Light Remnants Ring High: GW151226 and GW170608, Shot Noise, and the Cost of a Kilohertz-Scale Mode

The lightest remnants in the catalogue ring at frequencies several times higher than GW150914, in the region where photon shot noise governs the instruments. This paper computes the fundamental modes of the GW151226 and GW170608 remnants, quantifies the sensitivity penalty their frequency placement incurs relative to a mid-band mode, and states the ringdown signal-to-noise ratio each event can support under a simple, stated noise model. The GW151226 remnant rings at 787.3 Hz with a damping time of 1.41 ms and 1.11 cycles per e-folding, while the GW170608 remnant rings at 888.6 Hz. Under the stated noise approximation the shot-noise amplitude penalty is 3.94 for the first event and 4.44 for the second, relative to a mode at the two-hundred-hertz band minimum. Folding the penalty through the estimated ringdown energy share gives ringdown signal-to-noise ratios of about 0.7 and 0.7, below the level at which a stand-alone two-parameter ringdown measurement is informative. The two light remnants ring at 787.3 Hz and 888.6 Hz with shot-noise penalties of 3.94 and 4.44, leaving estimated ringdown signal-to-noise ratios of 0.7 and 0.7, so their spectroscopy awaits high-frequency sensitivity improvements. This study is computed from stated assumptions and published catalogue values; it is simulated, not measured.