The calculation of the upper limit on the rate of ringdowns described in section 9.4 was based on our ability to recover injected signals. For that study we used isolated ringdown signals. The question here was how would this change if the ringdown was preceded by an inspiral and merger. This investigation has shown that the presence
Figure 10.11: Hanford effective distance versus injected ringdown frequency for ringdown-only injections. The black vertical lines denote the template bank bound- aries.
Figure 10.12: Hanford effective distance versus injected ringdown frequency for IMR injections. The black vertical lines denote the template bank boundaries.
159
of an additional signal before the ringdown does not in any way hinder our ability to detect the signal. In fact, this model of an IMR injection improves our ability to detect coalescences with high ringdown frequencies i.e., low black hole masses.
This increases our efficiency, which also positively impacts the upper limit we can set. From this we can conclude that not only is the upper limit for the S4 ringdown search presented in section 9.4 still valid, it may be regarded as a conservative upper limit.
What is impacted, however, is our ability to correctly recover the black hole’s physical parameters; this study demonstrated that we can only correctly identify ringdown frequencies occurring below ∼ 200 Hz. However, this lower limit on the accurate recovery of the mass of a black hole corresponds to the upper limit to the scope of the binary black hole inspiral search. Thus, a low-mass binary black hole coalescence will be detected by both searches and correctly parameterized by the inspiral search, while high-mass coalescences should be detected and parameterized by the ringdown search (of course, only within the distance reach of the searches).
Chapter 11
The Future for Ringdown Searches
This thesis describes the first ringdown detection search in LIGO data and has demon- strated that the pipeline is an effective method of searching for triple coincident ringdown events. However this is just the beginning; with every science run comes increased sensitivity and the possibility of exploring a much larger population of as- trophysical sources.
In the course of the analysis we have gained an understanding of the character of ringdown waveforms in noisy data. In this chapter we list some of the unsolved issues, lessons learned, and future recommendations for this particular search. We discuss some new ideas for combining searches for the individual inspiral, merger and ringdown phases of the binary coalescence and discuss the parameter space available to future ringdown searches.
11.1 Notes for Future Searches with the current Pipeline
11.1.1 Searches for Triple Coincident Events
We saw that in the S4 search the rate of false alarms in triple coincidence was less than one event per run. Now that we have some understanding of the characteristics of simulated ringdown waveforms in data we can tolerate a somewhat higher level of background and use these known features to veto false alarms. This gives us
161
leeway to loosen some of the constraints on the search and gain sensitivity. We have demonstrated that the coincidence windows were sufficiently loose and that we did not lose any injections because of clustering. However the search signal to noise thresholds could be lowered further. Given that a triple coincidence search is limited by H2 we recommend lowering its SNR threshold. Decreasing the H2 threshold to 4 would allow triple coincident signals to be seen with SNRs as low as 8 in H1 and L1 (as opposed to 11 in the current search). Given the rate of false alarms in double coincidence, attaining this level of sensitivity without H2 is currently not possible.
11.1.2 Searches for Double Coincident Events
The results of the double coincidence analysis showed that the level of background with the current pipeline was too high to detect gravitational waves at threshold of 5.5. We are a long way from being able to claim a detection of gravitational wave ringdown from co-located detectors however requiring two site coincidence should in theory provide sufficiently strong evidence. We just discussed how to increase our sensitivity to triples without changing the pipeline. However increasing our sensitivity to doubles will require significant additions to the pipeline. We will need to work harder at reducing the level of false coincidences. One method of doing this is by implementing signal-based vetoes; vetoes based on our knowledge of a signals shape in the time and frequency domains [93]. These have been implemented in inspiral searches and are effective in reducing the false alarm rate. Caution has to be exercised however when implementing these in the ringdown search. The ringdown is a short duration single frequency waveform and is likely (but not necessarily) to be preceded by an inspiral and thus any signal-based vetoes must be tested on IMR waveforms to allow for this possibility.
11.1.3 Coincidence Test
The coincidence test described in this analysis in which we use the metric to define coincident windows is an vast improvement on the traditional rectangular coincidence
test. However the results of the injection (section 8.4.1) run revealed that the differ- ence in the time of arrival of the injected waveform was a strong function of frequency, particularly for the H1H2 pair (see figure 8.16). This plot showed that at high fre- quencies a much tighter time accuracy could be required. A frequency dependence time soincidence test should be considered for future searches as it is likely to reduce the false alarm rate considerably.
11.1.4 Extending the Template Bank
For the S4 search the region of frequency space searched over was from 50 Hz to 2 kHz. As mentioned in section 7.4.1 we had hoped to extend the template bank to encompass a frequency range of 40Hz to 4kHz. However in the course of tuning the search and following up on missed injections a peculiar feature was observed. In plots of SNR versus frequency for injections, such as is shown in figure 11.1, the SNR falls off from the injection frequency as expected, but then begins to increase on both sides of the peak. This was observed in varying degrees of severity in every injection looked at regardless of the frequency of the injection. This feature became problematic when the templates far from the injection had higher SNR than those close to the injected frequency. When this occurred in one detector the injection failed the coincidence test and if it occurred in two or three detectors the injection was found at the wrong frequency. In the example shown in figure 11.1 the injection was made at 200 Hz but was found close to 4 kHz. Weeks of investigations were dedicated to this problem but a solution was not found and so the smaller bank was reinstated. These “wings” are still observable with the smaller bank but the effect is small enough that they do not interfere with signal recovery.
This is an important problem to solve because the wider the frequency range we can search over, the larger the number of black hole ringdowns we are sensitive to.
In particular, in increasing the upper frequency bound to 4 kHz we become sensitive to gravitational waves from the entire mass range of non-spinning stellar mass black holes. This would provide an excellent overlap with the binary black hole inspiral
163 search.
Figure 11.1: A demonstration of the high SNR “wings” observed when the template bank was extended to include frequenies between 40 Hz and 4 kHz. This plot shows the SNR versus frequency for a ringdown injection with central frequency of 200 Hz.