Transport of Cosmic-Ray Electrons from 1 au to the Sun

Gamma rays are produced by cosmic-ray (CR) protons interacting with the particles at the solar photosphere and by CR electrons and positrons (CRes) via inverse Compton scattering of solar photons. The former comes from the solar disk while the latter extends beyond the disk. Evaluation of these emissions requires the flux and spectrum of CRs in the vicinity of the Sun, while most observations provide flux and spectra near the Earth, at around 1 au from the Sun. Past estimates of the quiet Sun gamma-ray emission use phenomenological modulation procedures to estimate spectra near the Sun. We show that CRe transport in the inner heliosphere requires a kinetic approach and use a novel approximation to determine the variation of CRe flux and spectrum from 1 au to the Sun including the effects of (1) the structure of the large-scale magnetic field, (2) small scale turbulence in the solar wind from several in situ measurements, in particular, those by Parker Solar Probe that extend this information to 0.1 au, and (3) most importantly, energy losses due to synchrotron and inverse Compton processes. We present results on the flux and spectrum variation of CRes from 1 au to the Sun for several transport models. In forthcoming papers we will use these results for a more accurate estimate of quiet Sun inverse Compton gamma-ray spectra, and, for the first time, the spectra of extreme ultraviolet to hard X-ray photons produced by synchrotron emission. These can be compared with the quiet Sun gamma-ray observation by the Fermi and X-ray upper limits set by RHESSI.