Prospects for Observing and Localizing Gravitational-Wave Transients with Advanced LIGO and Advanced Virgo

2.1 Commissioning and observing roadmap

The anticipated strain sensitivity evolution for aLIGO and AdV is shown in Figure 1. A standard figure of merit for the sensitivity of an interferometer is the BNS range R_BNS: the volume- and orientation-averaged distance at which a compact binary coalescence consisting of two 1.4 M_⊙ neutron stars gives a matched filter signal-to-noise ratio (SNR) of 8 in a sing le detector [58].¹ The BNS ranges for the various stages of aLIGO and AdV expected evolution are also provided in Figure 1.

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The commissioning of aLIGO is well under way. The original plan called for three identical 4-km interferometers, two at Hanford (H1 and H2) and one at Livingston (L1). In 2011, the LIGO Lab and IndIGO consortium in India proposed installing one of the aLIGO Hanford detectors (H2) at a new observatory in India (LIGO-India) [64]. As of early 2015, LIGO Laboratory has placed the H2 interferometer in long-term storage for possible use in India. Funding for the Indian portion of LIGO-India is in the final stages of consideration by the Indian government.

Advanced LIGO detectors began taking sensitive data in August 2015 in preparation for the first observing run. O1 formally began 18 September 2015 and ended 12 January 2016. It involved the H1 and L1 detectors; the detectors were not at full design sensitivity. We aimed for a BNS range of 40–80 Mpc for both instruments (see Figure 1), and both instruments were running with a 60–80 Mpc range. Subsequent observing runs will have increasing duration and sensitivity. We aim for a BNS range of 80–170 Mpc over 2016–2018, with observing runs of several months. Assuming that no unexpected obstacles are encountered, the aLIGO detectors are expected to achieve a 200 Mpc BNS range circa 2019. After the first observing runs, circa 2020, it might be desirable to optimize the detector sensitivity for a specific class of astrophysical signals, such as BNSs. The BNS range may then become 215 Mpc. The sensitivity for each of these stages is shown in Figure 1.

As a consequence of the planning for the installation of one of the LIGO detectors in India, the installation of the H2 detector has been deferred. This detector will be reconfigured to be identical to H1 and L1 and will be installed in India once the LIGO-India Observatory is complete. The final schedule will be adopted once final funding approvals are granted. If project approval comes soon, site development could start in 2016, with installation of the detector beginning in 2020. Following this scenario, the first observing runs could come circa 2022, and design sensitivity at the same level as the H1 and L1 detectors is anticipated for no earlier than 2024.

The time-line for the AdV interferometer (V1) [23] is still being defined, but it is anticipated that in 2016 AdV will join the aLIGO detectors in their second observing run (O2). Following an early step with sensitivity corresponding to a BNS range of 20–60 Mpc, commissioning is expected to bring AdV to a 60–85 Mpc in 2017–2018. A configuration upgrade at this point will allow the range to increase to approximately 65–115 Mpc in 2018–2020. The final design sensitivity, with a BNS range of 130 Mpc, is anticipated circa 2021. The corresponding BNS-optimized range would be 145 Mpc. The sensitivity curves for the various AdV configurations are shown in Figure 1.

The GEO 600 [76] detector will likely be operational in the early to middle phase of the AdV and aLIGO observing runs, i.e. 2015–2017. The sensitivity that potentially can be achieved by GEO in this time-frame is similar to the AdV sensitivity of the early and mid scenarios at frequencies around 1 kHz and above. GEO could therefore contribute to the detection and localization of high-frequency transients in this period. However, in the ∼ 100 Hz region most important for BNS signals, GEO will be at least 10 times less sensitive than the early AdV and aLIGO detectors, and will not contribute significantly.

Japan has begun the construction of an advanced detector, KAGRA [100, 28]. KAGRA is designed to have a BNS range comparable to AdV at final sensitivity. We do not consider KAGRA in this article, but the addition of KAGRA to the worldwide GW-detector network will improve both sky coverage and localization capabilities beyond those envisioned here [96].

