another. Because of the dynamic nature of the process, thermal pressure is expected to deviate from TE at transitional densities.

9. 9 Indeed, a parametric study (Gazol, VS & Kim 2005, ApJ) of randomly-driven turbulence shows:

10. 10 Effect of the driving scale for, M=1 (w.r.t. diffuse gas @ 7000K) for  50pc for  6.25pc for  12.5pc for  25pc As for decreases,  cros decreases,  eff approaches  of the gas. Simulations in 100-pc boxes, 512 2 resolution, random Fourier driving 2D histograms in P-  space Slope =  eff

11. 11 Effect of the Mach number M (w.r.t. the WNM) for =50pc for =6.25pc M=0.5 M=1 M=1.25 The dynamic range of P and n, and the mean slope of the distribution increase with M

12. 12 Fits to the points in P-  diagram give: As either M increases or for decreases,  cros /  cool decreases the gas behaves farther from thermal equilibrium and closer to adiabatic  is always >0 and increases with M and 1/ for = 1/ for

13. 13 Density PDF Temperature PDFs: ~ 50% of the mass at “unstable” temperatures. Cumulative PDF (VS, Gazol & Scalo 2000 ApJ) (Gazol, VS, Sánchez-Salcedo & Scalo 2001 ApJL) Qualitatively consistent with observations: Dickey et al. 1979; Heiles 2001; Kanekar et al. 2003. Implications: thermally unstable gas should be present in the ISM... Simulations of warm and cold media, with ionization heating only. (see also Wada & Norman 2001; de Avillez & Breitschwerdt 2004; Mac Low et al. 2005; Audit & Hennebelle 2005)

14. 14... and also large pressure fluctuations: de Avillez & Breitschwerdt 2004 Numerical simulations with SN driving, no B N(P) ~ P -5/2

15. 15 2.Dependence of PDFs on turbulent parameters –Functional form of density PDF depends on  eff (Passot & VS 1998). Due to variation of sound speed with density c ~  (  -1)/2, so effective Mach number of a compression depends on local density. –Width of PDF (standard deviation) depends on M rms. Isothermal case: lognormal (molecular clouds) General polytropic case: power law tails (~atomic ISM) Passot & Vázquez-Semadeni 1998  = 0.3  = 1.7

16. 16 – Apparently similar behavior for pressure PDF: for = 50 pc for = 6.25 pc M = 0.5 M = 1 M = 1.25 The high-P wing approaches a power law for high M. Low-  –like behavior The high-P wing drops rapidly, and its slope is independent of M High-  –like behavior Gazol et al. 2005

17. 17 Comparison with observations should constrain  eff Jenkins 2004 Observations of CI pressure PDF Also column density PDF? (VS & García 2001)

18. 18 III.B- , P correlations Numerical simulations of ideal MHD interstellar turbulence (without AD) show little correlation of magnetic pressure (B 2 ) with density. Padoan & Nordlund 1999 (isothermal) Passot, VS & Pouquet 1995 (multi-temperature) Ostriker, Stone & Gammie 2001 (isothermal) See also Hennebelle & Pérault 2000 (multi-temperature)

19. 19 de Avillez & Breitschwerdt (2004) (multi-temperature) Similarly for observations of B in atomic ISM (e.g., Crutcher et al. 2003; Heiles & Troland 2005)

20. 20 Interpretation (Passot & VS 2003) : Analytical+numerical study of magnetic pressure in driven MHD turbulence. Found different asymptotic B 2 -r scaling for different modes of nonlinear MHD (“simple”) waves: B 2 ~  2 Fast wave B 2 ~ c 1 – c 2  Slow wave B 2 ~  1/2—2 Alfvén wave Fast mode domination Slow mode domination log  log B 2 log 

21. 21  In a turbulent medium with superpositions of waves: Value of B at a given position and time is not a function of local , but of the history of wave passages at that position.  B 2 not characterized by a single response to compressions; randomizes the behavior of the restoring force. Alfvén mode, low M a Alfvén mode, high M a  1/2 22

22. 22 Thermal-magnetic pressure correlation: Generally uncorrelated..., (see also de Avillez & Breitschwerdt 2005; Mac Low et al. 2005) except at high densities, where P th is high and P mag is medium-to-high. Cold gas can have high or low P th. In latter case, P mag makes up for low P th (see also Inutsuka’s poster). 10 4 K < T 6100 < T < 10 4 K 310 < T < 6100 K 140 < T < 140 K 45 < T < 140 K T < 45 K n < 0.1 cm -3 0.1 < n < 0.6 cm -3 0.6 < n < 3.2 cm -3 3.2 < n < 7.0 cm -3 7.0 < n < 80 cm -3 80 cm -3 < n Diffuse cold gas Dense gas Sorted by temperatureSorted by density Gazol, Luis & Kim 2006

