Pick-up ion distributions and their influence on energetic neutral atom spectral curvature

This paper focuses on the analysis and significance of the spectral curvature of energetic neutral atoms (ENAs) detected by the Interstellar Boundary Explorer. The flux versus energy spectrum is analytically expressed in terms of the source proton distributions, namely: (1) the solar wind kappa distribution of protons and (2) the coexisting filled spherical shell distribution of pick-up ions (PUIs). The influence of PUIs on the spectral index and curvature is modeled and investigated in detail. It is analytically shown that (1) the PUI speed upper limit is restricted by the Earthward PUI velocity vector, (2) the PUI distribution causes a positive spectral curvature, and (3) the exact expressions of the spectral index and curvature can be used to extract information about the governing parameters of the parent proton distributions. The sky maps of the spectral curvature reveal a possible band-like configuration of positive spectral curvature that is missing in the original flux sky maps. This band can be roughly separated into the north/south polar regions and two ecliptic meridional "columns" located around the ecliptic longitudes 5° and 150°. The geometric locus between the two cones with noseward axis, and apertures 60° and 120°, configures the band-like region of (1) the positive curvature and (2) the maximum values of PUI distribution. Indeed, the observed curvature band is highly correlated with PUI distributions, and is possibly caused by the influence of PUIs on bending the spectrum from linear (log-log scale) to concave upward, thus increasing its spectral curvature.