Explain the vanishing of tidal jumps for circular orbits

Explain why the tidal-resonance jump amplitudes in the angular momentum $L_z$ and Carter constant $Q$ vanish in the circular-orbit limit $e\to0$.

Background

The computed duration-weighted jump amplitudes increase sharply with eccentricity and appear to vanish as eccentricity approaches zero. Although the paper offers a tentative geometric explanation for the growth at high eccentricity, it explicitly states that it lacks a rigorous explanation for the circular-orbit behavior and suggests that an overlooked symmetry may be responsible.

References

We do not have a rigorous explanation as to why the jumps vanish for circular orbits.

— Not All Resonances Are Created Equal: Prioritizing Tidal Resonances in EMRIs  (2609.03732 - Bonga et al., 3 Sep 2026) in Section 4, Jump amplitudes, subsection Prograde orbits