 Blackbody ionizing photon function

ID: blackbody-ionizing-photon-function

Q (E_{0}) = 8 π^{2} R_{s}^{2} (k T_{s})^{3} F (E_{0} / k T_{s}) / (h^{3} c^{2})

photons per time above threshold

E_{0}

. Integrating specific intensity over the outward hemisphere gives flux

π B_{ν}

; dividing the resulting spectral luminosity by photon energy and substituting

x = h ν / k T_{s}

F (y) = \sum_{m \geq 1} e^{- m y} (y^{2} / m + 2 y / m^{2} + 2/ m^{3})

follows by integrating the geometric-series expansion termwise.

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