The first dark matter halos form by direct collapse from peaks in the matter density field, and evidence from numerical simulations and other analyses suggests that the dense inner regions of these objects largely persist today. These halos would be the densest dark matter structures in the Universe, and their abundance can probe processes that leave imprints on the primordial density field, such as inflation or an early matter-dominated era. They can also probe dark matter through its free-streaming scale. The first halos are qualitatively different from halos that form by hierarchical clustering, as evidenced by their ρ ∝ r −3/2 inner density profiles. In this work, we present and tune models that predict the density profiles of these halos from properties of the density peaks from which they collapsed. These models predict the coefficient A of the ρ = Ar −3/2 small-radius asymptote of the density profile along with the maximum circular velocity vmax and associated radius rmax. These models are universal; they can be applied to any cosmology, and we confirm this by validating them using six N -body simulations carried out in wildly disparate cosmological scenarios. We find that these models can even predict the full population of halos with reasonable accuracy in scenarios with narrowly supported power spectra, although for broader power spectra, an understanding of the impact of halo mergers is needed. With their connection to the primordial density field established, the first dark matter halos will serve as probes of the early Universe and the nature of dark matter.

The plasmasphere is a highly dynamic toroidal region of cold, dense plasma around Earth.Plasma waves exist both inside and outside this region and can contribute to the loss and acceleration of high energy outer radiation belt electrons. Early observational studies found an apparent correlation on long time scales between the observed inner edge of the outer radiation belt and the modeled innermost plasmapause location. More recent work using high-resolution Van Allen Probes data has found a more complex relationship. For this study, we determine the standoff distance of the location of maximum electron flux of the outer belt MeV electrons from the plasmapause following rapid enhancement events. We find that the location of the outer radiation belt based on maximum electron flux is consistently outside the plasmapause, with a peak radial standoff distance of ΔL~1. We discuss the implications this result has for acceleration mechanisms. Plain Language SummaryWe present a statistical study of the location of particles, particularly electrons, in currents around the Earth whose intensity is increased, or enhanced, rapidly (within 1 day). We use over 5 years of particle intensity and plasma density data from the Van Allen Probes satellites. We find that these quick enhancement events occur when the particles are outside the edge of the plasmasphere, an ever-changing, often asymmetric donut-shaped region of plasma around the Earth. Specifically, we find that the locations of particles are correlated with the location of plasma waves outside the plasmasphere, which supports models of electron acceleration from interactions with these waves over short periods of time. Understanding these wave-particle interactions will improve our understanding of how the plasmasphere under differing conditions can either shield Earth from or worsen the impacts of geomagnetic activity and space weather.