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Binary black hole population inference combining confident and marginal events from the $\tt{IAS\text{-}HM}$ search pipeline

Ajit Kumar Mehta, Digvijay Wadekar, Isha Anantpurkar, Javier Roulet, Tejaswi Venumadhav, Tousif Islam, Jonathan Mushkin, Barak Zackay, Matias Zaldarriaga

TL;DR

This paper develops a hierarchical Bayesian framework to infer binary black hole population properties by incorporating both confident and marginal events detected by the IAS-HM pipeline during LVK O3. By linking the observed triggers to an astrophysical BBH population model via a reweighted probability $p_{astro}$ and a population-averaged sensitive volume $\overline{VT}$, the authors quantify how marginal events influence key population parameters such as the redshift evolution $\kappa$ and the mass-ratio slope $\beta_q$, while validating their method against LVK GWTC-3 results. When restricted to high-significance events, the IAS-HM results align with GWTC-3, but including marginal events shifts the inference toward stronger redshift evolution and more asymmetric mergers, though within prior ranges. The work highlights the value of incorporating marginal detections and independent pipelines for robust BBH population studies and motivates extended modeling (e.g., spins, IMBH components) with future data from O4 and beyond.

Abstract

We present the population properties of binary black hole mergers identified by the $\tt{IAS\text{-}HM}$ pipeline (which incorporates higher-order modes in the search templates) during the third observing run (O3) of the LIGO, Virgo, and KAGRA (LVK) detectors. In our population inference analysis, instead of only using events above a sharp cut based on a particular detection threshold (e.g., false alarm rate), we use a Bayesian framework to consistently include both marginal and confident events. We find that our inference based solely on highly significant events ($p_{\mathrm{astro}} \sim 1$) is broadly consistent with the GWTC-3 population analysis performed by the LVK collaboration. However, incorporating marginal events into the analysis leads to a preference for stronger redshift evolution in the merger rate and an increased density of asymmetric mass-ratio mergers relative to the GWTC-3 analysis, while remaining within its allowed parameter ranges. Using simple parametric models to describe the binary black hole population, we estimate a merger rate density of $32.4^{+18.5}_{-12.2}\ \mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ at redshift $z = 0.2$, and a redshift evolution parameter of $κ= 4.4^{+1.9}_{-2.0}$. Assuming a power-law form for the mass ratio distribution ($\propto q^β$), we infer $β= 0.1^{+1.9}_{-1.4}$, indicating a relatively flat distribution. These results highlight the potential impact of marginal events on population inferences and motivate future analyses with data from upcoming observing runs.

Binary black hole population inference combining confident and marginal events from the $\tt{IAS\text{-}HM}$ search pipeline

TL;DR

This paper develops a hierarchical Bayesian framework to infer binary black hole population properties by incorporating both confident and marginal events detected by the IAS-HM pipeline during LVK O3. By linking the observed triggers to an astrophysical BBH population model via a reweighted probability and a population-averaged sensitive volume , the authors quantify how marginal events influence key population parameters such as the redshift evolution and the mass-ratio slope , while validating their method against LVK GWTC-3 results. When restricted to high-significance events, the IAS-HM results align with GWTC-3, but including marginal events shifts the inference toward stronger redshift evolution and more asymmetric mergers, though within prior ranges. The work highlights the value of incorporating marginal detections and independent pipelines for robust BBH population studies and motivates extended modeling (e.g., spins, IMBH components) with future data from O4 and beyond.

Abstract

We present the population properties of binary black hole mergers identified by the pipeline (which incorporates higher-order modes in the search templates) during the third observing run (O3) of the LIGO, Virgo, and KAGRA (LVK) detectors. In our population inference analysis, instead of only using events above a sharp cut based on a particular detection threshold (e.g., false alarm rate), we use a Bayesian framework to consistently include both marginal and confident events. We find that our inference based solely on highly significant events () is broadly consistent with the GWTC-3 population analysis performed by the LVK collaboration. However, incorporating marginal events into the analysis leads to a preference for stronger redshift evolution in the merger rate and an increased density of asymmetric mass-ratio mergers relative to the GWTC-3 analysis, while remaining within its allowed parameter ranges. Using simple parametric models to describe the binary black hole population, we estimate a merger rate density of at redshift , and a redshift evolution parameter of . Assuming a power-law form for the mass ratio distribution (), we infer , indicating a relatively flat distribution. These results highlight the potential impact of marginal events on population inferences and motivate future analyses with data from upcoming observing runs.

