8.2 Recovery of Simulated Signals
8.2.2 Coincident Injections
Runninglalapps coincringreadon the output of the coincidence step gives us a list of the triggers identified with the injections, one coincidence for each injection (as discussed in section 5.5.6). These can be categorized as injections found in triple coincidence (referred to as triples in triple time, or simply triples) and injections found in coincidence in two detectors (doubles in triple time, or doubles). The doubles are further divided into those that were missed in the third detector because that time was vetoed and those that were simply not seen in the third detector. Note that intervals within triple time when one detector was vetoed are still regarded as triple time; we consider this a loss of efficiency (of detecting triples) rather than a loss
of live time. One could, in theory, account for the lost analysis time, however the extra complexity this entails in terms of bookkeeping is not justified given the small difference this makes.
8.2.2.1 Missed and Found Injections
Figure 8.2 shows a plot similar to that discussed above, the effective distance versus frequency of missed and found injections from the coincidence analysis. The injections found in triple coincidence are marked in blue and those injections found in two detectors are denoted by green, cyan, and magenta stars for H1H2, H1L1, and H2L1 doubles, respectively. The injections vetoed in one detector and found in the other two have a black circle surrounding the star to emphasize the fact that technically they were not missed in the third detector (although they are treated that way in the calculation of the efficiency). The doubles are shown on their own in figure 8.3. As before, the missed injections are marked in red. Our sensitivity to triples is limited by the least-sensitive instrument, H2, and thus the distance out to which we see triples depends on how far H2 can see. For that reason the distance at which we no longer find injections in triple coincidence is approximately the same as the distance that we start missing H2 injections in figure 8.1. Beyond this limit H1 and L1 are still sensitive enough to detect ringdowns, and so we see a thin line of H1L1 double coincidences beyond the distance at which the triples end. At high frequencies there is also a band of H1H2 injections mixed in with the triples. This is because during the S4 run the sensitivity in L1 decreased as the laser power was lower (as discussed in section 6.2), and thus injections made at large distances during this time were missed in L1 while those made when L1 was running with full power were found.
The remaining uncircled doubles (i.e., those missed in the third detector) scattered throughout the predominantly blue area should have been found in the third detector and were followed up on an injection-by-injection basis. Further investigation showed that these were predominantly due to excess noise in the third detector, causing the SNR to peak at a frequency other than the injected frequency, and as a result this detector failed the coincidence test. However, with these exceptions, this plot shows
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that we are recovering the all injections we would expect to recover, and this reassures us that the tools we are employing in the analysis are sound.
Figure 8.2: Hanford effective distance versus frequency for injections missed (red circles) and found in coincidence. Injections found in triple coincidence are marked as blue crosses, injections found in double coincidence are shown as green (H1H2) cyan (H1L1) and magenta (L1H2) stars and those that were vetoed are also marked with a black circle.
8.2.2.2 Efficiency of Finding Triple Coincidences
We evaluate the efficiencyεof finding triples, that is the fraction of injections found in triple coincidence, as a function of injected (physical) distance. This is implemented by binning the injections in logarithmic distance and calculating the efficiency in each bin. A plot of efficiency versus distance is shown in figure 8.4. The uncertainty in
Figure 8.3: Hanford effective distance versus frequency for injections found in double coincidence. The coloured stars represent each of the detector pairs (H1H2 doubles are marked in green, H1L1 in cyan and L1H2 in magenta). The black circles mark those doubles that were vetoed in the third detector.
the efficiency is assumed to be binomial,
σ2ε = ε(1−ε)
N , (8.1)
where N is the total number of injections made.
The first thing to note is that the efficiency is never unity, even at small distances, because, as mentioned in section 5.5 we apply category 2 and 3 vetoes, and thus some injections that otherwise may have been found as triples are found as doubles or not at all. The second feature of note is the gradual slope. This is because the plot encompasses all frequencies and, as is obvious from figure 8.2, the efficiency is a strong function of frequency. In chapter 9 we present analogous plots for smaller
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Figure 8.4: The efficiency of finding injections in triple coincidences as a function of physical distance for injections made between 45 Hz and 2.5 kHz.
frequency bands. Considering injections at all values of the central frequency, we see from figure 8.4 that the 50% efficiency point lies at a distance of approximately 4 Mpc.