Third-generation Gravitational-wave Detectors Research Articles

Toward establishing the presence or absence of horizons in coalescing binaries of compact objects by using their gravitational wave signals

The quest for distinguishing black holes (BH) from horizonless compact objects using gravitational wave (GW) signals from coalescing compact binaries can be helped by utilizing the phenomenon of tidal heating (TH), which leaves its imprint on binary waveforms through the horizon parameters. We investigate the effects of TH on GWs to probe the observability of the horizon parameters, mainly using Fisher matrix analysis to determine the errors and covariances between them. The horizon parameters are defined as $H_1$ and $H_2$ for the two binary components, with $H_{1,2} \in [0,1]$, and combined with the component masses and spins to form two new parameters, $H_{\rm eff5}$ and $H_{\rm eff8}$, to minimize their covariances in parameter estimation studies. In this work, we add the phase contribution due to TH in terms of $H_{\rm eff5}$ and $H_{\rm eff8}$ to a post-Newtonian waveform and examine the variation of their measurement errors with the binary's total mass, mass ratio, luminosity distance, and component spins. Since the Fisher matrix approach works well for high signal-to-noise ratio, we focus mainly on third-generation (3G) GW detectors Einstein Telescope and Cosmic Explorer and use LIGO and Virgo for comparison. We find that the region in the total binary mass where measurements of $H_{\rm eff5}$ and $H_{\rm eff8}$ are most precise are $\sim 20 - 30M_\odot$ for LIGO-Virgo and $\sim 50 - 80M_\odot$ for 3G detectors. Higher component spins allow more precise measurements of $H_{\rm eff5}$ and $H_{\rm eff8}$. For a binary situated at 200 Mpc with component masses $12M_\odot$ and $18M_\odot$, equal spins $\chi_1=\chi_2=0.8$, and $H_{\rm eff5}=0.6$, $H_{\rm eff8}=12$, the 1-$\sigma$ errors in these two parameters are $\sim 0.01$ and $\sim 0.04$, respectively, in 3G detectors. We substantiate our results from Fisher studies with a set of Bayesian simulations.

Impact of gravitational lensing on black hole mass function inference with third-generation gravitational wave detectors

ABSTRACT The recent rapid growth of the black hole (BH) catalogue from gravitational waves (GWs) has allowed us to study the substructure of black hole mass function (BHMF) beyond the simplest power–law distribution. However, the BH masses inferred from binary BH merger events, may be systematically ‘brightened’ or ‘dimmed’ by the gravitational lensing effect. In this work, we investigate the impact of gravitational lensing on the BHMF inference considering the detection of the third-generation GW detector – the Einstein Telescope (ET). We focus on high redshift, z = 10 in order to obtain the upper limits of this effect. We use Monte Carlo (MC) method to simulate the data adopting three original BHMFs under Un-Lensed and Lensed scenarios, then recover the parameters of BHMFs from the mock data, and compare the difference of results, respectively. We found that all the parameters are well recovered within one standard deviation(std., 1σ), and all three BHMF models are reconstructed within 68 per cent credible interval, suggesting that lensing would not change the main structure drastically, even at very high redshifts and with high precision of ET. And the modest influence beyond 50M⊙, depends on the modeling of the high mass tail or substructure of BHMF. We conclude that the impact of lensing on BHMF inference with ET can be safely ignored in the foreseeable future. Careful handling of lensing effects is required only when focusing on an accurate estimation of the high mass end of BHMF at high redshifts.

