Determine equipartition establishment from nonequipartition initial conditions

Determine whether planetesimals formed with nonequipartitioned semimajor-axis, eccentricity, and inclination dispersions evolve toward equipartition, and determine the timescale of that evolution, particularly beyond the simplified configurations tested in the N-body simulations.

Background

The paper’s main analysis assumes that narrow planetesimal rings begin in equipartition among semimajor-axis, eccentricity, and inclination dispersions. The appendix reports a limited suite of N-body experiments showing that some distributions and dispersion ratios tend toward equipartition, but that strongly nonequipartitioned configurations—especially those with initially enhanced semimajor-axis dispersion or suppressed inclination—can evolve slowly and remain far from equipartition over the simulated interval.

A broader treatment is therefore unresolved: the simulations do not establish whether equipartition is generally reached for realistic formation conditions, nor how the equilibration timescale depends on the initial orbital-element distributions and their degree of nonequipartition. This matters because the paper’s predicted radial widths, scale heights, and evolutionary scalings rely on equipartition assumptions.

References

As this study focuses on the case of equipartition between semimajor axis, eccentricity and inclination, we have not addressed in detail whether the initial conditions of planetesimals formed are in equipartition, and if not, the timescale over which they establish equipartition.

— Substructure evolution from protoplanetary to debris disks driven by mutually gravitating planetesimals and implications on Kepler resonances and free-floating planets  (2608.19329 - Han et al., 19 Aug 2026) in Appendix, Section “Establishing equipartition” (Appendix A)