At mid- and high-latitudes, energetic protons of magnetospheric origin precipitate down to the upper atmosphere, manifested as one of the most important coupling processes between the ionosphere and magnetosphere. The equatorward boundary of the energetic proton precipitation, or called isotropic boundary (IB), is usually believed to coincide with the boundary in the magnetosphere where field line curvature scattering of protons transits from strong to weak. In this study, we statistically examine the global distribution of the IB for 39 and 115 keV ring current protons as detected by the NOAA/Polar Operational Environmental Satellites in 2013–2018 and propose an empirical model of the IB as a function of solar wind conditions, magnetic local time, and geomagnetic activity index. The IB is well ordered by SYM-H index and interplanetary magnetic field B_z, moving to lower latitudes with more negative SYM-H index and B_z values, and with larger AE index and solar wind pressure. Energy dispersions of the IB are also explored, consistent with the scenario of field curvature scattering in the magnetosphere. This empirical model can be used as an indirect measure of the strength of the magnetospheric stretching and may be applied in magnetosphere-ionosphere mapping studies.
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