[Paper Review] Gravitational-wave confusion background from cosmological compact binaries: Implications for future terrestrial detectors

T. Regimbau, Scott A. Hughes|DSpace@MIT (Massachusetts Institute of Technology)|Jan 19, 2009

Pulsars and Gravitational Waves Research1 references4 citations

TL;DR

This paper investigates the gravitational-wave confusion background from cosmological compact binary mergers (NS-NS and NS-BH) and finds that future terrestrial detectors—particularly the Einstein Telescope with low-frequency sensitivity (f_L ≤ 5 Hz)—may enter a confusion-limited regime. At redshifts z ≈ 0.25–0.4 (for f_L = 5 Hz) or z ≈ 1 (for f_L = 1 Hz), the duty cycle exceeds unity, leading to overlapping signals that challenge source resolution and necessitate advanced data analysis to disentangle individual events.

ABSTRACT

Increasing the sensitivity of a gravitational-wave (GW) detector improves our ability to measure the characteristics of detected sources. It also increases the number of weak signals that contribute to the data. Because GW detectors have nearly all-sky sensitivity, they can be subject to a confusion limit: Many sources which cannot be distinguished may be measured simultaneously, defining a stochastic noise floor to the sensitivity. For GW detectors operating at present and for their planned upgrades, the projected event rate is sufficiently low that we are far from the confusion-limited regime. However, some detectors currently under discussion may have large enough reach to binary inspiral that they enter the confusion-limited regime. In this paper, we examine the binary inspiral confusion limit for terrestrial detectors. We consider a broad range of inspiral rates in the literature, several planned advanced gravitational-wave detectors, and the highly advanced "Einstein Telescope" design. Though most advanced detectors will not be impacted by this limit, the Einstein Telescope with a very low frequency "seismic wall" may be subject to confusion noise. At a minimum, careful data analysis will be require to separate signals which will appear confused. This result should be borne in mind when designing highly advanced future instruments.

Motivation & Objective

• To assess whether future ground-based gravitational-wave detectors will face a confusion-limited regime due to overlapping signals from cosmological compact binary coalescences.
• To evaluate the impact of low-frequency sensitivity (seismic wall) and detection horizon on the onset of confusion background for advanced detectors.
• To determine the redshift thresholds (z*) where the duty cycle of binary signals reaches unity (popcorn background) and z** where it reaches 10 (Gaussian stochastic background).
• To examine the feasibility of resolving individual sources using global fitting techniques in the presence of confusion noise.
• To guide the design of next-generation detectors by identifying critical sensitivity and rate thresholds where confusion becomes a limiting factor.

Proposed method

• Modeling the cosmic coalescence rates of NS-NS and NS-BH binaries using a range of published estimates (from 0.001 to 1.4 Myr⁻¹ Mpc⁻³).
• Calculating the detection horizon (z_DH) for various detectors (LIGO, Virgo, advanced LIGO/Virgo, Einstein Telescope) based on their low-frequency cutoff (f_L) and strain sensitivity.
• Defining the duty cycle Δ(z) = (event duration) / (average interval between events) to quantify source overlap at redshift z.
• Identifying z* where Δ(z*) = 1 (popcorn background) and z** where Δ(z**) = 10 (Gaussian stochastic confusion background).
• Assessing the detectability of sources at high redshifts and evaluating the signal-to-noise ratio of events near the detection horizon.
• Drawing analogies from LISA Mock Data Challenges and Big Bang Observatory studies to evaluate feasibility of global fitting for source separation in ET data.

Experimental results

Research questions

• RQ1 At what redshift does the duty cycle of compact binary signals exceed unity (Δ(z) = 1) for future terrestrial detectors, indicating the onset of a confusion-limited regime?
• RQ2 How does the low-frequency sensitivity (f_L) of the Einstein Telescope affect the redshift threshold for confusion background formation?
• RQ3 Can advanced data analysis techniques, such as global fitting of multiple overlapping signals, effectively resolve sources in a confusion-limited environment?
• RQ4 What are the implications of optimistic versus pessimistic coalescence rate estimates on the likelihood of forming a Gaussian stochastic confusion background?
• RQ5 To what extent does the low signal-to-noise ratio of distant sources near the detection horizon complicate confusion-limited source separation?

Key findings

• For the Einstein Telescope with f_L = 1 Hz, the redshift z* where the duty cycle Δ(z*) = 1 for NS-NS binaries is expected to occur well within the detection horizon, indicating a high likelihood of confusion.
• With f_L = 5 Hz, z* for NS-NS binaries is estimated at z* ≈ 0.25–0.4, and z** (for Gaussian background) at z** ≈ 0.6–1.2, unless coalescence rates are very low (ρ̇_c^o < 0.15 Myr⁻¹ Mpc⁻³).
• For NS-BH binaries, confusion is less likely with f_L = 5 Hz unless coalescence rates exceed 0.6 Myr⁻¹ Mpc⁻³, suggesting they may remain resolvable under most realistic rate estimates.
• The confusion background becomes significant when both the detection horizon is large and the low-frequency cutoff is low, as these factors increase both the number of sources and their time-in-band.
• Even for highly sensitive detectors like the Einstein Telescope, confusion noise may limit sensitivity unless advanced data analysis techniques are employed to disentangle overlapping signals.
• The study concludes that confusion is a non-negligible concern for next-generation detectors with low-frequency sensitivity, especially at z ~ 1, and must be factored into instrument design and data analysis strategy.