Future Gravitational Wave Detectors Research Articles

Gwfish: A simulation software to evaluate parameter-estimation capabilities of gravitational-wave detector networks

An important step in the planning of future gravitational-wave (GW) detectors and of the networks they will form is the estimation of their detection and parameter-estimation capabilities, which is the basis of science-case studies. Several future GW detectors have been proposed or are under development, which might also operate and observe in parallel. These detectors include terrestrial, lunar, and space-borne detectors. In this paper, we present gwfish,11github.com/janosch314/GWFish. a new software to simulate GW detector networks and to calculate measurement uncertainties based on the Fisher-matrix approximation. gwfish models the impact of detector motion on PE and makes it possible to analyze multiband scenarios, i.e., observation of a GW signal by different detectors in different frequency bands. We showcase a few examples for the Einstein Telescope (ET) including the sky-localization of binary neutron stars, and ET’s capability to measure the polarization of GWs.

Hunt for light primordial black hole dark matter with ultrahigh-frequency gravitational waves

Light primordial black holes may comprise a dominant fraction of the dark matter in our Universe. This paper critically assesses whether planned and future gravitational wave detectors in the ultra-high-frequency band could constrain the fraction of dark matter composed of sub-solar primordial black holes. Adopting the state-of-the-art description of primordial black hole merger rates, we compare various signals with currently operating and planned detectors. As already noted in the literature, our findings confirm that detecting individual primordial black hole mergers with currently existing and operating proposals remains difficult. Current proposals involving gravitational wave to electromagnetic wave conversion in a static magnetic field and microwave cavities feature a technology gap with respect to the loudest gravitational wave signals from primordial black holes of various orders of magnitude. However, we point out that one recent proposal involving resonant LC circuits represents the best option in terms of individual merger detection prospects in the range $(1\div 100) \, \text{MHz}$. In the same frequency range, we note that alternative setups involving resonant cavities, whose concept is currently under development, might represent a promising technology to detect individual merger events. We also show that a detection of the stochastic gravitational wave background produced by unresolved binaries is possible only if the theoretical sensitivity of the proposed Gaussian beam detector is achieved. Such a detector, whose feasibility is subject to various caveats, may be able to rule-out some scenarios for asteroidal mass primordial black hole dark matter. We conclude that pursuing dedicated studies and developments of gravitational wave detectors in the ultra-high-frequency band remains motivated and may lead to novel probes on the existence of light primordial black holes.

Surrogate model for gravitational wave signals from nonspinning, comparable-to large-mass-ratio black hole binaries built on black hole perturbation theory waveforms calibrated to numerical relativity

We present a reduced-order surrogate model of gravitational waveforms from non-spinning binary black hole systems with comparable to large mass-ratio configurations. This surrogate model, \texttt{BHPTNRSur1dq1e4}, is trained on waveform data generated by point-particle black hole perturbation theory (ppBHPT) with mass ratios varying from 2.5 to 10,000. \texttt{BHPTNRSur1dq1e4} extends an earlier waveform model, \texttt{EMRISur1dq1e4}, by using an updated transition-to-plunge model, covering longer durations up to 30,500 $m_1$ (where $m_1$ is the mass of the primary black hole), includes several more spherical harmonic modes up to $\ell=10$, and calibrates subdominant modes to numerical relativity (NR) data. In the comparable mass-ratio regime, including mass ratios as low as $2.5$, the gravitational waveforms generated through ppBHPT agree surprisingly well with those from NR after this simple calibration step. We also compare our model to recent SXS and RIT NR simulations at mass ratios ranging from $15$ to $32$, and find the dominant quadrupolar modes agree to better than $\approx 10^{-3}$. We expect our model to be useful to study intermediate-mass-ratio binary systems in current and future gravitational-wave detectors.