Finally, further upgrades to the LIGO and Virgo detectors, within their existing facilities (e.g., [63, 78, 11]) as well as future underground detectors (for example, the Einstein Telescope [93]) are envisioned in the future. These affect both the rates of observed signals as well as the localizations of these events, but this lies beyond the scope of this paper.

2.2 Envisioned observing schedule

Keeping in mind the important caveats about commissioning affecting the scheduling and length of observing runs, the following is a plausible scenario for the operation of the LIGO-Virgo network over the next decade:

• 2015–2016 (O1) A four-month run (beginning 18 September 2015 and ending 12 January 2016) with the two-detector H1L1 network at early aLIGO sensitivity (40–80 Mpc BNS range).

• 2016–2017 (O2) A six-month run with H1L1 at 80–120 Mpc and V1 at 20–60 Mpc.

• 2017–2018 (O3) A nine-month run with H1L1 at 120–170 Mpc and V1 at 60–85 Mpc.

• 2019+ Three-detector network with H1L1 at full sensitivity of 200 Mpc and V1 at 65–115 Mpc.

• 2022+ H1L1V1 network at full sensitivity (aLIGO at 200 Mpc, AdV at 130 Mpc), with other detectors potentially joining the network. Including a fourth detector improves sky localization [72, 109, 79, 91], so as an illustration we consider adding LIGO-India to the network. 2022 is the earliest time we imagine LIGO-India could be operational, and it would take several more years for it to achieve full sensitivity.

This time-line is summarized in Figure 2. The observational implications of this scenario are discussed in Section 4.

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3.1 Detection and false alarm rates

The rate of false alarm triggers above a given SNR depends critically upon the data quality of the advanced detectors; non-stationary transients or glitches [1, 10] produce an elevated background of loud triggers. For low-mass binary coalescence searches, the waveforms are well modeled, and signal consistency tests reduce the background significantly [27, 38, 107]. For burst sources which are not well modeled, or which spend only a short time in the detectors’ sensitive band, it is more difficult to distinguish between the signal and a glitch, and so a reduction of the FAR comes at a higher cost in terms of reduced detection efficiency.

Figure 3 shows the noise background as a function of detection statistic for the low-mass binary coalescence and burst searches with the 2009–2010 LIGO-Virgo data [19, 14].² For binary mergers, the background rate decreases by a factor of ∼ 100 for every unit increase in combined SNR ρ _c . Here ρ _c is a combined, re-weighted SNR [29, 19]. The re-weighting is designed to reduce the SNR of glitches while leaving signals largely unaffected. Consequently, for a signal, ρ _c is essentially the root-sum-square of the SNRs in the individual detectors. For bursts, we use the coherent network amplitude η, which measures the degree of correlation between the detectors [22, 86]. Glitches have little correlated energy and so give low values of η. Both ρ _c and η give an indication of the amplitude of the signal and can be used to rank events.

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For CBC signals, we conservatively estimate that a ρ _c threshold of 12 is required for a FAR below ∼ 10⁻² yr⁻¹ in aLIGO-AdV. To arrive at this estimate, we begin with Figure 3 which indicates that an SNR of around 10.5 corresponds to a FAR of 10⁻² yr⁻¹. However, this corresponds to only a subspace of the CBC parameter space and the background of the full search is a factor of six higher. Additionally, due to the improved low frequency sensitivity of the advanced detectors and the inclusion of templates for binaries with (aligned) component spins, at least ten times as many waveform templates are required to perform the search [84, 34, 88, 46]. The background increases approximately linearly with the number of templates required. Consequently, we expect a background around a factor of 100 higher than indicated by Figure 3, which leads us to quote a threshold of 12 for a FAR of 10⁻² yr⁻¹ [31]. A combined SNR of 12 corresponds to a single-detector SNR of 8.5 in each of two detectors, or 7 in each of three detectors.

