(a)χeff = 0 Template Bank (b)χeff≥0 Template Bank
Figure 6.6: Capturing aligned spin effects in high mass template banks. We show the expected fractional signal-to-noise recovery for a population of aligned-spin binary black holes using a bank of IMRPhe- nomB waveforms with (a) χeff = 0 and (b) χeff ≥ 0. The solid lines indicate the approximate fitting factor contours in theMtotal−χeff plane, averaging over the mass ratio dimension with 1≤m1/m2 ≤4.
The template banks are both constructed with SBank assuming the design iLIGO sensitivity [11] with flow= 40Hz. We find that with this sensitivity, a template bank that neglects spin achieves fitting factors exceeding the nominalF Fmin= 0.97 from aligned-spin systems over a wide region of parameter space, span- ning roughly−0.25≤χeff ≤0.2 over the entire mass range. As the mass of the system increases, the loss of signal-to-noise incurred from neglecting spin becomes small, and we therefore do not consider systems with total masses exceedingMtotal= 35M. Theχeff= 0 bank has∼700 templates, whereas theχeff ≥0 bank has∼3000 templates.
was increased to 0.98. Thus, under this assumption, the non-spinning template bank appears to be adequate for the detection of GWs from binary neutron stars.
6.4 Aligned spin template banks for the detection of merging
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on the improvement in signal recovery for aligned spin systems only.
TheIMRPhenomBwaveform model consists of a parametrized phenomenological fit to hybrid waveforms constructed from numerical relativity simulations of the late-inspiral [that is, fGW &
10−3/(GMtotal/c3), where fGW is the dominant mode gravitational wave frequency], merger and ringdown of binary black holes matched to a post-Newtonian approximation describing the early inspiral. As such, the validity of these waveforms have restrictions on the mass ratio and spins based on the availability of numerical simulations with which to fit. Specifically, theIMRPhenomBfamily is expected to be accurate only for low to moderate mass ratios and spins. Hence, in these studies, we consider only binaries for which 1≤m1/m2≤4 and−0.5≤χeff <0.85.
We choose to further focus only on the regions in the parameter space where the merger and ringdown stages are important for detection. For both an initial and advanced LIGO design sen- sitivity, the effects of merger and ringdown begin to contribute significantly to the SNR when the total mass of the binary exceeds Mtotal ≈ 12 M [18]. For lower mass systems, accurate and generically spinning post-Newtonian waveforms are available [92], and can be used to give a more detailed understanding the effects of spin on the search. We therefore consider only systems with Mtotal ≥10 M, giving a small safety factor between the transitional region and considering the degeneracy between the mass and spin parameters.
Since the finite size of neutron stars can have a significant impact on the gravitational waveform observed in the merger phase of coalescence, we restrict our attention to binary black holes and takemi= 3M as the minimal component mass. We note that from astrophysical considerations, neutron stars in coalescing compact binaries are not expected to have large spins. Further, from physical considerations of the possible neutron star equations of state, the dimensionless spin for a neutron cannot exceed∼0.7 without undergoing tidal disruption.
We consider two regimes separately. First, we consider the available gains in SNR by the use of aligned spin templates to analyze data with iLIGO sensitivity. This study is intended to presage our development of a pipeline, which includes aligned spin templates to recover aligned spin signals inreal LIGO noise. Then we turn our attention to signal recovery in data obtained at aLIGO sensitivities.
Here we immediately bump up against questions of the validity of the phenomenological models.
Nonetheless, as we discuss in this and the next chapter, preliminary studies pushing these waveforms to their maximum indicate that spin effects for aLIGO binary black hole searches will beextremely important. The development and validation of IMR waveforms with spin effects must be a top
priority for the success of these searches.
6.4.0.1 Initial LIGO sensitivity
As a proof of principle, we are going to demonstrate our analysis pipeline with spinning templates on initial LIGO data, where the computational scale is not a limiting factor. Here we investigate template banks covering an initial LIGO design sensitivity to determine the regions in parameter space which have the greatest potential for improvement in SNR recovery.
We usedSBank to construct banks of IMRPhenomBtemplates withχeff = 0 using the above mass parameter restrictions andflow= 40Hz. We then computed the fittings factors of this template bank towards aligned spin signals in the samem1−m2parameter space. In Fig. 6.6a, we show that a template bank withχeff = 0 already captures greater than 97% of the possible SNR over a wide mass and spin range. In particular, we note that theχeff = 0 bank covers signals withχeff <0 down to roughly χeff ∼ −0.25 over the entire mass range. From astrophysical considerations of binary evolution, spins positively aligned with the orbital angular momentum are considered the more likely scenario for binary black holes [26]. Given these factors, along with the potential for artifacts in the waveforms at large negative χeff, we develop our search using only χeff ≥0 templates. Note that sinceχeff is a mass-weighted sum of the two component spins, this restriction does not necessarily exclude the possibility that one of the black holes has an anti-aligned spin. We also see that as the total mass of the target system increases, the fractional loss of SNR incurred from neglecting spin decreases. This effect is due to the fact that higher mass systems merge at lower frequencies and have fewer cycles in the LIGO sensitive band, and consequently the matched filtering is more tolerant of imperfect templates. We thus expect that for systems with total masses exceedingMtotal= 35M, the benefits of including spin effects will be small.
