Seismic Noise Environment and Implications for Future Gravitational Wave Detection on the Moon

Lunar seismicity and tectonics

The proposed TianQin gravitational wave observatory is aiming to detect gravitational wave signals in the millihertz frequency band, through the method of space-borne laser interferometry. In total, three satellites will be launched, each following a geocentric orbit, with an orbital altitude of about one hundred thousand kilometers. They form into an equilateral triangle formation, with an orbital period of <sc>3.6 d.</sc> The orbital plane of TianQin is fixed almost constant, towards one specific gravitational wave source, RXJ0806.3+1527, so that TianQins response to this source is maximized, and this source can be used to calibrate and assess the facilities performance. It is widely anticipated that in the millihertz frequency band, there lurks a wide variety of gravitational wave sources, ranging from massive black hole binary mergers, extreme mass ratio inspirals, Galactic binary white dwarves, stellar mass binary compact objects inspirals, as well as stochastic gravitational wave background. Meanwhile, the expected source number in such frequency band would also be huge. The successful implementation of the TianQin project would pave the way towards exciting prospects of future gravitational wave research. By successfully performing gravitational wave observation, the TianQin gravitational wave observatory can open a new window for the study of gravitational wave astronomy, gravitational wave cosmology as well as gravitational wave physics. The science prospect of TianQin gravitational wave observation can be further enhanced through a combination with multi-band gravitational wave detection and multi-messenger astronomical observations, by collaboration with gravitational wave detectors operating in different frequency bands as well as with other probes focusing on different messengers like electro-magnetic signals, neutrinos or cosmic rays. The TianQin project will also greatly promote the construction of a high-precision space-time reference system, ultra-long-range laser interferometry, high-precision satellite platform, etc. The development of cutting-edge space technologies has important applications in the national economy as well as the national strategic needs. Currently, the TianQin project has made important progress in the precision gravity measurement facility, the payload research base, the laser ranging station, the simulation facility for space-borne gravitation wave detection on ground, and the series test satellite for the TianQin project. Based on the long-term accumulation of relevant technology, the TianQin project team proposed the goal of achieving gravitational wave detection in the 2030s, and a 0123 plan roadmap is formulated, aiming to perform, step by step, lunar or relay satellite laser ranging, testing key technology like space-borne laser interferometry and drag-free control, verifying high precision space-borne laser interferometry technology, and ultimately detecting gravitational wave. By the 2030s, the scientific cooperation between scientists from all over the world and the use of various means to jointly conduct exploration and research on the Universe will face great development. So far, the TianQin project has held many international seminars and received extensive international attention and active participation. Currently, the TianQin Collaboration Group has been formally established, with a collaboration group advisory committee also established, consisting of scientists with significant influence in the field of gravitational wave detection all over the world. The TianQin project will establish a collaborative research or comprehensive cooperation agreement with foreign universities or research organizations, and vigorously promote the China-led space-borne gravitational wave detection business. Through extensive international cooperation, the TianQin project will unite domestic and foreign strengths and strive to take the lead in realizing the gravitational wave detection in the window of millihertz band.

The extreme sensitivity required for direct observation of gravitational waves by the Advanced LIGO detectors means that environmental noise is increasingly likely to contaminate Advanced LIGO gravitational wave signals if left unaddressed. Consequently, environmental monitoring efforts have been undertaken and novel noise mitigation techniques have been developed which have reduced environmental coupling and made it possible to analyze environmental artifacts with potential to affect the 90 gravitational wave events detected from 2015–2020 by the Advanced LIGO detectors. So far, there is no evidence for environmental contamination in gravitational wave detections. However, automated, rapid ways to monitor and assess the degree of environmental coupling between gravitational wave detectors and their surroundings are needed as the rate of detections continues to increase. We introduce a computational tool, PEMcheck, for quantifying the degree of environmental coupling present in gravitational wave signals using data from the extant collection of environmental monitoring sensors at each detector. We study its performance when applied to 79 gravitational waves detected in LIGO’s third observing run and test its performance in the case of extreme environmental contamination of gravitational wave data. We find that PEMcheck’s automated analysis identifies only a small number of gravitational waves that merit further study by environmental noise experts due to possible contamination, a substantial improvement over the manual vetting that occurred for every gravitational wave candidate in the first two observing runs. Building on a first attempt at automating environmental coupling assessments used in the third observing run, this tool represents an improvement in accuracy and interpretability of coupling assessments, reducing the time needed to validate gravitational wave candidates. With the validation provided herein; PEMcheck will play a critical role in event validation during LIGO’s fourth observing run as an integral part of the data quality report produced for each gravitational wave candidate.

