4.7: Other Integrals
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[ "article:topic", "authorname:tatumj" ]
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 \(\text{Pa}\).