$$\require{cancel}$$

4.7: Other Integrals

Other integrals occurring in the theory of stellar atmospheres are (using the abbreviated notation)

$H = \frac{1}{4\pi} \int I \cos \theta d \omega = F/ (4\pi) \label{4.7.1}$

$= 0 \text{ if isotropic} \label{4.7.2}$

$K = \frac{1}{4\pi} \int I \cos^2 \theta d \omega = cP/(4\pi) \label{4.7.3}$

$= J/3 \text{ if isotropic}. \label{4.7.4}$

The SI units for $$F$$ are $$\text{W m}^{-2}$$. For $$I$$, $$J$$, $$H$$, $$K$$ they are $$\text{W m}^{−2} \ \text{sr}^{−1}$$. For $$P$$ they are $$\text{Pa}$$.