The Radial Transition of Open Magnetic Flux: A Multi-Mission Breakpoint Analysis

Authors: Jackson MacTaggart (University of Michigan), Susan Lepri (University of Michigan), Liang Zhao (University of Michigan), Lennard Fisk (University of Michigan)

Under simple radial expansion, the radial magnetic field is expected to scale as Br ∝ r^-2, so the open magnetic flux Br r^2 should remain approximately constant with heliocentric distance. Recent inner-heliospheric observations, particularly from Parker Solar Probe, suggest that the open magnetic flux may instead transition from an approximately constant trend at larger radii to a sloped radial dependence closer to the Sun. We quantify this transition using in-situ magnetic field measurements from Helios 1, Helios 2, Parker Solar Probe, and Solar Orbiter, combined with reconstructed spacecraft ephemerides from SPICE kernels. For each encounter and polarity, we estimate the dense core of the Br r^2 distribution with radial-bin quantiles and fit a robust segmented model with an outer constant branch and an inner sloped branch. The transition distance r_0 is identified by minimizing an L1 loss across candidate breakpoints. Preliminary results show that r_0 varies across spacecraft and encounters, but is distributed around 0.35 AU. We also show that past each breakpoint, the open magnetic flux plateaus near 3.3 nT AU^2, close to the expected value of 3.6 nT AU^2. This method provides a quantitative framework for locating departures from r^-2 scaling and investigating their relationship to solar-wind structure and solar-cycle evolution.