Dynamics of Multi-Phase Interstellar Medium Shu-ichiro Inutsuka (Kyoto Univ.) Collaboration with Hiroshi Koyama (Univ. Maryland) Tsuyoshi Inoue (Kyoto Univ.) Patrick Hennebelle (Paris Obs.) Masahiro Nagashima (Nagasaki Univ.) Keywords: radiative cooling/heating, thermal instability, MHD, supersonic velocity dispersion, etc.

Observed “Turbulence” in ISM Observation of Molecular Clouds line-width  v > C S Universal Supersonic Velocity Dispersion even in the clouds without star formation activity ⇒ should not due to star formation activity Numerical Simulation of (Isothermal) MHD Turbulence  Rapid Shock Dissipation or Cascade –Dissipation time « Lifetime of Molecular Clouds Gammie & Ostriker 1996, Mac Low 1997, Ostriker et al. 1999, Stone et al. 1999, etc… Recent Study on Origin of Supersonic Motion –Koyama & Inutsuka, ApJ 532, 980, 2000; ApJL 564, L97, 2002 –Kritsuk & Norman 2002a, ApJ 569, L127; 2002b ApJ 580, L51 –Audit & Hennebelle 2005, A&A 433, 1 –Heitsch, Burkert, Hartmann et al. 2005, ApJ 633, L113, Vazquez-Semadeni et al. 2006, etc...

Radiative Equilibrium WNM CNM Solid: N H =10 19 cm -2, Dashed: cm -2

Radiative Cooling & Heating Solid: Cooling, Dashed: Heating Koyama & Inutsuka (2000) ApJ 532, 980, based on Wolfire et al grains

Basic Equations radiative heating/cooling thermal conduction

Numerical Scheme 2D Eulerian Grid Scheme Second-Order Godunov Method –Exact Riemann Solver for “ P gas + P mag ” (Sano & Inutsuka 1999) –MoC-CT for Magnetic Field (Stone & Norman 1992) Radiative heating/cooling ( Koyama & Inutsuka 2002 ) Thermal Conduction –Classical (Parker 1953) † and saturated conduction We adopt 900 times large K in order to resolve Field length. –q sat K ▽ T/(q sat + K| ▽ T|), q sat =c s P gas Ambipolar Diffusion –Strong coupling approximation –Collision of H + and C + Ionization Equilibrium – CR ionization and radiative recombination of H atom

1D Shock Propagation into WNM Density-Pressure Diagram Density-Temperature Diagram –through unstable region unstable Koyama & Inutsuka 2000, ApJ 532, 980

1D Shock Propagation into CNM Density-Pressure Diagram Density-Temperature Diagram CNM becomes thermally unstable with shock. Koyama & Inutsuka 2000, ApJ 532,980 See also Hennebelle & Perault 1999, 2000 unstable

WNM Swept- Up by MHD Shock (3D)

Warning to Numerical Simulation Requirement for Spatial Resolution “ Field Condition ” We should resolve the structure of transition layer: F unstable F dashed line: Field 1965

No convergence for x  F /3 Koyama & Inutsuka (2004) ApJ, 602, L25

Hot Medium P=35000K/cm 3 2D/3D Calculation Hydro Code: 2nd-Order Godunov method –Exact Riemann Solver for “ P gas + P mag ” (Sano & Inutsuka 1999) –MoC-CT for Magnetic Field (Stone & Norman 1992) Thermal Conduction, and Radiative Cooling/Heating Boundary Conditions Upper Region: WNM –small density perturbations  A |k| n cos( kx +  ) Lower Region: Hot Medium Pressure driven SNR Boundary Condition –x- & y-direction ： periodic –z-direction: Free WNM 24km/s

Shock Propagation into WNM Hot Medium Color: Density Koyama & Inutsuka, 2001 Ambient ISM WNM

Shock Propagation into WNM

Summary of TI-driven Turbulence 2D/3D Calculation of The Propagation of Shock Wave into WNM via Thermal Instability ⇒ fragmentation of the cold layer into cold clumps with long-sustained supersonic velocity dispersion ( ～ km/s) 1D: Shock ⇒ E th ⇒ E rad 2D&3D: Shock ⇒ E th ⇒ E rad + E kin  v ～ a few km/s ＜ C S,WNM

2D Evolution from Unstable Equilibrium With Cooling/Heating and Thermal Conduction Without Physical Viscosity  Pr = 0

Evaporation of Spherical CNM in WNM Smaller CNM cloud evaporates: R~0.01pc clouds evaporate in ~Myr condensation evaporation Analytic Formula Nagashima, Koyama, Inutsuka & 2005, MN 361, L25 Nagashima, Inutsuka, & Koyama 2006, ApJL 652, in press (astro-ph/ ) Evaporation Timescale Size of CNM cloud CNM WNM RcRc

