How Far Will the Next Instruments Hear a Ringdown? Horizon Distances for Spectroscopy and Memory in a Tenfold-Sensitivity Network

A tenfold improvement in strain sensitivity, of the kind proposed for third-generation ground-based detectors, is usually summarised as a thousandfold increase in volume. This paper works out what that improvement buys specifically for the post-merger effort: the horizon distance at which a GW150914-like ringdown reaches stated signal-to-noise thresholds, the corresponding horizon for its memory step, and the number of usable spectroscopy events per year implied by published local merger rates. At the recorded distance of 440 Mpc the reference ringdown stands at signal-to-noise ratio 8; the present-network horizon for a spectroscopy-grade value of 20 is therefore 176 Mpc. A tenfold sensitivity gain moves the signal-to-noise 8 horizon to 4.40 Gpc and the spectroscopy-grade horizon to 1.76 Gpc. At a representative local rate of 20 per cubic gigaparsec per year, the spectroscopy horizon encloses 22.84 cubic gigaparsecs and implies about 457 usable spectroscopy events per year, before duty-cycle and selection corrections. Tenfold sensitivity moves the spectroscopy-grade ringdown horizon to 1.76 Gpc, implying roughly 457 usable events per year at the stated rate, and lifts the single-event memory horizon to 0.92 Gpc. This study is computed from stated assumptions and published catalogue values; it is simulated, not measured.