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Enrique Vázquez-SemadeniAdriana Gazol

CRyA UNAM, México

Collaborators:Thierry Passot (OCA)Jongsoo Kim (KASI)Dongsu Ryu (Chungnam U.)Ricardo González (CRyA UNAM)

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Contents1. 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

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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.

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– 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 (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.

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• 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?

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II. TURBULENCE IN THERMALLY BISTABLE MEDIA

1.Effects of net cooling (heating + cooling ):

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 ~ 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

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log n (cm-3)

adiabatic (fast)isobaric

TE (slow)

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~0.7~ -0.7

~0

~0.7

Pinstab

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.

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

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Effect of the driving scale for, M=1 (w.r.t. diffuse gas @

7000K)

for50pc

for6.25pc

for12.5pc

for25pc

As for decreases, cros decreases, eff approaches of the gas.

Simulations in 100-pc boxes, 5122 resolution, random Fourier driving

2D histograms in P- spaceSlope = eff

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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

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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

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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)

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... and also large pressure fluctuations:

de Avillez & Breitschwerdt 2004

Numerical simulations with SN driving, no B

N(P) ~ P-5/2

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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 Mrms.

Isothermal case: lognormal(molecular clouds)

General polytropic case: power law tails (~atomic ISM)

Passot & Vázquez-Semadeni 1998

= 0.3

= 1.7

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– Apparently similar behavior for pressure PDF:

for = 50 pc for = 6.25 pc

M = 0.5M = 1M = 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

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Comparison with observations should constrain eff

Jenkins 2004

Observations of CI pressure PDF

• Also column density PDF? (VS & García 2001)

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III. B-, P correlationsNumerical 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)

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• de Avillez & Breitschwerdt (2004) (multi-temperature)

• Similarly for observations of B in atomic ISM (e.g., Crutcher et al. 2003; Heiles & Troland 2005)

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• 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 ~ 2 Fast wave

B2 ~ c1 – c2 Slow wave

B2 ~ 1/2—2 Alfvén wave

Fast mode domination Slow mode domination

log

log

B2 log

B2

log

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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.

B2 not characterized by a single response to compressions; randomizes the behavior of the restoring force.

Alfvén mode, low Ma Alfvén mode, high Ma

1/2

2

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• 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).

104 K < T6100 < T < 104 K310 < T < 6100 K140 < T < 140 K45 < T < 140 KT < 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 temperature Sorted by density

Gazol, Luis & Kim 2006

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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 = v1/cWNM (control parameter)

n, T, P, -v1n, T, P, v1Physical setup: (see also Hennebelle & Pérault 1999; Koyama & Inutsuka 2000, 2002; Audit & Hennebelle 2005; Heitsch et al. 2005)

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• 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.

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• 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.

Simulation with L = 64 pc, M = 1.03, resol. = 4000

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• 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.

-v

v0

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• 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.

M = 1.03, t = 80 Myr M = 2.4, t = 26.7 Myr

P

64

pc

16

pc

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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

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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)

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Density field.

Lbox = 100 pc

resol. = 20482

x = 0.05 pc

Large-scale driving.

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– 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.)

~

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• 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.

• , 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.

VI. Summary

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• 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?

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The End