Observing Capabilities¶

This section summarizes the projected observing capabilities of the global gravitational-wave detector network as of March 2023, superseding the Living Review [5] on prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo, and KAGRA.

Timeline¶

The gravitational-wave observing schedule is divided into Observing Runs or epochs of months to years of operation at fixed sensitivity, down time for construction and commissioning, and transitional Engineering Runs between commissioning and observing runs. The long-term observing schedule is shown below. Since BNS mergers are a well-studied class of gravitational-wave signals, this figure gives the BNS range for a single-detector SNR threshold of 8 in each observing run.

Observing Run 4 (O4) started on May 24, 2023, and will continue for 20 calendar months from that date. We expect that up to four facilities (LHO, LLO, Virgo, and KAGRA) will contribute data during O4.

• LHO, LLO, and Virgo are currently operational. The BNS range spans approximately 150-170 Mpc for LHO and LLO while for Virgo it extends to about 45-55 Mpc. Virgo data will not be used for detection, but it will be used for sky localization, parameter estimation, and downstream analyses.

• These three facilities were offline for commissioning for about 2 months starting January 16, 2024. The second part of the observing run (O4b) started on April 10, 2024.

• KAGRA plans to join O4b in December 2024 with a with a BNS range of around 10 Mpc.

Downtime for upgrades and commissioning are depicted in the figure above by vertical gray bands.

Live Status¶

There are a handful of public web pages that report live status of the LIGO/Virgo/KAGRA detectors and alert infrastructure.

• Detector Status Portal: Daily summary of detector performance.

  https://gwosc.org/detector_status/
• GWIStat: Real-time detector up/down status and estimated range.

  https://online.ligo.org

Probability of the Detection of BNS and NSBH Mergers in O4b¶

With no significant BNS alert during O4a, despite the increase in the time-volume surveyed with respect to the end of O3, a pressing question is how likely the detection of at least one such source is in the remainder of O4. An estimate of the probability of a number \(N\) of detections of a given source class in a run can be obtained based on the number \(N'\) of detections in the previous runs (assuming these to be actual astrophysical signals), and on the ratio of the sensitive time-volume surveyed in the new run to that of previous runs, \(\mathcal{C}=VT/V'T'\). Here \(V\) is the sensitive volume of the detector network to the class of sources, \(T\) is the run duration, and primed quantities refer to past runs. Such probability has been derived by [1] (their Equation 42) assuming a uniform prior on the average rate, and by [2] (their Equation B3) for a more general choice of prior.

For compact binary merger gravitational wave sources whose signal, in the band of the detectors, is dominated by the inspiral (such as BNS and light NSBH) and for which the detection horizon is at redshift \(z\ll 1\), the sensitive volume scales with the chirp mass [3]. Therefore the ratio \(\mathcal{C}\) is insensitive to the mass distribution. Within such an approximation, we can calculate the \(\mathcal{C}\) ratio of O4b with respect to the combined previous runs in a relatively simple way based only on the BNS ranges of the LIGO and Virgo detectors during the previous runs and those expected in the O4b run. Refer to LIGO-P2400022 for a detailed derivation.

For the calculation, we assume a duration of \(T=297\) days for O4b (reflecting the current LIGO, Virgo, and KAGRA observing run plans) and we adopt BNS ranges of 150, 160 and 50 Mpc for LHO, LLO, and Virgo, respectively, based on pre-O4b detector logs available on the Detector Status Portal. We further assume the same detector duty cycles as in O3b. With these assumptions, the ratio of the O4b time volume to that of the combined previous runs is \(\mathcal{C}=0.86\). For BNS, we set the number of previously detected events to \(N'=2\) based on confident astrophysical signals from BNS detected in O2 and O3 [8]. For NSBH, we set it to \(N'=4\) based on the number of events with FAR less than 1 in 4 years in such class as reported in the GWTC-3 catalog [8], plus the number of high-probability NSBH candidates for which public alerts have been issued up to the end of O4a (as reported in GraceDB). Setting the prior on the average detection rate equal to the Jeffreys prior for a Poisson distribution, we obtain the results summarized in the following figure:

(Source code)

The red squares in the figure show the probability of obtaining at least \(N_\mathrm{O4b}\) BNS detections over O4b. In particular, it shows that the probability of at least one BNS detection is around 73%. This probability varies by less than 10% when adopting different priors or assuming the duty cycles of O3a instead of those of O3b.

The blue circles in the figure show the corresponding probability for NSBH. The probability of at least one NSBH detection in O4b is 94%. Adopting different priors affects this probability by a few percent.

We based the above results on an updated estimate of the time-volume surveyed since O1, and we assumed that no new BNS has been detected since GWTC-3. This means that our calculation implicitly makes use of a revised BNS local rate density. This can be made explicit, as follows. Given that we use no new information on the BNS mass distribution, and we assume \(N'\) is unchanged, our rate density estimate and the associated uncertainty scale as \(1/VT\). From our calculation, the \(VT\) surveyed in O4a is 0.85 times that spanned by the GWTC-3 observations. Therefore, the revised BNS rate density (combined 90% uncertainty range from the three models described in [9]) is 5 - 920 \(\mathrm{Gpc^{-3}\,yr^{-1}}\). We will provide further updates that incorporate offline search results, refined sensitivity estimates, and our revised understanding of the BNS population in forthcoming publications.

