Left panel: the dimensionless radial perturbation ξ(t) of the secondary core during the settling phase as a function of normalized time. The damped oscillator formalism captures the thermalization of the stellar debris, describing an initial expansion before settling into exponentially damped quasiperiodic oscillations. Right panel: the resulting synthetic hydrogen α line profile. The virial depths of the secondary core power the broad emission wings. Concurrently, the unvirialized outflowing gas driven by the initial expansion mechanically carves out a narrow absorption trough. The composite synthetic profile captures qualitative features of the complex Balmer profiles.