23. 23 IV.Thin CNM sheet formation (VS, Ryu, Passot, González & Gazol 2006 ApJ) –Fortuitous finding while investigating molecular cloud formation by colliding WNM streams. WNM inflow: –n = 0.34 cm -3 –T = 7100 K –P = 2400 K cm -3 –Mach number in WNM: M = v 1 /c WNM (control parameter) n, T, P, -v 1 n, T, P, v 1 Physical setup: (see also Hennebelle & Pérault 1999; Koyama & Inutsuka 2000, 2002; Audit & Hennebelle 2005; Heitsch et al. 2005)

24. 24 Analytical model for early stages: –Ingredients: Adiabatic shock. Quasi-stationary state after ~ cooling time (shocked layer thickness ~ 2 cooling lengths c ). Phase transition through TI to cold phase after cooling length.  P/ c ~ momentum flux drop across c. ~ c Predictions: Conditions in dense layer as function of M.

25. 25 Excellent agreement with 1D simulations: Cold dense layer has properties comparable to Heiles & Troland’s (2003) thin cold neutral medium sheets: –N ~ 2.5 x 10 19 cm -2 (after 1 Myr) –T ~ 25 K –n ~ 250 cm -3 –v f ~ 0.015 pc Myr -1 –P ~ 7000 K cm -3  Note higher-than-mean ISM P T because of dynamical origin. In pressure balance with inflow’s total (ram + thermal) pressure. Simulation with L = 64 pc, M = 1.03, resol. = 4000

26. 26 Linewidth ~ 1 km s -1 A signature of the inflow gas velocity, not of the internal turbulence. –Does not imply excessively short (10 4 yr) lifetimes. –N at t ~ 1 Myr comparable to observed value. -v  v 0

27. 27 Late stages (3D runs @ 200 3 ): –Turbulence apparently develops by NTSI-like instability in cooling gas: Shocked warm gas is everywhere subsonic, but large density contrast provided by phase transition. Time for turbulence development depends on inflow Mach number M: –~ 10 Myr for M ~ 2.5 –~ 50 Myr for M ~ 1. M = 1.03,  t = 80 Myr M = 2.4,  t = 26.7 Myr  P 64 pc 16 pc

28. 28 M = 1.03,  t = 80 Myr M = 2.4,  t = 26.7 Myr Thin CNM sheets may be the “little sisters” (low-M collisions) of molecular clouds

29. 29 V.Small-scale structure (Gazol, VS & Kim, in prep.) –Ongoing analysis of small-scale structures in high- resolution simulations of atomic ISM turbulence. –2048 2 simulation of randomly-driven turbulence at M rms ~1 in WNM (see also P. Hennebelle’s talk)

30. 30 Density field. L box = 100 pc resol. = 2048 2  x = 0.05 pc Large-scale driving.

31. 31 –Formation of sheets and cometary cloudlets. –Steady overdense (n > 100 cm -3 ) and over-pressured (P > 4000 K cm -3 ) mass fraction ~ 5-10% (compare to 2-4% reported by Stanimirovic & Heiles 2005). –Relatively common excursions to n > 1000 cm -3, P > 10 4 K cm -3, occasionally to n ~ 3000 cm -3, P ~ 3x10 4 K cm -3. (cooling function implies a transition to ~ isothermal regime at 10 K at n > 2000 cm -3.) ~

32. 32 ISM in statistical equilibrium, but not necessarily in local thermal and pressure equilibria. Structure and star formation provided by the fluctuations.  Theories must discuss variances as well as mean values. , P th and P mag all expected to fluctuate significantly in transonic, thermally bistable media such as atomic ISM. –Thermally unstable gas AND overdense, overpressured cloudlets are NON-equilibrium structures. P th for intermediate-density gas fluctuates because of competition between approach to thermal equilibrium and turbulent crossing time. P mag fluctuates because different trends for different MHD waves. Overdense, overpressured cloudlets are created by transient ram- pressure compressions. VI. Summary

33. 33 Thin CNM sheets can be transiently formed by transonic collisions of WNM streams, with lifetimes ~ 1 Myr. Structure down to the smallest resolved scales (a few x 0.1 pc), with high densities (n > 1000 cm -3 ) and pressures (P > 10 4 K cm -3 ). –Sufficient to account for observed frequency of TSAS?

34. 34 The End