Modulation of the Galactic Low-energy Proton Spectrum in the Inner Heliosphere

We study the energy spectra of 0.3-100 MeV protons and find that, at the lower part of the galactic particle spectrum, they are significantly steeper than the J(E) similar to E spectrum predicted by analytical approximations, such as the force-field model of modulation. We select a series of low-flux periods, and approximate the spectral form by J(E) = AE(-gamma) + CE nu, where the two terms describe solar/heliospheric and galactic components, respectively. By determining the best fit parameters to energy spectra, correlations are sought with solar activity indices and between the parameters themselves. In the majority of cases, nu turns out to be between 1.2 and 1.4, with an average of 1.32 +/- 0.12, significantly greater than the commonly expected nu = 1 predicted by the force-field approximation. In modulation theories nu > 1 corresponds to a negative Compton-Getting factor, which poses a challenge. Such an inversion may occur if the radial diffusion coefficient kappa(rr) < rV (where r is heliocentric distance and V solar wind speed), in which case a large fraction of the 10-100 MeV protons reaching 1 AU would have been cooled down within 1 AU and subsequently convected outward by the solar wind. We also find that the position of the intensity minimum of the proton spectrum dividing the solar and galactic populations shifts toward higher values with increasing solar activity. Correlations obtained with solar activity indicate that the slope of the solar/heliospheric spectrum is practically independent of solar activity. Observations are compared with numerical solutions of the modulation equation adopting simple spherical models. Possible interpretations are discussed.