We probe the present‐day stresses in the lunar interior by examining the slip directions of moonquakes in the A01 nest. In this nest, some deep moonquakes appear to slip “backwards,” in the opposite direction to other events. We assess whether these changes in slip direction result from a spatial variation in the tectonic stress or from a temporal variation in the tidal stress. To test these two options, we first show that a dominant tectonic stress implies deep moonquakes can only slip in one direction: forwards and backwards, while a dominant tidal stress could allow moonquakes to slip in more directions: any combination of forwards, backwards, left, and right. Then we look for the number of slip directions; we separate the deep moonquake waveforms into slip directions using a principal component analysis technique. We find two slip directions present in the A01 deep moonquake nest. The moonquakes slip in a variety of directions as time evolves. This observation implies that the tidal stresses drive deep moonquakes. Additionally, these results place a new constraint on the magnitude of the tectonic stresses at depth; they must be smaller than the modeled tidal stress of ∼0.1 MPa.

While deep moonquakes are seismic events commonly observed on the Moon, their source mechanism is still unexplained. The two main issues are poorly constrained source parameters and incompatibilities between the thermal profiles suggested by many studies and the apparent need for brittle properties at these depths. In this study, we reinvestigated the deep moonquake data to reestimate its source parameters and uncover the characteristics of deep moonquake faults that differ from those on Earth. We first improve the estimation of source parameters through spectral analysis using “new” broadband seismic records made by combining those of the Apollo long‐ and short‐period seismometers. We use the broader frequency band of the combined spectra to estimate corner frequencies and DC values of spectra, which are important parameters to constrain the source parameters. We further use the spectral features to estimate seismic moments and stress drops for more than 100 deep moonquake events from three different source regions. This study revealed that deep moonquake faults are extremely smooth compared to terrestrial faults. Second, we reevaluate the brittle‐ductile transition temperature that is consistent with the obtained source parameters. We show that the source parameters imply that the tidal stress is the main source of the stress glut causing deep moonquakes and the large strain rate from tides makes the brittle‐ductile transition temperature higher. Higher transition temperatures open a new possibility to construct a thermal model that is consistent with deep moonquake occurrence and pressure condition and thereby improve our understandings of the deep moonquake source mechanism.

This thesis investigates the direct measurement of the thermal noise spectral distribution. Long base line gravitational wave detectors, being commissioned around the world, are limited in sensitivity in the intermediate frequencies by the thermal noise. These detectors are utilising suspended test mirrors for the detection of gravitational waves by measuring their relative displacement. One of the fundamental noise sources in these detectors is the thermally induced displacement of the suspension onto and within the mirrors. This thermally induced motion of the test mirrors limits the displacement sensitivity of the gravitational wave detectors. Knowledge of the spectral behavior of thermal noise over a wide frequency range will improve predictions and understanding of the behavior of the suspension and test mirrors. ¶ In this thesis the direct measurement of the thermal noise spectral distribution of a mechanical flexure resonator is described. The mechanical flexure resonator is an unidirectional ’wobbly table’ made from copper-beryllium, which hinges around four thin flexures 15 mm wide, 1 mm high and ~116 µm thick. The mechanical flexure resonator has a resonant frequency of 192 Hz, with a quality factor of ~3000. ¶ ...

The growing catalog of gravitational wave (GW) detections by the LIGO-Virgo-KAGRA collaboration enables increasingly stringent tests of general relativity, particularly regarding possible violations of parity and Lorentz symmetry. Parity and Lorentz violations in gravity can modify both the damping rate and dispersion relation of GWs, leading to birefringence, frequency-dependent damping, and dispersion effects in the propagation of GWs. These effects result in amplitude and phase corrections of the waveforms of GWs produced by the coalescence of compact binaries, which enable us to constrain parity- and Lorentz-violating effects by analyzing GW signals detected by LIGO-Virgo-KAGRA detectors with the distorted waveforms. While most current analyses employ single-parameter methods-varying one deformation parameter at a time-modified gravity theories often predict multiple, coexisting deviations. In this work, we construct several specific multi-parameter GW waveform models incorporating parity- and Lorentz-violating effects and perform full Bayesian parameter estimation to compare multi-parameter and single-parameter constraints. We find that including multiple deformation parameters yields constraints on individual parameters that are generally comparable to those from single-parameter analyses, despite one specific model showing a degeneracy between the deformation parameters. Our results support the robustness of single-parameter tests for parity and Lorentz symmetry of gravity in current and future GW observations.

