Quasinormal Mode Excitation in the Horizon Shear of Near-Extremal Kerr Black Holes

The horizon shear of a near-extremal Kerr black hole perturbed by an eccentric extreme mass ratio inspiral shows low amplitude, high frequency oscillations (''wiggles") after periapsis passage. Previous works are unable to tie the frequency of the wiggles to the orbit, and argue they cannot be quasinormal modes (QNMs). We show that they are Kerr QNMs belonging to the damped-mode branch --- that is, modes whose decay rate stays finite as the spin approaches extremality. For an equatorial prograde orbit with $p = 3M$ and $e = 0.85$ and spins ranging from $a/M = 0.999$ to $a/M = 0.99999$, fits to the time-domain shear identify the fundamental $(\ell,m) = (2,1)$ and $(3,2)$ modes as the dominant and first subdominant excitations. Fitting each multipole separately gives frequencies to within two standard deviations of the Kerr values and provides evidence for the excitation of the fundamental $(3,1)$, $(4,1)$ and $(4,2)$ modes, though these are not resolvable in the full signal. We further argue that the same wiggles must be present in the tidal field that drives the shear. For $\ell \leq 4$ we find no evidence of QNM excitation in the $m = 0$ or the $m = \ell$ multipoles.