Gravitational radiation from inspiralling compact objects: Spin effects to the fourth post-Newtonian order

The linear- and quadratic-in-spin contributions to the binding potential and gravitational-wave flux from binary systems are derived to next-to-next-to-leading order in the Post-Newtonian (PN) expansion of general relativity, including finite-size and tail effects. The calculation is carried out through the worldline effective field theory framework. We find agreement in the overlap with the available PN literature and test-body limit. As a direct application, we complete the knowledge of spin effects in the evolution of the orbital phase for aligned-spin circular orbits to fourth PN order. We estimate the impact of the new results in the number of accumulated gravitational-wave cycles. We find they will play an important role in providing reliable physical interpretation of gravitational-wave signals from spinning binaries with future detectors such as LISA and the Einstein Telescope.

Low coherency of wind induced seismic noise: implications for gravitational wave detection

Seismic noise poses challenges for gravitational wave detection. Effective vibration isolation and methods to subtract unshieldable Newtonian noise (NN) are examples. Seismic arrays offer one way to deal with these issues by making use of correlations between seismic ground measurements and noise inside the detector. In this paper we find that wind induced seismic noise is incoherent and our results show that it can dramatically reduce the projected low frequency sensitivity of future gravitational wave detectors. To quantify this, we measure the coherence length of wind induced seismic noise from 0.06–20 Hz in three distinct locations: close to a building, among tall trees and in shrubs. We show that wind induced seismic noise is ubiquitous and reduces the coherence lengths from several hundred meters to 2–40 m for 0.06–0.1 Hz, from 60 m to 3–16 m for 1.5–2.5 Hz and from 35 m to 1–16 m around 16.6 Hz in the study area. This leads to significant loss of velocity resolution of the array for primary microseism and 5 times worse NN cancellation by Wiener filtering at 2 Hz, while it may not pose additional limitation to NN cancellation between 10–20 Hz.

Comparing second-order gravitational self-force and effective one body waveforms from inspiralling, quasicircular and nonspinning black hole binaries. II. The large-mass-ratio case

We compare recently computed waveforms from second-order gravitational self-force (GSF) theory to those generated by a new, GSF-informed, effective one body (EOB) waveform model for (spin-aligned, eccentric) inspiralling black hole binaries with large mass ratios. We focus on quasi-circular, nonspinning, configurations and perform detailed GSF/EOB waveform phasing comparisons, either in the time domain or via the gauge-invariant dimensionless function $Q_\omega\equiv \omega^2/\dot{\omega}$, where $\omega$ is the gravitational wave frequency. The inclusion of high-PN test-mass terms within the EOB radiation reaction (notably, up to 22PN) is crucial to achieve an EOB/GSF phasing agreement below 1~rad up to the end of the inspiral for mass ratios up to 500. For larger mass ratios, up to $5\times 10^4$, the contribution of horizon absorption becomes more and more important and needs to be accurately modeled. Our results indicate that our GSF-informed EOB waveform model is a promising tool to describe waveforms generated by either intermediate or extreme mass ratio inspirals for future gravitational wave detectors

Exploring compact binary populations with the Einstein Telescope

The Einstein Telescope (ET), a wide-band, future third generation gravitational wave detector, is expected to have detection rates of ∼105 − 106 binary black hole (BBH) detections and ∼7 × 104 binary neutron star (BNS) detections in one year. The coalescence of compact binaries with a total mass of 20–100 M⊙, typical of BH-BH or BH-NS binaries, will be visible up to redshift z ≈ 20 and even higher, thus facilitating the understanding of the dark era of the Universe preceding the birth of the first stars. The ET will therefore be a crucial instrument for population studies. We analysed the compact binaries originating in stars from (i) Population (Pop) I+II, (ii) Pop III, and (iii) globular clusters (GCs), with the single ET instrument, using the ET-D design sensitivity for the analysis. We estimated the constraints on the chirp mass, redshift, and merger rate as function of redshift for these classes of compact object binaries. We conclude that the ET as a single instrument is capable of detecting and distinguishing different compact binary populations separated in chirp mass – redshift space. While compact binaries originating in stars from Pop III are clearly distinguishable, owing to the separation in chirp mass – redshift space, the other two populations, Pop I+II, and GCs, can be distinguished with just 500 detections, corresponding to an observation time of ∼1 h. The mass distribution characteristics of such different compact binary populations can also be estimated with the single ET instrument.

