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physical effects in the search templates is the ability to manage the background trigger rates while exploiting the elevation of the signal. The methods described here have proven successful in miti- gating the background elevation relative to the signal to obtain a net gain in sensitivity. We point out, however, that the inclusion of spin effects in the templates does increase the background levels in proportion to the increase in the size of the bank, as shown in Fig. 7.3. We have highlighted in this section the use of exact template parameter coincidence and the autocorrelationχ2. These are just two features of thegstlalpipeline which are manifestly different from other studies, and lie at the core of the background rejection techniques currently implemented in the pipeline. Given that thegstlal pipeline has not previously been used for an analysis of this type, there are of course many other differences between this work and previous studies, but isolating the particular features which made these results possible is a difficult task.
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Figure 7.4: Improved sensitivity to spinning signals in simulated aLIGO noise. We compare the sensitive distances measured in the gstlalpipeline with (color) and without (black) spin effects in the templates.
The template bank covers the spaceMtotal∈[40,125]M and the simulated signals systems haveMtotal∈ [60,80]M, each restricted to mass ratiosm1/m2 ≤4. The template bank extends beyond the injection space in order to avoid template bank edge effects. We see that the inclusion of aligned spin effects in the template waveforms can increase the observable volume by more than a factor of two in this mass range for systems with the largest spins.
However, it is worth noting that if IMRPhenomBwere the only approximation we had available for aligned spin systems, this would be areal effect – we don’t have IMR aligned spin templates below Mtotal= 40M that are valid down to 10 Hz. Fortunately, more accurate models with a wider range of validity are currently being developed. As they are developed, we plan to insert these models into the SBank infrastructure to generate template banks with them and extend the study presented here down to even lower masses, where the effects of spin only become greater.
In Fig. 7.5, we illustrate the effect of waveform mismatch on the χ2. Recall that we have conducted our study in Gaussian noise. As a result, the χ2 is in some sense superfluous; theory indicates that SNR is an optimal statistic in Gaussian noise. Nonetheless, even in Gaussian noise,
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(a) Non-spin Templates (b) Aligned-spin Templates
Figure 7.5: The effect of waveform mismatch on theχ2statistic. We compare the values of the autocorrela- tionχ2statistic for an analysis of simulated spinning signals with and without aligned spin templates for our study in simulated aLIGO noise. The injections here are the same as those in Fig. 7.4 except that the upper limit on total mass is 100M. This figure illustrates the sensitivity of theχ2statistic to mismatch between the signal and the triggered template. In the non-spinning template case, theχ2 statistic can have values that rival that of non-Gaussian background triggers (cf. Fig. 3.4), although such triggers are not present in this study on Gaussian noise. Hence when recovering spinning signals with non-spinning templates, the loss of SNR is compounded by the waveform mismatch which appears in theχ2.
theχ2statistic reflects the consistency of the template with the signal in the data. We see that when we use non-spinning templates to search for aligned-spin systems, theχ2values lie dangerously near where we would expect non-Gaussian triggers to appear (compare to Fig. 3.4, although this figure uses the traditionalχ2in the IHOPEpipeline).
We have much further to go. We have completely neglected the mass rangeMtotal∈[15,40]M, relevant for IMR templates. We have at present no waveform which models both inspiral-merger- ringdown and precession. Without these, we are unable to quantify how well these aligned spin filters work for detecting generically (not necessarily aligned) spinning binary black holes. The inclusion of spin effects for binary black hole searches could very well prove to be vital to their successful detection, but we need the waveforms.
Chapter 8
Conclusions
I don’t understand why no adult knows that Sirius is the brightest star in the sky. I know Uncle Stephen would know.
My nephew Nicholas (age 5)
The LIGO experiment is one of the most important and exciting efforts in contemporary physics.
Discovering gravitational waves from coalescing compact binaries would open up a whole new way of studying the sky. What we have demonstrated is one small piece of a much larger puzzle. What is the impact of the results presented here? How will the answers to the exam be different next year?
We close our discussion in this thesis by zooming out and reminding the reader where this piece fits in the big picture.