Neutron star tidal deformability and equation of state constraints

Despite their long history and astrophysical importance, some of the key properties of neutron stars are still uncertain. The extreme conditions encountered in their interiors, involving matter of uncertain composition at extreme density and isospin asymmetry, uniquely determine the stars' macroscopic properties within General Relativity. Astrophysical constraints on those macroscopic properties, such as neutron star masses and radii, have long been used to understand the microscopic properties of the matter that forms them. In this article we discuss another astrophysically observable macroscopic property of neutron stars that can be used to study their interiors: their tidal deformation. Neutron stars, much like any other extended object with structure, are tidally deformed when under the influence of an external tidal field. In the context of coalescences of neutron stars observed through their gravitational wave emission, this deformation, quantified through a parameter termed the \emph{tidal deformability}, can be measured. We discuss the role of the tidal deformability in observations of coalescing neutron stars with gravitational waves and how it can be used to probe the internal structure of Nature's most compact matter objects. Perhaps inevitably, a large portion of the discussion will be dictated by GW170817, the most informative confirmed detection of a binary neutron star coalescence with gravitational waves as of the time of writing

Neutron star tidal deformability and equation of state constraints

Despite their long history and astrophysical importance, some of the key properties of neutron stars are still uncertain. The extreme conditions encountered in their interiors, involving matter of uncertain composition at extreme density and isospin asymmetry, uniquely determine the stars' macroscopic properties within General Relativity. Astrophysical constraints on those macroscopic properties, such as neutron star masses and radii, have long been used to understand the microscopic properties of the matter that forms them. In this article we discuss another astrophysically observable macroscopic property of neutron stars that can be used to study their interiors: their tidal deformation. Neutron stars, much like any other extended object with structure, are tidally deformed when under the influence of an external tidal field. In the context of coalescences of neutron stars observed through their gravitational wave emission, this deformation, quantified through a parameter termed the \emph{tidal deformability}, can be measured. We discuss the role of the tidal deformability in observations of coalescing neutron stars with gravitational waves and how it can be used to probe the internal structure of Nature's most compact matter objects. Perhaps inevitably, a large portion of the discussion will be dictated by GW170817, the most informative confirmed detection of a binary neutron star coalescence with gravitational waves as of the time of writing.Comment: invited review for General Relativity and Gravitation, published versio

Toward Realistic and Practical No-Hair Relations for Neutron Stars in the Non-Relativistic Limit

The gravitational properties of astrophysical objects depend sensitively on their internal structure. In Newtonian theory, the gravitational potential of a rotating star can be fully described by an infinite number of multipole moments of its mass distribution. Recently, this infinite number of moments for uniformly-rotating stars were shown semi-analytically to be expressible in terms of just the first three: the mass, the spin, and the quadrupole moment of the star. The relations between the various lower multipole moments were additionally shown to depend weakly on the equation of state, when considering neutron stars and assuming single polytropic equations of state. Here we extend this result in two ways. First, we show that the universality also holds for realistic equations of state, thus relaxing the need to use single polytropes. Second, we derive purely analytical universal relations by perturbing the equations of structure about an $n=0$ polytrope that reproduce semi-analytic results to $\mathcal{O}(1\%)$. We also find that the linear-order perturbation vanishes in some cases, which provides further evidence and a deeper understanding of the universality.Comment: 10 pages, 5 figures, published versio

Tidal heating and torquing of a Kerr black hole to next-to-leading order in the tidal coupling

We calculate the linear vacuum perturbations of a Kerr black hole surrounded by a slowly-varying external spacetime to third order in the ratio of the black-hole mass to the radius of curvature of the external spacetime. This expansion applies to two relevant physical scenarios: (i) a small Kerr black hole immersed in the gravitational field of a much larger external black hole, and (ii) a Kerr black hole moving slowly around another external black hole of comparable mass. This small-hole/slow-motion approximation allows us to parametrize the perturbation through slowly-varying, time-dependent electric and magnetic tidal tensors, which then enables us to separate the Teukolsky equation and compute the Newman-Penrose scalar analytically to third order in our expansion parameter. We obtain generic expressions for the mass and angular momentum flux through the perturbed black hole horizon, as well as the rate of change of the horizon surface area, in terms of certain invariants constructed from the electric and magnetic tidal tensors. We conclude by applying these results to the two scenarios described above.Comment: 15 pages, no figures, published versio

