We compute the internal modes of a non-spinning neutron star and its tidal metric perturbation in general relativity, and determine the effect of relativistic corrections to the modes on mode coupling and the criterion for instability. Claims have be
en made that a new hydrodynamic instability can occur in a neutron star in a binary neutron star system triggered by the nonlinear coupling of the companions tidal field to pairs of p-modes and g-modes in it as the binary inspirals toward merger. This PG instability may be significant since it can influence the binarys inspiral phase by extracting orbital energy, thereby potentially causing large deviations in their gravitational waveforms from those predicted by theoretical models that do not account for it. This can result in incorrect parameter estimation, at best, or mergers going undetected, at worst, owing to the use of deficient waveform models. On the other hand, better modeling of this instability and its effect on binary orbits can unravel a new phenomenon and shed light on stellar instabilities, via gravitational wave observations. So far, all mode-tide coupling instability studies have been formulated in Newtonian perturbation theory. Neutron stars are compact objects, so relativistic corrections might be important. We present and test a new code to calculate the relativistic eigenmodes of nonrotating relativistic stars. We use these relativistic tide and neutron star eigenmodes to compute the mode-tide coupling strength (MTCS) for a few selected equations of state. The MTCS thus calculated can be at most tens of percent different from its purely Newtonian value, but we confirm the dependencies on orbital separation and equation of state found by Newtonian calculations. For some equations of state, the MTCS is very sensitive to the neutron star crust region, demonstrating the importance of treating this region accurately.
An important physical phenomenon that manifests itself during the inspiral of two orbiting compact objects is the tidal deformation of each under the gravitational influence of its companion. In the case of binary neutron star mergers, this tidal def
ormation and the associated Love numbers have been used to probe properties of dense matter and the nuclear equation of state. Non-spinning black holes on the other hand have a vanishing (field) tidal Love number in General Relativity. This pertains to the deformation of the asymptotic gravitational field. In certain cases, especially in the late stages of the inspiral phase when the black holes get close to each other, the source multipole moments might be more relevant in probing their properties and the No-Hair theorem; contrastingly, these Love numbers do not vanish. In this paper, we track the source multipole moments in simulations of several binary black hole mergers and calculate these Love numbers. We present evidence that, at least for modest mass ratios, the behavior of the source multipole moments is universal.
We study how by careful monitoring of the presence or absence of tidal deformability (TD) and tidal-heating (TH) in the inspiral signal of compact object binaries in ground-based gravitational wave (GW) detectors, one can test if its components are b
lack holes or not. The former property (TD) is finite for neutron stars but vanishes for black holes (in general relativity), whereas the latter is finite for black holes and negligible for neutron stars, and affects the GW phase evolution of binaries in a distinctly different way. We introduce waveform parameters that characterize the strength of tidal-heating, and are zero when there is no horizon. We develop Bayesian methods that use TD and TH for distinguishing the presence or absence of horizons in a binary. This is timely owing to several claims that these stellar-mass objects, especially, with masses heavier than those of neutron stars, may not have a horizon but may be black hole mimickers or exotic compact objects (ECOs). It is also astrophysically important to have the tools to test the presence or absence of horizons in mass-gap binaries and, thereby, help detect the heaviest neutron star or the lightest black hole. A proper accounting of tidal-heating in binary waveform models will also be critical for an unbiased measurement of characteristics of the equation of state of neutron stars in GW observations of binaries containing them -- or even to probe the existence of ECOs. We show that purely based on GW waveforms it will not be possible to discern binary horizons in the mass gap in Advanced LIGO, Virgo and KAGRA detectors unless the binary is within a few tens of Mpc. However, third generation ground-based detectors will be able to do so for binaries a few hundred Mpc away.
In a binary black hole merger, it is known that the inspiral portion of the waveform corresponds to two distinct horizons orbiting each other, and the merger and ringdown signals correspond to the final horizon being formed and settling down to equil
ibrium. However, we still lack a detailed understanding of the relation between the horizon geometry in these three regimes and the observed waveform. Here we show that the well known inspiral chirp waveform has a clear counterpart on black hole horizons, namely, the shear of the outgoing null rays at the horizon. We demonstrate that the shear behaves very much like a compact binary coalescence waveform with increasing frequency and amplitude. Furthermore, the parameters of the system estimated from the horizon agree with those estimated from the waveform. This implies that even though black hole horizons are causally disconnected from us, assuming general relativity to be true, we can potentially infer some of their detailed properties from gravitational wave observations.
The defining feature of a classical black hole is being a perfect absorber. Any evidence showing otherwise would indicate a departure from the standard black-hole picture. Energy and angular momentum absorption by the horizon of a black hole is respo
nsible for tidal heating in a binary. This effect is particularly important in the latest stages of an extreme mass ratio inspiral around a spinning supermassive object, one of the main targets of the future LISA mission. We study how this effect can be used to probe the nature of supermassive objects in a model independent way. We compute the orbital dephasing and the gravitational-wave signal emitted by a point particle in circular, equatorial motion around a spinning supermassive object to the leading order in the mass ratio. Absence of absorption by the central object can affect the gravitational-wave signal dramatically, especially at high spin. This effect will make it possible to put an unparalleled upper bound on the reflectivity of exotic compact objects, at the level of ${cal O}(0.01)%$. This stringent bound would exclude the possibility of observing echoes in the ringdown of a supermassive binary merger.
