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Detection probability of light compact binary mergers in future observing runs of the current ground-based gravitational wave detector network

Om Sharan Salafia

TL;DR

The work presents a minimal Poisson-statistics framework to forecast future LVK detections of BNS and NSBH mergers using past event counts and the ratio of future-to-past time-volume, $\mathcal{C}=\lambda/\lambda'$. A closed-form posterior $p(N|N',\alpha,\mathcal{C})$ is derived, with priors $\alpha \in \{0,\tfrac12,1\}$, enabling mass-distribution independent predictions. The method is applied to O4 and O5, yielding O4c probabilities for additional BNS detections of $34\%-46\%$ and NSBH of $64\%-71\%$, and forecasting O5 counts around $N_{\mathrm{BNS,O5}}=28_{-21}^{+44}$ and $N_{\mathrm{NSBH,O5}}=65_{-38}^{+61}$; the local BNS rate density is updated to $2.8\,\mathrm{Gpc^{-3}\,yr^{-1}} \leq R_0 \leq 480\,\mathrm{Gpc^{-3}\,yr^{-1}}$. While simple, the approach highlights near-term detection prospects and provides a practical tool for planning electromagnetic follow-up, subject to refinement via injections and more detailed sensitivity modeling.

Abstract

With no binary neutron star (BNS) merger detected yet during the fourth observing run (O4) of the LIGO-Virgo-KAGRA (LVK) gravitational wave (GW) detector network, despite the time-volume (VT) surveyed with respect to the end of O3 increased by more than a factor of three, a pressing question is how likely the detection of at least one BNS merger is in the remainder of the run. I present here a simple and general method to address such a question, which constitutes the basis for the predictions that have been presented in the LVK Public Alerts User Guide during the hiatus between the O4a and O4b parts of the run. The method, which can be applied to neutron star - black hole (NSBH) mergers as well, is based on simple Poisson statistics and on an estimate of the ratio of the VT span by the future run to that span by previous runs. An attractive advantage of this method is that its predictions are independent from the mass distribution of the merging compact binaries, which is very uncertain at the present moment. The results, not surprisingly, show that the most likely outcome of the final part of O4 is the absence of any BNS merger detection. Still, the probability of a non-zero number of detections is 34-46\%. For NSBH mergers, the probability of at least one additional detection is 64-71\%. The prospects for the next observing run O5 are more promising, with predicted numbers $N_\mathrm{BNS,O5}=28_{-21}^{+44}$, and the NSBH detections to be $N_\mathrm{NSBH,O5}=65_{-38}^{+61}$ (median and 90\% symmetric credible range), based on the current LVK detector target sensitivities for the run. The calculations presented here also lead to an update of the LVK local BNS merger rate density estimate that accounts for the absence of BNS merger detections in O4 so far, that reads $2.8\,\mathrm{Gpc^{-3}\,yr^{-1}}\leq R_0\leq 480\,\mathrm{Gpc^{-3}\,yr^{-1}}$.

Detection probability of light compact binary mergers in future observing runs of the current ground-based gravitational wave detector network

TL;DR

The work presents a minimal Poisson-statistics framework to forecast future LVK detections of BNS and NSBH mergers using past event counts and the ratio of future-to-past time-volume, . A closed-form posterior is derived, with priors , enabling mass-distribution independent predictions. The method is applied to O4 and O5, yielding O4c probabilities for additional BNS detections of and NSBH of , and forecasting O5 counts around and ; the local BNS rate density is updated to . While simple, the approach highlights near-term detection prospects and provides a practical tool for planning electromagnetic follow-up, subject to refinement via injections and more detailed sensitivity modeling.

Abstract

With no binary neutron star (BNS) merger detected yet during the fourth observing run (O4) of the LIGO-Virgo-KAGRA (LVK) gravitational wave (GW) detector network, despite the time-volume (VT) surveyed with respect to the end of O3 increased by more than a factor of three, a pressing question is how likely the detection of at least one BNS merger is in the remainder of the run. I present here a simple and general method to address such a question, which constitutes the basis for the predictions that have been presented in the LVK Public Alerts User Guide during the hiatus between the O4a and O4b parts of the run. The method, which can be applied to neutron star - black hole (NSBH) mergers as well, is based on simple Poisson statistics and on an estimate of the ratio of the VT span by the future run to that span by previous runs. An attractive advantage of this method is that its predictions are independent from the mass distribution of the merging compact binaries, which is very uncertain at the present moment. The results, not surprisingly, show that the most likely outcome of the final part of O4 is the absence of any BNS merger detection. Still, the probability of a non-zero number of detections is 34-46\%. For NSBH mergers, the probability of at least one additional detection is 64-71\%. The prospects for the next observing run O5 are more promising, with predicted numbers , and the NSBH detections to be (median and 90\% symmetric credible range), based on the current LVK detector target sensitivities for the run. The calculations presented here also lead to an update of the LVK local BNS merger rate density estimate that accounts for the absence of BNS merger detections in O4 so far, that reads .

Paper Structure

This paper contains 9 sections, 26 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Poisson probability informed by previous occurrences of a rare event
  3. Application to compact binary mergers
  4. Evaluation of the effective sensitive volume for each run
  5. Application to BNS and NSBH mergers in O4
  6. Updated local BNS merger rate density estimate
  7. Predictions for O5
  8. Discussion and conclusions
  9. Sub-network time fractions

Figures (3)

  • Figure 1: BNS and NSBH merger detection probability in O4c. The red squares in the left-hand panel show the probability that exactly $N_\mathrm{O4c2}$ BNS mergers are detected by the LVK network during O4c2, based on the number $N'=2$ detected in previous runs, according to Eq. \ref{["eq:P(N|N')"]} and adopting the Jeffreys prior ($\alpha=1/2$). The blue circles refer to NSBH instead, assuming $N'=5$. In the right-hand panel, the probability of a number of detections $N\geq N_\mathrm{O4c2}$ in O4c2 is shown for the same two classes of sources.
  • Figure 2: Probability of at least one detection in the remainder of O4, as a function of time $t$ from the start of O4c2, for three different prior choices (different colours), keeping $N'=2$ fixed (i.e. assuming no detection, solid lines). The dashed line represents the probability of at least one hypothetical further detection after a third detection has been made during O4c2.
  • Figure 3: BNS merger detection probability in O5. The left-hand panel is the same as the corresponding panel in Fig. \ref{['fig:PNO4c']}, but for O5. The right-hand panel shows the corresponding cumulative probability.