Impact of site-dependent noise configurations on Einstein Telescope science at low frequency

Author(s)

Crescimbeni, Francesco, Di Giovanni, Matteo, Rozza, Davide, Contu, Andrea, Cardini, Alessandro, D'Urso, Domenico, Giunchi, Carlo, Naticchioni, Luca, Olivieri, Marco, Lindner, Mike, Rietbrock, Andreas, Pani, Paolo

Abstract

We investigate how site-dependent Newtonian noise configurations affect the scientific performance of the Einstein Telescope (ET), a third-generation gravitational-wave observatory. We compare the baseline triangular and 2L detector geometries, with arm lengths of 10km and 15km, respectively, under three site-dependent noise scenarios constructed from measurements in the Euregio Meuse-Rhine region, Lausitz, and Sardinia. The differences among the adopted sensitivities are concentrated mainly below 10Hz and thus have the greatest impact on science cases that rely on the early inspiral of light objects, or on massive systems whose characteristic frequencies lie in the low-frequency band. We quantify these effects for four ET science cases: (1) detection and parameter estimation of intermediate-mass black-hole binaries; (2) post-Newtonian tests of General Relativity based on the early inspiral; (3) black-hole ringdown spectroscopy with massive remnants; and (4) early-warning and sky-localization capabilities for binary neutron-star mergers. Using Bayesian parameter estimation, we find that improved low-frequency sensitivity can significantly enhance ET's scientific performance across all four cases. Within the configurations considered here, a 2L network in which at least one of the two L-shaped interferometers attains a noise level comparable to that assumed for the Sardinian site generally provides better performance than the triangular configurations. Conversely, strong degradation of the sensitivity below 10Hz can substantially reduce, and in some regimes offset, the scientific gains expected from increasing the arm length from 10km to 15km. These results highlight the importance of site selection and low-frequency noise mitigation, alongside network geometry, for fully realizing ET's scientific potential in the largely unexplored frequency band below 10Hz.

Figures

Caption

Site-dependent strain ASDs adopted in this work for the $10\,{\rm km}$ and $15\,{\rm km}$ configurations associated with various sites. The upper-left panel compares all the site-dependent curves with the corresponding nominal ET sensitivities, shown in gray. The remaining panels show the TERZ (top right), Sardinia (bottom left), and Lausitz (bottom right) configurations separately, using the same vertical scale. The TERZ curves correspond to the noise realization inferred from the borehole seismometer installed in the village of Terziet and should not be interpreted as a characterization of the entire EMR candidate region. The differences among the site-dependent, unmitigated Newtonian noise curves are concentrated mainly below approximately $10\,{\rm Hz}$. The Sardinia curves remain relatively close to the nominal targets, whereas the TERZ and Lausitz curves exhibit a stronger low-frequency degradation. Differences in site-dependent low-frequency noise can outweigh the benefit of longer arms when comparing detectors at different sites.

Caption

Top panel: locations of the different detector configurations on a map of Europe. Bottom panels: enlarged views of the three configurations, based on the coordinates listed in Tabs~\ref{tab:et_triangle_configurations} and~\ref{tab:et_l_configurations}.Black stars mark the borehole seismometers whose data enter the Newtonian-noise estimate (P2, TERZ, and DZA13), located approximately $1.5\,{\rm km}$, $0.4\,{\rm km}$, and $4.3\,{\rm km}$ from the nearest vertex of the corresponding triangular layout. The three bottom panels share the same scale, each spanning $30\,{\rm km}\times30\,{\rm km}$.

Caption

Top panel: locations of the different detector configurations on a map of Europe. Bottom panels: enlarged views of the three configurations, based on the coordinates listed in Tabs~\ref{tab:et_triangle_configurations} and~\ref{tab:et_l_configurations}.Black stars mark the borehole seismometers whose data enter the Newtonian-noise estimate (P2, TERZ, and DZA13), located approximately $1.5\,{\rm km}$, $0.4\,{\rm km}$, and $4.3\,{\rm km}$ from the nearest vertex of the corresponding triangular layout. The three bottom panels share the same scale, each spanning $30\,{\rm km}\times30\,{\rm km}$.