GWFAST: A Fisher Information Matrix Python Code for Third-generation Gravitational-wave Detectors

We introduce GWFAST (https://github.com/CosmoStatGW/gwfast), a Fisher information matrix Python code that allows for easy and efficient estimation of signal-to-noise ratios and parameter measurement errors for large catalogs of resolved sources observed by networks of gravitational-wave (GW) detectors. In particular, GWFAST includes the effects of the Earth’s motion during the evolution of the signal, supports parallel computation, and relies on automatic differentiation rather than on finite differences techniques, which makes possible the computation of derivatives with accuracy close to machine precision. We also release the library WF4Py (https://github.com/CosmoStatGW/WF4Py) implementing state-of-the-art GW waveforms in Python. In this paper we provide a documentation of GWFAST and WF4Py with practical examples and tests of performance and reliability. In the companion paper Iacovelli et al. we present forecasts for the detection capabilities of the second and third generation of ground-based GW detectors, obtained with GWFAST.

Constraints on compact dark matter from lensing of gravitational waves for the third-generation gravitational wave detector

ABSTRACT Since the first gravitational wave (GW) event from binary black hole (BBH) was detected by LIGO-Virgo, GWs have become a useful probe on astrophysics and cosmology. If compact dark matter (DM) objects e.g. primordial black holes, contribute a significant fraction of DM at wide mass range, they will cause microlensing in the GW signals with long wavelengths that are distinct from the lensing effects of electromagnetic signals from astrophysical objects. In this paper, we apply the lensing effect of GW from BBH to derive constraints on the abundance of compact DM for the Cosmic Explorer, a third-generation ground-based GW detector. We first consider two channels of formation of BBH that contribute to low- and high-redshift GW sources, including the astrophysical origin BBH scenario, and the primordial origin BBH scenario. Secondly, comparing with the method of optical depth, we use the Bayesian analysis to derive constraints on the abundance of compact DM with different mass function of lens taken into consideration. For a null search with 1000 detected GW events of BBH, we find that the abundance of compact DM could be constrained to $\lesssim 0.1\,\mathrm{ per}\,\mathrm{ cent}$ in the mass range $\ge 500\, {\rm M}_{\odot }$ at 68 per cent confidence level. In addition, if a GW event lensed by a compact DM object with $M_{\rm l}\in [100\, {\rm M}_{\odot },300\, {\rm M}_{\odot }]$ is detected in 100 detected GW events of BBH, we can derive that the estimation of the abundance of compact DM is from $2.3$ to $25.2$ per cent in this mass range with the Bayesian analysis.

Sensitivity of neutron star observations to three-nucleon forces

Astrophysical observations of neutron stars have been widely used to infer the properties of the nuclear matter equation of state. Beside being a source of information on average properties of dense matter, the data provided by electromagnetic and gravitational wave (GW) facilities are reaching the accuracy needed to constrain, for the first time, the underlying nuclear dynamics. In this work, we assess the sensitivity of current and future neutron star observations to directly infer the strength of repulsive three-nucleon forces, which are key to determine the stiffness of the equation of state. Using a Bayesian approach, we focus on the constraints that can be derived on three-body interactions from binary neutron star mergers observed by second- and third-generations of gravitational wave interferometers. We consider both single and multiple observations. For current detectors at design sensitivity, the analysis suggests that only low mass systems, with large signal-to-noise ratios, allow one to reliably constrain the three-body forces. However, our results show that a single observation with a third-generation interferometer, such as the Einstein Telescope or Cosmic Explorer, will constrain the strength of the repulsive three-nucleon potential with exquisite accuracy, turning third-generation GW detectors into new laboratories to investigate the properties of nucleon interactions.

Impacts of gravitational-wave standard siren observations from Einstein Telescope and Cosmic Explorer on weighing neutrinos in interacting dark energy models

Multi-messenger gravitational wave (GW) observation for binary neutron star merger events could provide a rather useful tool to explore the evolution of the Universe. In particular, for the third-generation GW detectors, i.e. the Einstein Telescope (ET) and the Cosmic Explorer (CE), proposed to be built in Europe and the U.S., respectively, lots of GW standard sirens with known redshifts could be obtained, which would exert great impacts on the cosmological parameter estimation. The total neutrino mass could be measured by cosmological observations, but such a measurement is model-dependent and currently only gives an upper limit. In this work, we wish to investigate whether the GW standard sirens observed by ET and CE could help improve the constraint on the neutrino mass, in particular in the interacting dark energy (IDE) models. We find that the GW standard siren observations from ET and CE can only slightly improve the constraint on the neutrino mass in the IDE models, compared to the current limit. The improvements in the IDE models are weaker than those in the standard cosmological model. Although the limit on neutrino mass can only be slightly updated, the constraints on other cosmological parameters can be significantly improved by using the GW observations.

