Gravitational-wave asteroseismology with fundamental modes from compact binary inspirals

Matched-filter searches for gravitational waves from coalescing compact binaries by the LIGO Scientific Collaboration use the FINDCHIRP algorithm: an implementation of the optimal filter with innovations to account for unknown signal parameters and to improve performance on detector data that has nonstationary and non-Gaussian artifacts. We provide details on the FINDCHIRP algorithm as used in the search for subsolar mass binaries, binary neutron stars, neutron star--black hole binaries, and binary black holes.

To enable detection and maximise the physics output of gravitational wave observations from compact binary systems, it is crucial the availability of accurate waveform models. The present work aims at giving an overview for non-experts of the (inspiral) waveforms used in the gravitational wave data analysis for compact binary coalescence. We first provide the essential elements of gravitational radiation physics within a simple Newtonian orbital dynamics and the linearized gravity theory, describing the adiabatic approximation applied to binary systems: the key element to construct the theoretical gravitational waveforms in practice. We next lay out the gravitational waveforms in the post-Newtonian approximation to General Relativity, and highlight the basic input for the inspiral waveform of the slowly evolving, spinning, nonprecessing, quasicircular binary black holes, namely, post-Newtonian energy, fluxes and the (absorption-corrected) balance equation. The post-Newtonian inspiral templates are then presented both in the time and frequency domain. Finally, including the merger and subsequent ringdown phase, we briefly survey the two families of the full waveform models of compact binary mergers currently implemented in LSC Algorithm Library Simulation: the effective-one-body approach and the phenomenological frequency domain model.

Due to our ignorance of the equation of state (EOS) beyond nuclear density, there is still no unique theoretical model for neutron stars (NSs). It is therefore surprising that universal EOS-independent relations connecting different physical quantities of neutron stars can exist. Lau et al. [ApJ, 714, 1234 (2010)] found that the frequency of the $f$-mode oscillation, the mass, and the moment of inertia are connected by universal relations. More recently, Yagi and Yunes [Science, 341, 365 (2013)] discovered the I-Love-Q universal relations among the mass, the moment of inertia, the Love number, and the quadrupole moment. In this paper, we study these universal relations in the Eddington-inspired Born-Infeld (EiBI) gravity. This theory differs from general relativity (GR) significantly only at high densities due to the nonlinear coupling between matter and gravity. It thus provides us an ideal case to test how robust the universal relations of NSs are with respect to the change of the gravity theory. Thanks to the apparent EOS formulation of EiBI gravity developed recently by Delsate and Steinhoff [Phys. Rev. Lett., 109, 021101 (2012)], we are able to study the universal relations in EiBI gravity using the same techniques as those in GR. We find that the universal relations in EiBI gravity are essentially the same as those in GR. Our work shows that, within the currently viable coupling constant, there exists at least one modified gravity theory that is indistinguishable from GR in view of the unexpected universal relations.

We propose a theoretical framework to address the singularity problem in black holes by introducing the concept of finite-density cores composed of ultra-dense crystalline matter formed under extreme pressure. By modifying the Einstein field equations to incorporate a scalar field representing quantum corrections and defining an anisotropic equation of state (EoS) for this exotic matter, we aim to unify classical and quantum descriptions without introducing singularities. Our model explores the possibility that subatomic particles, when subjected to pressures beyond those in neutron stars, form a crystalline lattice at scales approaching the Planck length. We present the modified field equations, the proposed EoS, and discuss the implications for black hole physics, quantum gravity, and potential observational signatures. The EoS is contained in a separate file in this project<br><br>The classical description of black holes in general relativity predicts singularities—points of infinite density and curvature—which pose significant challenges to our understanding of physics. Resolving these singularities is a crucial step toward unifying general relativity with quantum mechanics. In this work, we explore a novel approach by proposing that black holes have finite-density cores composed of ultra-dense crystalline matter formed under extreme pressure.Analogous to neutron stars, where matter is compressed to nuclear densities, we hypothesize that black holes compress matter even further. At these extreme conditions, subatomic particles form a crystalline lattice, possibly involving new states of matter where even electrons are broken down into smaller constituents. This exotic matter would only exist under specific temperatures and pressures near the Planck scale.

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within the frequency band of ground-based detectors, while compact binaries of WDs are important sources of GWs at lower frequencies to be covered by space interferometers (LISA). Major uncertainties in the current understanding of properties of NSs and BHs most relevant to the GW studies are discussed, including the treatment of the natal kicks which compact stellar remnants acquire during the core collapse of massive stars and the common envelope phase of binary evolution. We discuss the coalescence rates of binary NSs and BHs and prospects for their detections, the formation and evolution of binary WDs and their observational manifestations. Special attention is given to AM CVn-stars — compact binaries in which the Roche lobe is filled by another WD or a low-mass partially degenerate helium-star, as these stars are thought to be the best LISA verification binary GW sources.