Caption

Network SNR as a function of the injected source-frame total mass for sources at $z=1$, $z=4$ (top panels), and $z=7$, $z=10$ (bottom panels), all with mass ratio $q=0.74$ and zero spins. The source sky position, inclination, and polarization are held fixed across all configurations to the values given in Table~\ref{tab:IMBH_injected_parameters}.

Caption

Network SNR as a function of the injected source-frame total mass for sources at $z=1$, $z=4$ (top panels), and $z=7$, $z=10$ (bottom panels), all with mass ratio $q=0.74$ and zero spins. The source sky position, inclination, and polarization are held fixed across all configurations to the values given in Table~\ref{tab:IMBH_injected_parameters}.

Caption

Network SNR as a function of the injected source-frame total mass for sources at $z=1$, $z=4$ (top panels), and $z=7$, $z=10$ (bottom panels), all with mass ratio $q=0.74$ and zero spins. The source sky position, inclination, and polarization are held fixed across all configurations to the values given in Table~\ref{tab:IMBH_injected_parameters}.

Caption

Network SNR as a function of the injected source-frame total mass for sources at $z=1$, $z=4$ (top panels), and $z=7$, $z=10$ (bottom panels), all with mass ratio $q=0.74$ and zero spins. The source sky position, inclination, and polarization are held fixed across all configurations to the values given in Table~\ref{tab:IMBH_injected_parameters}.

Caption

Redshift horizon for equal-mass, nonspinning binaries as a function of the source-frame total mass, assuming a network SNR threshold of $8$ for all the considered networks.

Caption

Detector-frame chirp-mass relative error as a function of the source-frame total mass (left panel) and effective-spin (right panel) relative error for \(z=1\), for the four different detector configurations.

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Detector-frame chirp-mass relative error as a function of the source-frame total mass (left panel) and effective-spin (right panel) relative error for \(z=1\), for the four different detector configurations.

Caption

Half-width of the central $90\%$ credible interval, $\sigma_{90\%}$, of the parametrized PN-deviation posteriors for sources at $z=4$, for the detector configurations considered in this work. The left and right panels correspond to negative and non-negative PN terms, respectively (note the widely different vertical scales in the two panels).

Caption

Half-width of the central $90\%$ credible interval, $\sigma_{90\%}$, for the beyond-GR deviations in the intermediate regime as a function of the injected source-frame total mass. The injections are performed at \(z=4\) and \(\iota=0.2\), and the different curves correspond to the detector configurations considered in this work.

Caption

Half-width of the central $90\%$ credible interval, $\sigma_{90\%}$, for the beyond-GR deviations in the merger-ringdown regime as a function of the injected source-frame total mass. The injections are performed at $z=4$ and $\iota=0.2$, and the different curves correspond to the detector configurations considered in this work.

Caption

Symmetric $90\%$ credible half-width of the fractional ringdown deviations, $\delta f_{330}$ and $\delta \tau_{330}$, as functions of the injected remnant mass, for the different detector configurations.

Caption

Symmetric $90\%$ credible half-width of the fractional ringdown deviations, $\delta f_{330}$ and $\delta \tau_{330}$, as functions of the injected remnant mass, for the different detector configurations.

Caption

Warning time $t_{\rm warn}$ for a GW170817-like binary, averaged over sky position and polarization, as a function of the adopted network-SNR threshold $\rho_{\rm th}$. The different curves correspond to the detector configurations considered in this work, including the nominal 2L sensitivity. The upper horizontal axis shows the sky-averaged maximum frequency $f_{\rm max}$ at which the nominal 2L network crosses the corresponding SNR threshold.

Caption

Posterior distributions of the sky localization parameters for a GW170817-like event obtained using the full prior range of $\iota$. Panels a), b), and c) correspond to $T=10800\,\mathrm{s}$, $T=3600\,\mathrm{s}$, and $T=1800\,\mathrm{s}$ before merger, respectively. In each panel, the left plot shows the joint and marginalized posterior distributions of right ascension $\alpha$ and declination $\delta$, while the right plot shows the one-dimensional posterior probability density $p(\iota)$ of the inclination angle. The corresponding plot obtained by enforcing the prior $\iota\in[\pi/2,\pi]$, hence removing multimodalities, is presented in the Appendix, see Fig.~\ref{fig:posteriors_BNS_theta_geq_pi2}.

