Characterize the spin dependence of low-inclination jump amplitudes

Characterize the dependence of the tidal jump amplitudes on the black-hole spin parameter at low orbital inclination, including its dependence on the resonance indices $k$ and $m$.

Background

The jump-amplitude curves show that spin effects become less pronounced for highly inclined orbits, but the amplitudes for the (3,0,−2)(3,0,-2) resonance become spin-sensitive again as x→0x\to0. The paper observes that this low-xx behavior appears to depend mainly on the resonance indices kk and mm, but states that the nature of the dependence is unresolved.

References

The influence of the spin parameter at low $x$ seems to be dependent mostly on $k$ and $m$. The nature of this dependence is not yet understood.

— 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