Instrumental disturbances in the data can have a greater effect on the burst search. At frequencies above 200 Hz, the rate of background events falls off steeply as a function of amplitude. At lower frequencies, however, the data often exhibit a significant tail of loud background events that are not simply removed by multi-detector consistency tests. Although the advanced detectors are designed with many technical improvements, we anticipate that similar features will persist, particularly at low frequencies. Improvements to detection pipelines, which better distinguish between glitches and potential waveforms, can help eliminate these tails (e.g., [66]). For a given FAR, the detection threshold may need to be tuned for different frequency ranges; for the initial detectors, a threshold of η ≳ 4.5–6 (approximately equivalent to ρ _c ≳ 12 from Figure 3) was needed for a FAR of 1/8 yr⁻¹ [14]. The unambiguous observation of an electromagnetic counterpart could increase the detection confidence.

3.2 Sky localization

Following the detection by the aLIGO-AdV network of a GW transient, determining the source’s location is a question for parameter estimation. Typically, posterior probability distributions for the sky position are constructed following a Bayesian framework [110, 43, 98]. Information comes from the time of arrival, plus the phase and amplitude of the GW.

The triangulation approach underestimates how well a source can be localized, since it does not include all the relevant information. Its predictions can be improved by introducing the requirement of phase consistency between detectors [60]. Triangulation always performs poorly for a two-detector network, but, with the inclusion of phase coherence, can provide an estimate for the average performance of a three-detector network [31].³

Source localization using only timing for a two-site network yields an annulus on the sky; see Figure 4. Additional information such as signal amplitude, spin, and precession effects resolve this to only parts of the annulus, but even then sources will only be localized to regions of hundreds to thousands of square degrees [99, 31]. An example of a two-detector BNS localization is shown in Figure 5. The posterior probability distribution is primarily distributed along a ring, but this ring is broken, such that there are clear maxima.

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For three detectors, the time delays restrict the source to two sky regions which are mirror images with respect to the plane passing through the three sites. It is often possible to eliminate one of these regions by requiring consistent amplitudes in all detectors. For signals just above the detection threshold, this typically yields regions with areas of several tens to hundreds of square degrees. Additionally, for BNSs, it is often possible to obtain a reasonable estimate of the distance to the source [109, 31], which can be used to further aid electromagnetic observations [79, 32]. If there is significant difference in sensitivity between detectors, the source is less well localized and we may be left with the majority of the annulus on the sky determined by the two most sensitive detectors. With four or more detectors, timing information alone is sufficient to localize to a single sky region, and the additional baselines help to limit the region to under 10 deg² for some signals.

From Eq. (1), it follows that the linear size of the localization ellipse scales inversely with the SNR of the signal and the frequency bandwidth of the signal in the detector [31]. For GWs that sweep across the band of the detector, such as CBC signals, the effective bandwidth is ∼ 100 Hz, determined by the most sensitive frequencies of the detector. For shorter transients the bandwidth ρ _f depends on the specific signal. For example, GWs emitted by various processes in core-collapse supernovae are anticipated to have relatively large bandwidths, between 150–500 Hz [48, 82, 113, 83], largely independent of detector configuration. By contrast, the sky localization region for narrowband burst signals may consist of multiple disconnected regions and exhibit fringing features; see for example [72, 16, 51].

Some GW searches are triggered by electromagnetic observations, and in these cases localization information is known a priori. For example, in GW searches triggered by gamma-ray bursts [18, 7, 6] the triggering space-based telescope provides the localization. The detection of a GW transient associated with a gamma-ray burst would provide strong evidence for the burst progenitor; for example, BNS mergers are considered the likely progenitors of most short gamma-ray bursts. It is therefore important to have high-energy telescopes operating during the advanced-detector era. Furthermore, the rapid identification of a GW counterpart to such a trigger could prompt further spectroscopic studies and longer, deeper follow-up in different wavelengths that may not always be done in response to gamma-ray bursts. This is particularly important for gamma-ray bursts with larger sky localization uncertainties, such as those reported by the Fermi GBM, which are not followed up as frequently as bursts reported by Swift.

