Although each of these searches considered the pipeline sensitivity to spinning signals, neither anal- ysis used spinning templates. As discussed in Sec. 1.3, most predictions based on the formation of compact binaries indicate that the components will have significant spin. Furthermore, as we pointed out in Secs. 1.4 and 1.5, the spins of the component black holes are known to have a potentially large effect on the emitted waveform. Component spin is expected to have several effects on our searches, compared to its performance for non-spinning systems. First, the non-spinning templates used in our searches have reduced overlap with the spinning signals, leading to a loss of sensitivity.
Second, the signal-basedχ2 test values are expected to be higher than if exactly matched spinning templates were used, due to “unmatched” excess power in the signals; this would further reduce the search sensitivity.
In the low mass search, we considered the effects of spin only for NSBH and BBH systems, as described in Tbl. 4.3. Our simulations were performed using inspiral-only post-Newtonian waveform models, in which the neutron spin was assumed to be zero and the black hole spin was arbitrarily oriented with a uniform distribution in spin magnitude. We found through these simulations that the analysis was less sensitive to this population of spinning signals compared to an otherwise equivalent population without spin by about∼15–20%. These simulations answer the question of how far the search was sensitive to generically spinning systems in this mass range (given that the search was conducted with non-spinning templates) but it gives no indication of how well the search could have done with templates that include spin effects5. In Sec. 6.3, we’ll take a much closer look at how much signal-to-noise may be at stake if we ignore spin effects in aLIGO low mass searches.
In the high mass regime, we use theIMRPhenomBwaveform family [19], discussed in Sec. 1.5.2, which models IMR signals from BBH with aligned/anti-aligned spins. This waveform family is parametrized by two mass parameters and a single “effective spin” parameter χeff, defined in Eqn. 1.70. We performed two sets of IMRPhenomB injections, a non-spinning set and a spin- ning set. Both were uniformly distributed in total mass between 25 and 100M, and uniformly distributed in q/(q+ 1)≡ m1/M for a given M, between the limits 1 ≤q < 4. In addition, the spinning injections were assigned aligned spin componentsχi uniformly distributed between−0.85 and 0.85. To illustrate the effect of aligned spin on the search sensitivity, we plot in Fig. 4.5 the
5In particular, one should take note that no spinning IMR injections were performed in the low mass search, and in particular, none in the rangeMtotal∈ [12,25]M, where merger effects are known to be significant. This mass regime may be very relevant for spin, and it would be a worthwhile to measure the sensitivity of the search pipeline to aligned spin signals in this mass range.
average sensitive distance over the S6/VSR2-3 observation time, in bins of total mass M, for both non-spinning simulated signals and for injections withχ <0 andχ >0, respectively.
Fig. 4.5 indicates higher sensitivity to positive-χ signals even with the current non-spinning templates, but also shows that the search is significantly less sensitive to negative-χsignals at higher values of total massM. This result is expected because the intrinsic luminosity of a compact binary gravitational wave signal increases as the spins of the components increase. Interestingly, the search ismore sensitive to non-spinningIMRPhenomBsignals than it is to non-spinning EOBNR signal, a rough indication of the level of disagreement between to the waveform models. As with the low mass case, these simulations only show how the actual search performed with respect to detecting spinning signals; it gives no hint as to whether the inclusion of spin effects in the templates could improve the sensitivity further (except inasmuch as you place weight on the SenseMon calculation, which seems to indicate that the search is already quite nearly optimal). In the following chapters, we will see that this is not the case. There is plenty of signal-to-noise available from the use of spinning templates, enough to offset the increased background incurred by using larger template banks.
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Chapter 5
Towards Advanced LIGO Searches
Before we acquire great power, we must acquire wisdom to use it well.
Ralph Waldo Emerson
In the previous chapter, we reported on the results of two recent searches for gravitational waves from compact binary coalescence in the final initial LIGO (iLIGO) observational data [3, 4]. For the remainder of this work, we will focus on the projection of such analyses to aLIGO searches. We conduct two basic lines of inquiry: (i) how do the data analysis requirements scale from iLIGO to aLIGO and (ii) can the sensitivity of such searches benefit from the inclusion of additional physical effects. The first question is the subject of the present chapter.
Advanced LIGO instruments are expected to be sensitive to gravitational wave frequencies as low as f ∼10 Hz. In order to recover CBC signals from such data with maximal significance – and in particular to recover otherwise sub-threshold events – the filter templates must extend down to these low frequencies. However, the full exploitation of the low frequency sensitivity leads to a number of technical problems which are not fully solved in the IHOPEimplementation [5]. For example, the duration of the templates (which sets the analysis cost per filter) and the required number of templates are a very strong function of the low frequency cutoff. Furthermore, the increased length of the signal in the LIGO band presents the problem of how to detect a signal which may overlap with more than one stable lock stretch and how to estimate the background power spectral density (PSD) in data which are fully “contaminated” by signal.
One promising solution to these computational problems is to exploit the relatively simple fre- quency evolution of the CBC signal and the large redundancy between different filters in a template
bank. While the signals we are looking for may be as long as an hour and extend up to very high frequencies, the signal spends most of its time within a very small bandwidth, allowing for the down- sampling of the filters without significant loss of SNR. Additionally, template banks are by design highly redundant. As a result, an orthogonal decomposition of the template bank can greatly reduce the required number of templates. We filter with the non-physical orthogonal waveforms instead of the redundant physical templates and only reconstruct the SNR when an excess power is found within the orthogonal projection.
We have implemented these techniques in a new pipeline, known asgstlal [89,90], which is built upon a stream-based infrastructure known asGStreamer [91] and the sameLALlibrary [92] upon whichIHOPEis built. The stream-based infrastructure provides an elegant solution to a number of other computational problems, such as the ability to filter over gaps in the data, a crucial requirement for signals that exceed the length of a typical stable lock stretch. Furthermore, the use of stream- based technology allows for a tunable latency of trigger generation, ideal for electromagnetic followup of mergers involving neutron stars, for which there may be bright electromagnetic counterparts [93].
In the following chapters, we use thegstlal pipeline described here to address the problem of extending the search parameter space to include spin.