Impact of coalescence signals on the search for continuous gravitational waves with Einstein Telescope

This study evaluates the impact of the unresolved compact binary coalescence background on continuous gravitational wave searches in the Einstein Telescope, finding that it acts as an additional noise source that degrades detection sensitivity by approximately 7–10% around 7 Hz.

The Gist

Imagine the universe is a giant, quiet concert hall. For the last decade, our current gravitational wave detectors (like LIGO and Virgo) have been like sensitive microphones that have successfully recorded hundreds of loud, short "crashes"—these are Compact Binary Coalescences (CBCs), where massive objects like black holes and neutron stars smash into each other.

Now, scientists are building a super-powered microphone for the future called the Einstein Telescope (ET). This new telescope will be so sensitive it can hear much quieter sounds, including a specific type of signal called Continuous Waves (CWs). These CWs are like a steady, high-pitched hum emitted by spinning neutron stars that aren't perfectly round. Finding them would tell us secrets about the inside of these stars.

However, there is a catch. Because the new telescope is so sensitive, it won't just hear the loud crashes; it will hear so many of them happening at once that they will blend together into a constant, low-frequency "hiss" or background noise. This is the astrophysical background.

The Problem: The "Crowded Room"

The authors of this paper asked a simple question: Will this new background hiss drown out the steady hum (CWs) we are trying to find?

To answer this, they created a realistic simulation. Think of it like this:

1. The Quiet Room (ET0): They simulated the Einstein Telescope listening to pure silence (just its own internal electronic noise).
2. The Crowded Room (ETC): They simulated the same telescope, but this time, they filled the room with the "hiss" of thousands of overlapping black hole and neutron star collisions happening simultaneously.

They then tried to "hide" a fake continuous wave signal (the steady hum) in both rooms and used a special search tool called the Frequency-Hough pipeline to see if they could find it.

The Findings: The Low-Frequency Fog

The results showed that the background hiss does make a difference, but only in a specific part of the sound spectrum:

• The "Fog" is Low: The background noise is strongest at very low frequencies (around 7 Hz). Imagine trying to hear a whisper in a room where a low-frequency bass drum is beating constantly. That bass drum is the CBC background.
• The Impact: In this low-frequency "fog," the search tool became slightly less effective. The background noise made it harder to distinguish the steady hum from the static.
• The Numbers: The study found that this background noise worsened the telescope's ability to detect these signals by about 7% to 10% around that 7 Hz mark. In other words, if the telescope could normally hear a signal at a certain distance, the background noise might make it seem like the signal is 10% quieter or harder to catch.
• Higher Frequencies are Clear: At higher frequencies (above 17 Hz), the "crowd" of collisions thins out, and the background noise becomes negligible. The telescope works just as well as it would in the quiet room.

The Conclusion

The paper concludes that while the Einstein Telescope will be an incredible tool, the sheer number of black hole and neutron star collisions will create a "fog" at low frequencies. This fog won't stop us from finding continuous waves, but it will make the job slightly harder (about 7–10% harder) in that specific low-frequency range.

The authors suggest that future work will need to develop "noise-canceling" techniques to subtract these loud collisions from the data, clearing the fog so the steady hum of the spinning stars can be heard more clearly. Until then, this study serves as a realistic "worst-case scenario" warning for how the universe's own activity might interfere with our search for new signals.

Technical Summary

Technical Summary: Impact of Coalescence Signals on the Search for Continuous Gravitational Waves with Einstein Telescope

Problem Statement
The current network of gravitational wave (GW) detectors has identified hundreds of compact binary coalescences (CBCs). As detector sensitivity improves with third-generation observatories like the Einstein Telescope (ET), the superposition of these unresolved CBC signals is expected to form a stochastic astrophysical background. This background is predicted to be most prominent at low frequencies. While previous studies have investigated the impact of such backgrounds on primordial stochastic GW searches, a comprehensive assessment of how this CBC background affects the detection of continuous gravitational waves (CWs) from isolated, spinning neutron stars has not been completed. CW signals are inherently weaker than transient CBC signals and require long observation times; the presence of an additional astrophysical noise source could mask or mimic these weak signals, potentially degrading search sensitivity.

