Lensed gravitational waves: Scattering and applications

To successfully detect the ultrasmall gravitational wave signal ($\sim$$10^{-19}$ m), the ground-based laser interferometric gravitational wave detector should reduce all kinds of noise. This study summarizes the seismic noise that affects gravitational wave detection and the basic principle and method for mitigating the seismic noise. At present, a multistage suspension system and an active vibration isolation system are combined to further reduce seismic noise. We investigate and analyze the application of passive and active vibration isolation methods in ground-based gravitational wave detectors by reviewing the suspension and vibration isolation systems of current gravitational wave detectors, including LIGO, Virgo, KAGRA, and GEO600.

Since the direct detection of gravitational wave will give us a fruitful insight about the early universe or life of stars, laser interferometric gravitational wave detectors with the strain sensitivity of higher than 10−22 have been developed. In Japan, the space gravitational wave detector project named DECi-hertz Gravitational wave Observatory (DECIGO) has been promoted which consists of three satellites forming equilateral triangle-shaped Fabry–Perot laser interferometer with the arm length of 1000 km. The designed strain sensitivity of DECIGO is 2 × 10−24/√Hz around 0.1 Hz whose targets are gravitational waves originated from the inspiral and the merger of black hole or neutron star binaries and from the inflation at the early universe, and no ground-based gravitational wave detector can access this observation band. Before launching DECIGO in 2030s, a milestone mission named B-DECIGO is planned which is a downsized mission of DECIGO. B-DECIGO also has its own scientific targets in addition to the feasibility test for DECIGO. In the present paper, DECIGO and B-DECIGO projects are reviewed.

Direct detection of gravitational waves was for a long time the holy grail of observational astronomy. The situation changed in 2015 with the first registration of a gravitational wave signal (GW150914) by laboratory interferometers on Earth. Now, successful operating runs of LIGO/Virgo gravitational wave detectors, resulting in numerous observations of gravitational wave signals from coalescing double compact objects (mainly binary black hole mergers) with the first evidence of a coalescing binary neutron star system, has elevated multimessenger astronomy to an unprecedented stage. Double compact objects (binary black hole systems, mixed black hole–neutron star systems, and double neutron star systems) are the main targets of future ground-based and space-borne gravitational wave detectors, opening the possibility for multifrequency gravitational wave studies and yielding very rich statistics of such sources. This, in turn, makes it possible that certain, non-negligible amounts of double compact objects will have a chance of being strongly lensed. In this paper, we will discuss new perspectives for future detections of gravitational wave signals in the case of strong gravitational lensing. First, the expected rates of lensed gravitational wave signals will be presented. Multifrequency detections of lensed gravitational wave events will demand different treatments at different frequencies, i.e., wave approach vs. geometric optics approach. New possibilities emerging from such multifrequency detections will also be discussed.

The quest of direct detection of gravitational waves (GWs) has reached the most interesting stage. During GW observation using LIGO and partially VIRGO and GEO600 for three years, no GW events were observed within a ∼15 Mpc radius from the Earth. To detect several GW events per year, enhancement of strain sensitivity, about ten times as high as for these GW detectors, is in progress. In Japan, Large-scale Cryogenic Gravitational wave Telescope (LCGT) project has also started in 2010 to detect GWs and to form a GW detection network with other GW detectors. LCGT will be constructed at the Kamioka mine, Hida-city, Gifu-prefecture. It is located about 200 meters under the ground surface for stable operation. LCGT is also designed to utilize cryogenic mirrors and cryogenic mirror suspension wires to reduce thermal noises and to reach the quantum noise limiting sensitivity of 10−22 in rms strain.

