Enrique V ázquez-Semadeni Adriana Gazol CRyA UNAM, México

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

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

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 (104 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. Caveat: left out advection (transport by gas motions), self-gravity, magnetic fields, rotation,...(see Elmegreen 1991, 1994 for linear instability analysis). • Eturb , Emag, Ecr > Eth in ISM (Boulares & Cox 1990) • Eturb advection (transport) and inertia (notjust 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. 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. II. TURBULENCE IN THERMALLY BISTABLE MEDIA 1. Effects of net cooling (heating G + cooling L): 1.1 Net 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 ~ rgeff and effective polytropic exponent geff(Elmegreen 1991; Vázquez-Semadeni et al 1996, 2003): Thermal-equilibrium (TE, G=nL) value gTE for tcool << tcros geff Adiabatic value g for tcool >> tcros

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

8. 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. DPinstab gTE~ -0.7 gTE~0.7 gTE~0.7 gTE~0

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

10. Effect of the driving scalelfor, M=1 (w.r.t. diffuse gas @ 7000K) Simulations in 100-pc boxes, 5122 resolution, random Fourier driving lfor = 50pc lfor = 25pc Slope = geff 2D histograms in P-r space lfor = 12.5pc lfor = 6.25pc Aslfordecreases, tcrosdecreases, geffapproachesgof the gas.

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

12. Fits to the points in P-rdiagram give: g is always >0 and increases with M and 1/lfor = 1/lfor As either M increases orlfordecreases, tcros/tcooldecreases the gas behaves farther from thermal equilibrium and closer to adiabatic

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

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

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

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

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

18. III. B-r, P correlations Numerical simulations of ideal MHD interstellar turbulence (without AD) show little correlation of magnetic pressure (B2) 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. de Avillez & Breitschwerdt (2004)(multi-temperature) • Similarly for observations of B in atomic ISM(e.g., Crutcher et al. 2003; Heiles & Troland 2005)

20. Interpretation(Passot & VS 2003): Analytical+numerical study of magnetic pressure in driven MHD turbulence. • Found different asymptotic B2-r scaling for different modes of nonlinear MHD (“simple”) waves: • B2~ r2Fast wave B2~ c1 – c2r Slow wave B2 ~ r1/2—2Alfvén wave Fast mode domination Slow mode domination log B2 log B2 log r log r

21. Alfvén mode, low Ma Alfvén mode, high Ma • In a turbulent medium with superpositions of waves: Value of B at a given position and time is not a function of local r, but of the history of wave passages at that position. • B2 not characterized by a single response to compressions; randomizes the behavior of the restoring force. r2 r1/2

22. Thermal-magnetic pressure correlation: • Generally uncorrelated..., (see also de Avillez & Breitschwerdt 2005; Mac Low et al. 2005) • except at high densities, where Pth is high and Pmag is medium-to-high. • Cold gas can have high or low Pth. In latter case, Pmag makes up for low Pth(see also Inutsuka’s poster). Sorted by temperature Sorted by density Dense gas Diffuse cold gas 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 104 K < T 6100 < T < 104 K 310 < T < 6100 K 140 < T < 140 K 45 < T < 140 K T < 45 K Gazol, Luis & Kim 2006

23. n, T, P, v1 n, T, P, -v1 IV. Thin CNM sheet formation (VS, Ryu, Passot, González & Gazol 2006 ApJ) • Fortuitous finding while investigating molecular cloud formation by colliding WNM streams. Physical setup:(see also Hennebelle & Pérault 1999; Koyama & Inutsuka 2000, 2002; Audit & Hennebelle 2005; Heitsch et al. 2005) • WNM inflow: • n = 0.34 cm-3 • T = 7100 K • P = 2400 K cm-3 • Mach number in WNM: M = v1/cWNM (control parameter)

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

25. Simulation with L = 64 pc, M = 1.03, resol. = 4000 • 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 1019 cm-2 (after 1 Myr) • T ~ 25 K • n ~ 250 cm-3 • vf ~ 0.015 pc Myr-1 • P ~ 7000 K cm-3 Note higher-than-mean ISM PT because of dynamical origin. In pressure balance with inflow’s total (ram + thermal) pressure.

26. v 0 -v • Linewidth ~ 1 km s-1 • A signature of the inflow gas velocity, not of the internal turbulence. • Does not imply excessively short (104 yr) lifetimes. • N at t ~ 1 Myr comparable to observed value. r

27. Late stages (3D runs @ 2003): • 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. 16 pc 64 pc r P M = 1.03, Dt = 80 Myr M = 2.4, Dt = 26.7 Myr

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

29. V. Small-scale structure (Gazol, VS & Kim, in prep.) • Ongoing analysis of small-scale structures in high-resolution simulations of atomic ISM turbulence. • 20482 simulation of randomly-driven turbulence at Mrms~1 in WNM (see also P. Hennebelle’s talk)

30. Density field. Lbox = 100 pc resol. = 20482 Dx = 0.05 pc Large-scale driving.

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 > 104 K cm-3, occasionally to n ~ 3000 cm-3, P ~ 3x104 K cm-3. (cooling function implies a transition to ~ isothermal regime at 10 K at n > 2000 cm-3.) ~

32. VI. Summary • 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. • r, Pth and Pmag 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 . • Pth for intermediate-density gas fluctuates because of competition between approach to thermal equilibrium and turbulent crossing time. • Pmag fluctuates because different trends for different MHD waves. • Overdense, overpressured cloudlets are created by transient ram-pressure compressions.

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 > 104 K cm-3). • Sufficient to account for observed frequency of TSAS?

34. The End