Probing horizon scale quantum effects with Love

Future gravitational wave (GW) detectors have been projected to be able to probe the nature of compact objects in great detail. In this work, we study the potential observability of the small length scale physics near black hole horizon with the tidal deformability of the compact objects in an inspiraling binary. We find that it is possible to probe them with extreme mass ratio inspirals. We discuss how the quantum effects can affect the GW observables. This as a consequence is bound to shape our understanding of the quantum scale near the horizon.

Quasi-monocrystalline silicon for low-noise end mirrors in cryogenic gravitational-wave detectors

Mirrors made of silicon have been proposed for use in future cryogenic gravitational-wave detectors, which will be significantly more sensitive than current room-temperature detectors. These mirrors are planned to have diameters of $\ensuremath{\approx}50$ cm and a mass of $\ensuremath{\approx}200$ kg. While single-crystalline float-zone silicon meets the requirements of low optical absorption and low mechanical loss, the production of this type of material is restricted to sizes much smaller than required. Here we present studies of silicon produced by directional solidification. This material can be grown as quasi-monocrystalline ingots in sizes larger than currently required. We present measurements of a low room-temperature and cryogenic mechanical loss comparable with float-zone silicon. While the optical absorption of our test sample is significantly higher than required, the low mechanical loss motivates research into further absorption reduction in the future. While it is unclear if material pure enough for the transmissive detector input mirrors can be achieved, an absorption level suitable for the highly reflective coated end mirrors seems realistic. Together with the potential to produce samples much larger than $\ensuremath{\approx}50$ cm, this material may be of great benefit for realizing silicon-based gravitational-wave detectors.

High mechanical Q-factor measurement of Si using a 3D cantilever support.

Thermal noise in test mass substrates and coatings is a significant noise contribution in the detection band of current and proposed future gravitational wave detectors. Substrate thermal noise can be reduced by using high mechanical Q-factor materials and cooling the test mass mirrors. Silicon is a promising potential candidate for the next generation detector test masses. The low thermal expansion and high thermal conductivity of silicon allow efficient cryogenic operation, and a significant increase in the amount of optical power that can be used in the detectors by decreasing thermal deformation and aberration. Mechanical stress, damage, poor surface quality or contamination can result in increased loss and thermal noise. Therefore, the characterization of mechanical loss in silicon test masses is necessary. In this project, we developed a technique to measure high Q-factor mechanical modes. We used finite element modeling to optimize the design of the test mass support structure to minimize the loss coupling from the support structure over a wide frequency range. Mechanical Q-factors of the order of 107 were achieved for several modes of a 10cm diam. × 3cm cylindrical silicon test mass with such a support at room temperature.

Weak-Light Phase-Locking Time Delay Interferometry with Optical Frequency Combs.

In the future space-borne gravitational wave (GW) detector, the optical transponder scheme, i.e., the phase-locking scheme, will be utilized so as to maintain the signal-to-noise ratio (SNR). In this case, the whole constellation will share one common laser equivalently, which enables the considerable simplification of time delay interferometry (TDI) combinations. Recently, and remarkably, the unique combination of TDI and optical frequency comb (OFC) has shown a bright prospect for the future space-borne missions. When the laser frequency noise and the clock noise are synchronized using OFC as the bridge, the data streams will be reasonably simplified. However, in the optical transponder scheme, the weak-light phase-locking (WLPL) loops could bring additional noises. In this work, we analyze the phase-locking scheme with OFC and transfer characteristics of the noises including the WLPL noise. We show that the WLPL noise can be efficiently reduced by using the specific TDI combination, and the cooperation of phase-locking and frequency combs can greatly simplify the post-processing.