Gravitational wave signal from the inspirai of stellar-mass binary black hole can be used as standard sirens to perform cosmological inference. This inspirai covers a wide range of frequency bands, from the millihertz band to the audio-band, allowing for detections by both space-borne and ground-based gravitational wave detectors. In this work, we conduct a comprehensive study on the ability to constrain the Hubble constant using the dark standard sirens, or gravitational wave events that lack electromagnetic counterparts. To acquire the redshift information, we weight the galaxies within the localization error box with photometric information from several bands and use them as a proxy for the binary black hole redshift. We discover that TianQin is expected to constrain the Hubble constant to a precision of roughly 30% through detections of 10 gravitational wave events; in the most optimistic case, the Hubble constant can be constrained to a precision of <10%, assuming TianQin I+II. In the optimistic case, the multi-detector network of TianQin and LISA is capable of constraining the Hubble constant to within 5% precision. It is worth highlighting that the multi-band network of TianQin and Einstein Telescope is capable of constraining the Hubble constant to a precision of about 1%. We conclude that inferring the Hubble constant without bias from photo-z galaxy catalog is achievable, and we also demonstrate self-consistency using the P-P plot. On the other hand, high-quality spectroscopic redshift information is crucial for improving the estimation precision of Hubble constant.

After the first direct detection of gravitational waves (GW), detection of stochastic background of GWs is an important next step, and the first GW event suggests that it is within the reach of the second-generation ground-based GW detectors. Such a GW signal is typically tiny, and can be detected by cross-correlating the data from two spatially separated detectors if the detector noise is uncorrelated. It has been advocated, however, that the global magnetic fields in the Earth-ionosphere cavity produce the environmental disturbances at low-frequency bands, known as Schumann resonances, which potentially couple with GW detectors. In this paper, we present a simple analytical model to estimate its impact on the detection of stochastic GWs. The model crucially depends on the geometry of the detector pair through the directional coupling, and we investigate the basic properties of the correlated magnetic noise based on the analytic expressions. The model reproduces the major trend of the recently measured global correlation between the GW detectors via magnetometer. The estimated values of the impact of correlated noise also match those obtained from the measurement. Finally, we give an implication to the detection of stochastic GWs including upcoming detectors, KAGRA and LIGO India. The model suggests that LIGO Hanford-Virgo and Virgo-KAGRA pairs are possibly less sensitive to the correlated noise, and can achieve a better sensitivity to the stochastic GW signal in the most pessimistic case.

With the observation of a series of ground-based laser interferometer gravitational wave (GW) detectors such as LIGO and Virgo, nearly 100 GW events have been detected successively. At present, all detected GW events are generated by the mergers of compact binary systems and are identified through the data processing of matched filtering. Based on matched filtering, we use the GW waveform of the Newtonian approximate (NA) model constructed by linearized theory to match the events detected by LIGO and injections to determine the coalescence time and utilize the frequency curve for data fitting to estimate the parameters of the chirp masses of binary black holes (BBHs). The average chirp mass of our results is , which is very close to provided by GWOSC. In the process, we can analyze LIGO GW events and estimate the chirp masses of the BBHs. This work presents the feasibility and accuracy of the low-order approximate model and data fitting in the application of GW data processing. It is beneficial for further data processing and has certain research value for the preliminary application of GW data.

Gravitational Wave (GW) is very small temporal variation of space distortion which is caused from the change of enormous mass such as inspiral and merger of black hole binaries, explosion of supernovae, and the inflation in the early universe. In order to detect GW directly, long-baseline laser interferometers have been developed by many countries and, at long last, the first direct detection of GW was achieved by the ground-based Advanced LIGO detectors [1]. In Japan, not only the ground-based GW detector, KAGRA [2], but also the space GW detector, DECIGO (DECi-hertz Interferometer Gravitational wave Observatory) [3] have been promoted which is a 3-km triangle shaped laser interferometer with the detection band between 0.1 Hz and 10 Hz. We have developed space borne frequency and the intensity stabilized lasers for DECIGO whose required frequency and intensity noise level are df=1 Hz/VHz and δΙ/Ι =1×10−8 /√Hz at observation band around 1 Hz, respectively, and the high power output power up to 10 W is also required.

