4 Observing Scenario

In this section we estimate the sensitivity, possible number of detections, and localization capability for each of the observing runs laid out in Section 2.2. We discuss each future observing run in turn and also summarize the results in Table 1.

In the following, we estimate the expected number of BNS coalescence detections using both the lower and upper estimates on the BNS source rate density, 10 −810−5 Mpc − 3yr−1 [13*]. Given the detectors’ noise spectral densities, the ρc detection threshold can be converted into the (source sky-location and orientation averaged) BNS sensitive detection range RBNS [13*, 20]. From this, the BNS source rate density can be converted into an estimate of the number of expected detected events; this estimate carries the large error on the source rate density. Similar estimates may be made for NS–BH binaries using the fact that the NS–BH range is approximately a factor of 1.6 larger than the BNS range,5 though the uncertainty in the NS–BH source rate density is slightly larger [13*]. We assume a nominal ρc threshold of 12, at which the expected FAR is −2 −1 10 yr. However, such a stringent threshold may not be appropriate for selecting candidate triggers for electromagnetic follow-up. For example, selecting CBC candidates at thresholds corresponding to a higher background rate of 1 yr− 1 (100 yr− 1) would increase the number of true signals subject to electromagnetic follow-up by about 30% (90%). The area localization for these low-threshold signals is only fractionally worse than for the high-threshold population – by approximately 20% (60%). The localization of NS–BH signals is expected to be similar to that of BNS signals.

For typical burst sources, the GW waveform is not well known. However, the performance of burst searches is largely independent of the detailed waveform morphology [14, 51*], allowing us to quote an approximate sensitive range determined by the total energy EGW emitted in GWs, the central frequency f0 of the burst, the detector noise spectrum S(f ), and the single-detector SNR threshold ρdet [101],

[ G E ]1∕2 Rburst ≃ ---2-3-----GW2--2-- . (2 ) 2π c S(f0)f0ρ det
In this article, we quote ranges using E = 10−2M c2 GW ⊙ and f = 150 Hz 0; E = 10−2M c2 GW ⊙ is an optimistic value for GW emission from stellar collapse (see, e.g., [18]), the uncertainty in EGW means that the quoted burst ranges are more uncertain than their BNS counterparts. We use a single-detector SNR threshold of 8, corresponding to a typical ρc ≃ 12 and FAR of ∼ 0.3 yr−1. Due to the tail of the low-frequency background-rate-vs-amplitude distribution in Figure 3*, we see that varying the selection threshold from a background of −1 0.1 yr (ρc ≳ 15) to even −1 3 yr (ρc ≳ 10) would increase the number of true signals selected for electromagnetic follow-up by a factor (15∕10)3 ∼ 3, though the area localization for low-SNR bursts may be particularly challenging.

The run durations discussed below are in calendar time. Based on prior experience, we can reasonably expect a duty cycle of ∼ 80% for each instrument during observing runs.6 Assuming downtime periods are uncorrelated among detectors, this means that all detectors in a three-detector network will be operating in coincidence approximately 50% of the time and two of the three detectors will be operating an additional 40% of the time. For a four-detector network, three or more detectors will be operational around 80% of the time. Our estimates for the expected number of detections and the fraction of sources localized account for these duty cycles. The number of detections also account for the uncertainty in the detector sensitive ranges as indicated in Figure 1*.

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 EGW = 10−2M ⊙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 5 3 (0.5– 4) × 10 Mpc yr at the confident detection threshold of ρc = 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 2 ∼ 500 deg, and only 4% of events are expected to have CRBNS 0.9 smaller than 100 deg2; the searched area ABNS ∗ 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 ∼ 1012. The median BNS CR 0.9 is 2 ∼ 600 deg and 3% have BNS CR 0.9 smaller than 100 deg2; ABN∗S 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 ∼ 12 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 − 2 2 EGW = 10 M ⊙c. 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 (0.62) × 106 Mpc3yr, 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*.

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 CRBNS0.9 smaller than 20 deg2. The searched area is smaller than 20 deg2 for 44% of events and smaller than 2 5 deg 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 EGW = 10−2M ⊙c2. This gives a BNS search volume of (3 –10 ) × 106 Mpc3yr, 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 Mpc3yr, 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 Mpc3yr, 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].
View Image
Figure 8: Schematic network sensitivity and localization accuracy for face-on binary neutron-star (BNS) systems with advanced-detector networks. The ellipses show 90% confidence localization areas based upon timing triangulation alone, and the red crosses show regions of the sky where the signal would not be confidently detected. The top two plots show the localization expected for a BNS system at 80 Mpc by the LIGO Hanford (H)–LIGO Livingston (L)–Virgo (V) network (HLV) in the 2016 – 2017 run (left) and 2017 – 2018 run (right). The bottom two plots show the localization expected for a BNS system at 160 Mpc by the HLV network in the 2019+ run (left) and by the four-detector network (HILV) comprising three LIGO sites – in Hanford, Livingston and India (I) – and Virgo operating in 2022+ with all detectors at final design sensitivity (right). The inclusion of a fourth site in India provides good localization over the whole sky.

Table 1: Summary of a plausible observing schedule, expected sensitivities, and source localization with the advanced LIGO and Virgo detectors, which will be strongly dependent on the detectors’ commissioning progress. The burst ranges assume standard-candle emission of −2 2 10 M ⊙c in gravitational waves at 150 Hz and scale as 1∕2 E GW, so it is greater for more energetic sources (such as binary black holes). The binary neutron-star (BNS) localization is characterized by the size of the 90% credible region (CR) and the searched area. For 2015 – 2016 and 2016 – 2017, these have been calculated from parameter-estimation studies (neglecting detector calibration uncertainty) [31*, 99*] using LALInference [110]. The CRs for subsequent periods are estimated from timing triangulation (highlighted by italics), which is known to provide estimates on average a factor of ∼ 4 too large for a three-detector network [60*, 31*], hence these serve as a conservative bound. Both ranges as well as the BNS timing-triangulation localizations reflect the uncertainty in the detector noise spectra shown in Figure 1*. Differences in the shape of the detector noise curves and also relative sensitivities between detectors have an effect on the localization areas. The BNS detection numbers also account for the uncertainty in the BNS source rate density [13]. BNS detection numbers and localization estimates are computed assuming a signal-to-noise ratio greater than 12. Burst localizations are expected to be broadly similar to those derived from timing triangulation, but vary depending on the signal bandwidth; the median burst searched area (with a false alarm rate of ∼ 1 yr−1) may be a factor of ∼ 2 – 3 larger than the values quoted for BNS signals [51]. No burst detection numbers are given, since the source rates are currently unknown. Localization and detection numbers assume an 80% duty cycle for each instrument.
2015 – 2016 2016 – 2017 2017 – 2018 2019+ 2022+ (India)
Estimated run duration
4 months 6 months 9 months (per year) (per year)
Burst range/Mpc
LIGO 40 – 60 60 – 75 75 – 90 105 105
Virgo 20 – 40 40 – 50 40 – 80 80
BNS range/Mpc
LIGO 40 – 80 80 – 120 120 – 170 200 200
Virgo 20 – 60 60 – 85 65 – 115 130
Estimated BNS detections
0.0005 – 4 0.006 – 20 0.04 – 100 0.2 – 200 0.4 – 400
90% CR
% within
5 deg2 < 1 2 > 1–2 > 3–8 > 20
20 deg2 < 1 14 > 10 > 8–30 > 50
480 230
searched area
% within
5 deg2 6 20
20 deg2 16 44
88 29

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