Pulsars versus Dark Matter Interpretation of ATIC/PAMELA

TL;DR

The study analyzes the $e^{\pm}$ flux from pulsars and dark matter in light of ATIC, PAMELA, Fermi, and HESS data, using diffusion-loss propagation and a pulsar wind nebula framework to connect source spectra to Earth observations. It finds that a continuous pulsar distribution can reproduce low-to-mid energy data, while high-energy flux is sensitive to a few young nearby pulsars that could imprint bumps in the spectrum; smearing from spatial energy-loss variations can partially blur these features. Dark matter scenarios typically produce smoother spectra with a robust $n\approx2$ scaling at energies well below the DM mass, and simple DM models with TeV-scale masses and boost factors can mimic pulsar signals. Overall, distinguishing pulsars from DM is challenging with current data, though the presence or absence of high-energy spectral bumps and complementary gamma-ray observations may provide distinguishing evidence.

Abstract

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.

Figures (10)

• Figure 1: Time evolution of $e^+e^-$ flux on the Earth from a pulsar at a distance of 1 kpc with $\eta W_0 = 3\times 10^{49}\:$erg, an injection index $n = 1.6$, and an injection cutoff $M = 10$ TeV. The diffusion and energy losses are described in Sec. \ref{['sec:prop']}. We assume the delta-function approximation for the emission from the pulsar, $Q({\bf x}, E, t) = Q(E) \delta({\bf x})\delta(t)$. The flux from a young pulsar (the 3 kyr curve on the right) has an exponential suppression because the electrons have not had enough time to diffuse from the pulsar to the Earth. The cutoff moves to the left due to cooling of electrons and becomes sharper. After reaching a maximal value, the flux decreases since the electrons diffuse over a large volume.
• Figure 2: Electron and positron flux from a single pulsar together with a primary background $\sim E^{-3.3}$ and a secondary background $\sim E^{-3.6}$. The pulsar is at a distance of 0.3 kpc. It has $\eta W_0 = 2.2 \times 10^{49}$ erg, age of 200 kyr, and injection index and cutoff $n = 1.6$ and $M = 10$ TeV, respectively. The propagation parameters are described in Sec. \ref{['sec:prop']}. The cutoff $M \gg 1$ TeV results in a significant bump around 1 TeV which is consistent with the ATIC data. For a smaller injection cutoff $M \sim 1$ TeV, the flux from the pulsar takes the form of a power law with an exponential cutoff that can be used to fit the Fermi and PAMELA data (see, e.g., Malyshev:2009zh).
• Figure 3: The expected spectrum from the continuous flux distribution and that from pulsars in the ATNF catalog pulsar Manchester:2004bp. The latter is calculated using $\eta = 0.065$, $n = 1.5$, and a pulsar time scale $\tau = 1$ kyr for each pulsar. This last fact, in conjunction with its spin-down age and current spin-down luminosity, is used to calculate each pulsar's initial rotational energy through Eq. (\ref{['iniW0']}). We also use the value of the propagation parameters given in Sec. \ref{['sec:prop']}. Several hundred pulsars contribute below 300 GeV and the continuous distribution provides a good approximation for these energies. Above 300 GeV, there are only $\sim10$ contributing pulsars, and the observed flux in this energy range is strongly dependent on their individual properties. The reason for the significant discrepancy between these two curves above 2 TeV has to do with the actual local distribution of pulsars versus the averaged flux seen by many observers in the Galaxy, as discussed in Sec. \ref{['sec:stat_cut']}.
• Figure 4: The predicted flux from pulsars in the ATNF catalog calculated using the same procedure as in Fig. \ref{['4ATNFdistr']} but accounting for spatial variations of energy losses as described in Appendix \ref{['Smearing-app']}. The assumed backgrounds are the same as in Fig. \ref{['SinglePsr']}.
• Figure 5: Statistical cutoff as a function of the diffusion index and the birth rate of pulsars in the Galaxy. The cutoff in $e^+ e^-$ flux from pulsars is determined by the age of the youngest pulsar within the diffusion distance from the Earth. The average such cutoff is a universal quantity that depends on the properties of ISM (the energy losses and the diffusion coefficient) and on the pulsar birth rate, but it is insensitive to the properties of the injection spectrum from the pulsars. We assume $D_0 = 100\, \text{pc}^2 \text{kyr}^{-1}$ and $b_0 = 5\times 10^{-6} \text{GeV}^{-1} \text{kyr}^{-1}$.