This program is a reworking of the program `optimal` to be run on
simulated 40-meter data. Instead of searching for binary inspiral,
`qn_optimal` searches for an injected quasinormal ringdown waveform.
Refer to the sections on optimal filtering
and the `optimal` program for a detailed discussion.

The program is setup to inject a quasinormal ringdown, produced by the
routine `qn_qring()`, due to a black hole of mass ,
dimensionless angular momentum parameter , and fractional mass
loss of . The injection occurs at a time of
and the source distance is set to
. The filter is
constructed from the same waveform.

The following is some sample output from `qn_optimal`:

max snr: 3.74 (offset 30469) data start: 466.77 variance: 0.72159 max snr: 4.03 (offset 50156) data start: 479.80 variance: 0.78550 Max SNR: 9.26 (offset 70785) variance 0.796263 If ringdown, estimated distance: 0.114364 Mpc, start time: 499.999968 Distribution: s= 40, N>3s= 0 (expect 353), N>5s= 0 (expect 0) POSSIBLE RINGDOWN: Distribution does not appear to have outliers max snr: 3.58 (offset 70974) data start: 505.86 variance: 0.77432 ... max snr: 3.62 (offset 123006) data start: 1339.81 variance: 0.70885 Max SNR: 67.01 (offset 126129) variance 4.637304 If ringdown, estimated distance: 0.009777 Mpc, start time: 1365.618108 Distribution: s= 40, N>3s= 320 (expect 353), N>5s= 780 (expect 0) Distribution has outliers! Reject Max SNR: 93.03 (offset 1295) variance 4.444335 If ringdown, estimated distance: 0.005934 Mpc, start time: 1365.998780 Distribution: s= 40, N>3s= 109 (expect 353), N>5s= 280 (expect 0) Distribution has outliers! Reject max snr: 2.71 (offset 127389) data start: 1378.90 variance: 0.29810 ... max snr: 4.85 (offset 118137) data start: 2152.18 variance: 0.91870 Max SNR: 12.74 (offset 69426) variance 1.332324 If ringdown, estimated distance: 0.081144 Mpc, start time: 2172.249524 Distribution: s= 39, N>3s= 0 (expect 353), N>5s= 0 (expect 0) POSSIBLE RINGDOWN: Distribution does not appear to have outliers max snr: 3.65 (offset 35976) data start: 2178.24 variance: 0.77820 max snr: 3.76 (offset 122854) data start: 2191.28 variance: 0.67849

As can be seen, `qn_optimal` is able to find the ringdown and
correctly estimates its distance and time of arrival.

- Author: Jolien Creighton, jolien@tapir.caltech.edu

Includes/qn_optimal.tex

Bruce Allen 2000-11-19