Galactic secondary positron flux at the Earth

TL;DR

This work addresses the origin and propagation of Galactic secondary positrons to interpret the PAMELA positron fraction rise. It combines up-to-date spallation cross sections with a Green-function solution to the diffusion-energy-loss equation in a cylindrical halo, and it brackets uncertainties using MIN/MED/MAX propagation models while exploring energy losses and optional reacceleration or convection. The authors find that the secondary e+ flux can reproduce observations within about an order of magnitude, but the inferred presence and size of any excess depend sensitively on the assumed electron spectrum and propagation parameters. They show most secondaries originate locally (within a few kiloparsecs) due to energy losses, and that improvements in electron flux measurements are crucial to robustly identify any primary positron component. The results provide a robust astrophysical background for secondary e+ and set the stage for tighter constraints with AMS-02 data on cosmic-ray transport and potential new physics.

Abstract

Secondary positrons are produced by spallation of cosmic rays within the interstellar gas. Measurements have been typically expressed in terms of the positron fraction, which exhibits an increase above 10 GeV. Many scenarios have been proposed to explain this feature, among them some additional primary positrons originating from dark matter annihilation in the Galaxy. The PAMELA satellite has provided high quality data that has enabled high accuracy statistical analyses to be made, showing that the increase in the positron fraction extends up to about 100 GeV. It is therefore of paramount importance to constrain theoretically the expected secondary positron flux to interpret the observations in an accurate way. We find the secondary positron flux to be reproduced well by the available observations, and to have theoretical uncertainties that we quantify to be as large as about one order of magnitude. We also discuss the positron fraction issue and find that our predictions may be consistent with the data taken before PAMELA. For PAMELA data, we find that an excess is probably present after considering uncertainties in the positron flux, although its amplitude depends strongly on the assumptions made in relation to the electron flux. By fitting the current electron data, we show that when considering a soft electron spectrum, the amplitude of the excess might be far lower than usually claimed. We provide fresh insights that may help to explain the positron data with or without new physical model ingredients. PAMELA observations and the forthcoming AMS-02 mission will allow stronger constraints to be aplaced on the cosmic--ray transport parameters, and are likely to reduce drastically the theoretical uncertainties.

Figures (12)

• Figure 1: Comparison between various parameterizations of the positron production cross--section at different incident proton energies.
• Figure 2: Comparison of the effect due to different parameterizations for the cosmic ray proton spectra on the positron source term, as a function of the positrons energy. The additional effect induced by the different nuclear physics parameterizations is also shown. The galactic protons density is taken at 1 hydrogen atom per cm$^{3}$.
• Figure 3: The integral $\eta$ is plotted as a function of the ratio ${{\lambda{\rm D}$λ_ D$}}/{z_\text{max}}$. Because $\eta$ can be interpreted as the the fraction of the positron sphere intersected by the Galactic disk, we infer that it should be unity for ${{\lambda{\rm D}$λ_ D$}} \ll {z_\text{max}}$. In the converse regime, $\eta$ is proportional to the ratio ${z_\text{max}}/{{\lambda{\rm D}$λ_ D$}}$. See text for further details.
• Figure 4: Interstellar secondary positron flux $E^{3.5} \Phi_{e^{+}}$ as a function of the energy at Earth, for different values of the energy loss timescale $\tau_E$. The longer the timescale, the larger the flux. The scaling relation $\phi\propto \sqrt{\tau_E}$ is also reported.
• Figure 5: Secondary positron flux as a function of the positron energy. The blue hatched band corresponds to the CR propagation uncertainty in the IS prediction, whereas the yellow strip refers to TOA fluxes. The long--dashed curves feature our reference model with the Kamae2006 parameterization of nuclear cross--sections, the bess_shikaze_etal_07 injection proton and helium spectra and the MED set of propagation parameters. The MIN, MED and MAX propagation parameters are displayed in Tab. \ref{['table:prop']}. Data are taken from CAPRICE 2000ApJ...532..653B, HEAT 1997ApJ...482L.191B, AMS Aguilar:2007yf2000PhLB..484...10A and MASS 2002AA...392..287G.