Ten Milliseconds of Disagreement: How the Choice of Ringdown Start Time Biases Recovered Frequency and Damping

Two analyses of the same ringdown can report different frequencies and damping times while fitting the same data, simply because they begin at different times after the peak. This paper quantifies that systematic in a controlled setting: a synthetic two-component signal, fundamental plus overtone, is fitted with a single damped sinusoid at a sequence of start times, and the drift of the recovered parameters is computed. The true fundamental parameters of the synthetic signal are 249.1 Hz and 4.05 ms, with an overtone starting at eight tenths of the fundamental amplitude. A single-mode fit begun at the peak recovers a frequency biased by 0.3 per cent and a damping time biased by -29.1 per cent, the compromise the incomplete model is forced into. By a start time of 10 ms the damping-time bias has fallen to -0.3 per cent, and the first start at which both biases lie below five per cent is 6 ms after the peak. A single-mode fit at the peak is biased by -29.1 per cent in damping time, the bias falls to -0.3 per cent by 10 ms, and both parameter biases drop below five per cent only from a start time of 6 ms. This study is computed from stated assumptions and published catalogue values; it is simulated, not measured.