Long-term rigidity of the runaway pair

Establish whether the separation of the positive–negative active-mass binary remains rigid at late times by conducting higher-resolution evolutions, particularly a run at N = 192, and determine whether the observed late-time gap opening is a numerical grid artifact or a physical effect.

Background

The matched pair maintains its separation to approximately 1% through t = 200, but the base-grid evolution later develops substantial gap opening as the trailing phantom star slows. Resolution studies show that the opening decreases strongly with finer grids, suggesting a discretization artifact, yet the available extrapolation extends far beyond the time interval covered by the resolution ladder. The authors identify a higher-resolution late-time run as necessary to settle whether rigidity persists.