Connection-angle dependence of proton anisotropy in ground-level enhancement events

Ground-level enhancements (GLEs) probe the earliest, highest-energy solar energetic particles and thus provide a unique window into particle release and transport from the low corona to 1 AU. We present a uniform, event-resolved analysis of the early anisotropy for ten well-observed GLEs, combining consistently reconstructed neutron-monitor pitch-angle distributions (PADs) with Parker-spiral footpoint mapping. We find a clear, monotonic decline in initial anisotropy with increasing magnetic connection angle: well-connected events exhibit strong, persistent forward-directed beams, while poorly connected events show systematically weaker and more rapidly decaying anisotropies. This relationship holds across a wide range of flare classes and coronal mass ejection (CME) speeds, demonstrating that magnetic connectivity and interplanetary transport, rather than eruption magnitude, dominate the directional properties of the earliest relativistic arrivals at Earth. A principal component analysis was applied to time-resolved spectral and angular parameters to separate source-driven changes from transport effects. By explicitly identifying and removing secondary sunward (back-scattered) components—attributable to scattering and reflection from solar-wind structures and transient interplanetary features—from the PAD fits, we isolated the intrinsic relaxation of the primary forward beam and show that apparent departures from simple exponential decay are frequently attributable to reflected or delayed populations rather than prolonged source injection. The empirical anisotropy--connection-angle relation reported here provides an event-resolved, quantitative benchmark that constrains focused-transport and shock-acceleration models and offers immediate operational value: rapid footpoint estimates can meaningfully limit expected initial beaming and directional radiation risk.