Inspiraling compact binaries have been identified as one of the most promising sources of gravitational waves for interferometric detectors. Most of these binaries are expected to have circularized by the time their gravitational waves enter the instrument's frequency band. However, the possibility that some of the binaries might still possess a significant eccentricity is not excluded. We imagine a situation in which eccentric signals are received by the detector but not explicitly searched for in the data analysis, which uses exclusively circular waveforms as matched filters. We ascertain the likelihood that these filters, though not optimal, will nevertheless be successful at capturing the eccentric signals. We do this by computing the loss in signal-to-noise ratio incurred when searching for eccentric signals with those nonoptimal filters. We show that for a binary system of a given total mass, this loss increases with increasing eccentricity. We show also that for a given eccentricity, the loss decreases as the total mass is increased.

Extending the electromagnetic and gravitational radiations from binary black holes with electric and magnetic charges in circular orbits in Liu et al. (Phys. Rev. D 102:103520, 2020), we calculate the total emission rates of energy and angular momentum due to gravitational and electromagnetic radiations from dyonic binary black holes in precessing elliptical orbits. It is shown that the emission rates of energy and angular momentum due to gravitational and electromagnetic radiations have the same dependence on the conic angle for different orbits. Moreover, we obtain the evolutions of orbits and find that a circular orbit remains circular while an elliptic orbit becomes quasi-circular due to electromagnetic and gravitational radiations. Using the evolution of orbits, we derive the waveform models for dyonic binary black hole inspirals and show the amplitudes of the gravitational waves for dyonic binary black hole inspirals differ from those for Schwarzschild binary black hole inspirals, which can be used to test electric and magnetic charges of black holes.

Detections of gravitational waves emitted by binary black holes allow for tests of General Relativity in the strong-field regime. In particular, deviations from General Relativity can be observed by comparing incoming signals to waveform templates that include parametrized deviations from General Relativity. However, it is essential that the General Relativity sector of these templates accounts for all predictable physics. Otherwise, missing physics might be mimicked by the "beyond General Relativity" sector of the templates, leading the analysis to report apparent deviations from General Relativity. Current parametrized tests implement templates that omit physical phenomena such as orbital eccentricity and higher-order modes. In this paper, we show how the omission of higher modes can lead to false deviations from General Relativity when these effects are strong enough. We study the extent of these deviations as a function of the mass ratio and the orbital orientation. We find that significant false deviations can arise when current tests are performed on signals emitted by asymmetric binaries whose orbital angular momentum is orthogonal to the line-of-sight. We estimate that the Advanced LIGO-Virgo network operating at its design sensitivity can observe false violations with a significance above $5 \sigma$ as often as once per year. Similar results are expected for other tests of General Relativity that use modified waveform models. Hence, we stress the necessity of accurate waveform models that include physical effects such as higher-order modes to trust future tests of General Relativity.

In testing gravity a model-independent way, one of crucial tests is measuring the propagation speed of a gravitational wave (GW). In general relativity, a GW propagates with the speed of light, while in the alternative theories of gravity the propagation speed could deviate from the speed of light due to the modification of gravity or spacetime structure at a quantum level. Previously we proposed the method measuring the GW speed by directly comparing the arrival times between a GW and a photon from the binary merger of neutron stars or neutron star and black hole, assuming that it is associated with a short gamma-ray burst. The sensitivity is limited by the intrinsic time delay between a GW and a photon at the source. In this paper, we extend the method to distinguish the intrinsic time delay from the true signal caused by anomalous GW speed with multiple events at cosmological distances, also considering the redshift distribution of GW sources, redshift-dependent GW propagation speed, and the statistics of intrinsic time delays. We show that an advanced GW detector such as Einstein Telescope will constrain the GW propagation speed at the precision of ~10^{-16}. We also discuss the optimal statistic to measure the GW speed, performing numerical simulations.

