Specific intensity
Definition: Radiative energy transported per projected area, time, solid angle, and frequency.
Why it matters here: It helps answer Which quantities must be specified to solve the transfer equation along a ray? within the numerical model described here.
Relationships: Connect it to Optical depth, the governing expression \(\frac{dI_\nu}{d\tau_\nu}=S_\nu-I_\nu,\quad I(\tau)=I_0e^{-\tau}+S(1-e^{-\tau})\), and the computed diagnostic developed later in the lecture.
Boundary or common confusion: The grey constant-source slab is an approximation. Frequency coupling, scattering source functions, geometry, and non-LTE populations can change the equation being solved.
Optical depth
Definition: A dimensionless path integral of opacity that measures attenuation strength.
Why it matters here: It helps answer Which quantities must be specified to solve the transfer equation along a ray? within the numerical model described here.
Relationships: Connect it to Source function, the governing expression \(\frac{dI_\nu}{d\tau_\nu}=S_\nu-I_\nu,\quad I(\tau)=I_0e^{-\tau}+S(1-e^{-\tau})\), and the computed diagnostic developed later in the lecture.
Boundary or common confusion: The grey constant-source slab is an approximation. Frequency coupling, scattering source functions, geometry, and non-LTE populations can change the equation being solved.
Source function
Definition: The ratio of emissivity to opacity, setting the intensity approached in an optically thick medium.
Why it matters here: It helps answer Which quantities must be specified to solve the transfer equation along a ray? within the numerical model described here.
Relationships: Connect it to Formal solution, the governing expression \(\frac{dI_\nu}{d\tau_\nu}=S_\nu-I_\nu,\quad I(\tau)=I_0e^{-\tau}+S(1-e^{-\tau})\), and the computed diagnostic developed later in the lecture.
Boundary or common confusion: The grey constant-source slab is an approximation. Frequency coupling, scattering source functions, geometry, and non-LTE populations can change the equation being solved.
Formal solution
Definition: The analytic integral solution of the transfer equation for specified source function and boundary intensity.
Why it matters here: It helps answer Which quantities must be specified to solve the transfer equation along a ray? within the numerical model described here.
Relationships: Connect it to Boundary intensity, the governing expression \(\frac{dI_\nu}{d\tau_\nu}=S_\nu-I_\nu,\quad I(\tau)=I_0e^{-\tau}+S(1-e^{-\tau})\), and the computed diagnostic developed later in the lecture.
Boundary or common confusion: The grey constant-source slab is an approximation. Frequency coupling, scattering source functions, geometry, and non-LTE populations can change the equation being solved.
Boundary intensity
Definition: Radiation entering the modeled ray at the starting surface.
Why it matters here: It helps answer Which quantities must be specified to solve the transfer equation along a ray? within the numerical model described here.
Relationships: Connect it to Specific intensity, the governing expression \(\frac{dI_\nu}{d\tau_\nu}=S_\nu-I_\nu,\quad I(\tau)=I_0e^{-\tau}+S(1-e^{-\tau})\), and the computed diagnostic developed later in the lecture.
Boundary or common confusion: The grey constant-source slab is an approximation. Frequency coupling, scattering source functions, geometry, and non-LTE populations can change the equation being solved.