Bremsstrahlung Collisions between charged particles. How did the particles get there? Lets us look at an astrophysical gasin equilibrium. Since it is mostly H, take pure H. H is composed of e- & p+ à must come into equilibrium. Ionization Equilibrium Will they stick together of merely pass by? Will the H split up or not? Energy in building compared to energy in thermal velocity. Heat to T, let enough time pass so all particles collide. Then how many atoms N+ are ionized compared to how many No are neutral. Given by Sara’s equation: Where does this come from? From Boltymann Equation based on quantum mechanical definition of temperature – must be ttrue by definition Very general application What energy states are available in our simple 2 state system? 0 (unionized) (ionized) gB(v,T) à quantum mechanical function\ Saha Equation rue only in thermal equilibrium. Thrue if collisions up and down determine balance Interstellar gas is very thin. What if radiation dominates recombination? Saha equation is then inapplicable— Boltzmann does not hold Microprocesses Dominate Einstein coefficients domintae collision rate. Take Lya – 10-4 sec to recombine At v = 1.6 * 106 cm s-1 In 10-4 s, moves 160 cm If no collisions, then Saha does not hold In this room, n ~ 1021 cm-3     Ready for Bremsstrahlung Take pure H at T >> 104 K (totally ionized) Basic collisions: ep, ee, pp (ee and pp have no dipole compontent, weak emitters) Electron-proton interactions dominate put these together and assume imagine uniform beam then Ebdb = E * 2p b db But frequency distribution but where integrating: total power erg cm-3 c-1   density of electrons collision E emitted by collision at V at v fequency averaged over b density of ions (stationary)     need f(v)d3v and En(n) First, En(n) Emits at n if t ~1/w = 1/(2pn) sum all radiation at n from all b’s Second:                 Example Take a ball of gas volume = V Pure H => ne = np Temp = T P=1.4*10-27T1/2n2V E=nV 3/2 kT t = E/P = sec Flare – measure t –watch intensity Measure T --watch spectrum   Line Emission Put heavy elements back in X ~ Z2 à Heavy elements can be partially ionized in a gas. FeI, FeII … FeXVII at 107K After heavy elements stripped then pure bremsstrahlung holds as derived. But at intermediate T line emission can dominate When an electron collies with an ion the ound electronscan get bumped into a higher state. Will then radiatively decay. This is efficient because electrons have just the right amount of energy to excite the ions. Line Emission dominates: at some T, pure bremsstrahlung <1% of emission Thus the small impurities dominate         Compton Scattering In this frame both particles merely reverse direction But this is not the case in the general fram of reference Electron has Photon has         initially: after: In a plasma repeated Compton scattering will blur features by 0.024 Å per scatter. Comptonize spectrum is smooth. Inverse Compton Effect Take relativistic electrons and send a beam of photons through If g = 104 n =108ni take an optical photon 5000 Å after scatter 5*10-5 Å = 2*108 eV Even microwave background T = 3° à T = 3*108K (x-rays) Power distribution of electrons à Power law spectrum