Gravitational Wave Modes Research Articles

Constraining extra gravitational wave polarizations with Advanced LIGO, Advanced Virgo, and KAGRA and upper bounds from GW170817

General metric theories of gravity in four-dimensional spacetimes can contain at most six polarization modes (two spin-0, two spin-1 and two spin-2) of gravitational waves (GWs). It has been recently shown that, with using four GW non-coaligned detectors, a direct test of the spin-1 modes can be done in principle separately from the spin-0 and spin-2 modes for a GW source in particular sky positions [Hagihara et al., Phys. Rev. D 98, 064035 (2018)]. They have found particular sky positions that satisfy a condition of killing completely the spin-0 modes in a so-called null stream which is a linear combination of the signal outputs to kill the spin-2 modes. The present paper expands the method to discuss a possibility that the spin-0 modes are not completely but effectively suppressed in the null streams to test the spin-1 modes separately from the other modes, especially with an expected network of Advanced LIGO, Advanced Virgo and KAGRA. We study also a possibility that the spin-1 modes are substantially suppressed in the null streams to test the spin-0 modes separately from the other modes, though the spin-1 modes for any sky position cannot be completely killed in the null streams. Moreover, we find that the coefficient of the spin-0 modes in the null stream is significantly small for the GW170817 event, so that an upper bound can be placed on the amplitude of the spin-1 modes as $< 6 \times 10^{-23}$.

Prospects for gravitational-wave polarization tests from compact binary mergers with future ground-based detectors

There exist six possible polarization modes of gravitational waves in a general metric theory of gravity, while two tensor polarization modes are allowed in general relativity. The properties and number of polarization modes depend on gravity theories. For transient signals, the number of the detectors needs to be basically equal to the number of the gravitational-wave polarization modes for separation of polarizations. However, a single detector having great sensitivity at lower frequency could be effectively regarded as a virtual detector network including a set of detectors along its trajectory due to a long gravitational-wave signal from a compact binary and the Earth's rotation. Thus, time-varying antenna pattern functions can help test the polarizations of gravitational waves. We study the effects of the Earth's rotation on the polarization test and show a possibility to test the nontensorial polarization modes from future observations of compact binary mergers with ground-based gravitational detectors such as Einstein telescope and Cosmic Explorer.

Gravitational-wave amplitudes for compact binaries in eccentric orbits at the third post-Newtonian order: Tail contributions and postadiabatic corrections

We compute the tail contributions to the gravitational-wave mode amplitudes for compact binaries in eccentric orbits at the third post-Newtonian order of general relativity. We combine them with the already available instantaneous pieces and include the post-adiabatic corrections required to fully account for the effects of radiation-reaction forces on the motion. We compare the resulting waveform in the small eccentricity limit to the circular one, finding perfect agreement.

Synchrosqueezing transforms: From low- to high-frequency modulations and perspectives

The general aim of this paper is to introduce the concept of synchrosqueezing transforms (SSTs) that was developed to sharpen linear time–frequency representations (TFRs), like the short-time Fourier or the continuous wavelet transforms, in such a way that the sharpened transforms remain invertible. This property is of paramount importance when one seeks to recover the modes of a multicomponent signal (MCS), corresponding to the superimposition of AM/FM modes, a model often used in many practical situations. After having recalled the basic principles of SST and explained why, when applied to an MCS, it works well only when the modes making up the signal are slightly modulated, we focus on how to circumvent this limitation. We then give illustrations in practical situations either associated with gravitational wave signals or modes with fast oscillating frequencies and discuss how SST can be used in conjunction with a demodulation operator, extending existing results in that matter. Finally, we list a series of different perspectives showing the interest of SST for the signal processing community.

Gravitational waves in F(R) gravity: Scalar waves and the chameleon mechanism

We discuss the scalar mode of gravitational waves emerging in the context of $F(R)$ gravity by taking into account the chameleon mechanism. Assuming a toy model with a specific matter distribution to reproduce the environment of detection experiment by a ground-based gravitational wave observatory, we find that chameleon mechanism remarkably suppresses the scalar wave in the atmosphere of Earth, compared with the tensor modes of the gravitational waves. We also discuss the possibility to detect and constrain scalar waves by the current gravitational observatories and advocate a necessity of the future space-based observations.

Exact amplitudes of six polarization modes for gravitational waves

The formalism of the exact six polarization modes of gravitational waves is constructed in terms of both the small metric perturbations and the Newman-Penrose scalars. The obtained formulae are applicable to any metric-compatible gravity theories whose gravitational waves propagate along either the null or non-null geodesics. Once a gravity theory, specifically its linearized wave equation, is written, comparison to the observed data of the laser interferometer experiments is direct.

