8 The Interstellar Medium EmissionLine Nebulae H II

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

<n> ~1 cm-3 in spiral arms n. He/n. H~0. 1 (n. O + n. C + n. Ne)/n. H ~ 3 x 10 -4 “Face-on”? (M 51)

GAS Clouds Nebulae GMCs Diffuse Nebulae M R n T Heating Cooling 104 -107 M 20 -80 pc ~10 pc 200 -106 cm-3 ~10 K CRs, Xrays H 2, CO, Dust 102 -104 M 0. 1 -1 M ≤ 0. 1 pc ~102 cm-3 103 -104 cm-3 ~8000 K 10, 000 -15, 000 K Hot Young Stars Hot Old Stars Mostly O+2, O+1, N+1 Intercloud Medium “Warm” “Hot” T n Heating Cooling ~70 K ~0. 3 -20 cm-3 CRs, Xrays, UV C+, Fe+, CO, Dust Also Novae & Supernovae ejecta Planetary 5 x 105 K ~0. 03 cm-3 shocks, Xrays, hard UV Ions, Bremsstrahlung

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.

Ionization and Excitation in TE 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 gi, the relative populations of i with respect to the ground i=0 is: 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 >> x thermal equilibrium b. times >> t statistical equilibrium c. distances >> x no equilibrium d. none of the above no 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~104: xm=2 x 1010 cm tm=400 s versus sizes ~ 3 x 1018 cm ages ~ 3 x 1013 s So: electron-ion (and electron-electron) interactions: • mechanical equilibrium • maxwellian velocity distribution

Matter-Radiation Radiative lifetimes of atoms < 10 sec, and usually < 10 -8 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

Luminosity The 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 Sν 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 Rate In Steady State

Ionized Gas Clouds Ionization cross sections of H 0, He 0 and He+ from Osterbrock’s AGN 2 13. 6 e. V 24. 6 e. V 54. 4 e. V

(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*~4 x 104 K and nneb~10 cm-3, Now, or so For nearly pure H,

DEFINE then, H is almost totally ionized!

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, αB 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 Aul~108 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, tcollisions~102 -103 sec, so tcoll <<<< trec, allowing the particles in the gas to maintain a maxwellian velocity distribution.

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