Gravitational wave (GW) analysis is attracting widespread attention as an emerging research field. As the presence of substantial noise in GW signals, and the characteristics of inspiral and merger stage are different, coupled with the sidelobe effect caused by window length, traditional time–frequency analysis methods face significant challenges in accurately analyzing the frequency variations of GW signals. This poses a major limitation in the precise analysis stage following GW detection. Therefore, we proposed a novel method of seasonal-trend decomposition using Loess with multilayer perceptron (STLMLP), for predicting and validating the accuracy and effectiveness of GW frequency variations. Experiment results on three noiseless GW templates demonstrate that STLMLP exhibits the adaptability and highest prediction accuracy for the dynamic frequency variations of GW signals compared to five state-of-the-art machine learning and deep learning methods. Furthermore, experiments conducted on three noisy actual GW data compared with the state-of-the-art method of Fourier-based synchrosqueezing transform in the signal processing domain confirm that STLMLP maintains lower error in predicting frequency change over the whole duration of the actual noisy GW signals.

The formation mechanism of AM CVn binary has not been well understood yet. Accurate measurements of the mass transfer rate can help us to determine the formation mechanism. But unfortunately such observation by electromagnetic means is quite challenging. One possible formation channel of AM CVn binary is a semidetached white dwarf binary. Such system emits strong gravitational wave radiation which could be measured by the future space-based detectors. We can simultaneously extract the mass transfer rate and the orbital period from the gravitational wave signal. We employ a post-Keplerian waveform model of gravitational wave and carry out a Fisher analysis to estimate the measurement accuracy of mass transfer rate through gravitational wave detection. Special attention is paid to the observed sources in Gaia Data Release 2. We found that we can accurately measure the mass transfer rate for those systems. Comparing to electromagnetic observations, gravitational wave detection improves the accuracy more than two orders of magnitude. Our results imply that the gravitational wave detection will help much in understanding the formation mechanism of AM CVn binaries.

The LIGO and Virgo gravitational-wave observatories are complex and extremely sensitive strain detectors that can be used to search for a wide variety of gravitational waves from astrophysical and cosmological sources. In this thesis, I motivate the search for the gravitational wave signals from coalescing black hole binary systems with total mass between 25 and 100 solar masses. The mechanisms for formation of such systems are not well-understood, and we do not have many observational constraints on the parameters that guide the formation scenarios. Detection of gravitational waves from such systems — or, in the absence of detection, the tightening of upper limits on the rate of such coalescences — will provide valuable information that can inform the astrophysics of the formation of these systems. I review the search for these systems and place upper limits on the rate of black hole binary coalescences with total mass between 25 and 100 solar masses. I then show how the sensitivity of this search can be improved by up to 40% by the the application of the multivariate statistical classifier known as a random forest of bagged decision trees to more effectively discriminate between signal and non-Gaussian instrumental noise. I also discuss the use of this classifier in the search for the ringdown signal from the merger of two black holes with total mass between 50 and 450 solar masses and present upper limits. I also apply multivariate statistical classifiers to the problem of quantifying the non-Gaussianity of LIGO data. Despite these improvements, no gravitational-wave signals have been detected in LIGO data so far. However, the use of multivariate statistical classification can significantly improve the sensitivity of the Advanced LIGO detectors to such signals.

The nonlinear memory effect is a fascinating prediction of general relativity (GR), in which oscillatory gravitational-wave (GW) signals are generically accompanied by a monotonically-increasing strain which persists in the detector long after the signal has passed. This effect is directly accessible to GW observatories, and presents a unique opportunity to test GR in the dynamical and nonlinear regime. In this article we calculate, for the first time, the nonlinear memory signal associated with GW bursts from cusps and kinks on cosmic string loops, which are an important target for current and future GW observatories. We obtain analytical waveforms for the GW memory from cusps and kinks, and use these to calculate the ‘memory of the memory’ and other higher-order memory effects. These are among the first memory observables computed for a cosmological source of GWs, with previous literature having focused almost entirely on astrophysical sources. Surprisingly, we find that the cusp GW signal diverges for sufficiently large loops, and argue that the most plausible explanation for this divergence is a breakdown in the weak-field treatment of GW emission from the cusp. This shows that previously-neglected strong gravity effects must play an important rôle near cusps, although the exact mechanism by which they cure the divergence is not currently understood. We show that one possible resolution is for these cusps to collapse to form primordial black holes (PBHs); the kink memory signal does not diverge, in agreement with the fact that kinks are not predicted to form PBHs. Finally, we investigate the prospects for detecting memory from cusps and kinks with current and future GW observatories, considering both individual memory bursts and the contribution of many such bursts to the stochastic GW background. We find that in the scenario where the cusp memory divergence is cured by PBH formation, the memory signal is strongly suppressed and is not likely to be detected. However, alternative resolutions of the cusp divergence may in principle lead to much more favourable observational prospects.