We show how observations of gravitational waves from binary neutron star (BNS) mergers over the next few years can be combined with insights from nuclear physics to obtain useful constraints on the equation of state (EoS) of dense matter, in particul
ar, constraining the neutron-matter EoS to within 20% between one and two times the nuclear saturation density $n_0approx 0.16 {text{fm}^{-3}}$. Using Fisher information methods, we combine observational constraints from simulated BNS merger events drawn from various population models with independent measurements of the neutron star radii expected from x-ray astronomy (the Neutron Star Interior Composition Explorer (NICER) observations in particular) to directly constrain nuclear physics parameters. To parameterize the nuclear EoS, we use a different approach, expanding from pure nuclear matter rather than from symmetric nuclear matter to make use of recent quantum Monte Carlo (QMC) calculations. This method eschews the need to invoke the so-called parabolic approximation to extrapolate from symmetric nuclear matter, allowing us to directly constrain the neutron-matter EoS. Using a principal component analysis, we identify the combination of parameters most tightly constrained by observational data. We discuss sensitivity to various effects such as different component masses through population-model sensitivity, phase transitions in the core EoS, and large deviations from the central parameter values.
In order to identify the rapidly-fading, optical transient counterparts of gravitational wave (GW) sources, an efficient follow-up strategy is required. Since most ground-based optical observatories aimed at following-up GW sources have a telescope w
ith a small field-of-view (FOV) as compared to the GW sky error region, we focus on a search strategy that involves dividing the GW patch into tiles of the same area as the telescope FOV to strategically image the entire patch. We present an improvement over the optimal telescope-scheduling algorithm outlined in Rana et al. (2016), by combining the tiling and galaxy-targeted search strategies, and factoring the effects of the source airmass and telescope slew, along with setting constraints, into the scheduling algorithm in order to increase the chances of identifying the GW counterpart. We propose two separate algorithms: the airmass-weighted algorithm, a specific solution to the Hungarian algorithm that maximizes probability acquired, while minimizing the image airmass, and the slew-optimization algorithm that minimizes the overall slew angle covered between images for the given probability acquired by the optimal telescope-scheduling algorithm in Rana et al. (2016). Using the observatory site of the GROWTH-India telescope as an example, we generate 100s of skymaps to test the performance of our algorithms. Our results indicate that slew-optimization can reduce the cumulative slew angle in the observing schedule by 100s of degrees, saving several of minutes of observing time without the loss of tiles and probability. Further, we demonstrate that as compared to the greedy algorithm, the airmass-weighted algorithm can acquire up to 20 % more probability and 30 sq. deg. more in areal coverage for skymaps of all sizes and configurations.
We investigate the use of particle swarm optimization (PSO) algorithm for detection of gravitational-wave signals from compact binary coalescences. We show that the PSO is fast and effective in searching for gravitational wave signals. The PSO-based
aligned-spin coincident multi-detector search recovers appreciably more gravitational-wave signals, for a signal-to-noise ratio (SNR) of 10, the PSO based aligned-spin search recovers approximately 26 $%$ more events as compared to the template bank searches. The PSO-based aligned-spin coincident search uses 48k matched-filtering operations, and provides a better parameter estimation accuracy at the detection stage, as compared to the PyCBC template-bank search in LIGOs second observation run (O2) with 400k template points. We demonstrate an effective PSO-based precessing coincident search with 320k match-filtering operations per detector. We present results of an all-sky aligned-spin coherent search with 576k match-filtering operations per detector, for some examples of two-, three-, and four-detector networks constituting of the LIGO detectors in Hanford and Livingston, Virgo and KAGRA. Techniques for background estimation that are applicable to real data for PSO-based coincident and coherent searches are also presented.
We show how gravitational-wave observations with advanced detectors of tens to several tens of neutron-star binaries can measure the neutron-star radius with an accuracy of several to a few percent, for mass and spatial distributions that are realist
ic, and with none of the sources located within 100 Mpc. We achieve such an accuracy by combining measurements of the total mass from the inspiral phase with those of the compactness from the postmerger oscillation frequencies. For estimating the measurement errors of these frequencies we utilize analytical fits to postmerger numerical-relativity waveforms in the time domain, obtained here for the first time, for four nuclear-physics equations of state and a couple of values for the mass. We further exploit quasi-universal relations to derive errors in compactness from those frequencies. Measuring the average radius to well within 10% is possible for a sample of 100 binaries distributed uniformly in volume between 100 and 300 Mpc, so long as the equation of state is not too soft or the binaries are not too heavy.
Bose-Einstein condensates (BECs) have been proposed as candidate states of matter for the interior of neutron stars. Specifically, Chavanis and Harko obtained the mass-radius relation for a BEC star and proposed that the recently discovered neutron s
tars with masses around 2$M_odot$ are BEC stars. They employed a barotropic equation of state (EOS), with one free parameter, that was first found by Colpi, Wasserman, and Shapiro (CSW), to describe them and derive stable equilibrium configurations of spinning BEC stars in General Relativity. In this work we show that while it is true that BECs allow for compact object masses as heavy as the heaviest observed ones, such stars cannot simultaneously have radii that are small enough to be consistent with the latest observations, in spite of the flexibility available in the EOS in the form of the free parameter. In fact, our conclusion applies to any spinning relativistic boson star that obeys the CSW EOS.
