Above is the model I fit my data too in Xspec. Xspec is a piece of software where you can model spectra from observations with their set models. It handles things like absorption, reddening, etc. to produce spectral energy distributions. This is a blackbody spectrum with normalization proportional to the surface area.
kT is measured in keV.
norm = K = $R_{km}^2/D_{10}^2$, where $R_{km}$ is the source radius in km and $D_{10}$ is the distance to the source in units of 10 kpc.
I understand that in this form it is the energy flux. But I can't understand where this $1.0344\times10^{-3}$ comes from.
I know that $$B_{\nu}=\frac{2h\nu^{3}}{c^{2}}\frac{1}{\exp(\frac{h\nu}{kT})-1}.$$
I'm modelling radiation from a star for example, and therefore:
$$F=\int I\cos\theta \,\mathrm d\Omega = B_{\nu} \int_{0}^{2\pi}\,\mathrm d\phi\int_{0}^{\theta_{c}}\sin\theta \cos\theta \,\mathrm d\theta,$$
such that $\theta_{c}=\sin^{-1}R/r$, where $R$ is the radius of the star and $r$ is the distance to from the observer to the star.
This gives $$F=\pi B_{\nu}\left(\frac{R}{r}\right)^{2}$$
Therefore, my specific flux for a blackbody is:
$$F_{\nu}=\frac{2\pi h\nu^{3}}{c^{2}}\frac{1}{\exp(\frac{h\nu}{kT})-1}\frac{R^{2}}{r},$$ where $R$ is the radius of the star and $r$ is the distance to from the observer to the star.
Is my calculation of the specific flux wrong? Or am I just not seeing an obvious unit conversion somewhere in the first $A(E)$ equation.
Also, I think the $\mathrm dE$ is included in $A(E)$ here, so try to ignore that. I'm mostly confused where the $1.0344\times10^{-3}$ comes from.