Finally, all GW data are stored permanently, so that it is possible to perform retroactive analyses at any time.

3.2.1 Localization of binary neutron stars

Providing prompt localizations for GW signals helps to maximise the chance that electromagnetic observatories can catch a counterpart. Sky maps will be produced at several different latencies, with updates coming from more computationally expensive algorithms that refine our understanding of the source. For BNS signals, rapid sky localization is performed using BAYESTAR [98], a Bayesian parameter-estimation code that computes source location using output from the detection pipeline. It can produce sky maps (as in Figure 5) with latencies of only a few seconds. A similar approach to low-latency localization has been separately developed by [42], who find results consistent with bayestar.

At higher latency, CBC parameter estimation is performed using the stochastic sampling algorithms of LALInference [110]. LALInference constructs posterior probability distributions for system parameters (not just location, but also mass, orientation, etc. [3]) by matching GW templates to the detector strain [44, 65]. Computing these waveforms is computationally expensive; this expense increases as the detectors’ low-frequency sensitivity improves and waveforms must be computed down to lower frequencies. The quickest LALInference BNS follow-up is computed using waveforms that do not include the full effects of component spin [99, 31], sky locations can then be reported with latency of hours to a couple of days. Parameter estimation is then performed using more accurate waveform approximates (those that include the full effects of spin precession), which can take weeks or months [57]. Methods of reducing the computational cost are actively being investigated (e.g., [37, 89, 36]).

There is negligible difference between the low-latency bayestar and the mid-latency non-spinning LALInference analyses if the BNS signal is loud enough to produce a trigger in all detectors: if there is not, LALInference currently gives a more precise localization, as it still uses information from the non-triggered detector [99, 98]. It is hoped to improve bayestar localization in the future by including information about sub-threshold signals. Provided that BNSs are slowly spinning [77], there should be negligible difference between the mid-latency non-spinning LALInference and the high-latency fully spinning LALInference analyses [57].

Results from an astrophysically motivated population of BNS signals, assuming a detection threshold of a SNR of 12, are shown in Figure 6 [99, 31]. Sky localization is measured by the 90% credible region CR_0.9, the smallest area enclosing 90% of the total posterior probability, and the searched area A_*, the area of the smallest credible region that encompasses the true position [97]: CR_0.9 gives the area of the sky that must be covered to expect a 90% chance of including the source location, and A_* gives the area that would be viewed before the true location using the given sky map. Results from both the low-latency bayestar and mid-latency non-spinning LALInference analyses are shown. These are discussed further in Section 4.1 and Section 4.2. The two-detector localizations get slightly worse going from O1 to O2. This is because although the detectors improve in sensitivity at every frequency, with the assumed noise curves the BNS signal bandwidth is lower in O2 for a given SNR because of enhanced sensitivity at low frequencies [99]. Despite this, the overall sky-localization in O2 is better than in O1. As sky localization improves with the development of the detector network [96, 72, 109, 91], these results mark the baseline of performance for the advanced-detector era.

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3.2.2 Localization of bursts

The lowest latency burst sky maps are produced as part of the coherent WaveBurst (cWB) [71, 73] detection pipeline, earlier versions of which were used in prior burst searches [12, 14, 70]. Sky maps are produced using a constrained likelihood algorithm that coherently combines data from all the detectors; unlike other approaches, this is not fully Bayesian. The resulting sky maps currently show calibration issues.⁴ The confidence is over-estimated at low levels and under-estimated at high levels. However, the searched areas are consistent with those from other burst techniques, indicating that cWB maps can be used to guide observations. The cWB sky maps calculated with a latency of a few minutes; following detection, further parameter-estimation codes analyze the data.

