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Heating and Cooling

Heating and Cooling

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Heating and Cooling

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

  2. 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 Transparent ISM Mechanisms

  3. Cosmic Rays • H ionization produces primary electrons with <E> ~ 35 eV. Counting secondaries, <Ee>=3.4 eV. • Field, Goldsmith, Habing took ζCR = 4  10-16 s-1 • Observations now suggest ζCR = 2  10-17 s-1 • ionization-sensitive molecules (HD, OH, H3+) • short path-lengths of low energy CRs

  4. Photoionization Heating

  5. X-ray Ionization Heating • Transfers energy from 106 K gas to gas with T << 104 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 < 103): excitation of molecular rotational and vibrational lines and atomic fine structure lines

  10. Diffuse ISM Cooling Curve ~ T-0.7 Bremsstrahl. ~ T1/2 Gaetz & Salpeter 1983

  11. Heating interiors cosmic rays grain heating by visible & IR edges (PDRs) grain & PAH UV photoelectric H2 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 Opaque ISM Mechanisms

  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, H2, H2O, and O most important • detailed models of chemistry required to determine full cooling function

  13. Neufeld, Lepp, & Melnick 1995

  14. Homonuclear species like H2 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 heating cooling

  17. Balbus 1986 Thermal Instability

  18. If tcool increases as T increases, then system is unstable

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

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

  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 vf2 = cs2 + vA2

  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