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

Abstract

We present a possible observing scenario for the Advanced LIGO and Advanced Virgo gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We determine the expected sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron-star systems, which are considered the most promising for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and 90% credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5 deg² to 20 deg² will require at least three detectors of sensitivity within a factor of ∼ 2 of each other and with a broad frequency bandwidth. Should the third LIGO detector be relocated to India as expected, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.

Keywords: Data analysis; Electromagnetic counterparts; Gravitational waves; Gravitational-wave detectors.

Figure 1

aLIGO (left) and AdV (right) target strain sensitivity as a function of frequency. The binary neutron-star (BNS) range, the average distance to which these signals could be detected, is given in megaparsec. Current notions of the progression of sensitivity are given for early, mid and late commissioning phases, as well as the final design sensitivity target and the BNS-optimized sensitivity. While both dates and sensitivity curves are subject to change, the overall progression represents our best current estimates.

Figure 2

The planned sensitivity evolution and observing runs of the aLIGO and AdV detectors over the coming years. The colored bars show the observing runs, with the expected sensitivities given by the data in Figure 1. There is significant uncertainty in the start and end times of the observing runs, especially for those further in the future, and these could move forward or backwards by a few months relative to what is shown above. The plan is summarised in Section 2.2.

Figure 3

False alarm rate versus detection statistic for compact binary coalescence (CBC) and burst searches on 2009–2010 LIGO-Virgo data. Left: Cumulative rate of background events for a subset of the CBC search parameter space, as a function of the threshold ranking statistic ρ_c [19]. Different methods were used to estimate the background for rate for high and low ρ_c, which is why there is an apparent gap in the data points. The background for the full search was approximately a factor of six higher. Right: Cumulative rate of background events for the burst search, as a function of the coherent network amplitude η [14]. For ease of comparison, we have also plotted the approximate equivalent ρ_c for the burst search (an exact identification is not possible as the search methods differ). The burst events are divided into two sets based on their central frequency.

Figure 4

Source localization by triangulation for the aLIGO-AdV network. The locations of the three detectors are indicated by black dots, with LIGO Hanford labeled H; LIGO Livingston as L, and Virgo as V. The locus of constant time delay (with associated timing uncertainty) between two detectors forms an annulus on the sky concentric about the baseline between the two sites (labeled by the two detectors). For three detectors, these annuli may intersect in two locations. One is centered on the true source direction (S), while the other (S′) is its mirror image with respect to the geometrical plane passing through the three sites. For four or more detectors there is a unique intersection region of all of the annuli. Figure adapted from [41].

Figure 5

Posterior probability density for sky location for an example binary neutron-star coalescence observed with a two-detector network. Left: Map produced by the low-latency BAYESTAR code [99, 98]. Right: Map produced by the higher-latency (non-spinning) LALInference [110], which also produces posterior estimates for other parameters. These algorithms are discussed in Section 3.2.1. The star indicates the true source location. The event has a network signal-to-noise ratio of ρ_c = 13.2 using a noise curve appropriate for the first aLIGO run (O1, see Section 4.1). The plot is a Mollweide projection in geographic coordinates. Image reproduced with permission from [31], copyright by APS; further mock sky maps for the first two observing runs can be found at www.ligo.org/scientists/first2years/ for binary neutron-star signals and www.ligo.org/scientists/burst-first2years/ for burst signals.

Figure 6

Anticipated binary neutron-star sky localization during the first two observing runs (top: O1, see Section 4.1; bottom: O2, see Section 4.2). The plots show the cumulative fractions of events with sky-localization areas smaller than the abscissa value. Left: Sky area of 90% credible region , the (smallest) area enclosing 90% of the total posterior probability. Right: Searched area , the area of the smallest credible region containing the true position. Results are shown for the low-latency bayestar [98] and higher-latency (non-spinning) LALInference (LI) [110] codes. The O2 results are divided into those where two detectors (2-det) are operating in coincidence, and those where three detectors (3-det) are operating: assuming a duty cycle of ∼ 80% for each instrument, the two-detector network would be operating for ∼ 40% of the total time and the three-detector network ∼ 50% of the time. The shaded areas indicate the 68% confidence intervals on the cumulative distributions. A detection threshold of a signal-to-noise ratio of 12 is used and results are taken from [31, 99].

Figure 7

Simulated sky localization for Gaussian (G; top left), sine-Gaussian (SG; top right), broadband white-noise (WN; bottom left) and binary black-hole (BBH; bottom right) bursts during the first two observing runs (O1, see Section 4.1, and O2, see Section 4.2). The plots show the cumulative fractions of events with searched areas A_* smaller than the abscissa value. Results are shown for the low-latency coherent WaveBurst (cWB) [70, 71, 73] and higher-latency LALInferenceBurst (LIB) [110] codes. The O2 results consider only a three-detector (3-det) network; assuming an instrument duty cycle of ∼ 80%, this would be operational ∼ 50% of the time. The shaded areas indicate the 68% confidence intervals on the cumulative distributions. A detection threshold of a false alarm rate of approximately 1 yr⁻¹ is used and results are taken from [51].

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.