\epsilon(\nu,\gamma(E)) \frac{dn}{dE}(r(\ell),z(\ell)), 
\label{flux}$$ where $r(\ell) = |r_e-\ell \cos(\theta)|$ and $z=\ell \sin(\theta)$ if we restrict out attention to angles $\theta$ above and below the galactic center, the sun is positioned at $r = r_e = 8 {\rm kpc}$ and $z=0$, and $\ell_{\rm max}$ is set by the height of the diffusion zone. We now turn to presenting our results utilizing the formalism outlined above.

After propagation, we fit the haze using the flux from Eq. \[flux\] in the all WMAP bands. The overall normalization of the curve depends on both the magnetic field, $B_0$ in Eq. \[eq:B-field\], the average pulsar power $W_0$, and the average pulsar efficiency times pulsar production rate $f_e
\dot{N}_{100}$. The range for $\dot{N}_{100}$ is 1-3 per century, following the rate of core collapse of supernovae in our galaxy. [@Raffelt:2007nv]. We have taken $\dot{N}_{100} = 2.8$, following [@FaucherGiguere:2005ny]. In addition, owing to uncertainties in the subtraction, we also allow a constant background at all angles to be added in the fit.

The index $\alpha$ in Eq. \[eq:source\] and ${E_{\rm cut}}$ are important in fitting the frequency structure of the Haze observed by WMAP. The cutoff energy ${E_{\rm cut}}$ is required to be above a minimum value $\gtrsim 40$ 