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

Author(s)

Codazzo, Elena, Mirasola, Lorenzo, Di Giovanni, Matteo, Astone, Pia, D'Antonio, Sabrina, Palomba, Cristiano, Lazzaro, Claudia, Contu, Andrea, Riggio, Alessandro, Sanna, Andrea

Abstract

The current network of gravitational wave detectors has already revealed hundreds of compact binary coalescences (CBCs), including binary neutron stars, binary black holes, and black hole-neutron star systems. As detector sensitivity improves, the superposition of these signals is expected to form an astrophysical background that becomes increasingly relevant for future observatories. In third generation detectors, such as the Einstein Telescope (ET), this background will be most prominent at low frequencies, potentially affecting the search for continuous gravitational waves (CWs) from spinning neutron stars. In this work, we evaluate the impact of the CBC background on CW detection using the Frequency-Hough pipeline, with a focus on the low-frequency performance in ET sensitivity conditions. Through realistic simulations of the unresolved CBC background, we find that it acts as an additional noise source, most strongly affecting the detection of CW signals around 7 Hz, worsening the FH sensitivity by about 7-10%.

Figures

ASDs of the three compact binary coalescence populations in the frequency range [2, 256]\,Hz: BBH (black), BNS (blue), and BHNS (gray). Their sum is shown in red. The green curve corresponds to ET noise alone, while the brown curve shows ET noise plus the CBC background. The two spectra are very similar on this scale, with no significant visible differences, although a small deviation will be discussed in the following. All spectra refer to day 13 of the timeseries and are computed using the Welch method with 128\,s Hann-windowed segments at a sampling frequency of 512\,Hz.
Caption ASDs of the three compact binary coalescence populations in the frequency range [2, 256]\,Hz: BBH (black), BNS (blue), and BHNS (gray). Their sum is shown in red. The green curve corresponds to ET noise alone, while the brown curve shows ET noise plus the CBC background. The two spectra are very similar on this scale, with no significant visible differences, although a small deviation will be discussed in the following. All spectra refer to day 13 of the timeseries and are computed using the Welch method with 128\,s Hann-windowed segments at a sampling frequency of 512\,Hz.
(\textit{left}) Ratio between the ASD of the data containing the CBC background injected into ET simulated noise and the ASD of ET noise alone, for day 13 of the timeseries. The ASDs were estimated using the Welch method with 128\,s Hann-windowed segments at a sampling frequency of 512\,Hz. (\textit{right}) Evolution of the number of inspiral binaries over the simulated month (solid line) as a function of frequency. Inverted triangles indicate the central frequencies of the 19 bands, each 1\,Hz wide, used in the analyses.
Caption (\textit{left}) Ratio between the ASD of the data containing the CBC background injected into ET simulated noise and the ASD of ET noise alone, for day 13 of the timeseries. The ASDs were estimated using the Welch method with 128\,s Hann-windowed segments at a sampling frequency of 512\,Hz. (\textit{right}) Evolution of the number of inspiral binaries over the simulated month (solid line) as a function of frequency. Inverted triangles indicate the central frequencies of the 19 bands, each 1\,Hz wide, used in the analyses.
(\textit{left}) Ratio between the ASD of the data containing the CBC background injected into ET simulated noise and the ASD of ET noise alone, for day 13 of the timeseries. The ASDs were estimated using the Welch method with 128\,s Hann-windowed segments at a sampling frequency of 512\,Hz. (\textit{right}) Evolution of the number of inspiral binaries over the simulated month (solid line) as a function of frequency. Inverted triangles indicate the central frequencies of the 19 bands, each 1\,Hz wide, used in the analyses.
Caption (\textit{left}) Ratio between the ASD of the data containing the CBC background injected into ET simulated noise and the ASD of ET noise alone, for day 13 of the timeseries. The ASDs were estimated using the Welch method with 128\,s Hann-windowed segments at a sampling frequency of 512\,Hz. (\textit{right}) Evolution of the number of inspiral binaries over the simulated month (solid line) as a function of frequency. Inverted triangles indicate the central frequencies of the 19 bands, each 1\,Hz wide, used in the analyses.