Toward a gravitational self-force-informed effective-one-body waveform model for nonprecessing, eccentric, large-mass-ratio inspirals

Building upon several recent advances in the development of effective-one-body models for spin-aligned eccentric binaries with individual masses $(m_1,m_2)$ we introduce a new EOB waveform model that aims at describing inspiralling binaries in the large mass-ratio regime, $m_1\gg m_2$. The model exploits the current state-of-the-art TEOBResumS-Dali model for eccentric binaries, but the standard EOB potentials $(A,\bar{D},Q)$, informed by Numerical Relativity (NR) simulations, are replaced with the corresponding functions that are linear in the symmetric mass ratio $\nu\equiv m_1 m_2/(m_1+m_2)^2$ taken at 8.5PN accuracy. To improve their strong-field behavior, these functions are: (i) suitably factorized and resummed using Pad\'e approximants and (ii) additionally effectively informed to state-of-the-art numerical results obtained by gravitational self-force theory (GSF). For simplicity, the spin-sector of the model is taken to be the one of TEOBResumS-Dali, though removing the NR-informed spin-orbit effective corrections. We propose the current GSF-informed EOB framework as a conceptually complete analytical tool to generate waveforms for eccentric Extreme (and Intermediate) Mass Ratio Inspirals for future gravitational wave detectors.

Searching for dark clumps with gravitational-wave detectors

Dark compact objects (``clumps'') transiting the Solar System exert accelerations on the test masses (TM) in a gravitational-wave (GW) detector. We reexamine the detectability of these clump transits in a variety of current and future GW detectors, operating over a broad range of frequencies. TM accelerations induced by clump transits through the inner Solar System have frequency content around $f\ensuremath{\sim}\ensuremath{\mu}\mathrm{Hz}$. Some of us [Fedderke et al., Phys. Rev. D 105, 103018 (2022)] recently proposed a GW detection concept with $\ensuremath{\mu}\mathrm{Hz}$ sensitivity, based on asteroid-to-asteroid ranging. From the detailed sensitivity projection for this concept, we find both analytically and in simulation that purely gravitational clump--matter interactions would yield one detectable transit every $\ensuremath{\sim}20\text{ }\text{ }\mathrm{yrs}$, if clumps with mass ${m}_{\mathrm{cl}}\ensuremath{\sim}{10}^{14}\text{ }\text{ }\mathrm{kg}$ saturate the dark-matter (DM) density. Other (proposed) GW detectors using local TMs and operating in higher frequency bands are sensitive to smaller clump masses and have smaller rates of discoverable signals. We also consider the case of clumps endowed with an additional attractive long-range clump--matter fifth force significantly stronger than gravity (but evading known fifth-force constraints). For the $\ensuremath{\mu}\mathrm{Hz}$ detector concept, we use simulations to show that, for example, a clump--matter fifth-force $\ensuremath{\sim}{10}^{3}$ times stronger than gravity with a range of $\ensuremath{\sim}\mathrm{AU}$ would boost the rate of detectable transits to a few per year for clumps in the mass range ${10}^{11}\text{ }\text{ }\mathrm{kg}\ensuremath{\lesssim}{m}_{\mathrm{cl}}\ensuremath{\lesssim}{10}^{14}\text{ }\text{ }\mathrm{kg}$, even if they are a $\ensuremath{\sim}1%$ subcomponent of the DM. The ability of $\ensuremath{\mu}\mathrm{Hz}$ GW detectors to probe asteroid-mass-scale dark objects that may otherwise be undetectable bolsters the science case for their development.

Squeezed States of Light for Future Gravitational Wave Detectors at a Wavelength of 1550nm.

The generation of strongly squeezed vacuum states of light is a key technology for future ground-based gravitational wave detectors (GWDs) to reach sensitivities beyond their quantum noise limit. For some proposed observatory designs, an operating laser wavelength of 1550nm or around 2 μm is required to enable the use of cryogenically cooled silicon test masses for thermal noise reduction. Here, we present for the first time the direct measurement of up to 11.5dB squeezing at 1550nm over the complete detection bandwidth of future ground-based GWDs ranging from 10kHz down to below 1Hz. Furthermore, we directly observe a quantum shot-noise reduction of up to (13.5±0.1) dB at megahertz frequencies. This allows us to derive a precise constraint on the absolute quantum efficiency of the photodiode used for balanced homodyne detection. These results hold important insight regarding the quantum noise reduction efficiency in future GWDs, as well as for quantum information and cryptography, where low decoherence of nonclassical states of light is also of high relevance.