In Fig. 6.6b, we demonstrate the coverage of the parameter space obtained by including only waveforms for non-negative aligned spins (χeff ≥0) in the template bank. The improvement in SNR recovery obtained by using such a bank comes at the cost of having more than three times as many templates in the bank. For the non-spinning case, we constructed a bank with ∼700 templates, while to cover the positively aligned signals, we require ∼ 3000 templates. The increase in the number of templates will increase the number of background triggers, and detecting a signal at a given false probability requires raising the SNR threshold used for detection.
The characteristics of the background can change in complicated ways when new template wave-
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(a) 25 Hz cutoff (b) 10 Hz cutoff
Figure 6.7: Importance of spin for aLIGO binary black hole searches.The two plots above show the coverage of a non-spinning template bank to aligned spin target signals, as in Fig. 6.6a, but for a late aLIGO design spectrum. To the left, we show the signal recovery by a non-spinning template bank integrating from 25 Hz. To the right, we show the same for higher mass systems integrating from 10 Hz. Note the regime of validity for theIMRPhenomBwaveforms requires one to make sacrifices between the low frequency cutoff for integration and the mass range covered by the template bank. For maximal signal recovery in aLIGO, we must have valid IMR waveforms that extend down to 10 Hz in the entire BBH mass range.
forms are introduced to a search. The results presented in Fig. 6.6 do not reflect the impact of non-Gaussianity in the data, nor do they capture the effects of multi-detector coincidence require- ments, the use ofχ2 statistics, increased false alarms due to larger template banks, or other effects which are important in realistic search pipelines. In the following chapter, we describe the imple- mentation of these spinning template banks in a search pipeline. We show that even in non-Gaussian data, we are able to sufficiently suppress the extra background to achieve a net gain in the search sensitivity.
6.4.0.2 Advanced LIGO sensitivity
In Fig. 6.7, we show how the results presented for iLIGO extend to an aLIGO sensitivity. Here we note that we are limited by the range of validity of the IMRPhenomB waveform family. Thus, we show two cases: (i) low mass IMR aligned spin with 25 Hz lower frequency cutoff and (ii) high mass aligned spin with 10 Hz lower frequency cutoff. The simulation results indicate, on the basis of SNR, that spin effects are very important for binary black holes in aLIGO and up to even higher masses than in iLIGO. In the next chapter, we demonstrate an analysis of simulated aLIGO noise and show that in fact these expectations hold even after considering false alarm rates.
Chapter 7
A Sensitive Search Pipeline for Binary Black Holes with Aligned Spin
When it is obvious that the goals cannot be reached, don’t adjust the goals, adjust the action steps.
Confucius
In the previous chapter, we showed that the inclusion of spin effects in templates for compact binary searches may significantly increase the detection rate if such spinning systems are common in astrophysical populations of binary black holes. Our discussion there was based on the expected improvement in signal-to-noise in idealized pipelines running on data with Gaussian background.
In reality, pipeline implementations, even in Gaussian noise, require compromises between optimal- ity and computational feasibility. Furthermore, LIGO data contain non-Gaussian artifacts which can mimic the gravitational wave signals we are trying to detect. This latter problem becomes considerably worse the shorter the template waveforms, as is the case for binary black holes.
In this chapter, we demonstrate the implementation of a sensitive search pipeline ingstlalfor binary black holes whose components have significant spin. We demonstrate an analysis of simulated binary black holes signal in the range Mtotal∈[15,25]M added to iLIGO detector noise, showing that the pipeline recovers 45% more volume from highly spinning binaries than the equivalent search using non-spinning templates, even in the presence of realistic non-Gaussian noise. After demon- strating this analysis in real iLIGO data, we extend our results to an analysis of simulated Gaussian data with a late aLIGO spectra. In this case, our simulated signals fromMtotal∈[60,100]M and
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we find more than a factor of two increase in sensitive volume for the highest spinning systems. As in the previous chapter, we will see that the improvement in recoverable search volume obtained by the inclusion of spin effects is dramatic when considering aLIGO sensitivities, but that covering the whole inspiral-merger-ringdown parameter space in this regime is limited by the availability of accurate waveform models.