Adding Silent Steps: A Stacking Budget for Gravitational-Wave Memory Across a Catalogue of Mergers

If one merger's memory step is a few per cent of its peak strain, the natural response is to add many mergers together. This paper computes how that addition actually scales when the events differ in distance, radiated energy, and orientation, using a representative set of published catalogue events, and states how many comparable events a stated detection threshold requires. The eight catalogue events give individual memory signal-to-noise ratios led by GW150914 at 0.67 under the stated effective noise scale of 2.0e-23. Combined in quadrature, the eight events reach a stacked signal-to-noise ratio of 0.95, well short of a detection threshold of 5. The three largest contributors carry a fraction 0.802 of the total quadrature weight, so the stack is dominated by its loudest members and the effective catalogue is much smaller than the nominal count of 8. Eight representative catalogue events stack to a memory signal-to-noise ratio of 0.95 under the stated noise assumption, with the top three carrying 0.80 of the weight, and about 222 comparable events are needed to reach 5. This study is computed from stated assumptions and published catalogue values; it is simulated, not measured.