the component of the magnetic field perpendicular to the line-of-sight. The pulsars do not contribute significantly to the Haslam map. There must be a different source of $e^+e^-$ with energies at or below GeV that contribute dominantly to the Haslam map. Thus, for an assumed magnetic field spatial distribution, the Haslam maps determine the spatial distribution of these lower energy electrons. It is clear from the Haslam maps that these lower energy electrons must be distributed more diffusely than the pulsar distribution assumed here. More detailed work on this subject would require a computation of the secondary positrons along with primary $e^+e^-$ produced by supernova remnants, away from the galactic disk. The secondary positrons, which are sub-dominant at multi-GeV energies in the solar neighborhood, will contribute significantly at $\sim {\rm GeV}$ and lower energies because of their steeper spectrum [@Strong:2004de] and there are large uncertainties in these calculations [@Delahaye:2008ua].

Our assumptions about energy losses differ from earlier work exploring constraints with the haze [@Hooper:2008zg]. We do not assume a spatially constant ratio of energy density of starlight to the magnetic field energy density to fit the haze data (as discussed also in Ref. [@Grajek:2008jb]); we parametrize our ignorance of the 