Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817

Continuous Gravitational Waves from Neutron Stars: Current Status and Prospects

Gravitational waves astronomy allows us to study objects and events invisible in electromagnetic waves. It is crucial to validate the theories and models of the most mysterious and extreme matter in the Universe: the neutron stars. In addition to inspirals and mergers of neutrons stars, there are currently a few proposed mechanisms that can trigger radiation of long-lasting gravitational radiation from neutron stars, such as e.g., elastically and/or magnetically driven deformations: mountains on the stellar surface supported by the elastic strain or magnetic field, free precession, or unstable oscillation modes (e.g., the r-modes). The astrophysical motivation for continuous gravitational waves searches, current LIGO and Virgo strategies of data analysis and prospects are reviewed in this work.

Constraining the Neutron Star Equation of State Using Multiband Independent Measurements of Radii and Tidal Deformabilities

Using a Bayesian approach, we combine measurements of neutron star macroscopic observables obtained by astrophysical and gravitational observations to derive joint constraints on the equation of state (EOS) of matter at supranuclear density. In our analysis, we use two sets of data: (i) the masses and tidal deformabilities measured in the binary neutron star event GW170817, detected by LIGO and Virgo, and (ii) the masses and stellar radii measured from observations of nuclear bursts in accreting low-mass x-ray binaries. Using a phenomenological parametrization of the equation of state, we compute the posterior probability distributions of the EOS parameters, using which we infer the posterior distribution for the radius and the mass of the two neutron stars of GW170817. The constraints we set on the radii are tighter than previous bounds.

Observational diversity of magnetized neutron stars

Young and rotation-powered neutron stars (NSs) are commonly observed as rapidly-spinning pulsars. They dissipate their rotational energy by emitting pulsar wind with electromagnetic radiation and spin down at a steady rate, according to the simple steadily-rotating magnetic dipole model. In reality, however, multiwavelength observations of radiation from the NS surface and magnetosphere have revealed that the evolution and properties of NSs are highly diverse, often dubbed as 'NS zoo'. In particular, many of young and highly magnetized NSs show a high degree of activities, such as sporadic electromagnetic outbursts and irregular changes in pulse arrival times. Importantly, their magnetic field, which are the strongest in the universe, makes them ideal laboratories for fundamental physics. A class of highly-magnetized isolated NSs is empirically divided into several subclasses. In a broad classification, they are, in the order of the magnetic field strength (B) from the highest, 'magnetars' (historically recognized as soft gamma-ray repeaters and/or anomalous x-ray pulsars), 'high-B pulsars', and (nearby) x-ray isolated NSs. This article presents an introductory review for non-astrophysicists about the observational properties of highly-magnetized NSs, and their implications. The observed dynamic nature of NSs must be interpreted in conjunction with transient magnetic activities triggered during magnetic-energy dissipation process. In particular, we focus on how the five fundamental quantities of NSs, i.e. mass, radius, spin period, surface temperature, and magnetic fields, as observed with modern instruments, change with evolution of, and vary depending on the class of, the NSs. They are the foundation for a future unified theory of NSs.

Constraints on Microscopic and Phenomenological Equations of State of Dense Matter from GW170817

We discuss the constraints on the equation of state (EOS) of neutron star matter obtained by the data analysis of the neutron star-neutron star merger in the event GW170807. To this scope, we consider two recent microscopic EOS models computed starting from two-body and three-body nuclear interactions derived using chiral perturbation theory. For comparison, we also use three representative phenomenological EOS models derived within the relativistic mean field approach. For each model, we determine the β -stable EOS and then the corresponding neutron star structure by solving the equations of hydrostatic equilibrium in general relativity. In addition, we calculate the tidal deformability parameters for the two neutron stars and discuss the results of our calculations in connection with the constraints obtained from the gravitational wave signal in GW170817. We find that the tidal deformabilities and radii for the binary’s component neutron stars in GW170817, calculated using a recent microscopic EOS model proposed by the present authors, are in very good agreement with those derived by gravitational waves data.

