Spectral shapes of the fluxes of electrons and positrons and the average residence time of cosmic rays in the Galaxy

Abstract

The cosmic ray energy spectra encode very important information about the mechanisms that generate relativistic particles in the Milky Way, and about the properties of the Galaxy that control their propagation. Relativistic electrons and positrons traveling in interstellar space lose energy much more rapidly than more massive particles such as protons and nuclei, with a rate that grows quadratically with the particle energy E. One therefore expects that the effects of energy loss should leave observable signatures in the e ∓ spectra, in the form of softenings centered at the critical energy E * . This quantity is determined by the condition that the total energy loss suffered by particles during their residence time in the Galaxy is of the same order of the initial energy. If the electrons and positrons are accelerated in discrete (quasi) point-like astrophysical objects, such as Supernova explosions or Pulsars, the stochastic nature of the sources should also leave observable signatures in the e ∓ energy spectra and angular distributions above a second (higher) critical energy E † , determined by the condition that particles with E E † can propagate only for a maximum distance shorter than the average separation between sources. In this work we discuss the theoretically expectations for the signatures of the energy loss effects on the electron and positron spectra, and compare these predictions with the existing observations. Recent measurements of the (e − + e + ) flux have discovered the existence of a prominent spectral break at E 1 TeV. This spectral feature can perhaps be identified with the critical energy E * . An alternative hypothesis is to assmume that E * has a much lower value of order few GeV. Resolving this ambiguity is of great importance for our understanding of Galactic cosmic rays.PACS numbers: 98.35Gi,95.85Pw,95.85Ry I. INTRODUCTIONThe fluxes of cosmic rays (CR) that are observable near the Earth, in a very broad energy interval that extends from GeV's to PeV's (and possibly to much higher energy) are formed by particles of Galactic origin. These CR particles are injected in interstellar space by sources distributed in the entire Milky Way, and remain confined in the Galaxy for an extended period of time because of the existence of the Galactic magnetic fields. The CR fluxes are in very good approximation isotropic, but their energy distributions contain very important information about their sources and about the properties of the Galaxy that control CR propagation. At low energy (E 30 GeV) the CR spectra are also distorted by the electromagnetic fields that fill the heliosphere, generating time dependent solar modulations.A fundamental problem for CR astrophysics is to disentangle the roles of the sources and of propagation in the formation of the CR fluxes, reconstructing from the observations the "source spectra" (that is the spectra with which the particles are injected in interstellar space by the sources), and the distortion effects generated by propagation.Relativistic, electrically ch...

Features in cosmic-ray lepton data unveil the properties of nearby cosmic accelerators

“…The result is shown in Figure 1d. We notice that the DRAGON output is in good agreement with analytical computations [14,49] predicting a propagated spectral index Γ = Γ inj + δ 2 + 1 2 above few GeV.…”

“…However, the discovery of an increasing positron fraction above 10 GeV by PAMELA [9], later confirmed and better characterized by AMS-02 [10], was then corroborated by the measurement of the absolute e + spectrum by both experiments [11,12] showing than the anomaly cannot be attributed to a steeper-than-expected e − spectrum and that a primary origin of Galactic high-energy positrons needs to be identified. More recently, the AMS-02 Collaboration provided a clear evidence of a cutoff in the e + spectrum at about ∼ 300 GeV [13] which may shed light on the nature of their source(s) and is not expected in alternative transport scenarios where CR positrons are entirely interpreted as secondaries of CR nuclei [14].…”

Cosmic ray models

“…The spectrum E 3 F (E) has a peak at 10 GeV and is affected by solar modulations at energies E < ∼ 20 GeV, as one can see from the differences between the data of PAMELA and AMS-02 which measured the electron flux at different times, for more details see Ref. [198]. Between 20 and 50 GeV, the spectrum hardens gradually and is then up to 500 GeV well described by a power law with spectral index α e − 3.17.…”

“…The alternative option advocated in Ref. [198] identifies the break in the electron flux at 1 TeV seen by the H.E.S.S. collaboration as the softening caused by the energy losses of electrons.…”

Quasielastic Lepton Scattering off Two-Component Dark Matter in Hypercolor Model

“…[20,[48][49][50] for details of the procedure). This flux of electron component of cosmic rays is known with a sufficient accuracy and is a power function of electron energy with some detail of this dependence in various energy regions [51][52][53][54]. Knowing only total cross sections of neutrino production, we can evaluate the fluxes of neutrinos produced by scattering of electrons with energies in some intervals ∆ E = E e,2 − E e,1 as:…”