Atmospheric Newtonian noise modeling for third-generation gravitational wave detectors

The sensitivity and the frequency bandwidth of third-generation gravitational-wave (GW) detectors are such that the Newtonian noise (NN) signals produced by atmospheric turbulence could become relevant. We build models for atmospheric NN that take into account finite correlation times and inhomogeneity along the vertical direction, and are therefore accurate enough to represent a reliable reference tool for evaluating this kind of noise. We compute the NN spectral density from our models and compare it with the expected sensitivity curve of the Einstein Telescope (ET) with the xylophone design. The noise signal decays exponentially for small values of the frequency and the detector's depth, followed by a power-law for large values of the parameters. We find that, when the detector is built at the earth's surface, the NN contribution in the low-frequency band is above the ET sensitivity curve for strong wind. Building the detector underground is sufficient to push the noise signal under the ET sensitivity curve, but the decrement is close to marginal for strong wind. In light of the slow decay with depth of the NN, building the detector underground could be only partially effective as passive noise mitigation.

The χeff − z correlation of field binary black hole mergers and how 3G gravitational-wave detectors can constrain it

Understanding the origin of merging binary black holes is currently one of the most pressing quests in astrophysics. We show that if isolated binary evolution dominates the formation mechanism of merging binary black holes, one should expect a correlation between the effective spin parameter, χeff, and the redshift of the merger, z, of binary black holes. This correlation comes from tidal spin-up systems preferentially forming and merging at higher redshifts due to the combination of weaker orbital expansion from low metallicity stars given their reduced wind mass loss rate, delayed expansion and have smaller maximal radii during the supergiant phase compared to stars at higher metallicity. As a result, these tightly bound systems merge with short inspiral times. Given our fiducial model of isolated binary evolution, we show that the origin of a χeff − z correlation in the detectable LIGO–Virgo binary black hole population is different from the intrinsic population, which will become accessible only in the future by third-generation gravitational-wave detectors such as Einstein Telescope and Cosmic Explorer. Given the limited horizon of current gravitational-wave detectors, z ≲ 1, highly rotating black hole mergers in the LIGO–Virgo observed χeff − z correlation are dominated by those formed through chemically homogeneous evolution. This is in contrast to the subpopulation of highly rotating black holes in the intrinsic population, which is dominated by tidal spin up following a common evolve event. The different subchannel mixture in the intrinsic and detected population is a direct consequence of detector selection effects, which allows for the typically more massive black holes formed through chemically homogeneous evolution to be observable at larger redshifts and dominate the LIGO–Virgo sample of spinning binary black holes from isolated evolution at z > 0.4. Finally, we compare our model predictions with population predictions based on the current catalog of binary black hole mergers and find that current data favor a positive correlation of χeff − z as predicted by our model of isolated binary evolution.

Computational challenges for multimodal astrophysics.

In the coming decades, we will face major computational challenges, when the improved sensitivity of third-generation gravitational wave detectors will be such that they will be able to detect a high number (of the order of 7 × 104 per year) of multi-messenger events from binary neutron star mergers, similar to GW 170817. In this Perspective, we discuss the application of multimodal artificial intelligence techniques for multi-messenger astrophysics, fusing the information from different signal emissions.

