8 -The Interstellar Medium

Emission-Line Nebulae H II Regions Planetary Nebulae Supernova Remnants

Reflection Nebulae

Dark Clouds Giant Molecular Clouds Bok Globules Diffuse Clouds

~1 cm -3 in spiral arms n He /n H ~0.1 (n O + n C + n N + n Ne )/n H ~ 3x10 -4 “Face-on”? (M 51)

GAS CloudsGMCsDiffuse NebulaePlanetary Nebulae M M  M  M  R20-80 pc~10 pc≤ 0.1 pc n cm -3 ~10 2 cm cm -3 T~10 K~8000 K10,000-15,000 K HeatingCRs, XraysHot Young StarsHot Old Stars CoolingH 2, CO, Dust Mostly O +2, O +1, N +1 Intercloud Medium “ Warm ”“ Hot ” T~70 K5x10 5 K n~ cm -3 ~0.03 cm -3 Heating CRs, Xrays, UVshocks, Xrays, hard UV Cooling C +, Fe +, CO, DustIons, Bremsstrahlung Also Novae & Supernovae ejecta

DUST Solid Grains C, Si, O, + …? T≤ 1200 K Absorb & Scatter starlight Polarization Transmission & Scattering Thermal Emission

Equilibrium States Thermal Equilibrium Detailed balancing for interacting systems Atomic States Atomic Energy Levels energy E 1 E 2 = energy E 2 E 1 Matter particles only “ mechanical equilibrium ” Matter + Radiation “ thermodynamic equilibrium ” – “ TE ” In TE, all distributions are homogeneous and isotropic, and can be characterized by a single given temperature T.

For atoms in ionization state j (j=0 for neutrals), having an ionization energy, and excitation state i, with an excitation energy relative to the ground level, and a statistical weight for occupation g i, the relative populations of i with respect to the ground i=0 is: Ionization and Excitation in TE And the relative populations of two adjacent ionization states is:

Statistical Equilibrium Energy In = Energy Out of a particular state This is a less stringent condition than TE. The type of equilibrium that exists will depend on the way that the particles in the system interact. If the mean free path and mean free time between collisions are x and t, If the temperature is constant over:we have: a. times >> t, distances >> xthermal equilibrium b. times >> tstatistical equilibrium c. distances >> xno equilibrium d. none of the aboveno equilibrium If both matter and radiation are in thermal equilibrium (including with one another), we have TE. Sometimes, the conditions are not in “ perfect TE ” everywhere in the system. Nevertheless, if it is sufficiently close enough not to affect the processes sufficiently at a particular location, that location is said to be in Local Thermodynamic Equilibrium – LTE.

Interactions Particle-Particle Photon-Particle Example – H II Region electron-ion collisions Typical n and T: n~10 and T~10 4 : x m =2x10 10 cmversus sizes ~ 3x10 18 cm t m =400 s versus ages ~ 3x10 13 s So: electron-ion (and electron-electron) interactions: mechanical equilibrium maxwellian velocity distribution

Matter-Radiation Radiative lifetimes of atoms < 10 sec, and usually < sec, much shorter than matter-matter collisions usually do not have detailed balancing. Upward collisional transition is followed by downward radiative transition. Radiation Field: VERY ANISOTROPIC! “Dilution Factor”: T~T * inside Ω T<T * outside Ω The photon field is not in thermal equilibrium, and Thermodynamic Equilibrium is not present. Cannot use Boltzmann & Saha equations to determine the excitation & ionization states!

GAS RADIATION PHYSICS Radiation Transfer - Basics Using conservation of energy and assuming a plane-parallel geometry (good for most situations): Specific Intensity Mean Intensity Flux

LuminosityThe net energy emitted (Watts or ergs/s) Flux of Radiation at a distance r from a star of luminosity L: Surface Area = 4πr 2 Note that this true for the surface of the star, It can also be shown that: In general, a location in the nebula will be illuminated by both the star and the rest of the nebula, so:

BASIC EQUATION OF TRANSFER OF RADIATION If we know what S ν is we can solve the equation of transfer.

For no incident radiation,

Ionization Rate For ionizations due to photons from all directions and frequencies: For an atom of number density n A cm -3 Recombination RateIn Steady State

Ionization cross sections of H 0, He 0 and He + from Osterbrock’s AGN eV 24.6 eV 54.4 eV Ionized Gas Clouds

(from here, borrowing many tables & figures from Osterbrock’s AGN 2 book)

EXAMPLE – Inside a Typical H II Region Here, Near a “ typical ” hot ionizing star, T * ~4x10 4 K and n neb ~10 cm -3, Now,so orFor nearly pure H,

DEFINE H is almost totally ionized! then,

Of course, a star cannot ionize an infinite volume. As the ionizing photons are consumed with distance from the star, H 0 will build up. Eventually, photons will only penetrate ~ 1 mean free path before being absorbed. Approximate idealized H II region – “ Strömgren* Sphere ” * (after Bengt Strömgren)

How big can this nebula be? If we equate the rate of ionizing photons produced by the star to the recombination rate in the nebula (assuming steady state), we get For hydrogen, α B would include only recombinations to the n=2 quantum level and higher. Recombinations to n=1 will produce a photon which will ionize some neutral H atom elsewhere, so cannot be counted in the net recombination rate. In a typical nebula, a typical recombination rate is:

After that, the radiative rate downward by deexcitation cascades goes as A ul ~10 8 s -1. So once recombination occurs, almost all H 0 is in the ground (n=1) electronic state. In a more realistic nebula, H + and He + regions will exist, and may not have their outer radii coincide.

Similarly, the metal ions may have numerous ionization zones.

If the recombination rate per unit volume is then the recombination time per ion is On the other hand, t collisions ~ sec, so t coll <<<< t rec, allowing the particles in the gas to maintain a maxwellian velocity distribution.

Other Processes Dielectric Recombination Capture of e - excites a second e - 2 EXCITED ELECTRONS This dominates the C ++ + e - C + reaction. Charge-Exchange Reaction Inside an H II region, At the edge of an H II region,