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GRB051103 LIGO data release

Omegagrams

The figures below show "omegagrams" (also known as "qscans") of short stretches (in this case, 16 seconds) of data from LIGO detectors. These are analogous to time-frequency spectrograms, which display excess signal "energy" above a whitened noise background, in time and frequency.

Omegagrams differ from spectrograms in that the noisy data are expanded in a basis set that consists of sine-Gaussians rather than the sine waves that are used in ordinary spectrograms. Sine-Gaussians are sine waves of a specified frequency, with a slowly-varying Gaussian amplitude envelope. They are characterized by their peak time, central frequency, and quality factor Q; Q is a measure of the number of sinusoidal cycles within the more slowly-varying Gaussian amplitude envelope.

In an omegagram, the peak time and central frequency of a sine-Gaussian is varied across the plot, for a small set of values of Q. The central frequencies are logarithmically-spaced. The data are whitened and band-passed, and then the "overlap" of the data with each sine-Gaussian is computed and stored as a time-frequency pixel value. Pixels are clustered into tiles (rectangular groups of pixels). The overlapping tiles are smoothed in time and frequency, and then plotted. The color scale is auto-scaled to highlight any significant signal energy in a tile or a clustered group of tiles; this is referred to as the "normalized tile energy".

This rather complex but flexible and powerful procedure makes it easier to see faint, short duration (transient) periods of excess energy in the LIGO sensitive band (between 40 and 1000 Hz).

For Gaussian noise in the absence of signal, these plots are typically mostly blue, with speckles of lighter blue from Gaussian fluctuations.

Omegagram of +-8 s around the GRB051103 trigger, at LHO (H2):
Omegagram, trigger, H2

Omegagram of +-8 s around the GRB051103 trigger, at LLO (L1): Note that the red blob near the bottom between 2 and 4 seconds is a detector data glitch which is mostly below 40 Hz, so it does not get picked up by our waveform templates, which start at 40 Hz because the detector noise rises sharply at lower frequencies. The omegagram goes into a higher-Q (45) mode, since the excess is most significant with higher-Q sine-Gaussians.
Omegagram, trigger, L1

Omegagram of +-8 s around an off-source segment (194 s before the GRB051103 trigger), at LHO (H2):
Note that this off-source segment contains the loudest (highest SNR) coincident trigger in the search; but it isn't loud enough to be visible in this plot.
Omegagram, off-source, H2

Omegagram of +-8 s around an off-source segment (194 s before the GRB051103 trigger), at LLO (L1):
Note that this off-source segment contains the loudest (highest SNR) coincident trigger in the search; but it isn't loud enough to be visible in this plot.
Omegagram, off-source, L1

What would a signal from a binary neutron star (BNS) inspiral look like?

It depends on how far away it is.

We compare its "effective distance" with the "inspiral horizon distance".
The "effective distance" is the physical distance to the source, corrected for the detector response if the source is not optimally located and oriented on the sky. If not optimal, it is larger than the actual physical distance.
The "inspiral horizon distance" of the detector is the distance at which an optimally located and oriented BNS would be seen in that detector with an SNR of 8.

So, an estimate of the SNR of a signal in a detector is:
SNR ~ 8 * (detector's inspiral horizon distance) / (source effective distance)

If GRB051103 came from M81 at physical distance of 3.6 Mpc, the "effective distance" of the source is at least that distance; but if the source is pointed towards us (as it may be since GRBs are believed to be strongly beamed), the effective distance may be not much farther; say 4 Mpc.
Near the GRB051103 trigger, the inspiral horizon distance of the H2 and L1 detectors were 8.1 Mpc and 18.0 Mpc, respectively.
So we expect a signal to have an SNR of ~ 16 in H2 and 36 in L1. So both detectors should be able to see the signal with high SNR. (Recall from the above that the loudest trigger in the GRB051103 search had SNR=5.2 in H2 and 5.9 in L1).

For comparison, here are omegagrams of simulated BNS GW signals hardware-injected into the H1 detector in October 2010 (there were no hardware injections into the detectors near GRB051103). Note the ratios of horizon distance to effective distance.

Omegagram of a simulated BNS at effective distance 5.5 Mpc, in the H1 detector with inspiral horizon distance = 44 Mpc; SNR ~ 64:
Omegagram, simulated BNS at 5.5 Mpc, H1

Omegagram of a simulated BNS at effective distance 22.0 Mpc, in the H1 detector with inspiral horizon distance = 44 Mpc; SNR ~ 16:
Omegagram, simulated BNS at 22 Mpc, H1

Omegagram of a simulated BNS at effective distance 32.2 Mpc, in the H1 detector with inspiral horizon distance = 44 Mpc; SNR ~ 11. The signal is too weak to be seen in an omegagram, but it still would be loud in our search. The omegagram software finds the highest energy tile with lower Q.
Omegragram, simulated BNS 32.2 Mps, H1

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