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.
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 Saras 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?
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
Einstein coefficients domintae collision rate.
Take Lya 10-4 sec to recombine
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
erg cm-3 c-1
density of electrons collision E emitted by collision at V
at v fequency averaged over b
density of ions
need f(v)d3v and En(n)
Emits at n if t ~1/w = 1/(2pn)
sum all radiation at n from all bs
Take a ball of gas volume = V
Pure H => ne = np
Temp = T
E=nV 3/2 kT
t = E/P =
Flare measure t watch intensity
Measure T --watch spectrum
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
In this frame both particles merely reverse direction
But this is not the case in the general fram of reference
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
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