Detection and identification of interesting events in single‐station seismic data with little prior knowledge and under tight time constraints is a typical scenario in planetary seismology. The Apollo lunar seismic data, with the only confirmed events recorded on any extraterrestrial body yet, provide a valuable test case. Here we present the application of a stochastic event detector and classifier to the data of station Apollo 16. Based on a single‐waveform example for each event class and some hours of background noise, the system is trained to recognize deep moonquakes, impacts, and shallow moonquakes and performs reliably over 3 years of data. The algorithm's demonstrated ability to detect rare events and flag previously undefined signal classes as new event types is of particular interest in the analysis of the first seismic recordings from a completely new environment. We are able to classify more than 50% of previously unclassified lunar events, and additionally find over 200 new events not listed in the current lunar event catalog. These events include deep moonquakes as well as impacts and could be used to update studies on temporal variations in event rate or deep moonquakes stacks used in phase picking for localization. No unambiguous new shallow moonquake was detected, but application to data of the other Apollo stations has the potential for additional new discoveries 40 years after the data were recorded. Besides, the classification system could be useful for future seismometer missions to other planets, e.g., the InSight mission to Mars.

We present an effective, low-dimensionality frequency-domain template for the gravitational wave (GW) signal from the stellar remnants from binary neutron star (BNS) coalescence. A principal component decomposition of a suite of numerical simulations of BNS mergers is used to construct orthogonal basis functions for the amplitude and phase spectra of the waveforms for a variety of neutron star (NS) equations of state and binary mass configurations. We review the phenomenology of late merger/post-merger GW emission in BNS coalescence and demonstrate how an understanding of the dynamics during and after the merger leads to the construction of a universal spectrum. We also provide a discussion of the prospects for detecting the post-merger signal in future GW detectors as a potential contribution to the science case for third generation instruments. The template derived in our analysis achieves match across a wide variety of merger waveforms and strain sensitivity spectra for current and potential GW detectors. Using a simple Monte Carlo simulation, we find a preliminary estimate of the typical uncertainty in the determination of the dominant post-merger oscillation frequency of . Using recently derived correlations between and the NS radii, this suggests potential constraints on the radius of a fiducial NS of ∼429 m. Such measurements would only be possible for nearby (∼30 Mpc) sources with advanced LIGO but become more feasible for planned upgrades to advanced LIGO and other future instruments, leading to constraints on the high density NS equation of state which are independent and complementary to those inferred from the pre-merger inspiral GW signal. We study the ability of a selection of future GW instruments to provide constraints on the NS equation of state via the postmerger phase of BNS mergers.

We propose two distinct atom interferometer gravitational wave detectors, one terrestrial and another satellite-based, utilizing the core technology of the Stanford 10m atom interferometer presently under construction. The terrestrial experiment can operate with strain sensitivity {approx} 10{sup -19}/{radical}Hz in the 1 Hz-10 Hz band, inaccessible to LIGO, and can detect gravitational waves from solar mass binaries out to megaparsec distances. The satellite experiment probes the same frequency spectrum as LISA with better strain sensitivity {approx} 10{sup -20}/{radical}Hz. Each configuration compares two widely separated atom interferometers run using common lasers. The effect of the gravitational waves on the propagating laser field produces the main effect in this configuration and enables a large enhancement in the gravitational wave signal while significantly suppressing many backgrounds. The use of ballistic atoms (instead of mirrors) as inertial test masses improves systematics coming from vibrations and acceleration noise, and reduces spacecraft control requirements.

As gravitational wave astronomy prepares for the first detections of gravitational waves from compact-object binary inspirals, theoretical work is required on the study of (i) gravitational-wave sources, (ii) the signals emitted by those sources, and (iii) the searches for those signals in detector data. This thesis describes work on all three fronts. (i) We discuss intermediate-mass-ratio inspirals (IMRIs) of black holes or neutron stars into intermediate-mass black holes (IMBHs) that could be detected with Advanced LIGO. We analyze different mechanisms of IMRI formation and compute IMRI event rates of up to tens of events per year for Advanced LIGO. We study the spin evolution of IMBHs that grow through a series of minor mergers. We explore how a deviation of an IMRI's central body from a Kerr black hole influences geodesics, including the possibility of chaotic orbital dynamics. We also address the scientific consequences of extreme-mass-ratio inspiral (EMRI) detections by LISA for astrophysics and general relativity, and the difficulties associated with detecting and analyzing EMRI signals. (ii) We study the periodic standing-wave approximation (PSWA), which can potentially provide accurate waveforms in the last inspiral cycles of a comparable-mass black-hole binary. Using a simple model, we find that the solution to Einstein's equations for inspiraling black holes can be recovered to a high accuracy by the addition a perturbative radiation-reaction field to the standing-wave, noninspiraling solution. (iii) We demonstrate the utility of searching for and analyzing tracks in time-frequency spectrograms of a gravitational-wave signal as a means of estimating the parameters of a massive black-hole binary inspiral, as observed by LISA.