Bb: blackbody model¶
The surface energy flux of a blackbody emitter is given by
\[F_\nu = \pi B_\nu = \frac{2\pi h\nu^3/c^2}{e^{h\nu/kT}-1}\]
(Chapter 1 of Rybicki & Lightman 1986). We transform this into a spectrum with energy units (conversion from Hz to keV) and obtain for the total photon flux:
\[S(E){\mathrm d}E = 2\pi c [10^3e/hc]^3 \frac{E^2}{e^{E/T}-1} {\mathrm d}E\]
where now \(E\) is the photon energy in keV, \(T\) the temperature in keV and \(e\) is the elementary charge in Coulomb. Inserting numerical values and multiplying by the emitting area \(A\), we get
\[N(E) = 9.883280\times 10^{7}\, E^2A/(e^{E/T}-1)\]
where N(E) is the photon spectrum in units of \(10^{44}\) photons/s/keV and \(A\) the emitting area in \(10^{16}\) \(\mathrm{m}^2\).
The parameters of the model are:
norm : Normalisation \(A\) (the emitting area, in units of
\(10^{16}\) \(\mathrm{m}^2\). Default value: 1.t : The temperature \(T\) in keV. Default value: 1 keV.Recommended citation: Kirchhoff (1860).