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4.7: Other Integrals

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  • 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 \(\text{Pa}\).