Impact and detectability of spin-tidal couplings in neutron star inspirals

The gravitational wave signal from a binary neutron star merger carries the imprint of the deformability properties of the coalescing bodies, and then of the equation of state of neutron stars. In current models of the waveforms emitted in these events, the contribution of tidal deformation is encoded in a set of parameters, the tidal Love numbers. More refined models include tidal-rotation couplings, described by an additional set of parameters, the rotational tidal Love numbers, which appear in the waveform at $6.5$ post-Newtonian order. For neutron stars with spins as large as $\sim0.1$, we show that neglecting tidal-rotation couplings may lead to a significant error in the parameter estimation by third-generation gravitational wave detectors. By performing a Fisher matrix analysis we assess the measurability of rotational tidal Love numbers, showing that their contribution in the waveform could be measured by third-generation detectors. Our results suggest that current models of tidal deformation in late inspiral should be improved in order to avoid waveform systematics and extract reliable information from gravitational wave signals observed by next generation detectors.

Signal space in the triangular network of the Einstein Telescope

The proposed third-generation gravitational-wave detectors Einstein Telescope will have a triangular design that consists of three colocated interferometers. Summing the strain outputs from the three interferometers will cancel any gravitational-wave signal and the resultant signal-free stream is known as null stream. The null stream is in a fixed subspace of the observation space of Einstein telescope where no gravitational-wave signal can exist. In this paper, we establish the decomposition of the observation space of Einstein Telescope into the signal space that contains all possible gravitational-wave signals and the null space that contains the null stream. We show that the results of Bayesian parameter estimation and model selection using the strain data in the signal space are identical to that using the full set of strain data. This implies that one could use a fraction of the strain data to extract all information of the source which reduces the memory usage and speeds up the likelihood evaluation. We also discuss the existence of a fixed null space in Einstein Telescope allows the unbiased estimation of the noise properties in the signal-free subspace.

Improvement of the parameter measurement accuracy by the third-generation gravitational wave detector Einstein Telescope

The Einstein Telescope (ET) has been proposed as one of the third-generation gravitational wave (GW) detectors. The sensitivity of ET would be a factor of 10 better than the second-generation GW detector, advanced LIGO (aLIGO); thus, the GW source parameters could be measured with much better accuracy. In this work, we show how the precision in parameter estimation can be improved between aLIGO and ET by comparing the measurement errors. We apply the TaylorF2 waveform model defined in the frequency domain to the Fisher matrix method which is a semi-analytic approach for estimating GW parameter measurement errors. We adopt as our sources low-mass binary black holes with the total masses of M ⩽ 16M ⊙ and the effective spins of −0.9 ⩽ χ eff ⩽ 0.9 and calculate the measurement errors of the mass and the spin parameters using 104 Monte-Carlo samples randomly distributed in our mass and spin parameter space. We find that for the same sources ET can achieve times better signal-to-noise ratio than aLIGO and the error ratios (σ λ,ET/σ λ,aLIGO) for the chirp-mass, symmetric mass ratio, and effective spin parameters can be lower than 7% for all binaries. We also consider the equal-mass binary neutron stars with the component masses of 1, 1.4, and 2M ⊙ and find that the error ratios for the mass and the spin parameters can be lower than 1.5%. In particular, the measurement error of the tidal deformability can also be significantly reduced by ET, with the error ratio of 3.6%–6.1%. We investigate the effect of prior information by applying the Gaussian prior on the coalescence phase ϕ c to the Fisher matrix and find that the error of the intrinsic parameters can be reduced to of the original priorless error if the standard deviation of the prior is similar to .

Cosmography with standard sirens from the Einstein Telescope

We discuss the power of third-generation gravitational wave detectors to constrain cosmographic parameters in the case of electromagnetically bright standard sirens focusing on the specific case of the Einstein Telescope. We analyze the impact that the redshift source distribution, the number of detections and the observational error in the luminosity distance have on the inference of the first cosmographic parameters, and show that with a few hundreds detections the Hubble constant can be recovered at sub-percent level whereas the deceleration parameter at a few percent level, both with negligible bias.

