\pi z_0 r_0^2 (1-e^{-r_{disk}/r_0}(1+r_{disk}/r_0))\,,\nonumber
\label{eq:pulsardist}\end{aligned}$$ where $r_{disk} = 15 \mbox{ kpc}$, $r_0 = 4 \mbox{ kpc}$ and $z_0 =
100 \mbox{ pc}$.

The distribution of pulsars close to the center is not well constrained – consequently the value of $r_0=4 \mbox{ kpc}$ that we use should be taken as a very rough estimate. We have chosen this value based on the dynamical models of the thin disk, which assign values for $r_0$ in the range of 2 to 4 kpc. We have adopted 4 kpc for our fiducial model and later explore the effect on the morphology of making $r_0$ smaller. In detail, we expect the pulsar distribution to track the galactic star formation rate in the disk (rather than the thin disk density), but the observational constraints on the star formation in the disk [@Boissier:1999ts] in the inner couple of kpc are weak. One may consider using the observed distribution of pulsars to reconstruct the true pulsar distribution in the galaxy after correcting for incompleteness. The distances to these pulsars are estimated through the dispersion measure, and this depends sensitively on the assumed distribution of electrons. The uncertainties inherent in this procedure makes it hard to pin down the 