(\textit{left}) False alarm probability ($p_{\rm fa}$) as a function of frequency, for ET0 (dark blue squares) and ETC (dark red stars). The $p_{\rm fa}$ is estimated by running the analyses without any CW injections, such that every recovered candidate corresponds to a false alarm. In both cases, the $p_{\rm fa}$ remains smaller than 0.02\%. (\textit{right}) Comparison of CR from ET0 and ETC analyses for a studied injected amplitude. We perform a linear fit and report its slope as a function of frequency. Error bars indicate the 95\% confidence intervals. Values smaller than unity show a reduction in the recovered CR; thus, values below one indicate a detected effect in the presence of CBCs.
Caption (\textit{left}) False alarm probability ($p_{\rm fa}$) as a function of frequency, for ET0 (dark blue squares) and ETC (dark red stars). The $p_{\rm fa}$ is estimated by running the analyses without any CW injections, such that every recovered candidate corresponds to a false alarm. In both cases, the $p_{\rm fa}$ remains smaller than 0.02\%. (\textit{right}) Comparison of CR from ET0 and ETC analyses for a studied injected amplitude. We perform a linear fit and report its slope as a function of frequency. Error bars indicate the 95\% confidence intervals. Values smaller than unity show a reduction in the recovered CR; thus, values below one indicate a detected effect in the presence of CBCs.
(\textit{left}) False alarm probability ($p_{\rm fa}$) as a function of frequency, for ET0 (dark blue squares) and ETC (dark red stars). The $p_{\rm fa}$ is estimated by running the analyses without any CW injections, such that every recovered candidate corresponds to a false alarm. In both cases, the $p_{\rm fa}$ remains smaller than 0.02\%. (\textit{right}) Comparison of CR from ET0 and ETC analyses for a studied injected amplitude. We perform a linear fit and report its slope as a function of frequency. Error bars indicate the 95\% confidence intervals. Values smaller than unity show a reduction in the recovered CR; thus, values below one indicate a detected effect in the presence of CBCs.
Caption (\textit{left}) False alarm probability ($p_{\rm fa}$) as a function of frequency, for ET0 (dark blue squares) and ETC (dark red stars). The $p_{\rm fa}$ is estimated by running the analyses without any CW injections, such that every recovered candidate corresponds to a false alarm. In both cases, the $p_{\rm fa}$ remains smaller than 0.02\%. (\textit{right}) Comparison of CR from ET0 and ETC analyses for a studied injected amplitude. We perform a linear fit and report its slope as a function of frequency. Error bars indicate the 95\% confidence intervals. Values smaller than unity show a reduction in the recovered CR; thus, values below one indicate a detected effect in the presence of CBCs.
(\textit{Upper panel}) Empirical upper limits at the 95\% confidence level as a function of frequency, see text for more details on their calculation. (\textit{Lower panel}) Ratio of ET0 to ETC upper limits. A clear discrepancy is observed in the low-frequency region, where the CBC background is expected to affect CW searches more strongly. At higher frequencies, the upper limits cluster around unity, as expected.
Caption (\textit{Upper panel}) Empirical upper limits at the 95\% confidence level as a function of frequency, see text for more details on their calculation. (\textit{Lower panel}) Ratio of ET0 to ETC upper limits. A clear discrepancy is observed in the low-frequency region, where the CBC background is expected to affect CW searches more strongly. At higher frequencies, the upper limits cluster around unity, as expected.
Example of the linear fit between CR$_{ET0}$ and CR$_{ETC}$ for the [7,8]\,Hz frequency band. The red line represents the best-fit linear relation, and the dashed line shows the bisector. The fitted slope $0.912\pm0.006$ indicates a reduction of CR in the ETC analysis due to the presence of the CBC background.
Caption Example of the linear fit between CR$_{ET0}$ and CR$_{ETC}$ for the [7,8]\,Hz frequency band. The red line represents the best-fit linear relation, and the dashed line shows the bisector. The fitted slope $0.912\pm0.006$ indicates a reduction of CR in the ETC analysis due to the presence of the CBC background.
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