Room for Departure: Deviation Budgets for the Ringdown Spectrum From Published Measurement Uncertainties

Tests of the Kerr spectrum are often summarised by quoting a fractional deviation parameter for frequency and damping time. This paper computes, from the published uncertainties of the two best-measured events, how large those deviation parameters are actually allowed to be, and then asks what classes of proposed departure that allowance excludes and what it leaves untouched. For GW150914 the combined measurement and prediction uncertainties allow a fractional frequency deviation of 0.084 and a fractional damping deviation of 0.183 at the one-standard-deviation scale. For GW190521 the corresponding allowances are 0.217 in frequency and 0.418 in damping, wider in proportion to that event's looser ringdown, despite its greater mass and radiated energy. Combining the two events in quadrature tightens the frequency allowance to 0.078, an illustration of how quickly a population, even of two, improves on its best member when the errors are independent. Published uncertainties allow fractional deviations of 0.084 in frequency and 0.183 in damping for GW150914 and 0.217 and 0.418 for GW190521, tightening to 0.078 in frequency when combined, which presses ten-per-cent departure models and leaves the torsion-frame shift untouched. This study is computed from stated assumptions and published catalogue values; it is simulated, not measured.