We present a Python based parameter inference system for the gravitational wave (GW) measured in the millihertz band. This system includes the following features: the GW waveform originated from the massive black hole binaries (MBHB), the stationary instrumental Gaussian noise, the higher-order harmonic modes, the full response function from the time delay interferometry and the Gaussian likelihood function with the dynamic nested parameter sampler. In particular, we highlight the role of higher-order modes. By including these modes, the luminosity distance estimation precision can be improved roughly by a factor of 50, compared with the case with only the leading order (ℓ = 2, ∣m∣ = 2) mode. This is due to the response functions of different harmonic modes on the inclination angle are different. Hence, it can help to break the distance-inclination degeneracy. Furthermore, we show the robustness of testing general relativity (GR) by using higher-order harmonics. Our results show that the GW from MBHB can simultaneously constrain four of the higher harmonic amplitudes (deviation from GR) with 95% confidence level of c21=0.54−1.05+0.82 , c32=−0.65−1.42+3.02 , c33=0.56−0.96+0.79 and c44=1.57−2.19+3.22 , respectively.

Gravitational wave (GW) observations of binary black hole (BBH) coalescences provide a unique opportunity to test general relativity (GR) in the strong-field regime. To ensure the reliability of these tests, it is essential to identify and address potential sources of error, particularly those arising from missing physics in the waveform models used in GW data analysis. This paper investigates potential biases in these tests arising from strong gravitational lensing, an effect not currently incorporated into the standard framework for GR tests. In the geometric optics approximation, strong lensing produces three types of images: Type I, Type II, and Type III. While Type I and Type III images do not distort the signal, Type II images introduce a characteristic phase shift that can mimic GR deviations for signals with higher-order modes, precession, or eccentricity. We assess the response of four standard GR tests on simulated Type II lensed BBH signals, including the two parameterized tests (TIGER and FTI), the modified dispersion relation test and the inspiral-merger-ringdown consistency test. We focus on precessing waveforms for binaries with total masses of $20M_{\odot}$ and $80M_{\odot}$, and dimensionless spins of 0.5 and 0.95, considering a fixed signal-to-noise ratio of 25 using the design A+ sensitivity of the LIGO-Virgo network. Our findings indicate that more mass-asymmetric and higher-spin binaries show larger false deviations from GR in the TIGER and modified dispersion relation tests when applying GR tests to Type II lensed signals. These results highlight the risk of false GR violations as detector sensitivity improves in future observational runs. Therefore, it is crucial to consider the possibility of strong lensing before drawing conclusions about deviations from GR in GW signals.

Gravitational waves are basically ripples in spacetime predicted by Einstein&#39;s General Theory of Relativity (1915), have revolutionized our understanding of the universe since their first detection in 2015 by the LIGO. These waves are typically generated by extreme cosmological events such as the mergers of two or more black holes, neutron stars, and other compact objects. Black holes, regions of spacetime where gravity is so intense that not even light can escape, are both significant sources and subjects of gravitational wave studies. The observation of gravitational waves from binary black hole mergers has provided unprecedented insights into the nature of black holes, their mass distribution, and the environments in which they form. This paper reviews the current state of research on gravitational waves and black holes, focusing on their astrophysical origins, the mechanisms of wave generation, and the information encoded in the wave signals. I have discussed how gravitational wave detections have confirmed the existence of stellar-mass black hole binaries, revealed new populations of black holes, and provided tests of general relativity in the strong-field regime. Additionally, this study highlights the potential of gravitational wave astronomy to address unresolved questions, such as the formation channels of black hole binaries, the detection of primordial black holes, and the role of black holes in galaxy evolution. By bridging observational data with theoretical models, gravitational wave observations are opening new frontiers in our understanding of both black holes and the fundamental nature of gravity.

The Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo Interferometer Collaborations have now detected all three classes of compact binary mergers: binary black hole (BBH), binary neutron star (BNS), and neutron star-black hole (NSBH). For coalescences involving neutron stars, the simultaneous observation of gravitational and electromagnetic radiation produced by an event, has broader potential to enhance our understanding of these events, and also to probe the equation of state (EOS) of dense matter. However, electromagnetic follow-up to gravitational wave (GW) events requires rapid real-time detection and classification of GW signals, and conventional detection approaches are computationally prohibitive for the anticipated rate of detection of next-generation GW detectors. In this work, we present the first deep learning based results of classification of GW signals from NSBH mergers in real LIGO data. We show for the first time that a deep neural network can successfully distinguish all three classes of compact binary mergers and separate them from detector noise. Specifically, we train a convolutional neural network (CNN) on ∼500,000 data samples of real LIGO noise with injected BBH, BNS, and NSBH GW signals, and we show that our network has high sensitivity and accuracy. Most importantly, we successfully recover the two confirmed NSBH events to-date (GW191219 and GW200115) and the two confirmed BNS mergers to-date (GW170817 and GW190425), together with ∼90% of all BBH candidate events from the third Gravitational Wave Transient Catalog, GWTC-3. These results are an important step towards low-latency real-time GW detection, enabling multi-messenger astronomy.

