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Evaluating statistical significance for massive black hole binary mergers with space-based gravitational wave detectors

Hong-Yu Chen, En-Kun Li, Yi-Ming Hu

Abstract

Important scientific discoveries should be backed by high statistical significance. In the 2030s, multiple space-based gravitational wave detectors are expected to operate. While many works aim to achieve quick and reliable detection and parameter estimation of millihertz gravitational wave sources, dedicated studies are lacking to assess the significance of space-based detectors. In this work, we propose a framework to assess the statistical significance of massive black hole binaries (MBHBs) detections with space-based gravitational wave detectors. We apply this algorithm to simulated data with Gaussian stationary noise and the complex LDC-2a dataset to measure the false alarm rate and significance of MBHB signals. We also analyze factors affecting the significance of MBHBs and design a method to mitigate multi-source confusion interference. In Gaussian noise conditions, MBHBs with a signal-to-noise ratio of about 7 can achieve $3 σ$ significance, and those with a signal-to-noise ratio of about 8 achieve $4 σ$. Our analysis demonstrates that all MBHB signals in the LDC-2a dataset have a significance exceeding $4.62 σ$.

Evaluating statistical significance for massive black hole binary mergers with space-based gravitational wave detectors

Abstract

Important scientific discoveries should be backed by high statistical significance. In the 2030s, multiple space-based gravitational wave detectors are expected to operate. While many works aim to achieve quick and reliable detection and parameter estimation of millihertz gravitational wave sources, dedicated studies are lacking to assess the significance of space-based detectors. In this work, we propose a framework to assess the statistical significance of massive black hole binaries (MBHBs) detections with space-based gravitational wave detectors. We apply this algorithm to simulated data with Gaussian stationary noise and the complex LDC-2a dataset to measure the false alarm rate and significance of MBHB signals. We also analyze factors affecting the significance of MBHBs and design a method to mitigate multi-source confusion interference. In Gaussian noise conditions, MBHBs with a signal-to-noise ratio of about 7 can achieve significance, and those with a signal-to-noise ratio of about 8 achieve . Our analysis demonstrates that all MBHB signals in the LDC-2a dataset have a significance exceeding .
Paper Structure (9 sections, 2 equations, 4 figures, 3 tables)

This paper contains 9 sections, 2 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Theoretical background
  3. Statistical significance
  4. Assessment of significance
  5. Result
  6. Gaussian Noise
  7. LDC-2a Sangria Dataset
  8. Summary
  9. Detectors

Figures (4)

  • Figure 1: The significance evaluation pipeline for MBHBs in space-based GW detectors.
  • Figure 2: The left panel shows the theoretical noise A/E channel PSD of TianQin (red), LISA (blue), and LISA with foreground (green). The right panel illustrates the SNR distribution of false alarms, which is compared with the survival function of the Rayleigh distribution (lighter areas). The blue dashed line denotes the results of LISA after the low-frequency hard cutoff. The left-hand axis of the right panel shows the cumulative count rate (FAR) at different SNRs. The right-hand axis is the significance corresponding to different FARs.
  • Figure 3: The SNR distribution of false alarms, similar with Fig. \ref{['fig:CCRofGaussianNoise']}, but for Sangria dataset with two kinds of PSD.
  • Figure 4: The histograms of the distribution of false alarms with $\rho \geq$ 5 (left panels) or 8 (right panels) in terms of chirp mass and luminosity distance for different PSDs.