Solar Energetic Particle Track Accumulation in Edgeworth-Kuiper Belt Dust Grains

Interplanetary dust grains (IDPs) originate from a variety of sources and are dynamically transported across the solar system. While in transport, high-$Z$ solar energetic particles (SEPs) with energies of $\sim$1 MeV/nuc leave damage tracks as they pass through IDPs. SEP track densities can be used as a measure of a grain's space exposure and in turn, help to constrain their lifetimes and origins. Stratospherically collected IDPs with relatively high track densities ($>10^{10}$ cm$^{-2}$) have been interpreted as originating from the Edgeworth-Kuiper Belt. To further test this hypothesis, we use a dynamical dust grain tracing model to explore the accumulation of SEP tracks within EKB dust grains. We demonstrate that, neglecting collisions, dust grains with radii up to 500 $\mu$m are capable of transiting from the EKB to 1 au despite gravitational perturbations from the outer planets, albeit with decreasing probability as a function of size. Despite this, we find that EKB grains cannot accumulate sufficient tracks to match those reported in the terrestrial stratospheric IDP collection when applying SEP track accumulation rates established from lunar samples at 1 au and assuming the SEP flux scales with heliocentric distance as $r^{-1.7}$. By exploring the radial scaling of the SEP flux, we find that a shallower SEP radial distribution of $r^{-1.0}$ does allow for the accumulation of $>$$10^{10}$ tracks cm$^{-2}$ in EKB dust grains that reach 1 au. We urge further research into the propagation and distribution of high-$Z$ SEPs throughout the heliosphere in order to better constrain track accumulation in IDPs.