On combining information from multiple gravitational wave sources

In the coming years, advanced gravitational wave detectors will observe signals from a large number of compact binary coalescences. The majority of these signals will be relatively weak, making the precision measurement of subtle effects, such as deviations from general relativity, challenging in the individual events. However, many weak observations can be combined into precise inferences, if information from the individual signals is combined in an appropriate way. In this study we revisit common methods for combining multiple gravitational wave observations to test general relativity, namely (i) multiplying the individual likelihoods of beyond-general-relativity parameters and (ii) multiplying the Bayes Factor in favor of general relativity from each event. We discuss both methods and show that they make stringent assumptions about the modified theory of gravity they test. In particular, the former assumes that all events share the same beyond-general-relativity parameter, while the latter assumes that the theory of gravity has a new unrelated parameter for each detection. We show that each method can fail to detect deviations from general relativity when the modified theory being tested violates these assumptions. We argue that these two methods are the extreme limits of a more generic framework of hierarchical inference on hyperparameters that characterize the underlying distribution of single-event parameters. We illustrate our conclusions first using a simple model of Gaussian likelihoods, and also by applying parameter estimation techniques to a simulated dataset of gravitational waveforms in a model where the graviton is massive. We argue that combining information from multiple sources requires explicit assumptions that make the results inherently model-dependent.Comment: 9 pages, 3 figure

Phenomenological model for the gravitational-wave signal from precessing binary black holes with two-spin effects

The properties of compact binaries, such as masses and spins, are imprinted in the gravitational-waves they emit and can be measured using parameterised waveform models. Accurately and efficiently describing the complicated precessional dynamics of the various angular momenta of the system in these waveform models is the object of active investigation. One of the key models extensively used in the analysis of LIGO and Virgo data is the single-precessing-spin waveform model IMRPhenomPv2. In this article we present a new model IMRPhenomPv3 which includes the effects of two independent spins in the precession dynamics. Whereas IMRPhenomPv2 utilizes a single-spin frequency-dependent post-Newtonian rotation to describe precession effects, the improved model, IMRPhenomPv3, employs a double-spin rotation that is based on recent developments in the description of precessional dynamics. Besides double-spin precession, the improved model benefits from a more accurate description of precessional effects. We validate our new model against a large set of precessing numerical-relativity simulations. We find that IMRPhenomPv3 has better agreement with the inspiral portion of precessing binary-black-hole simulations and is more robust across a larger region of the parameter space than IMRPhenomPv2. As a first application we analyse, for the first time, the gravitational-wave event GW151226 with a waveform model that describes two-spin precession. Within statistical uncertainty our results are consistent with published results. IMRPhenomPv3 will allow studies of the measurability of individual spins of binary black holes using GWs and can be used as a foundation upon which to build further improvements, such as modeling precession through merger, extending to higher multipoles, and including tidal effects.Comment: 15 pages, 5 figure

Gravitational Waveforms for Precessing, Quasicircular Compact Binaries with Multiple Scale Analysis: Small Spin Expansion

We obtain analytical gravitational waveforms in the frequency-domain for precessing, quasi-circular compact binaries with small spins, applicable, for example, to binary neutron star inspirals. We begin by calculating an analytic solution to the precession equations, obtained by expanding in the dimensionless spin parameters and using multiple-scale analysis to separate timescales. We proceed by analytically computing the Fourier transform of time-domain waveform through the stationary phase approximation. We show that the latter is valid for systems with small spins. Finally, we show that these waveforms have a high overlap with numerical waveforms obtained through direct integration of the precession equations and discrete Fourier transformations. The resulting, analytic waveform family is ideal for detection and parameter estimation of gravitational waves emitted by inspiraling binary neutron stars with ground-based detectors.Comment: 37 pages, 14 figures, final published versio