

Optically Thick Case Radiative Transfer Until now: But what if absorption occours? But what if it gets very thick? Then dI_{n} = 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 E_{U}  E_{L} = hn Then Boltzman tells us: also, in equilibrium A_{UL} = spontaneous emission I_{n}B_{UL} = stimulated emission N_{L}B_{LU}I_{n }= 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 l_{m}=5000 lT = 25*10^{6} Next look at low n end hn << kT RayleighJeans 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 * 10^{5 }* 4 * 10^{45} = 2 * 10^{51} ergs t = 15 * 10^{9} years  very close to correct! What is the theral timescale of the Sun? Thermal content at core 10^{6}K Takes 10^{6 }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*10^{18 }cm deg Chemical energy dissipates 1000 years Gravitational energy dissipates in 3*10^{7} 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 