Large-scale Monolithic Fused-Silica Mirror Suspension for Third-Generation Gravitational-Wave Detectors

Thermal noise from the suspension fibers used in the mirror pendulums in current gravitational-wave detectors is a critical noise source. Future detectors will require improved suspension performance with the specific ability to suspend much heavier masses to reduce radiation pressure noise, while retaining good thermal noise performance. In this paper we propose and experimentally demonstrate a design for a large-scale fused-silica suspension, demonstrating its suitability for holding an increased mass of 160 kg. We demonstrate the concepts for improving thermal noise via longer suspension fibers supporting a higher static stress. We present a full thermal noise analysis of our prototype, meeting requirements for conceptual third-generation detector designs such as the high frequency interferometer of the Einstein Telescope, and closely approaching that required for Cosmic Explorer.

Probing the Large-scale Structure of the Universe Through Gravitational Wave Observations

The improvements in the sensitivity of the gravitational wave (GW) network enable the detection of several large redshift GW sources by third-generation GW detectors. These advancements provide an independent method to probe the large-scale structure of the universe by using the clustering of the binary black holes (BBHs). The black hole catalogs are complementary to the galaxy catalogs because of large redshifts of GW events, which may imply that BBHs are a better choice than galaxies to probe the large-scale structure of the universe and cosmic evolution over a large redshift range. To probe the large-scale structure, we used the sky position of the BBHs observed by third-generation GW detectors to calculate the angular correlation function and the bias factor of the population of BBHs. This method is also statistically significant as 5000 BBHs are simulated. Moreover, for the third-generation GW detectors, we found that the bias factor can be recovered to within 33% with an observational time of ten years. This method only depends on the GW source-location posteriors; hence, it can be an independent method to reveal the formation mechanisms and origin of the BBH mergers compared to the electromagnetic method.

Laser parameters requirement for third-generation ground-based gravitational wave detection

Gravitational waves (GWs), predicted by the general relativity of Albert Einstein, are ripples in space-time caused by massive accelerating objects. Since the first direct observation of GWs in 2015, more and more binary black hole mergers and neutron star merger were detected by the laser interferometer gravitational-wave observatory (LIGO) and the Virgo interferometric detector. The construction of the third-generation (3G) gravitational wave detector(GWD), whose sensitivity is ten times that of the second-generation (2G) GWD (Advanced LIGO and Virgo), can not only push the gravitational wave astronomy towards the edge of the observable universe, but also test the fundamental laws of physics and study the nature of matter. By utilizing the abandoned underground mines, Shanxi university proposes to construct a 3G ground-based gravitational wave detector with an arm length of 10 km and a strain sensitivity of 10<sup>–24</sup> Hz<sup>–1/2</sup>, improving the location accuracy of wave source by participating in the global GWD network. The construction of 3G GWD has many technical challenges, including ultrahigh large-scale vacuum system, ultrastable seismic isolation system, high-precision control system, high-quality laser and quantum source. Theoretically, the sensitivity of GWD with equal arm length is not limited by the laser source noise. However, in the actual scenario, the sensitivity is limited by the differences in arm length, arm cavity linewidth, arm reflectivity, arm mass, arm power, and the laser parameters. In this work, based on the design sensitivity (10<sup>–24</sup> Hz<sup>–1/2</sup>) of dual-recycled Fabry-Perot Michelson interferometer, we propose the requirements for an ultra low-noise laser, including wavelength, amplitude noise, frequency noise, beam pointing noise and fundamental mode purity. The results show that in order to achieve the design sensitivity at the Fourier frequency of 100 Hz, the wavelength of the laser source should be 1.5 μm, the output power should be higher than 200 W, the amplitude noise should be better than 10<sup>–8</sup> Hz<sup>–1/2</sup>, and the frequency noise should be better than 100 Hz/Hz<sup>1/2</sup>. To achieve the sensitivity of 10<sup>–24</sup> Hz<sup>–1/2</sup> at 10 Hz analysis frequency, the requirements for the amplitude and frequency noise of the laser source are much more stringent. This study lays a solid foundation for the analysis of laser source noise and the decomposition of interferometer indexes .

