Reconstruction of the dark matter density profile from cosmic positron anomaly data

In this work we continue our investigations of the possibility of explanation of the positron anomaly (PA) in cosmic rays with the help of annihilating or decaying dark matter (DM) component by varying its space distribution. In the contrast of our previous studies, where we first assumed some specific spatial distribution of DM component and looked at how it agrees with data, here we solve, in some sense, the inverse problem: we search for distribution, in a mathematical way, which satisfies observational data. A unique algorithm has been implemented which, using linear algebra and adaptive grid methods, adjusts distribution to the data. It allows telling in principle whether or not is possible to solve PA problem by variation of spatial distribution of DM sources. A positive result has been formally obtained. A class of solutions can be identified. Though the distributions obtained at the chosen injection spectra may seem slightly realistic, nonetheless it demonstrates a quite powerful possibility in explaining PA that could be realized in more realistic models.