Evaporation of Spherical CNM in WNM If the ambient pressure is larger, the critical size of the stable cloud is smaller. Nagashima, Inutsuka, & Koyama 2006, ApJL 652, in press Ambient Pressure Critical Radius

Instability of Transition Layer important in maintaining the “turbulence” Cold Medium Warm Medium Evaporation Front Thickness

Instability of Transition Layer Similar Mechanisms… 1) Darrieus-Landau (DL) Instability Flame-Front Instability # Important in SNe Ia # Effect of Magnetic Field See Dursi (astroph/ ) 2) Corrugation Instability in MHD Slow Shock – Edelman 1990 – Stone & Edelman 1995 unburnedburned Flame Front Thickness

Linear Analysis of New Instability Growth Rate (Myr -1 ) Cold Medium Warm Medium Evaporation Front T 2 WNM CNM T 1 11 22 Field length wavenumber k y /2  pc   step function approx. isobaric approx. unstable Inoue, Inutsuka, & Koyama 2006, ApJ 652, in press (astro-ph/ )

Non-Linear Development of TI without External Forcing Amplitude of Turbulent Velocity vs. Domain Length Turbulent Motions Driven by Thermal Instability Koyama & Inutsuka 2006, astro-ph/ Pr = 2/3 Pr = 0.05

Equilibrium with Various Column Density Column Density Inutsuka & Koyama 1999

Allowed Region of 2-Phase Medium 4.0 Inutsuka & Koyama 1999

How long does WNM survive inside Molecular Clouds? When column density is sufficiently large, N H > cm -2 or A v > 1 mag ambient radiation field does not provide sufficient radiative heating for WNM. WNM simply cools down.

Various Timescales Dynamical Timescale of ISM  10 6 yr Ionization Equilibrium…  n p   n e n p recombination coeff.    2.6· (10 4 K /T ) 0.7 cm 3 s -1 ionization due to Cosmic Rays:   1.8· s -1 ionization degree: x = n e /n WNM  (n WNM /1cm -3 ) -1/2 Recombination Timescale  rec  1Myr Cooling Rate   erg cm -3 s -1 Cooling Timescale? x e =0.1 x e =0.01

Cooling Timescale of WNM in Molecular Clouds: no heating case Hennebelle & Inutsuka 2006 ApJ 647, 404 WNM cannot survive without heating. cooling within 1Myr P = 10P ISM P = P ISM x e =0.01 Equilibrium ionization x e =0.1

Is there any heating to WNM inside Molecular Clouds? When column density is sufficiently large, N H > cm -2 or A v > 1 mag ambient radiation field does not provide sufficient radiative heating for WNM. Without any heating WNM simply cools down very quickly.

Is there any heating? Obs... Ubiquitous Supersonic Motion Theory...Rapid Dissipation of Supersonic Motions  Heating due to Dissipation What is the effect of dissipation of supersonic motions? How effective in gas heating?

Schematic Picture Hennebelle & Inutsuka 2006 ApJ 647, 404

Heating due to Dissipation of MHD Waves  B  B  E wave  B 2 /8  Assume B  G (n WNM / 1cm -3 ) 0.5 (e.g., Heiles & Troland) Damping Timescale: t damp = 2  i /(V A 2 k 2 )   (v rms /km s -1 ) 0.75 cm 3 g -1 s -1 Glassgold et al Heating Rate:  E wave /t damp   (1cm 3 /n WNM ) 0.5 (1pc/ ) 2 erg -1 s -1 & Cooling Rate:  WNM  erg cm -3 s -1

WNM in Molecular Clouds: Thermal Equilibrium with MHD Wave Heating Hennebelle & Inutsuka 2006 ApJ 647, 404 P MC =nT=10 4 (n/10 3 )(T/10K) Heating is sufficient for WNM to survive in MC. Interstellar Radiation Case MHD Wave Heating

Summary Shock waves in ISM create turbulent CNM embedded in WNM. In TI-driven turbulence in Multi-Phase ISM –Evaporation/Condensation of CNM clouds –New Instability in Evaporation Front Can WNM Survive in Molecular Clouds? –Possible: Dissipation of MHD Waves Future Work RHD calculation of the evolution of two phase medium… When self-gravity becomes important?

Radiative Equilibrium: Column Density Dependence Inutsuka & Koyama 2000 Cooling Timescale

Turbulence in Molecular Clouds Linewidth-Size Relation (Larson’s Law) cm -2. N H cm -2 L (pc) Heyer & Brunt 2004