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

TL;DR

This work treats the positron anomaly as an inverse problem and seeks the DM-source spatial distribution that best explains AMS-02 and Fermi-LAT data without violating gamma-ray constraints. It introduces a linear-algebra framework that partitions the Galaxy into regions, computes region-specific spectra, and solves a nonnegative least-squares problem to recover region coefficients, yielding a DM density $ ho(x,y,z)=\sum_i \sqrt{k_i}\,\rho_i(x,y,z)$. By employing an adaptive grid and an exclusion-based procedure to explore near-optimal solutions under a constrained objective $ abla^2$, the authors demonstrate a formal positive result and identify a class of density profiles that can explain PA within realistic bounds. The approach provides a data-driven pathway to constrain DM distributions and informs more physically realistic models, with potential implications for interpreting PA while maintaining gamma-ray compatibility.

Abstract

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.

Figures (10)

• Figure 1: Calculation procedure scheme. On the left, green colour conditionally denotes partitioned areas of unit density, as well as their corresponding spectra in the centre. On the right, orange colour corresponds to the final sum of these spectra compared to experimental data.
• Figure 2: Positron fluxes \ref{['subfig:xy_e_e']}, \ref{['subfig:xy_mu_e']} and $\gamma$-radiation \ref{['subfig:xy_e_g']}, \ref{['subfig:xy_mu_g']} for all possible values of parameters $\alpha_i$ compared to AMS-02 and Fermi-LAT data, respectively. Cases of annihilation via $e^{+}e^{-}$ channel \ref{['subfig:xy_e_e']}, \ref{['subfig:xy_e_g']} and via $\mu^{+}\mu^{-}$ channel \ref{['subfig:xy_mu_e']}, \ref{['subfig:xy_mu_g']}. $\Delta \chi^{2}$ is 10% of $\chi^{2}_{min} = 2.5$ for the $e^+e^-$channel and $\chi^{2}_{min} = 1.3$ for the $\mu^+\mu^-$ channel. Black lines show used background.
• Figure 3: Upper bound on the source density obtained by choosing the parameter $\Delta \chi^{2}$ equal to 10% of $\chi^{2}_{min}$. Cases of annihilation via $e^+e^-$\ref{['subfig:xy_e_up']} and $\mu^+\mu^-$\ref{['subfig:xy_mu_up']} channels.
• Figure 4: The density profile obtained by imposing the condition of the minimum of the highest density. Cases of annihilation via $e^+e^-$\ref{['subfig:xy_e']} and $\mu^+\mu^-$\ref{['subfig:xy_mu']} channels.
• Figure 5: Set of positron fluxes \ref{['subfig:rz_e_e']}, \ref{['subfig:rz_mu_e']} and $\gamma$-radiation \ref{['subfig:rz_e_g']}, \ref{['subfig:rz_mu_g']} for all possible values of parameters $\alpha_i$ compared to AMS-02 PhysRevLett.110.141102PhysRevLett.113.121101AGUILAR20211 and Fermi-LAT Ackermann:2014usa data, respectively. Cases of annihilation via $e^{+}e^{-}$ channel \ref{['subfig:rz_e_e']}, \ref{['subfig:rz_e_g']} and via $\mu^{+}\mu^{-}$ channel \ref{['subfig:rz_mu_e']}, \ref{['subfig:rz_mu_g']}. $\Delta \chi^{2}$ is 10% of $\chi^{2}_{min} = 3.3$ for the $e^+e^-$channel and $\chi^{2}_{min} = 3.0$ for the $\mu^+\mu^-$ channel. Black lines show the background used.