about the diffusion constant at the center of the galaxy. We will discuss the effect of changing the diffusion constant on the morphology of the haze later.

The synchrotron emission from the positrons along the line of sight receives contributions from a large number of pulsars. Since pulsars are being created on time scales of 100 years in the galaxy and this is much shorter than the diffusion time scale and the assumed $10^5$ yr time lag, we expect a steady state calculation to work well. In the limit that the diffusion equation can be solved in a steady state, the source function reduces to $$Q(\vec{x},E)= \rho(\vec{x}) Q(E),$$ with $Q(E)$ given by Eq. \[eq:source\] and $\rho(\vec{x})$ given by Eq. \[eq:rho\]. This gives us explicitly Q(E,) &=& 1.5 10\^[-26]{} ( ) ( ) ( )\^[2-]{}\
&& ((0.4)/(2-)) 100\^[-1.6]{} (E/[GeV]{})\^[-]{} e\^[-E/E\_[cut]{}]{}\
&& e\^[-r/()-|z|/() ]{} \^[-1]{} \^[-1]{} \^[-3]{}, for our fiducial $r_0$, $z_0$ and $r_{\rm disk}$ values.

We use GALPROP [@Strong:1998pw; @Moskalenko:1997gh] to compute the diffusion, and check the results with an ordinary partial differential equation solver. The diffusion coefficient is K(E) = K\_0 ( )\^, where we take $K_0 = 5 \times 10^{28}$ cm$^2$/s and the index $\delta = 0.33$ as our 