Methodology
The authors evaluate the impact of the CBC background on CW detection using the Frequency-Hough (FH) pipeline, a semi-coherent search method designed for all-sky CW searches. The study employs a comparative analysis framework involving two distinct datasets:

1. ET0: Simulated ET instrumental noise only.
2. ETC: The same simulated ET noise with an injected astrophysical CBC background.

The astrophysical background was constructed by simulating individual inspiral waveforms for Binary Black Hole (BBH), Binary Neutron Star (BNS), and Black Hole–Neutron Star (BHNS) populations. These populations were drawn from established catalogs representing various formation channels (isolated and dynamical) and extended to redshifts up to $z \sim 14$. The waveforms were generated using the TaylorT2 approximant and summed to create a 31-day time series representing the unresolved background.

The analysis utilized Band Sampled Data (BSD) files covering the frequency range [0, 250] Hz. The FH pipeline was applied to 19 specific 1-Hz wide frequency bands between 5 Hz and 249 Hz. To assess sensitivity, 10 simulated CW signals with random sky locations and parameters were injected into each dataset for 150 different sky points, totaling 228,000 injections. The detection efficiency was evaluated by comparing the Critical Ratio (CR) of recovered candidates and determining the 95% confidence level upper limits ($h_{0}^{95\%}$) for signal amplitude. The study did not employ mitigation strategies (such as subtracting loud CBCs), thereby representing a "worst-case scenario" for the pipeline's performance.

Key Contributions

• First Comprehensive Assessment: This work presents the first investigation into the influence of the unresolved CBC background on CW searches for isolated neutron stars specifically within the context of the Einstein Telescope.
• Realistic Simulation: The authors generated a realistic astrophysical background by summing waveforms from BBH, BNS, and BHNS populations, accounting for the specific spectral density contributions of each population type.
• Pipeline Validation: The study validates the robustness of the FH pipeline in the presence of this new noise source by quantifying changes in detection statistics and sensitivity limits.

Results

• Spectral Impact: The CBC background introduces an excess in the noise amplitude spectral density (ASD) below 20 Hz, with a peak contribution around 7 Hz. This peak is primarily driven by the high overlap of BNS signals at low frequencies.
• False Alarm Probability: The false-alarm probability ($p_{fa}$) remained below 0.02% across all frequencies for both ET0 and ETC datasets, confirming that the pipeline's ability to distinguish noise fluctuations from signals remains robust even with the added background.
• Sensitivity Degradation: The presence of the CBC background systematically reduces the Critical Ratio (CR) of detected candidates, particularly at low frequencies.
  • In the frequency band [7, 8] Hz, where the background impact is maximal, the slope of the linear fit between CR values in ET0 and ETC analyses drops to approximately 0.91.
  • Consequently, the 95% confidence upper limits on signal amplitude ($h_{0}^{95\%}$) are worsened by approximately 7–10% in the ETC scenario compared to the ET0 scenario at these low frequencies.
  • At higher frequencies ($f \ge 17$ Hz), the impact diminishes, and the sensitivity limits for both datasets converge.

Significance and Claims
The paper claims that while the degradation in sensitivity is moderate (7–10%), it is non-negligible for future CW searches with third-generation detectors. The authors state that this variation could significantly affect the required observation time and the detectability of CW signals, whose intrinsic amplitudes are currently unknown.

The study concludes that if the CBC background is not mitigated, it will act as an additional noise source that limits the performance of the FH pipeline in the low-frequency regime. The authors emphasize that while their findings represent a worst-case scenario (without signal subtraction), developing dedicated techniques to suppress the effect of overlapping CBC events will be a crucial direction for future work to ensure that CW searches are not limited by this astrophysical foreground. The authors also note that while the analysis used a single detector arm configuration, the qualitative impact is expected to remain consistent across different ET configurations, though quantitative variations may exist.