magnetic field in the center of the galaxy directly. This allows us to make more direct contact with studies aiming to fit cosmic ray and diffuse photon backgrounds.

We plot in Fig. \[fig:Rdep\] the electron flux spectrum at various positions with respect to the galactic center. The diffusion softens the spectrum considerably, implying a larger flux in the lower frequency bands of the WMAP haze. The question is then whether the spectrum remains sufficiently hard to explain the WMAP haze in the all frequency bands, from 22 to 93 GHz. We examine this next.

After propagation, at any given point in space, the flux in synchrotron radiation (in erg/s/Hz) in the presence of the magnetic field is computed according to the relation [@Ghisellini:1988] $$\epsilon(\nu,\gamma)=\frac{4 \pi \sqrt{3} e^2 \nu_B}{c} x^2 \left(K_{4/3}(x) K_{1/3}(x)- \frac{3}{5} x [K_{4/3}^2(x)-K_{1/3}^2(x)] \right)$$ with $x = \nu/(3\gamma^2 \nu_B)$, $\nu_B = eB/(2\pi m_e)$, and $\gamma(E)$ the electron’s boost.

The total flux (in kJy/sr) in a given frequency at a given angle from the galactic center is computed by folding the synchrotron power with the electron distribution at any given point. The flux is then obtained by integrating along the line of sight: $$\Phi(\nu) = \frac{1}{4\pi}\int_0^{\ell_{\rm max}} d\ell
\int_0^{\infty} dE\, 