Primordial gravitational waves in Horndeski gravity

We investigate the propagation of primordial gravitational waves within the context of the Horndeski theories, for this, we present a generalized transfer function quantifying the sub-horizon evolution of gravitational waves modes after they enter the horizon. We compare the theoretical prediction of the modified primordial gravitational waves spectral density with the aLIGO, Einstein telescope, LISA, gLISA and DECIGO sensitivity curves. Assuming reasonable and different values for the free parameters of the theory (in agreement with the event GW170817 and stability conditions of the theory), we note that the gravitational waves amplitude can vary significantly in comparison with general relativity. We find that in some cases the gravitational primordial spectrum can cross the sensitivity curves for DECIGO detector with the maximum frequency sensitivity to the theoretical predictions around 0.05 - 0.30 Hz. From our results, it is clear that the future generations of space based interferometers can bring new perspectives to probing modifications in general relativity.

Constraining the non-Einsteinian polarizations of gravitational waves by pulsar timing array

Pulsar timing array (PTA) provides an excellent opportunity to detect the gravitational waves (GWs) in nanoHertz frequency band. In particular, due to the larger number of "arms" in PTA, it can be used to test gravity by probing the non-Einsteinian polarization modes of GWs, including two spin-1 shear modes labeled by "$sn$" and "$se$", the spin-0 transverse mode labeled by "$b$" and the longitudinal mode labeled by "$l$". In this paper, we investigate the capabilities of the current and potential future PTAs, which are quantified by the constraints on the amplitudes parameters $(c_b,c_{sn},c_{se},c_{l})$, by observing an individual supermassive black hole binary in Virgo cluster. We find that for binary with chirp mass $M_{c}=8.77 \times 10^{8} \mathrm{M_{\odot}}$ and GW frequency $f=10^{-9}\mathrm{Hz}$, the PTA at current level can detect these GW modes if $c_b > 0.00106$, $c_l > 0.00217$, $c_{se} > 0.00271$, $c_{sn} > 0.00141$, which will be improved by about two orders if considering the potential PTA in SKA era. Interesting enough, due to effects of the geometrical factors, we find that in SKA era, the constraints on the $l$, $sn$, $se$ modes of GWs are purely dominated by several pulsars, instead of the full pulsars in PTA.

Propagation of gravitational waves in teleparallel gravity theories

We investigate propagation of gravitational waves in the most general teleparallel gravity model with second order field equations around the Minkowski background. We argue that in this case the most general Lagrangian at the first order of perturbations is given by the linear combination of quadratic invariants and hence coincides with the well-known new general relativity model. We derive the linearized field equations and analyze them using the principal polynomial and the Newman-Penrose formalism. We demonstrate that all gravitational wave modes propagate at the speed of light and there are up to six possible polarizations. We show that two tensorial modes of general relativity are always present and the number of extra polarizations depends on the free parameters of the new general relativity model.

Tracking Black Hole Kicks from Gravitational-Wave Observations.

Coalescing binary black holes emit anisotropic gravitational radiation. This causes a net emission of linear momentum that produces a gradual acceleration of the source. As a result, the final remnant black hole acquires a characteristic velocity known as recoil velocity or gravitational kick. The symmetries of gravitational wave emission are reflected in the interactions of the gravitational wave modes emitted by the binary. In this Letter, we make use of the rich information encoded in the higher-order modes of the gravitational wave emission to infer the component of the kick along the line of sight (or radial kick). We do this by performing parameter inference on simulated signals given by numerical relativity waveforms for nonspinning binaries using numerical relativity templates of aligned-spin (nonprecessing) binary black holes. We find that for suitable sources, namely those with mass ratio q≥2 and total mass M∼100 M_{⊙}, and for modest radial kicks of 120 km/s, the 90% credible intervals of our posterior probability distributions can exclude a zero kick at a signal-to-noise ratio of 15, using a single Advanced LIGO detector working at its early sensitivity. The measurement of a nonzero radial kick component would provide the first observational signature of net transport of linear momentum by gravitational waves away from their source.