The first direct detection of gravitational wave has been realized by LIGO 100 years after Einstein’s theoretical prediction. It opens a new window for human to observe our Universe and initiates the age of Gravitational Wave Astronomy. The data analysis of gravitational wave detection is a typically signal extraction problem and the matched filtering technique has shown to be an optimal method in extracting weak signal buried in strong Gaussian noises. Matched filtering requires the accurate gravitational waveforms. It is also essential for the parameter estimation of the gravitational wave source, with which the GW150914 was recognized as a binary of 29 and 36 solar masses black holes merging about 1.3 billion light years away. Nowadays, other laser interferometric gravitational wave detectors such as Virgo, KAGRA and the third LIGO in the India, IndIGO, are under construction. The space-borne detection projects including eLISA, Taiji and TianQin are also in progress. The pulsar timing approach with FAST, SKA and other radio telescope arrays to detect gravitational wave are also in the rapid development. It is foreseeable the gravitational wave astronomy in the wide frequency band from 10–10 to 1000 Hz will be realized in the near future. As such, the matched filtering plays an important role, and correspondingly the theoretical research of gravitational wave source models becomes urgent and important. For astrophysical realistic objects without symmetries in general, the analytical treatment of Einstein equation becomes nearly intractable. The numerical relativity then becomes an essential method and tool for solving the Einstein equation. We briefly introduce the state of art research of numerical relativity in the viewpoint of gravitational wave astronomy.

In Japan, not only the ground-based gravitational wave (GW) detector mission KAGRA but also the space GW detector mission DECIGO (DECi-hertz Interferometer Gravitational wave Observatory) and its milestone mission B-DECIGO have been promoted. The designed strain sensitivity of DECIGO and B-DECIGO are δL/L < 10−23. Since the GW detector requires high power and highly-stable light source, we have developed the light source with high frequency and intensity stability for DECIGO and B-DECIGO. The frequency of the Yb-doped fiber DFB lasers are stabilized to the iodine saturated absorption at 515 nm, and the intensity of the laser at 1 Hz (observation band) is stabilized by controlling the pump source of an Yb-doped fiber amplifier. The intensity of the laser at 200 kHz (modulation band) is also stabilized using an acousto-optic modulator to improve the frequency stability of the laser. In the consequences, we obtain the frequency stability of δf = 0.4 Hz/√Hz (in-loop) at 1 Hz, and the intensity stability of δI/I = 1.2 × 10−7/√Hz (out-of-loop) and δI/I = 1.5 × 10−7/√Hz (in-loop) at 1 Hz and 200 kHz, respectively.

Topics of LIGO Physics: Template Banks for the Inspiral of Precessing, Compact Binaries, and Design of the Signal-Recycling Cavity for Advanced LIGO

Dark matter (DM) occupies the majority of matter content in the universe and is probably cold (CDM). However, modifications to the standard CDM model may be required by the small-scale observations, and DM may be self-interacting (SIDM) or warm (WDM). Here we show that the diffractive lensing of gravitational waves (GWs) from binary black hole mergers by small halos ($\ensuremath{\sim}{10}^{3}--{10}^{6}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$; minihalos) may serve as a clean probe to the nature of DM, free from the contamination of baryonic processes in the DM studies based on dwarf/satellite galaxies. The expected lensed GW signals and event rates resulting from CDM, WDM, and SIDM models are significantly different from each other, because of the differences in halo density profiles and abundances predicted by these models. We estimate the detection rates of such lensed GW events for a number of current and future GW detectors, such as the Laser Interferometer Gravitational Observatories (LIGO), the Einstein Telescope (ET), the Cosmic Explorer (CE), Gravitational-wave Lunar Observatory for Cosmology (GLOC), the Deci-Hertz Interferometer Gravitational Wave Observatory (DECIGO), and the Big Bang Observer (BBO). We find that GLOC may detect one such event per year assuming the CDM model, DECIGO (BBO) may detect more than several (hundreds of) such events per year, by assuming the CDM, WDM (with mass $&gt;30\text{ }\text{ }\mathrm{keV}$) or SIDM model, suggesting that the DM nature may be strongly constrained by DECIGO and BBO via the detection of diffractive lensed GW events by minihalos. Other GW detectors are unlikely to detect a significant number of such events within a limited observational time period. However, if the inner slope of the minihalo density profile is sufficiently steeper than the Navarro-Frenk-White profile, e.g., the pseudo-Jaffe profile, one may be able to detect one to more than 100 such GW events by ET and CE.

