Pulsars versus Dark Matter Interpretation of ATIC/PAMELA

In this paper, we study the flux of electrons and positrons injected by pulsars and by annihilating or decaying dark matter in the context of recent ATIC, PAMELA, Fermi, and HESS data. We review the flux from a single pulsar and derive the flux from a distribution of pulsars. We point out that the particle acceleration in the pulsar magnetosphere is insufficient to explain the observed excess of electrons and positrons with energy E ~ 1 TeV and one has to take into account an additional acceleration of electrons at the termination shock between the pulsar and its wind nebula. We show that at energies less than a few hundred GeV, the flux from a continuous distribution of pulsars provides a good approximation to the expected flux from pulsars in the Australia Telescope National Facility (ATNF) catalog. At higher energies, we demonstrate that the electron/positron flux measured at the Earth will be dominated by a few young nearby pulsars, and therefore the spectrum would contain bumplike features. We argue that the presence of such features at high energies would strongly suggest a pulsar origin of the anomalous contribution to electron and positron fluxes. The absence of features either points to a dark matter origin or constrains pulsar models in such a way that the fluctuations are suppressed. Also we derive that the features can be partially smeared due to spatial variation of the energy losses during propagation.

💡 Research Summary

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This paper addresses the striking excess of high‑energy cosmic‑ray electrons and positrons reported by ATIC, PAMELA, Fermi‑LAT, and HESS, and evaluates two competing explanations: nearby pulsars and annihilating or decaying dark matter (DM). The authors begin by formulating the transport equation for relativistic electrons and positrons in the Milky Way, incorporating spatial diffusion with an energy‑dependent diffusion coefficient, and energy losses dominated by synchrotron radiation and inverse‑Compton scattering on the interstellar radiation field. They adopt standard Galactic propagation parameters (e.g., (D(E)=D_0 (E/1;{\rm GeV})^\delta) with (\delta\approx0.33)) and solve the Green’s‑function for a point source, which will later be used for both pulsar and DM contributions.

Pulsar Scenario
The authors distinguish two acceleration stages in a pulsar’s life. The first stage occurs within the magnetosphere, where the available potential drop can accelerate electrons up to a few hundred GeV at most. This is insufficient to account for the observed TeV‑scale excess, so a second stage—acceleration at the termination shock between the pulsar wind and its surrounding nebula—is introduced. Using shock‑physics arguments (compression ratio, shock speed, magnetic field amplification), they derive a power‑law injection spectrum (Q(E)\propto E^{-\gamma}) with (\gamma\simeq1.5!-!2.0) and a cutoff energy that can reach several TeV.

For energies below a few hundred GeV, the authors demonstrate that the cumulative contribution of the entire ATNF pulsar catalog can be approximated by a smooth, continuous distribution of sources. By weighting each catalog entry with its spin‑down power, age, and distance, they obtain a background that reproduces the measured spectrum’s gentle rise.

At higher energies, however, the propagation distance becomes limited by rapid energy losses, and only a handful of young, nearby pulsars (e.g., Geminga, Monogem, Vela) can contribute appreciably. The flux from each such source is given by the point‑source Green’s function multiplied by its individual injection spectrum and an exponential attenuation factor (\exp