At higher latency, burst signals are analyzed by LALInferenceBurst (LIB), a stochastic sampling algorithm similar to the LALInference code used to reconstruct CBC signals [110], and BayesWave, a reversible jump Markov-chain Monte Carlo algorithm that models both signals and glitches [43]. LIB uses a sine-Gaussian waveform (in place of the CBC templates used by LALInference), and can produce sky maps in a few hours. BayesWave uses a variable number of sine-Gaussian wavelets to model a signal and glitches while also fitting for the noise spectrum using BayesLine [75]; it produces sky maps with a latency of a few days. Sky maps produced by LIB and BayesWave should be similar, with performance depending upon the actual waveform.

A full study of burst localization in the first two years of the aLIGO-AdV network was completed in [51]. This study was conducted using cWB and LIB. Sky localization was quantified by the searched area. Using an approximate FAR threshold of 1 yr⁻¹, the median localization was shown to be ∼ 100–200 deg² for a two-detector network in 2015–2016 and ∼ 60–110 deg² for a three-detector network in 2016–2017, with the localization and relative performance of the algorithms depending upon the waveform morphology. Results for Gaussian, sine-Gaussian, broadband white-noise and BBH waveforms are shown in Figure 7 (for the two-detector O1 network and the three-detector O2 network, cf. Figure 6). The largest difference between the codes here is for the white-noise bursts; for a three-detector network, LIB achieves better localization than cWB for Gaussian and sine-Gaussian bursts. The variety of waveform morphologies reflect the range of waveforms that could be detected in a burst search [16].

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4.1 2015–2016 run (O1): aLIGO 40–80 Mpc

This is the first advanced-detector observing run, lasting four months, starting 18 September 2015 and ending 12 January 2016. The aLIGO sensitivity is expected to be similar to the early band in Figure 1, with a BNS range of 40–80 Mpc, and a burst range of 40–60 Mpc for E_GW = 10⁻² M_⊙c². Our experience so far indicates that sensitivity will probably be at the better end of this span, with a BNS range potentially in the interval 60–80 Mpc.

A four-month run gives a BNS search volume of (0.5–4) × 10⁵ Mpc³ yr at the confident detection threshold of ρ _c = 12. The search volume is (4/3)πR³ × T, where R is the range and T is the observing time incorporating the effects of the detectors’ duty cycles. We therefore expect 0.0005–4 BNS detections. A BNS detection is likely only if the most optimistic astrophysical rates hold.

With the two-detector H1-L1 network any detected events are unlikely to be well localized. A full parameter-estimation study using realistic detector noise and an astrophysically-motivated source catalog has been completed for 2015–2016 [31].⁷ This used a noise curve in the middle of the early range shown in Figure 1 (the early curve specified in [30]). The distribution of results is shown in Figure 6. It was found that using an SNR threshold of 12, the median 90% credible region for BNS signals is ∼ 500 deg², and only 4% of events are expected to have \({\rm{CR}}_{0.9}^{{\rm{BNS}}}\) smaller than 100 deg²; the searched area \(A_{\ast}^{{\rm{BNS}}}\) is smaller than 20 deg² for 16% of events and smaller than 5 deg² in 6%. If a FAR threshold of 10⁻² yr⁻¹ is used without the SNR cut, these localizations change because of the inclusion of an additional population of events with SNRs ∼ 10–12. The median \({\rm{CR}}_{0.9}^{{\rm{BNS}}}\) is ∼ 600 deg² and 3% have \({\rm{CR}}_{0.9}^{{\rm{BNS}}}\) smaller than 100 deg²; \(A_{\ast}^{{\rm{BNS}}}\) is smaller than 20 deg² for 14% of events and smaller than 5 deg² for 4%.

Equivalent (but not directly comparable) results for bursts are found in [51]. Specific results depend upon the waveform morphology used, but the median searched area is ∼ 1–2 times larger than for BNS signals; part of this difference is due to the burst study using a less-stringent FAR threshold of ∼ 1 yr⁻¹. The distribution of searched areas for four waveform morphologies are shown in Figure 7.

