The gradient of diffuse gamma-ray emission in the Galaxy

We show that the well-known discrepancy, known for about two decades, between the radial dependence of the Galactic cosmic ray nucleon distribution, as inferred most recently from EGRET observations of diuse -rays above 100 MeV, and of the most likely cosmic ray source distribution (supernova remnants, superbubbles, pulsars) can be explained purely by propagation eects. Contrary to previous claims, we demonstrate that this is possible, if the dynamical coupling between the escaping cosmic rays and the thermal plasma is taken into account, and thus a self-consistent calculation of a Galactic Wind is carried out. Given a dependence of the cosmic ray source distribution on Galactocentric radius r, our numerical wind solutions show that the cosmic ray outflow velocity, V (r;z )= u0 +VA0, also depends both on r, as well as on vertical distance z ,w ithu0 and VA0 denoting the thermal gas and the Alfv en velocities, respectively, at a reference level zC. The latter is by denition the transition boundary from diusion to advection dominated cosmic ray transport and is therefore also a function of r. In fact, the cosmic ray escape time averaged over particle energies decreases with increasing cosmic ray source strength. Thus an increase in cosmic ray source strength is counteracted by a reduced average cosmic ray residence time in the gas disk. This means that pronounced peaks in the radial distribution of the source strength result in mild radial -ray gradients at GeV energies, as it has been observed. The eect might be enhanced by anisotropic diusion, assuming dierent radial and vertical diusion coecients. In order to better understand the mechanism described, we have calculated analytic solutions of the stationary diusion-advection equation, including anisotropic diusion in an axisymmetric geometry, for a given cosmic ray source distribution and a realistic outflow velocity eld V (r;z), as inferred from the self-consistent numerical Galactic Wind simulations performed simultaneously. At TeV energies the -rays from the sources themselves are expected to dominate the observed \diuse" flux from the disk. Its observation should therefore allow an empirical test of the theory presented.