Probing gravitational wave polarizations with Advanced LIGO, Advanced Virgo, and KAGRA

Assuming that, for a given source of gravitational waves (GWs), we know its sky position, as is the case of GW events with an electromagnetic counterpart such as GW170817, we discuss a null stream method to probe GW polarizations including spin-0 (scalar) GW modes and spin-1 (vector) modes, especially with an expected network of Advanced LIGO, Advanced Virgo and KAGRA. For two independent null streams for four non-co-aligned GW detectors, we study a location on the sky, exactly at which the spin-0 modes of GWs vanish in any null stream for the GW detector network, though the strain output at a detector may contain the spin-0 modes. Our numerical calculations show that there exist seventy sky positions that satisfy this condition of killing the spin-0 modes in the null streams. If a GW source with an electromagnetic counterpart is found in one of the seventy sky positions, the spin-1 modes will be testable separately from the spin-0 modes by the null stream method. In addition, we study a superposition of the two null streams to show that any one of the three modes (one combined spin-0 and two spin-1 modes) can be eliminated by suitably adjusting a weighted superposition of the null streams and thereby a set of the remaining polarization modes can be experimentally tested.

Polarization test of gravitational waves from compact binary coalescences

Gravitational waves have only two polarization modes in general relativity. However, there are six possible modes of polarization in a generic metric theory of gravity. Thus, tests of gravitational-wave polarization can be tools for pursuing the nature of space-time structure. The observations of gravitational waves with a worldwide network of interferometric detectors such as Advanced LIGO, Advanced Virgo, and KAGRA will make it possible to obtain the information of gravitational-wave polarization from detector signals. We study the separability of the polarization modes for the inspiral gravitational waves from the compact binary coalescences systematically. Unlike some other waveforms such as burst, the binary parameters need to be properly considered. We show that three polarization modes of gravitational waves would be separable with the global network of three detectors to some extent, depending on the signal-to-noise ratio and the duration of the signal. We also show that with four detectors the three polarization modes would be more easily distinguished by breaking a degeneracy of the polarization modes and even the four polarization modes would be separable.

Gravitational waves from spinning binary black holes at the leading post-Newtonian orders at all orders in spin

We determine the binding energy, the total gravitational wave energy flux, and the gravitational wave modes for a binary of rapidly spinning black holes, working in linearized gravity and at leading orders in the orbital velocity, but to all orders in the black holes' spins. Though the spins are treated nonperturbatively, surprisingly, the binding energy and the flux are given by simple analytical expressions which are finite (respectively third- and fifth-order) polynomials in the spins. Our final results are restricted to the important case of quasi-circular orbits with the black holes' spins aligned with the orbital angular momentum.

Towards asteroseismology of core-collapse supernovae with gravitational-wave observations – I. Cowling approximation

Gravitational waves from core-collapse supernovae are produced by the excitation of different oscillation modes in the proto-neutron star (PNS) and its surroundings, including the shock. In this work we study the relationship between the post-bounce oscillation spectrum of the PNS-shock system and the characteristic frequencies observed in gravitational-wave signals from core-collapse simulations. This is a fundamental first step in order to develop a procedure to infer astrophysical parameters of the PNS formed in core-collapse supernovae. Our method combines information from the oscillation spectrum of the PNS, obtained through linear-perturbation analysis in general relativity of a background physical system, with information from the gravitational-wave spectrum of the corresponding non-linear, core-collapse simulation. Using results from the simulation of the collapse of a 35 $M_{\odot}$ presupernova progenitor we show that both types of spectra are indeed related and we are able to identify the modes of oscillation of the PNS, namely g-modes, p-modes, hybrid modes, and standing-accretion-shock-instability (SASI) modes, obtaining a remarkably close correspondence with the time-frequency distribution of the gravitational-wave modes. The analysis presented in this paper provides a proof-of-concept that asteroseismology is indeed possible in the core-collapse scenario, and it may serve as a basis for future work on PNS parameter inference based on gravitational-wave observations.

Excitation of high frequency voices from intermediate-mass-ratio inspirals with large eccentricity

The coalescence of a stellar-mass compact object together with an intermediate-mass black hole, also known as an intermediate-mass-ratio inspiral, is usually not expected to be a viable gravitational wave source for the current ground-based gravitational wave detectors, due to the generally lower frequency of such a source. In this paper, we adopt the effective-one-body formalism as the equation of motion, and obtain the accurately calculated gravitational waveforms by solving the Teukolsky equation using the frequency-domain method. We point out that high frequency modes of gravitational waves can be excited by large eccentricities of intermediate-mass-ratio inspirals. These high frequency modes can extend to more than 10 Hz, and enter the designed sensitive band of Advanced LIGO and Advanced Virgo. We propose that such kinds of highly eccentric intermediate-mass-ratio inspirals could be feasible sources and potentially observable by the ground-based gravitational wave detectors, like the Advanced LIGO and Advanced Virgo.

