1. Heating and Cooling 10 March 2003 Astronomy G9001 - Spring 2003 Prof. Mordecai-Mark Mac Low

2. Transparent ISM Mechanisms Heating –cosmic rays –photoionization UV soft X-rays –grain photoelectric heating –shock heating Cooling –molecular rotation, vibration –atomic fine structure, metastable –resonance lines –bremsstrahlung –recombination –dust emission Wolfire et al. 1995, Spitzer PPISM

3. Cosmic Rays H ionization produces primary electrons with ~ 35 eV. Counting secondaries, =3.4 eV. Field, Goldsmith, Habing took ζ CR = 4  10 -16 s -1 Observations now suggest ζ CR = 2  10 -17 s -1 –ionization-sensitive molecules (HD, OH, H 3 + ) –short path-lengths of low energy CRs

4. Photoionization Heating

5. X-ray Ionization Heating Transfers energy from 10 6 K gas to gas with T << 10 4 K, with a small contribution from extragalactic sources To calculate local contribution, must take absorption into account Can maintain high electron densities even if heating rate is low. heat from each primary e - absorption of X-rays

6. Grain Photoelectric Heating Small grains (PAHs, a < 15Å) can be efficiently photoionized by FUV (Bakes & Thielens 1994). –10% of flux absorption –50% of photoelectron production

7. Efficiency of Grain Heating grains neutral grains charged

8. Shock Heating Extremely inhomogeneous Produces high-pressure regions that interact with surroundings Traditionally, included in equilibrium thermodynamical descriptions anyway

9. Cooling Radiative cooling requires available energy levels for collisional excitation Cold gas (10 < T < 10 3 ): excitation of molecular rotational and vibrational lines and atomic fine structure lines

10. Gaetz & Salpeter 1983 Bremsstrahl. ~ T 1/2 ~ T -0.7 Diffuse ISM Cooling Curve

11. Opaque ISM Mechanisms Heating –interiors cosmic rays grain heating by visible & IR –edges (PDRs) grain & PAH UV photoelectric H 2 pumping by FUV Cooling –gas molecular rotation, vibration atomic fine structure, metastable radiative transfer determines escape of energy from gas –grains grain emission in FIR gas-grain coupling Hollenbach & Tielens 1999, Neufeld et al 1995

12. Cooling in Opaque gas Emission from an optically thick line reaches the blackbody value: velocity gradients allow escape of radiation through line wings many molecular and atomic lines can contribute in some regimes, but CO, H 2, H 2 O, and O most important detailed models of chemistry required to determine full cooling function

13. Neufeld, Lepp, & Melnick 1995

14. Homonuclear species like H 2 do not have low-lying energy levels Rarer polar species contribute most to cooling in 10 K gas Fine structure lines most important at surfaces of PDRs

15. Isothermal Equation of State For densities 10 -19 < ρ < 10 -13 cm -3, cooling is very efficient down to about 10 K Gas remains isothermal in this regime, ultimately due to cooling of dust grains by IR emission. Compressibility is high: P ~ ρ When even dust becomes optically thick, gas becomes adiabatic, subject to compressional heating, such as during protostellar collapse.

16. Energy Equation heatingcooling

17. Thermal Instability Balbus 1986

18. If t cool increases as T increases, then system is unstable

19. (Isobaric) Thermal Instability Perturb temperature of points along the thermal equilibrium curve Stable if they return to equilibrium Unstable if they depart from equilibrium

20. Two-Phase Models Wolfire et al 1995 log ρ (cm -3 )

21. Three-Phase Model Attempt to extend FGH two-phase model to include presence of hot gas (McKee & Ostriker 1977) Hot gas not technically stable (no continuous heating, only intermittent), but has long cooling timescale (determined by evaporation off of clouds in MO77 Pressure fixed by action of local SNR Temperature of cold phases fixed by points of stability on phase diagram as in two- phase model

22. Turbulent Flow Equilibrium models only appropriate for quasi-static situations If compressions and rarefactions occur on the cooling timescale, then gas will lie far from equilibrium Conversely, rapid cooling or heating can generate turbulent flows (Kritsuk & Norman)

23. MHD Courant Condition Similarly, the time step must include the fastest signal speed in the problem: either the flow velocity v or the fast magnetosonic speed v f 2 = c s 2 + v A 2

24. Lorentz Forces Update pressure term during source step Tension term drives Alfvén waves –Must be updated at same time as induction equation to ensure correct propagation speeds –operator splitting of two terms

25. Added Routines Stone & Norman 1992b