Follow-up observations of a GW signal would be difficult, but not impossible. Localizations provided by another instrument, such as a gamma-ray burst telescope, could improve the possibility of locating an optical or a radio counterpart.

4.2 2016–2017 run (O2): aLIGO 80–120 Mpc, AdV 20–60 Mpc

This is envisioned to be a six-month run with three detectors. The aLIGO performance is expected to be similar to the mid band in Figure 1, with a BNS range of 80–120 Mpc, and a burst range of 60–75 Mpc for E_GW = 10⁻² M_⊙c². The AdV range may be similar to the early band, approximately 20–60 Mpc for BNS and 20–40 Mpc for bursts. This gives a BNS search volume of (0.6–2) × 10⁶ Mpc³ yr, and an expected number of 0.006–20 BNS detections.

Source localization for various points in the sky for CBC signals for the three-detector network is sketched in Figure 8.

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BNS sky localization for 2016–2017 (in addition to 2015–2016) has been investigated in [99]. This assumed a noise curve which lies in the middle of the mid range in Figure 1 for aLIGO (the mid curve specified in [30]) and the geometric mean of the upper and lower bounds of the mid region in Figure 1 for AdV. The distribution of results is shown in Figure 6. Performing parameter estimation on an astrophysically-motivated BNS population, with an SNR threshold of 12 (in addition to a FAR cut of 10⁻² yr⁻¹), it was found that the median 90% credible region for BNS signals is ∼ 200 deg², and 20% of events are expected to have \({\rm{CR}}_{0.9}^{{\rm{BNS}}}\) smaller than 20 deg². The searched area is smaller than 20 deg² for 44% of events and smaller than 5 deg² for 20%. The burst study [51] gives approximately equivalent results, producing median searched areas a factor of ∼ 2–3 larger than the BNS results; these results are shown in Figure 7.

4.3 2017–2018 run (O3): aLIGO 120–170 Mpc, AdV 60–85 Mpc

This is envisioned to be a nine-month run with three detectors. The aLIGO and AdV sensitivities will be similar to the late and mid bands of Figure 1 respectively, with BNS ranges of 120–170 Mpc and 60–85 Mpc, and burst ranges of 75–90 Mpc and 40–50 Mpc for E_GW = 10⁻² M_⊙c². This gives a BNS search volume of (3–10) × 10⁶ Mpc³ yr, and an expected 0.04–100 BNS detections. Source localization for CBC signals is illustrated in Figure 8. While the greater range compared to the 2016–2017 run increases the expected number of detections, the detector bandwidths are marginally smaller. This slightly degrades the localization capability for a source at a fixed SNR.

4.4 2019+ runs: aLIGO 200 Mpc, AdV 65–130 Mpc

At this point we anticipate extended runs with the detectors at or near design sensitivity. The aLIGO detectors are expected to have a sensitivity curve similar to the design curve of Figure 1. AdV may be operating similarly to the late band, eventually reaching the design sensitivity circa 2021. This gives a per-year BNS search volume of 2 × 10⁷ Mpc³ yr, giving an expected 0.2–200 confident BNS detections annually. Source localization for CBC signals is illustrated in Figure 8. The fraction of signals localized to areas of a few tens of square degrees is greatly increased compared to previous runs. This is due to the much larger detector bandwidths, particularly for AdV; see Figure 1.

4.5 2022+ runs: aLIGO (including India) 200 Mpc, AdV 130 Mpc

The four-site network incorporating LIGO-India at design sensitivity would have both improved sensitivity and better localization capabilities. The per-year BNS search volume increases to 4 × 10⁷ Mpc³ yr, giving an expected 0.4–400 BNS detections annually. Source localization is illustrated in Figure 8. The addition of a fourth detector site allows for good source localization over the whole sky [96, 109, 79, 91].