Optically Thick Case Radiative Transfer Until now: But what if absorption occours? But what if it gets very thick? Then dIn = 0 Let us look at this more closely. Consider the particles doing the absorbing and emitting. Take two states upper, U, and lower, L. Separate them by EU - EL = hn Then Boltzman tells us: also, in equilibrium AUL = spontaneous emission InBUL = stimulated emission NLBLUIn = absorption combine let T --> infinity, therefore I --> infinity then So in general, in equilibrium Can be shown using box normalization and quantum mechanics that (in most circustances) Blackbody radiation erg cm-2 s-1 Hz-1 st Wien Law A*K Remember, sun: T=5000 lm=5000 lT = 25*106 Next look at low n end hn << kT Rayleigh-Jeans law Can’t measure T if Area unknown very inconvient if hn = kT region hidden   Finally -- total emission From a flat dA     Review Basic   Radiation from a charge   Cyclotron   Synchrotron   Bremsstrahlung   Compton Scattering   Blackbody   Sun is a star Star is a ball of gas with an energy source in the middle Chemical Energy Gravitational Energy   Nuclear 1MeV per particle instead of 2eV E = 5 * 105 * 4 * 1045 = 2 * 1051 ergs t = 15 * 109 years -- very close to correct! What is the theral timescale of the Sun? Thermal content at core 106K Takes 106 years to change significantly Lets make a star Ball of gas at mass M Collapses Gravitationally For a few thousand years chemical processes have an effect (very short time) Gravity holds it together Thermal Pressure holds it up Balance the two and you have a star P = nkT ideal gas law RT=1.5*1018 cm deg Chemical energy dissipates 1000 years Gravitational energy dissipates in 3*107 years Keeps contracting until nuclear burning sets in at T=15 million Equilibrium is achieved If R decreases then T increases If T increases L increases If L increases T increases more If T increases R increases Stable equilibrium is achieved