4.1.4. 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).