Caption

Posterior distributions of the sky localization parameters for a GW170817-like event obtained using the full prior range of $\iota$. Panels a), b), and c) correspond to $T=10800\,\mathrm{s}$, $T=3600\,\mathrm{s}$, and $T=1800\,\mathrm{s}$ before merger, respectively. In each panel, the left plot shows the joint and marginalized posterior distributions of right ascension $\alpha$ and declination $\delta$, while the right plot shows the one-dimensional posterior probability density $p(\iota)$ of the inclination angle. The corresponding plot obtained by enforcing the prior $\iota\in[\pi/2,\pi]$, hence removing multimodalities, is presented in the Appendix, see Fig.~\ref{fig:posteriors_BNS_theta_geq_pi2}.

Caption

Posterior distributions of the sky localization parameters for a GW170817-like event obtained using the full prior range of $\iota$. Panels a), b), and c) correspond to $T=10800\,\mathrm{s}$, $T=3600\,\mathrm{s}$, and $T=1800\,\mathrm{s}$ before merger, respectively. In each panel, the left plot shows the joint and marginalized posterior distributions of right ascension $\alpha$ and declination $\delta$, while the right plot shows the one-dimensional posterior probability density $p(\iota)$ of the inclination angle. The corresponding plot obtained by enforcing the prior $\iota\in[\pi/2,\pi]$, hence removing multimodalities, is presented in the Appendix, see Fig.~\ref{fig:posteriors_BNS_theta_geq_pi2}.

Caption

Posterior distributions of the sky localization parameters for a GW170817-like event obtained using the full prior range of $\iota$. Panels a), b), and c) correspond to $T=10800\,\mathrm{s}$, $T=3600\,\mathrm{s}$, and $T=1800\,\mathrm{s}$ before merger, respectively. In each panel, the left plot shows the joint and marginalized posterior distributions of right ascension $\alpha$ and declination $\delta$, while the right plot shows the one-dimensional posterior probability density $p(\iota)$ of the inclination angle. The corresponding plot obtained by enforcing the prior $\iota\in[\pi/2,\pi]$, hence removing multimodalities, is presented in the Appendix, see Fig.~\ref{fig:posteriors_BNS_theta_geq_pi2}.

Caption

Posterior distributions of the sky localization parameters for a GW170817-like event obtained using the full prior range of $\iota$. Panels a), b), and c) correspond to $T=10800\,\mathrm{s}$, $T=3600\,\mathrm{s}$, and $T=1800\,\mathrm{s}$ before merger, respectively. In each panel, the left plot shows the joint and marginalized posterior distributions of right ascension $\alpha$ and declination $\delta$, while the right plot shows the one-dimensional posterior probability density $p(\iota)$ of the inclination angle. The corresponding plot obtained by enforcing the prior $\iota\in[\pi/2,\pi]$, hence removing multimodalities, is presented in the Appendix, see Fig.~\ref{fig:posteriors_BNS_theta_geq_pi2}.

Caption

Posterior distributions of the sky localization parameters for a GW170817-like event obtained using the full prior range of $\iota$. Panels a), b), and c) correspond to $T=10800\,\mathrm{s}$, $T=3600\,\mathrm{s}$, and $T=1800\,\mathrm{s}$ before merger, respectively. In each panel, the left plot shows the joint and marginalized posterior distributions of right ascension $\alpha$ and declination $\delta$, while the right plot shows the one-dimensional posterior probability density $p(\iota)$ of the inclination angle. The corresponding plot obtained by enforcing the prior $\iota\in[\pi/2,\pi]$, hence removing multimodalities, is presented in the Appendix, see Fig.~\ref{fig:posteriors_BNS_theta_geq_pi2}.

Caption

Left panel: relative uncertainties on the source-frame component masses as functions of the injected source-frame total mass, for the four detector configurations considered. Right panel: corresponding relative uncertainties on the individual spins. In both panels, solid and dashed curves refer to the primary and secondary components, respectively.

Caption

Left panel: relative uncertainties on the source-frame component masses as functions of the injected source-frame total mass, for the four detector configurations considered. Right panel: corresponding relative uncertainties on the individual spins. In both panels, solid and dashed curves refer to the primary and secondary components, respectively.