Core-collapse supernovae (CCSNe) are among the most energetic explosions in the universe, liberating the prodigious amount of ~ 1053 erg, the binding energy of their compact remnants, neutron stars or stellar mass black holes. While 99% of this energy is emitted in neutrinos, 1% goes into the internal and asymptotic kinetic energy of the ejecta, and it is reasonable to assume that a tiny fraction is radiated in gravitational waves (GWs). Ever since the first experimental efforts to detect GWs, CCSNe have been considered prime sources of gravitational waves for interferometric detectors. Besides neutrinos, which have already been observed in the context of stellar core collapse of SN1987A, GWs could provide us access to the electromagnetically hidden compact inner core of some such cataclysmic events, supplying us for example with valuable information about the angular momentum distribution and the baryonic equation of state, both of which are uncertain. Furthermore, they might even help to constrain theoretically predicted SN mechanisms. However, GW astronomy strongly depends on the extensive data processing of the detector output on the basis of reliable GW estimates, which only recently have become feasible with the emerging power of supercomputers. The work presented in this thesis is concerned with numerical CCSN models and their imprints in GWs. I performed an extensive series of more than 30 three-dimensional magnetohydrodynamical (MHD) core-collapse simulations. My models are based on a 15M [...] progenitor stemming from stellar evolution calculations, an effective general relativistic potential and either the Lattimer-Swesty (with three possible compressibilities) or the Shen equation of state (EoS) for hot, dense matter. Furthermore, the neutrino transport is tracked by computationally efficient algorithms for the radiative transfer of massless fermions. I systematically investigated the effects of the microphysical finite-temperature nuclear EoS, the initial rotation rate, both the toroidal and the poloidal magnetic fields, and multidimensional gravitational potentials on the GW signature. Based on the results of these calculations, I obtained the largest – and also one of the most realistic – catalogue of GW signatures from 3D MHD stellar core collapse simulations at present. I stress the importance of including postbounce neutrino physics, since it quantitatively alters the GW signature. Non- and slowly-rotating models show GW emission caused by prompt and protoneutron star (PNS) convection. Moreover, the signal stemming from prompt convection allows for the distinction between the two different nuclear EoS indirectly by different properties of the fluid instabilities. For simulations with moderate or even fast rotation rates, I only find the axisymmetric type I wave signature at core bounce. In line with recent results, I could confirm that the maximum GW amplitude scales roughly linearly with the ratio of rotational to gravitational energy (T/|W|) at core bounce below a threshold value of about 10%. Furthermore, I point out that PNS can become dynamically unstable to rotational instabilities at T/|W| values as low as ~ 2% at core bounce. Apart from these two points, I show that it is generally very difficult to discern the effects of the individual features of the input physics in a GW signal from a rotating CCSN that can be attributed unambiguously to a specific model. Weak magnetic fields do not notably influence the dynamical evolution of the core and thus the GW emission. However, for strong initial poloidal magnetic fields ≥ 1012G, the combined action of flux-freezing and field winding leads to conditions where the ratio of magnetic field pressure to matter pressure reaches about unity which leads to the onset of a jet-like supernova explosion. The collimated bipolar out-stream of matter is then reflected in the emission of a type IV GW signal. In contradiction to axisymmetric simulations, I find evidence that nonaxisymmetric fluid modes can counteract or even suppress jet formation for models with strong initial toroidal magnetic fields. I emphasize the importance of including multidimensional gravitational potentials in rapidly rotating 3D CCSN simulations: taking them into account can alter the resulting GW amplitudes up to a factor of 2 compared to simulations which encounter gravity only by a monopolar approximation. Moreover, I show that the postbounce dynamics occuring in the outer layers (at radii R ≥ 200km) of models run with 3D gravity deviates vastly from the ones run with a 1D or 2D gravitational potential. The latter finding implies that both spherically symmetric and axisymmetric treatments of gravity are too restrictive for a quantitative description of the overall postbounce evolution of rapidly rotating CCSN models. The results of models with continued neutrino emission show that including deleptonization during the postbounce phase is an indispensable issue for the quantitative prediction of GWs from core-collapse supernovae, because it can alter the GW amplitude up to a factor of 10 compared to a pure hydrodynamical treatment. My collapse simulations indicate that corresponding events in our Galaxy would be detectable either by LIGO, if the source is rotating, or at least by the advanced LIGO detector, if it is not or only slowly rotating.

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.