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Measuring gravitational waves from binary black hole coalescences: I. Signal to noise for inspiral, merger, and ringdown

Eanna E. Flanagan, Scott A. Hughes

TL;DR

The paper develops a comprehensive framework to estimate the signal-to-noise ratios of gravitational waves from binary black hole coalescences across three phases—inspiral, merger, and ringdown—for initial and advanced ground-based detectors (LIGO/VIRGO) and space-based LISA. It combines energy-spectrum models for each phase with detector noise curves and three detection strategies (matched filtering, band-pass filtering, and noise-monitoring) to map out detectability and potential gains from merger templates. Key findings show BBHs could be among the first LIGO detections, with merger and ringdown channels expanding reach to higher masses, while LISA can achieve extremely large SNRs for supermassive BBHs, enabling precision measurements and tests of general relativity. The analysis also highlights the importance of numerical-relativity merger templates for maximizing detection rates and extracting information from strong-field gravity signals.

Abstract

We estimate the expected signal-to-noise ratios (SNRs) from the three phases (inspiral,merger,ringdown) of coalescing binary black holes (BBHs) for initial and advanced ground-based interferometers (LIGO/VIRGO) and for space-based interferometers (LISA). LIGO/VIRGO can do moderate SNR (a few tens), moderate accuracy studies of BBH coalescences in the mass range of a few to about 2000 solar masses; LISA can do high SNR (of order 10^4) high accuracy studies in the mass range of about 10^5 to 10^8 solar masses. BBHs might well be the first sources detected by LIGO/VIRGO: they are visible to much larger distances (up to 500 Mpc by initial interferometers) than coalescing neutron star binaries (heretofore regarded as the "bread and butter" workhorse source for LIGO/VIRGO, visible to about 30 Mpc by initial interferometers). Low-mass BBHs (up to 50 solar masses for initial LIGO interferometers; 100 for advanced; 10^6 for LISA) are best searched for via their well-understood inspiral waves; higher mass BBHs must be searched for via their poorly understood merger waves and/or their well-understood ringdown waves. A matched filtering search for massive BBHs based on ringdown waves should be capable of finding BBHs in the mass range of about 100 to 700 solar masses out to 200 Mpc (initial LIGO interferometers), and 200 to 3000 solar masses out to about z=1 (advanced interferometers). The required number of templates is of order 6000 or less. Searches based on merger waves could increase the number of detected massive BBHs by a factor of order 10 or more over those found from inspiral and ringdown waves, without detailed knowledge of the waveform shapes, using a "noise monitoring" search algorithm. A full set of merger templates from numerical relativity could further increase the number of detected BBHs by an additional factor of up to 4.

Measuring gravitational waves from binary black hole coalescences: I. Signal to noise for inspiral, merger, and ringdown

TL;DR

The paper develops a comprehensive framework to estimate the signal-to-noise ratios of gravitational waves from binary black hole coalescences across three phases—inspiral, merger, and ringdown—for initial and advanced ground-based detectors (LIGO/VIRGO) and space-based LISA. It combines energy-spectrum models for each phase with detector noise curves and three detection strategies (matched filtering, band-pass filtering, and noise-monitoring) to map out detectability and potential gains from merger templates. Key findings show BBHs could be among the first LIGO detections, with merger and ringdown channels expanding reach to higher masses, while LISA can achieve extremely large SNRs for supermassive BBHs, enabling precision measurements and tests of general relativity. The analysis also highlights the importance of numerical-relativity merger templates for maximizing detection rates and extracting information from strong-field gravity signals.

Abstract

We estimate the expected signal-to-noise ratios (SNRs) from the three phases (inspiral,merger,ringdown) of coalescing binary black holes (BBHs) for initial and advanced ground-based interferometers (LIGO/VIRGO) and for space-based interferometers (LISA). LIGO/VIRGO can do moderate SNR (a few tens), moderate accuracy studies of BBH coalescences in the mass range of a few to about 2000 solar masses; LISA can do high SNR (of order 10^4) high accuracy studies in the mass range of about 10^5 to 10^8 solar masses. BBHs might well be the first sources detected by LIGO/VIRGO: they are visible to much larger distances (up to 500 Mpc by initial interferometers) than coalescing neutron star binaries (heretofore regarded as the "bread and butter" workhorse source for LIGO/VIRGO, visible to about 30 Mpc by initial interferometers). Low-mass BBHs (up to 50 solar masses for initial LIGO interferometers; 100 for advanced; 10^6 for LISA) are best searched for via their well-understood inspiral waves; higher mass BBHs must be searched for via their poorly understood merger waves and/or their well-understood ringdown waves. A matched filtering search for massive BBHs based on ringdown waves should be capable of finding BBHs in the mass range of about 100 to 700 solar masses out to 200 Mpc (initial LIGO interferometers), and 200 to 3000 solar masses out to about z=1 (advanced interferometers). The required number of templates is of order 6000 or less. Searches based on merger waves could increase the number of detected massive BBHs by a factor of order 10 or more over those found from inspiral and ringdown waves, without detailed knowledge of the waveform shapes, using a "noise monitoring" search algorithm. A full set of merger templates from numerical relativity could further increase the number of detected BBHs by an additional factor of up to 4.

Paper Structure

This paper contains 28 sections, 150 equations, 6 figures.

Table of Contents

  1. INTRODUCTION AND SUMMARY
  2. Coalescences of black hole binaries
  3. Status of theoretical calculations of the gravitational-wave signal
  4. Purpose of this paper
  5. Estimating the signal-to-noise ratios: method and assumptions
  6. Signal-to-noise ratios: results and implications
  7. Organization of this paper
  8. DERIVATION OF GENERAL FORMULAE FOR SIGNAL-TO-NOISE RATIOS AND DETECTION THRESHOLDS
  9. Searches for gravitational-wave bursts: band-pass filtering and matched filtering
  10. Searches for gravitational-wave bursts: noise monitoring
  11. Signal-to-noise ratio for matched filtering in terms of waves' energy spectrum
  12. THE GRAVITATIONAL-WAVE SIGNAL FROM COALESCING BLACK HOLES
  13. The three phases of the gravitational-wave signal
  14. Energy spectrum of the emitted gravitational radiation from the merger phase
  15. Energy spectrum of the radiation from the inspiral phase
  16. ...and 13 more sections

Figures (6)

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