Caption

Comparison of the posterior distributions for two IMBH systems with source-frame total masses $M_{\rm src}=1200\,M_\odot$ and $M_{\rm src}=2400\,M_\odot$, both with mass ratio $q=0.74$, observed with the 2L configuration. The detector-frame chirp mass is normalized to its injected value, while the right ascension, declination, and polarization angle are shown as offsets from their respective injected values. Dashed black lines mark the injected parameters. The one-dimensional marginalized posteriors are normalized to unit peak for ease of comparison, and the contours enclose the $50\%$ and $90\%$ credible regions.

Caption

Same as Fig.~\ref{fig:posteriors_BNS_standard} but imposing $\pi/2 \leq \iota \leq \pi$ as a prior, thus forcing the absence of multimodalities. Panels a), b), and c) correspond to $T=10800\,\mathrm{s}$, $T=3600\,\mathrm{s}$, and $T=1800\,\mathrm{s}$ before merger, respectively. In each panel, the left plot shows the joint and marginalized posterior distributions of right ascension $\alpha$ and declination $\delta$, while the right plot shows the one-dimensional posterior probability density $p(\iota)$ of the inclination angle.

Caption

Same as Fig.~\ref{fig:posteriors_BNS_standard} but imposing $\pi/2 \leq \iota \leq \pi$ as a prior, thus forcing the absence of multimodalities. Panels a), b), and c) correspond to $T=10800\,\mathrm{s}$, $T=3600\,\mathrm{s}$, and $T=1800\,\mathrm{s}$ before merger, respectively. In each panel, the left plot shows the joint and marginalized posterior distributions of right ascension $\alpha$ and declination $\delta$, while the right plot shows the one-dimensional posterior probability density $p(\iota)$ of the inclination angle.

Caption

Same as Fig.~\ref{fig:posteriors_BNS_standard} but imposing $\pi/2 \leq \iota \leq \pi$ as a prior, thus forcing the absence of multimodalities. Panels a), b), and c) correspond to $T=10800\,\mathrm{s}$, $T=3600\,\mathrm{s}$, and $T=1800\,\mathrm{s}$ before merger, respectively. In each panel, the left plot shows the joint and marginalized posterior distributions of right ascension $\alpha$ and declination $\delta$, while the right plot shows the one-dimensional posterior probability density $p(\iota)$ of the inclination angle.

Caption

Same as Fig.~\ref{fig:posteriors_BNS_standard} but imposing $\pi/2 \leq \iota \leq \pi$ as a prior, thus forcing the absence of multimodalities. Panels a), b), and c) correspond to $T=10800\,\mathrm{s}$, $T=3600\,\mathrm{s}$, and $T=1800\,\mathrm{s}$ before merger, respectively. In each panel, the left plot shows the joint and marginalized posterior distributions of right ascension $\alpha$ and declination $\delta$, while the right plot shows the one-dimensional posterior probability density $p(\iota)$ of the inclination angle.

Caption

Same as Fig.~\ref{fig:posteriors_BNS_standard} but imposing $\pi/2 \leq \iota \leq \pi$ as a prior, thus forcing the absence of multimodalities. Panels a), b), and c) correspond to $T=10800\,\mathrm{s}$, $T=3600\,\mathrm{s}$, and $T=1800\,\mathrm{s}$ before merger, respectively. In each panel, the left plot shows the joint and marginalized posterior distributions of right ascension $\alpha$ and declination $\delta$, while the right plot shows the one-dimensional posterior probability density $p(\iota)$ of the inclination angle.

Caption

Same as Fig.~\ref{fig:posteriors_BNS_standard} but imposing $\pi/2 \leq \iota \leq \pi$ as a prior, thus forcing the absence of multimodalities. Panels a), b), and c) correspond to $T=10800\,\mathrm{s}$, $T=3600\,\mathrm{s}$, and $T=1800\,\mathrm{s}$ before merger, respectively. In each panel, the left plot shows the joint and marginalized posterior distributions of right ascension $\alpha$ and declination $\delta$, while the right plot shows the one-dimensional posterior probability density $p(\iota)$ of the inclination angle.