Prospects of discovering subsolar primordial black holes using the stochastic gravitational wave background from third-generation detectors

ABSTRACT Primordial black holes (PBHs) are dark matter candidates that span broad mass ranges from 10−17 M⊙ to ∼100 M⊙. We show that the stochastic gravitational wave background can be a powerful window for the detection of subsolar mass PBHs and shed light on their formation channel via third-generation gravitational wave detectors such as Cosmic Explorer and the Einstein Telescope. By using the mass distribution of the compact objects and the redshift evolution of the merger rates, we can distinguish astrophysical sources from PBHs and will be able to constrain the fraction of subsolar mass PBHs ≤1 M⊙ in the form of dark matter $f_\mathrm{PBH}\le 1{{\ \rm per\ cent}}$ at $68{{\ \rm per\ cent}}$ C.L. even for a pessimistic value of a binary suppression factor. In the absence of any suppression of the merger rate, constraints on fPBH will be less than $0.001{{\ \rm per\ cent}}$. Furthermore, we will be able to measure the redshift evolution of the PBH merger rate with about $1{{\ \rm per\ cent}}$ accuracy, making it possible to uniquely distinguish between the Poisson and clustered PBH scenarios.

Multimodal Analysis of Gravitational Wave Signals and Gamma-Ray Bursts from Binary Neutron Star Mergers

A major boost in the understanding of the universe was given by the revelation of the first coalescence event of two neutron stars (GW170817) and the observation of the same event across the entire electromagnetic spectrum. With third-generation gravitational wave detectors and the new astronomical facilities, we expect many multi-messenger events of the same type. We anticipate the need to analyse the data provided to us by such events not only to fulfil the requirements of real-time analysis, but also in order to decipher the event in its entirety through the information emitted in the different messengers using machine learning. We propose a change in the paradigm in the way we do multi-messenger astronomy, simultaneously using the complete information generated by violent phenomena in the Universe. What we propose is the application of a multimodal machine learning approach to characterize these events.

Probing modified gravitational wave propagation with strongly lensed coalescing binaries

It has been recently shown that quadruply lensed gravitational-wave (GW) events due to coalescing binaries can be localized to one or just a few galaxies, even in the absence of an electromagnetic counterpart. We discuss how this can be used to extract information on modified GW propagation, which is a crucial signature of modifications of gravity at cosmological scales. We show that, using quadruply lensed systems, it is possible to constrain the parameter ${\mathrm{\ensuremath{\Xi}}}_{0}$ that characterizes modified GW propagation, without the need of imposing a prior on ${H}_{0}$. A LIGO/Virgo/Kagra network at target sensitivity might already get a significant measurement of ${\mathrm{\ensuremath{\Xi}}}_{0}$, while a third-generation GW detector such as the Einstein Telescope could reach a very interesting accuracy.

Early warning of precessing compact binary merger with third-generation gravitational-wave detectors

Rapid localization of gravitational-wave events is important for the success of the multi-messenger observations. The forthcoming improvements and constructions of gravitational-wave detectors will enable detecting and localizing compact-binary coalescence events even before mergers, which is called early warning. The performance of early warning can be improved by considering modulation of gravitational wave signal amplitude due to the Earth rotation and the precession of a binary orbital plane caused by the misaligned spins of compact objects. In this paper, for the first time we estimate localization precision in the early warning quantitatively, taking into account an orbital precession. We find that a neutron star-black hole binary at $z=0.1$ can typically be localized to $100\,\mathrm{deg}^2$ and $10\,\mathrm{deg^2}$ at the time of $12$ -- $15 \,\mathrm{minutes}$ and $50$ -- $300\,\mathrm{seconds}$ before merger, respectively, which cannot be achieved without the precession effect.