Regularization of a scalar charged particle for generic orbits in Kerr spacetime

A scalar charged particle moving in a curved background spacetime will emit a field affecting its own motion; the resolving of this resulting motion is often referred to as the self-force problem. This also serves as a toy model for the astrophysically interesting compact body binaries, extreme mass ratio inspirals, targets for the future space-based gravitational wave detector, LISA. In the modelling of such systems, a point-particle assumption leads to problematic singularities which need to be safely removed to solve for the motion of the particle regardless of the scenario: scalar, electromagnetic or gravitational. Here, we concentrate on a scalar charged particle and calculate the next order of the Detweiler-Whiting singular field and its resulting regularisation parameter when employing the mode-sum method of regularisation. This enables sufficiently faster self-force calculations giving the same level of accuracy with significantly less $\ell$ modes. Due to the similarity of the governing equations, this also lays the groundwork for similar calculations for an electromagnetic or mass charged particle in Kerr spacetime and has applications in other regularisation schemes like the effective source and matched expansion.

Intermediate mass-ratio inspirals with dark matter minispikes

The dark matter (DM) distributed around an intermediate massive black hole (IMBH) forms an overdensity region called DM minispike. We consider the binary system which consists of an IMBH with DM minispike and a small black hole inspiralling around the IMBH in eccentric orbits. The factors which affect the evolution of the orbit include the gravity of the system, the dynamical friction and accretion of the small black hole caused by the DM minispike, and the radiation reaction of gravitational waves (GWs). Using the method of osculating orbit, we find that when the semi-latus rectum $p\ensuremath{\ll}{10}^{5}{R}_{s}$ (${R}_{s}$ is the Schwarzschild radius of the IMBH) the dominated factors are the dynamical friction and accretion from the DM minispike, and the radiation reaction. When $p\ensuremath{\gg}{10}^{5}{R}_{s}$, the gravity from the DM minispike dominates the orbital evolution. The existence of DM minispike leads to the deviation from the Keplerian orbit, such as extra orbital precession, henceforth extra phase shift in the GW waveform. By calculating the signal-to-noise ratio for GWs with and without DM minispikes and the mismatch between them, we show that the effect of the DM minispike in GW waveforms can potentially be detected by future space-based GW detectors such as LISA, Taiji, and Tianqin.

Probing dark matter spikes via gravitational waves of extreme-mass-ratio inspirals

The exact properties of dark matter remain largely unknown despite the accumulating evidence. If dark matter is composed of weakly interacting massive particles, it would be accreted by the black hole in the galactic center and form a dense, cuspy spike. Dynamical friction from this spike may have observable effects in a binary system. We consider extreme-mass-ratio inspiral (EMRI) binaries comprising massive black holes harbored in dark matter spikes and stellar mass objects in elliptic orbits. We find that the gravitational-wave waveforms in the frequency domain can be substantially modified. In particular, we show that dark matter can suppress the characteristic strain of a gravitational wave at low frequency but enhance it at a higher domain. These effects are more dramatic as the dark matter density increases. The results indicate that the signal-to-noise ratio of EMRIs can be strongly reduced near 10−3−0.3 Hz but enhanced near 1.0 Hz with a higher sensitivity, which can be probed via the future space-borne gravitational-wave (GW) detectors, LISA and TAIJI. The findings will have important impacts on the detection and parameter inference of EMRIs.

