HelMod in the Works: From Direct Observations to the Local Interstellar Spectrum of Cosmic-Ray Electrons

Abstract

The local interstellar spectrum (LIS) of cosmic-ray (CR) electrons for the energy range 1 MeV to 1 TeV is derived using the most recent experimental results combined with the state-of-the-art models for CR propagation in the Galaxy and in the heliosphere. Two propagation packages, GALPROP and HELMOD, are combined to provide a single framework that is run to reproduce direct measurements of CR species at different modulation levels, and at both polarities of the solar magnetic field. An iterative maximum-likelihood method is developed that uses GALPROP-predicted LIS as input to HELMOD, which provides the modulated spectra for specific time periods of the selected experiments for model-data comparison. The optimized HelMod parameters are then used to adjust GALPROP parameters to predict a refined LIS with the procedure repeated subject to a convergence criterion. The parameter optimization uses an extensive data set of proton spectra from 1997 to 2015. The proposed CR electron LIS accommodates both the low-energy interstellar spectra measured by Voyager 1 as well as the high-energy observations by PAMELA and AMS-02 that are made deep in the heliosphere; it also accounts for Ulysses counting rate features measured out of the ecliptic plane. The interstellar and heliospheric propagation parameters derived in this study agree well with our earlier results for CR protons, helium nuclei, and anti-protons propagation and LIS obtained in the same framework.

The cosmic-ray content of the Orion-Eridanus superbubble

“…This emission probes CR electrons with energies near 10 GeV in the magnetic fields of the cirrus and superbubble shells. The LIS electron spectrum has a spectral index of −3.5 around this energy (Boschini et al 2018). Despite the enhanced field strengths in the superbubble shell, we observe the same synchrotron intensities in the Eridu and West Rim directions for which we have magnetic field measurements (paper I).…”

Strong new limits on light dark matter from neutrino experiments

“…For energies above several GeV, solar modulation is negligible, but for lower energies, it suppresses the CR flux at Earth, contributing to the peak mentioned above. Voyager 1 has measured the local interstellar spectra (LIS) of CR electrons and various nuclei down to energies of 1-10 MeV [38], and recent papers have computed the LIS down to the lowest energies of the Voyager electron, proton, and helium spectra [39][40][41]. The LIS has been shown to agree well with the CR spectra elsewhere in the galaxy as inferred by gamma-ray observations, with the CR density increasing somewhat at smaller galactic radii [42][43][44]; we therefore use for the galactic CR spectra the LIS computed in Refs.…”

“…The LIS has been shown to agree well with the CR spectra elsewhere in the galaxy as inferred by gamma-ray observations, with the CR density increasing somewhat at smaller galactic radii [42][43][44]; we therefore use for the galactic CR spectra the LIS computed in Refs. [39,40], which were also used in Refs. [27] and [28], respectively.…”

Light Dark Matter at Neutrino Experiments

“…As anticipated in the Introduction we focus on cosmicray electrons. We use their flux as provided in [11] for energies between 2 MeV and 90 GeV. To compute J(b, l) we use an NFW DM density profile [12] with ρ DM (r = 8.5 kpc) = 0.42 GeV/cm 3 and r s = 20 kpc.…”

“…Figure 2, the shape of our limits is driven by the CR electron of larger energies. Following [11], we have included their spectra only up to 90 GeV. For more than a decade above those energies the spectral index of electrons does not become softer [17], and this would e.g.…”