The direct detection of gravitational waves by ground-based interferometric gravitational wave detectors in recent years has opened a new window of the universe, allowing the astrophysical observations of previously unexplored phenomena, such as the collisions of black holes and neutron stars. However, small thermodynamic fluctuations of the density of the thin films that compose the mirrors used within the gravitational wave detectors, such as the LIGO and Virgo detectors, give rise to noise which limits these instruments at their most sensitive frequencies. This "Brownian Thermal Noise" can be related to the inherent internal friction of the mirror materials through the fluctuation-dissipation theorem. Therefore, the improved sensitivity of gravitational wave detectors depends, to some extent, upon the development of optical thin films with low internal friction. The past two decades have therefore seen the growth of internal friction experiments undertaken within the gravitational wave detection community. This article attempts to summarize the results of these investigations and to highlight current research directions in order to foster a stronger dialogue with the larger internal friction and mechanical spectroscopy community.

Next generation ground-based gravitational wave (GW) detectors are expected to detect ∼104–105 binary black holes (BBHs) per year. Understanding the formation pathways of these binaries is an open question. Orbital eccentricity can be used to distinguish between the formation channels of compact binaries, as different formation channels are expected to yield distinct eccentricity distributions. Due to the rapid decay of eccentricity caused by the emission of GWs, measuring smaller values of eccentricity poses a challenge for current GW detectors due to their limited sensitivity. In this study, we explore the potential of next generation GW detectors such as Voyager, Cosmic Explorer (CE), and Einstein Telescope (ET) to resolve the eccentricity of BBH systems. Considering a GWTC-3 like population of BBHs and assuming some fiducial eccentricity distributions as well as an astrophysically motivated eccentricity distribution (Zevin et al. 2021), we calculate the fraction of detected binaries that can be confidently distinguished as eccentric. We find that for Zevin eccentricity distribution, Voyager, CE, and ET can confidently measure the non-zero eccentricity for ${\sim} 3\%$, 9%, and 13% of the detected BBHs, respectively. In addition to the fraction of resolvable eccentric binaries, our findings indicate that Voyager, CE, and ET require typical minimum eccentricities ≳0.02, 5 × 10−3, and 10−3 at 10 Hz GW frequency, respectively, to identify a BBH system as eccentric. The better low-frequency sensitivity of ET significantly enhances its capacity to accurately measure eccentricity.

The direct detection of gravitational waves (GWs) was recently achieved by the Laser Interferometer Gravitational-wave Observatory (LIGO) team, which opened a new era of gravitational wave astronomy. With the operation of Advanced LIGO to scientific operation period, and in the next few years the other second generation detectors, such as Advanced Virgo and LIGO-India continuing to be built and put into use, there will be more and more GW signals being detected. Recently, GW signals from NS-NS merger and its electromagnetic (EM) counterpart have also been detected. Because of the faint nature of GW signals, detecting an EM emission signal coincident with a GW signal in both trigger time and spatial direction is essential to confirm the astrophysical origin of the GW signals and study the astrophysical properties of the GW sources (e.g. host galaxy, distance). Due to the poor localization ability of GW wave detectors (Advanced LIGO ~ 10–100 of square degrees), the detection of EM counterpart for GW events with large field of view high energy observational equipment is an urgent demand. Einstein Probe (EP) has a large field of view, all day long observation ability, high sensitivity, fast slewing and pointing capability, fast data downloading and other advantages, provides an ideal facility for the detection of EM counterpart for GW events. The successful operation of the Einstein Probe will promote the development of gravitational wave astronomy and gravitational wave cosmology, and make China in the international leading position for the study of the EM counterpart for the GW source.