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Example: qn_optimal program

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 $M=50M_\odot$, dimensionless angular momentum parameter $\hat{a}=0.98$, and fractional mass loss of $\epsilon=0.03$. The injection occurs at a time of  $500\,{\mathrm{s}}$ and the source distance is set to  $100\,{\mathrm{kpc}}$. 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