Explain the persistence of grouped retrograde resonance contours

Explain why retrograde resonance contours with a fixed radial index $n$ remain close together as the black-hole spin increases, despite the high-spin regime.

Background

For retrograde orbits, the paper finds that the resonance-band structure persists even at high spin, unlike in the prograde case. The authors propose that the larger orbital radii and weaker gravitational influence may account for the grouping, but explicitly identify this explanation as uncertain.

References

Why the contours for a given $n$ remain close together despite the high $a$ values is less clear. One possible explanation is that, because the retrograde resonance contours lie farther from the central BH, the gravitational influence is weaker, so the contours behave more similarly and stay grouped together.

— Not All Resonances Are Created Equal: Prioritizing Tidal Resonances in EMRIs  (2609.03732 - Bonga et al., 3 Sep 2026) in Section 2, Resonance contours, subsection Retrograde orbits