Induced gravitational waves from slow-roll inflation after an enhancing phase

The primordial spectrum of fluctuations may present a large peak as a result of enhancing features during inflation. This may include, but is not limited to, bumps in the inflaton's potential, phases of ultra-slow-roll or turns in multi-field space. However, in many models, inflation does not end immediately after the enhancing feature and it is likely to continue with a second phase of slow-roll. We show that the resulting induced gravitational waves may probe the primordial spectrum from the second inflationary phase, even if its amplitude is too small to directly induce detectable gravitational waves. This is because, if there are sharp peaks in the primordial spectrum, the total gravitational wave spectrum is not simply the sum of gravitational waves induced by a peaked andscale-invariant primordial spectra separately, but cross terms from interaction between these modes also become important. We also find that such cross terms always have a characteristic slope. We discuss the parameter space that may be probed by future gravitational wave detectors in the presence of these signals.

Impact of correlated seismic and correlated Newtonian noise on the Einstein Telescope

Correlated noise could impact the search for the gravitational wave background at future Earth-based gravitational-wave detectors. Due to the small distance ($\sim$ 400 m) between the different interferometers of the Einstein Telescope, correlated seismic noise could have a significant effect. To this extent, we study the seismic correlations at the Earth's surface, as well as underground, between seismometers and geophones separated by several hundreds of meters, in the frequency range 0.05 Hz - 50 Hz. Based on these correlated seismic fields we predict the levels of correlated Newtonian noise (NN). We construct upper limits on the allowed seismic coupling function such that correlated seismic noise does not affect the search for an isotropic gravitational wave background. Assuming a facility located 300 m below the surface, the impact on the search for a gravitational wave background of correlated NN from Rayleigh waves are found to be problematic up to $\sim$ 5 Hz. The NN from body waves, however, constitutes a serious threat to the search of a gravitational wave background. Correlated NN from body waves could be up to five to seven orders of magnitude above the planned sensitivity at $\sim$ 3 Hz and it could impede any search for a gravitational wave background below 40 Hz. With a factor 10 of NN reduction via NN cancellation in each interferometer, the effects of the NN on the stochastic search could be eliminated above 30 Hz.

Investigating the detection rates and inference of gravitational-wave and radio emission from black hole neutron star mergers

Context. Black hole neutron star (BHNS) mergers have recently been detected through their gravitational-wave (GW) emission. While no electromagnetic emission has yet been confidently associated with these systems, observing any such emission could provide information on, for example, the neutron star equation of state. Black hole neutron star mergers could produce electromagnetic emission as a short gamma-ray burst (sGRB) and/or an sGRB afterglow upon interaction with the circum-merger medium. Aims. We make predictions for the expected detection rates with the Square Kilometre Array Phase 1 (SKA1) of sGRB radio afterglows associated with BHNS mergers. We also investigate the benefits of a multi-messenger analysis in inferring the properties of the merging binary. Methods. We simulated a population of BHNS mergers, making use of recent stellar population synthesis results, and estimated their sGRB afterglow flux to obtain the detection rates with SKA1. We investigate how this rate depends on the GW detector sensitivity, the primary black hole spin, and the neutron star equation of state. We then performed a multi-messenger Bayesian inference study on a fiducial BHNS merger. We simulated its sGRB afterglow and GW emission as input to this study, using recent models for both, and take systematic errors into account. Results. The expected rates of a combined GW and radio detection with the current-generation GW detectors are likely low. Due to the much increased sensitivity of future GW detectors such as the Einstein Telescope, the chances of an sGRB localisation and radio detection increase substantially. The unknown distribution of the black hole spin has a big influence on the detection rates, however, and it is a large source of uncertainty. Furthermore, when placing our fiducial BHNS merger at 50 and 100 Mpc, we are able to infer both the binary source parameters and the parameters of the sGRB afterglow simultaneously if we combine the GW and radio data. The radio data provide useful extra information on the binary parameters, such as the mass ratio, but this is limited by the systematic errors involved. For our fiducial binary at 200 Mpc, it is considerably more difficult to adequately infer the parameters of the system. Conclusions. The probability of finding an sGRB afterglow of a BHNS merger is low in the near future but will rise significantly when the next-generation GW detectors come online. Combining information from GW data with radio data is crucial for characterising the jet properties. A better understanding of the systematics will further increase the amount of information on the binary parameters that can be extracted from this radio data.