Paper Structure

This paper contains 14 sections, 22 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Population likelihood
  3. Events and Data
  4. $\tt{CogwheelPop}$: Likelihood implementation and Sampling
  5. Discussion
  6. O3 LVK and $\tt{IAS\text{-}HM}$ events with $\mathrm{IFAR} > 1\, \rm{yr}$
  7. $\tt{IAS\text{-}HM}$ events with $\mathrm{IFAR} > 0.2\, \rm{yr}$
  8. Conclusion
  9. Computation of the reference $p_{\rm{astro}}$ of the triggers
  10. $\tt{POWER\ LAW} + \tt{PEAK}$ model of BBH Parameters
  11. Primary mass ($m_1$) and mass ratio ($q$)
  12. Spin model
  13. Merger rate density $R(z)$
  14. Priors for the hyperparameters

Figures (5)

  • Figure 1: Top panels: Inferred differential merger-rate densities for primary mass $m_1$ and secondary mass $m_2$. We compare $\tt{IAS\text{-}HM}$ O3-catalog (including confident and marginal events with $\mathrm{IFAR}>0.2$ yr) to the GWTC-3 ($\mathrm{O1+O2+O3}$) population model. Medians and $90\%$ credible bands are shown. The $m_1$ distribution remains broadly consistent with GWTC-3, while the $m_2$ distribution is consistent within uncertainties but assigns slightly higher probability at the upper end of the spectrum. Bottom panels: Inferred differential merger-rate density as a function of mass ratio $q$ (left) and the redshift evolution $R(z)$ (right). The $q$ distribution is noticeably flatter than GWTC-3, favoring more asymmetric mergers. For $R(z)$, the $\tt{IAS\text{-}HM}$ inference favors a steeper rise with redshift, consistent with the larger growth rate ($\kappa$) obtained when marginal events are included.
  • Figure 2: We first check that we obtain results consistent with the LVK analysis when we include only our higher significance ($\mathrm{IFAR} > 1$ yr) events in our analysis. We show posterior distributions of the $\tt{POWER\ LAW} + \tt{PEAK}$ hyperparameters for the GWTC-3 analysis (green), GWTC-3 O3-only analysis (blue), our $\tt{CogwheelPop}$ reproduction of the GWTC-3 O3-only result (purple), and the $\tt{IAS\text{-}HM}$ catalog with the same $\mathrm{IFAR} > 1$ yr threshold (orange). Note that $\tt{CogwheelPop}$IshaInPrep is the population inference code used in our analysis (which is a generalized version of the $\tt{cogwheel}$Rou22_cogwheel parameter estimation package for hierarchical Bayesian inference) and $\tt{Zenodo}$ corresponds to the hyperposterior samples taken from zenodoLVKPop. The close match between $\tt{IAS\text{-}HM}$ and GWTC-3 posteriors highlights the consistency between results of independent search pipelines.
  • Figure 3: Similar to Fig. \ref{['fig:Hyperparams_post_0']}, but also including marginal-significance events ($\mathrm{IFAR} \geq 0.2$ yr) from the $\tt{IAS\text{-}HM}$ catalog (orange) in our population inference analysis. Results are compared to the GWTC-3 (green) and GWTC-3 O3-only (blue) posteriors. The major differences upon including marginal events is that the redshift evolution parameter $\kappa$ increases and the mass-ratio slope $\beta_q$ is flatter.
  • Figure 4: Median posterior estimates of mass ratio $q$ and redshift $z$ for the $\tt{IAS\text{-}HM}$ events with $\mathrm{IFAR}>0.2$ yr which are not in GWTC-3 lvc_gwtc3_o3_ab_catalog_2021. Circular markers show medians under the standard LVK PE prior. Triangular markers show medians after reweighting with our population model and marginalizing over hyperparameter uncertainties, with their color gradient indicating the IFAR values. Shifts toward higher $q$ and $z$ after reweighting reflect the coupling between the inferred $\kappa$ and $\beta_q$, as evident in Figure \ref{['fig:Hyperparams_post_1']}.
  • Figure 5: Astrophysical probabilities, $p_{\mathrm{astro}}$, for events (ordered here by their trigger time, $t_\mathrm{gps}$) with $\mathrm{IFAR} > 0.2$ yr ($x$-axis), computed using the injection set described in Appendix \ref{['app:p_astro']}. For comparison, we also show the $p_{\mathrm{astro}}$ values assigned directly by the $\tt{IAS\text{-}HM}$ pipeline, which estimates them by comparing the ranking score densities of coincident triggers between the Livingston and Hanford detectors with those of other (i.e., background) triggers.