= Mean ionizing photon energy of a power-law spectrum
{title2=$\langle E\rangle=\frac{s}{s-1}h\nu_0\quad(s>1)$}
For $L_\nu=A\nu^{-s}$ above an ionization threshold $\nu_0$, the energy luminosity is $A\nu_0^{1-s}/(s-1)$ and the photon rate is $A\nu_0^{-s}/(sh)$. Their ratio is the displayed emitted mean energy. For slope two it is twice the threshold energy. Absorption weighting, a high-energy cutoff and secondary ionizations can change the energy deposited per ionization; emitted and locally absorbed spectra must not be conflated.
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