On the ambiguity in the notion of transverse traceless modes of gravitational waves

Somewhat surprisingly, in many of the widely used monographs and review articles the term Transverse-Traceless modes of linearized gravitational waves is used to denote two entirely different notions. These treatments generally begin with a decomposition of the metric perturbation that is local in the momentum space (and hence non-local in physical space), and denote the resulting transverse traceless modes by $h_{ab}^{\TT}$. However, while discussing gravitational waves emitted by an isolated system --typically in a later section-- the relevant modes are extracted using a `projection operator' that is local in physical space. These modes are also called transverse-traceless and again labeled $h_{ab}^{\TT}$, implying that this is just a reformulation of the previous notion. But the two notions are conceptually distinct and the difference persists even in the asymptotic region. We show that this confusion arises already in Maxwell theory that is often discussed as a prelude to the gravitational case. Finally, we discuss why the distinction has nonetheless remained largely unnoticed, and also point out that there are some important physical effects where only one of the notions gives the correct answer.

Rigid covariance as a natural extension of Painlevé–Gullstrand space-times: gravitational waves

The group of rigid motions is considered to guide the search for a natural system of space-time coordinates in General Relativity. This search leads us to a natural extension of the space-times that support Painlev\'{e}--Gullstrand synchronization. As an interesting example, here we describe a system of rigid coordinates for the cross mode of gravitational linear plane waves.

Gravitational waves in Friedman–Lemaitre–Robertson–Walker cosmology, material perturbations and cosmological rotation, and the Huygens principle

We analyze propagation equations for the polar modes of gravitational waves in cosmological space-times. We prove that polar gravitational waves must perturb the density and non-azimuthal components of the velocity of material medium of the Friedman–Lemaitre–Robertson–Walker spacetimes. Axial gravitational waves can influence only the azimuthal velocity, leading to local cosmological rotation. The whole gravitational dynamics reduces to the single ‘master equation’ that has the same form for polar and axial modes. That allows us to conclude that the status of the Huygens principle is the same for axial and polar gravitational waves. In particular, this principle is valid exactly in radiation spacetimes with the vanishing cosmological constant, and it is broken otherwise.

Equation of state effects and one-arm spiral instability in hypermassive neutron stars formed in eccentric neutron star mergers

We continue our investigations of the development and importance of the one-arm spiral instability in long-lived hypermassive neutron stars (HMNSs) formed in dynamical capture binary neutron star mergers. Employing hydrodynamic simulations in full general relativity, we find that the one-arm instability is generic in that it can develop in HMNSs within a few tens of milliseconds after merger for all equations of state in our survey. We find that mergers with stiffer equations of state tend to produce HMNSs with stronger m = 2 azimuthal mode density deformations, and weaker m = 1 components, relative to softer equations of state. We also find that for equations of state that can give rise to double-core HMNSs, large m = 1 density modes can already be present due to asymmetries in the two cores. This results in the generation of l = 2, m = 1 gravitational wave modes even before the dominance of a one-arm mode that ultimately arises following merger of the two cores. Our results further suggest that stiffer equations of state give rise to HMNSs generating lower m = 1 gravitational wave frequencies. Thus, if gravitational waves from the one-arm instability are detected, they could in principle constrain the neutron star equation of state. We estimate that, depending on the equation of state, the one-arm mode could potentially be detectable by second generation gravitational wave detectors at ∼10 Mpc and by third generation ones at ∼100 Mpc. Finally, we provide estimates of the properties of dynamical ejecta, as well as the accompanying kilonovae signatures.

Gravitational wave asteroseismology with protoneutron stars

We examine the time evolution of the frequencies of the gravitational wave after the bounce within the framework of relativistic linear perturbation theory using the results of one dimensional numerical simulations of core-collapse supernovae. Protoneutron star models are constructed in such a way that the mass and radius of protoneutron star become equivalent to the results obtained from the numerical simulations. Then, we find that the frequencies of gravitational waves radiating from protoneutron stars strongly depend on the mass and radius of protoneutron stars, but almost independently of the profiles of electron fraction and entropy per baryon inside the star. Additionally, we find that the frequencies of gravitational waves can be characterized by the square root of the average density of protoneutron star irrespectively the progenitor models, which are completely different from the empirical formula for cold neutron stars. The dependence of the spectra on the mass and radius is different from that of the $g$-mode: the oscillations around the surface of protoneutron stars due to the convection and the standing accretion-shock instability. Careful observations of the these modes of gravitational waves can determine the evolution of the mass and radius of protoneutron stars after core-bounce. Furthermore, the expected frequencies of gravitational waves are around a few hundred hertz in the early stage after bounce, which must be a good candidate for the ground-based gravitational wave detectors.