Public Alert Rate and Localization Accuracy¶

Here we provide predicted public alert rates, distances, and localization uncertainties for BNS, NSBH, and BBH mergers in O4 and O5, based on a Monte Carlo simulation of detection and localization of events. We note that these numbers assume Virgo’s participation, and so are optimistic relative to what is expected early in O4.

The methodology and results of the simulation are described in [7] (also see [5] and [6]).

Source code to reproduce these simulations is available at https://github.com/lpsinger/observing-scenarios-simulations/tree/v2 or https://doi.org/10.5281/zenodo.5206852.

Sky localization FITS files from these simulations are provided at doi:10.5281/zenodo.7026209.

Detection Threshold¶

The network SNR threshold for detection was set to 8 in order to approximately reproduce the rate of public alerts that were sent in O3 (see [6]).

Detector Network¶

The detector amplitude spectral density (Hz\(^{-1/2}\)) curves used for the simulation are available in LIGO-T2200043-v3. The filenames for each detector and observing run are given in the table below.

These noise curves correspond to the high ends of the BNS ranges shown in the timeline figure above, with the exception of Virgo in O4, for which it represents the low end.

We assume that each detector has an independent observing duty cycle of 70%.

Source Distribution¶

We draw masses and spins of compact objects from a global maximum a posteriori fit of all O3 compact binary observations [9]. The distribution and its parameters are described below.

Masses

The 1D source-frame component mass distribution is the “Power Law + Dip + Break” model based on [10], and is given by:

defined for \(1 \leq m / M_\odot \leq 100\). It consists of four terms:

• a high-mass tapering function \(l(m|M_\mathrm{max},\eta_\mathrm{max}) = \left(1 + \left(m / M_\mathrm{max}\right)^{\eta_\mathrm{max}}\right)^{-1}\),

• a low-mass tapering function \(h(m|M_\mathrm{min},\eta_\mathrm{min}) = 1 - l(m|M_\mathrm{min},\eta_\mathrm{min})\),

• a function \(n(m| M^\mathrm{gap}_\mathrm{low}, M^\mathrm{gap}_\mathrm{high}, \eta_\mathrm{low}, \eta_\mathrm{high}, A) = 1 - A \, l(m|M^\mathrm{gap}_\mathrm{high}, \eta_\mathrm{high}) \, h(m|M^\mathrm{gap}_\mathrm{low}, \eta_\mathrm{low})\) that suppresses masses in the hypothetical “mass gap” between NSs and BHs, and

• a piecewise power law.

The joint 2D distribution of the primary mass \(m_1\) and the secondary mass \(m_2\) builds on the 1D component mass distribution and adds a pairing function that weights binaries by mass ratio:

defined for \((m_1 \geq m_2) \cap ((m_1 \leq 60 M_\odot) \cup (m_2 \geq 2.5 M_\odot))\). The two figures below show the 1D and joint 2D component mass distributions (using a linear probability density scale).

(Source code)

Spins

The spins of the binary component objects are isotropically oriented. Component objects with masses less than 2.5 \(M_\odot\) have spin magnitudes that are uniformly distributed from 0 to 0.4, and components with greater masses have spin magnitudes that are uniformly distributed from 0 to 1.

Sky Location, orientation

Sources are isotropically distributed on the sky and have isotropically oriented orbital planes.

Redshift

Sources are uniformly distributed in differential comoving volume per unit proper time.

Rate

The total rate density of mergers, integrated across all masses and spins, is set to \(240_{-140}^{+270}\,\mathrm{Gpc}^{-3}\mathrm{yr}^{-1}\) ([9], Table II, first row, last column).

Parameters

The parameters of the mass and spin distribution are given below.

Summary Statistics¶

The table below summarizes the estimated public alert rate and sky localization accuracy in O4 and O5. All values are given as a 5% to 95% confidence intervals.

Merger rate per unit comoving volume per unit proper time is the astrophysical rate of mergers in the reference frame that is comoving with the Hubble flow. It is averaged over a distribution of masses and spins that is assumed to be non-evolving.

Sensitive volume is the quotient of the rate of detected events per unit observer time and the merger rate per unit comoving volume per unit proper time. The definition is given in the glossary entry for sensitive volume. To calculate the detection rate, multiply the merger rate by the sensitive volume.

The quoted confidence interval represents the uncertainty from the Monte Carlo simulation.

Annual number of public alerts is the number of alerts in one calendar year of observation. The quoted confidence interval incorporates both the log-normal distribution of the merger rate and Poisson counting statistics, but does not include the Monte Carlo error (which is negligible compared to the first two sources of uncertainty).

The remaining sections all give median values over the population of detectable events.

Median luminosity distance is the median luminosity distance in Mpc of detectable events. The quoted confidence interval represents the uncertainty from the Monte Carlo simulation.

Median 90% credible area is the area in deg\(^2\) of the smallest (not necessarily simply connected) region on the sky that has a 90% chance of containing the true location of the source.

Median 90% credible volume is the median comoving volume enclosed in the smallest region of space that has a 90% chance of containing the true location of the source.

Cumulative Histograms¶

Below are cumulative histograms of the 90% credible area, 90% credible comoving volume, and luminosity distance of detectable events in O3, O4, and O5.