The gradient of diffuseγ-ray emission in the Galaxy

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Abstract
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 diffuse γ-rays above 100 MeV, and of the most likely cosmic ray source distribution (supernova remnants, superbubbles, pulsars) can be explained purely by propagation effects. 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, , also depends both on r, as well as on vertical distance z, with u 0 and denoting the thermal gas and the Alfvén velocities, respectively, at a reference level z C. The latter is by definition the transition boundary from diffusion 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 γ-ray gradients at GeV energies, as it has been observed. The effect might be enhanced by anisotropic diffusion, assuming different radial and vertical diffusion coefficients. In order to better understand the mechanism described, we have calculated analytic solutions of the stationary diffusion-advection equation, including anisotropic diffusion in an axisymmetric geometry, for a given cosmic ray source distribution and a realistic outflow velocity field , as inferred from the self-consistent numerical Galactic Wind simulations performed simultaneously. At TeV energies the γ-rays from the sources themselves are expected to dominate the observed “diffuse” flux from the disk. Its observation should therefore allow an empirical test of the theory presented.
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