Radial and Longitudinal Dependence of Solar 4-13 MeV and 27-37 MeV Proton Peak Intensities and Fluences: Helios and IMP 8 Observations

We study the radial and longitudinal dependence of 4-13 and 27-37 MeV proton peak intensities and fluences measured within 1 AU of the Sun during intense solar energetic particle events. Data are from the IMP 8 and the two Helios spacecraft. We analyze 72 events and compute the total event fluence (F) and the peak intensity (J), distinguishing between the event's absolute maximum intensity and that neglecting local increases associated with the passage of shocks or plasma structures. Simultaneous measurements of individual events by at least two spacecraft show that the dominant parameter determining J and F is the longitudinal separation (ϕ) between the parent active region and the footpoint of the field line connecting each spacecraft with the Sun, rather than the spacecraft radial distance (R). We perform a multiparameter fit to the radial and longitudinal distributions of J and F for events with identified solar origin and that produce intensity enhancements in at least two spacecraft. This fit determines simultaneously the radial and longitudinal dependences of J and F. Radial distributions of events observed by at least two spacecraft show ensemble-averaged variations ranging from R^-2.7 to R^-1.9 for 4-13 and 27-37 MeV proton peak intensities, and R^-2.1 to R^-1.0 for 4-13 and 27-37 MeV proton event fluences, respectively. Longitudinal distributions of J and F are approximated by the form e, where ϕ₀ is the distribution centroid and k is found to vary between ~1.3 and ~1.0 rad^-2. Radial dependences are less steep than both those deduced from diffusion transport models by Hamilton et al. in 1990 and those recommended by Shea et al. in 1988 to extrapolate J and F from R = 1 to R < 1 AU.