Yuki Takeuchi
Reading assignment 1
Ch1.1
The spectrum correspond to waves which have various wavelength and frequency. λν=c Temperature and energy E=hν T=E/k
ch1.2
Flux = the measure of energy of all rays passing through a given area dAdt. Flux from isotropic source = assuming there are two spherical sources S and S' with radii r and r'. by conservation of energy, energy passing both elements are the same; F(r)*4πr^2 = F(r')*4πr'^2. => F= const/r^2 if S' is fixed.
ch1.3
radiation is the energy carried by individual rays, but we need to consider the energy carried by sets of rays rather than individual ray because single ray essentially does not carry energy.
Specific Intensity = describes the rate of radiative transfer of energy at a specific point P.
Net Flux = integration of flux over solid angle with direction n. F = ∫IcosθdΩ
Momentum flux = momentum flux along ray at angle θ is dF/c. and integrate it over solid angle.
Specific Energy Density = the energy per unit volume per unit frequency range. Total radiation density = integrating specific density over all frequency. Radiation Pressure P = 1/3 u which is also useful for thermodynamics of blackbody radiation.
Ch1.4
Emission => dI = jds Spontaneous emission coefficient: dE = jdVdΩdt Monochromatic emission coefficient: dE = jdVdΩdtdν (where j_ν = 1/4pi P)
- spontaneous emission can be defined as emissivity ε.
So, spontaneous emission can be dE = ερdVdtdν(dΩ/4π) then, compare those dE to get j = ερ/4pi
Absorption => dI = -αIds derivation is similar to emission above
Radiative transfer equation can be obtained by combining emission and absorption. => (dI/ds)=-αI+j Case.1) Emission only α=0 Case.2) Absorption Only j = 0
Also, transfer equation can be simpler by introducing optical depth τ =>(dI/dτ)=-I+S where S = j/α
Ch1.5
Kirchhoffs law for Thermal emission S = B(T) j = αB(T) If S>B, then I>B. If S<B, then I<B. Transfer equation becomes (dI/dτ)=-I+B(T) for blackbody radiation I = B for Thermal radiation S = B
Blackbody radiation adiabatic laws TV^(1/3) - const. pV^(4/3) = const.
Planck spectrum Derivation requires two parts. 1)density of photon state 2)average energy per photon state Also, planck law has 5 different properties. 1)hν<<kT:Rayleigh-Jean law (applied at low frequency) 2)hν>>kT:Wien Law 3)Monotonicity with temperature (On blackbody curve, one with higher temp. lies entirely above the other. ) 4)Wien Displacement Law (peak frequency of blackbody law shifts linearly with temperature.) 5)Relation of Radiation Constants to Fundamental Constants In addition Characteristic Temp. is related to Planck constant. a)Brightness Temp.I = B(T)used in radio astronomy and where Rayleigh-Jeans law is applicable. b)Color Temp.(By fitting the data to a blackbody curve without regard to vertical scale, a color temp. is obtained.) c)Effective temp. (Obtained by integrate flux over all frequency.
Reading assignment 2
ch1.6
spontaneous emission (transition prob. A_21) = when particle drop from energy level 2 to 1, the particle emit photon. And this occurs even if radiation field does not exist.
absorption (transition prob. B_12J) = this occur when a particle absorb photon and excited to from level 1 to 2. probability for this even is prop. to the density of photon, and the function is normalizeable.
A and B are both Einstein coefficient.
stimulated emission (transition prob. = B_21J) = when particle in level 2 is stimulated by other particle such as photon, the particle emit photon and drop from level 2 to 1.
Relation b/w Einstein coefficient by introducing n1, n2, and ,n3 being number density of atoms in level 1 and 2, the einstein coefficients are combined in one equation as in page 29 eq 1.69. Since J = B in thermodynamic equilibrium, the final relation of Einstein relation become g_1B_12 = g_2B_21 and A_21 = 2hv^3 / c^2 B_21 as eq 1.72 this einstein relation can include non-thermal emission in not TE.
LTE = this happen when the matter is in TE with itself.