Multimessenger Bayesian parameter inference of a binary neutron star merger

The combined detection of a binary neutron star merger in both gravitational waves (GWs) and electromagnetic (EM) radiation spanning the entire spectrum – GW170817/AT2017gfo/GRB170817A – marks a breakthrough in the field of multimessenger astronomy. Between the plethora of modelling and observations, the rich synergy that exists among the available data sets creates a unique opportunity to constrain the binary parameters, the equation of state of supranuclear density matter, and the physical processes at work during the kilonova and gamma-ray burst. We report, for the first time, Bayesian parameter estimation combining information from GW170817, AT2017gfo, and GRB170817 to obtain truly multimessenger constraints on the tidal deformability $\tilde{\Lambda } \in [302,860]$, total binary mass M ∈ [2.722, 2.751] M⊙, the radius of a 1.4 solar mass neutron star $R \in [11.3,13.5] \,\,\rm km$ (with additional $0.2\ \rm km$ systematic uncertainty), and an upper bound on the mass ratio of q ≤ 1.27, all at 90 per cent confidence. Our joint novel analysis uses new phenomenological descriptions of the dynamical ejecta, debris disc mass, and remnant black hole properties, all derived from a large suite of numerical relativity simulations.

Impact of the Nuclear Equation of State on the Stability of Hybrid Neutron Stars

We construct a set of equations of state (EoS) of dense and hot matter with a 1st order phase transition from a hadronic system to a deconfined quark matter state. In this two-phase approach, hadrons are described using the relativistic mean field theory with different parametrisations and the deconfined quark phase is modeled using vBag, a bag–type model extended to include vector interactions as well as a simultaneous onset of chiral symmetry restoration and deconfinement. This feature results in a non–trivial connection between the hadron and quark EoS, modifying the quark phase beyond its onset density. We find that this unique property has an impact on the predicted hybrid (quark core) neutron star mass–radius relations.

Binary Neutron Star (BNS) Merger: What We Learned from Relativistic Ejecta of GW/GRB 170817A

Gravitational Waves (GW) from coalescence of a Binary Neutron Star (BNS) and its accompanying short Gamma-Ray Burst (GRB) GW/GRB 170817A confirmed the presumed origin of these puzzling transients and opened up the way for relating properties of short GRBs to those of their progenitor stars and their surroundings. Here we review an extensive analysis of the prompt gamma-ray and late afterglows of this event. We show that a fraction of polar ejecta from the merger had been accelerated to ultra-relativistic speeds. This structured jet had an initial Lorentz factor of about 260 in our direction, which was O ( 10 ∘ ) from the jet’s axis, and was a few orders of magnitude less dense than in typical short GRBs. At the time of arrival to circum-burst material the ultra-relativistic jet had a close to Gaussian profile and a Lorentz factor ≳ 130 in its core. It had retained in some extent its internal collimation and coherence, but had extended laterally to create mildly relativistic lobes—a cocoon. Its external shocks on the far from center inhomogeneous circum-burst material and low density of colliding shells generated slowly rising afterglows, which peaked more than 100 days after the prompt gamma-ray. The circum-burst material was somehow correlated with the merger. As non-relativistic outflows or tidally ejected material during BNS merger could not have been arrived to the location of the external shocks before the relativistic jet, circum-burst material might have contained recently ejected materials from resumption of internal activities, faulting and mass loss due to deformation and breaking of stars crusts by tidal forces during latest stages of their inspiral but well before their merger. By comparing these findings with the results of relativistic Magneto-Hydro-Dynamics (MHD) simulations and observed gravitational waves we conclude that progenitor neutron stars were most probably old, had close masses and highly reduced magnetic fields.

Neutron Star Mass and Radius Measurements

Constraints on neutron star masses and radii now come from a variety of sources: theoretical and experimental nuclear physics, astrophysical observations including pulsar timing, thermal and bursting X-ray sources, and gravitational waves, and the assumptions inherent to general relativity and causality of the equation of state. These measurements and assumptions also result in restrictions on the dense matter equation of state. The two most important structural parameters of neutron stars are their typical radii, which impacts intermediate densities in the range of one to two times the nuclear saturation density, and the maximum mass, which impacts the densities beyond about three times the saturation density. Especially intriguing has been the multi-messenger event GW170817, the first observed binary neutron star merger, which provided direct estimates of both stellar masses and radii as well as an upper bound to the maximum mass.

Detecting the Hadron-Quark Phase Transition with Gravitational Waves

The long-awaited detection of a gravitational wave from the merger of a binary neutron star in August 2017 (GW170817) marks the beginning of the new field of multi-messenger gravitational wave astronomy. By exploiting the extracted tidal deformations of the two neutron stars from the late inspiral phase of GW170817, it is now possible to constrain several global properties of the equation of state of neutron star matter. However, the most interesting part of the high density and temperature regime of the equation of state is solely imprinted in the post-merger gravitational wave emission from the remnant hypermassive/supramassive neutron star. This regime was not observed in GW170817, but will possibly be detected in forthcoming events within the current observing run of the LIGO/VIRGO collaboration. Numerous numerical-relativity simulations of merging neutron star binaries have been performed during the last decades, and the emitted gravitational wave profiles and the interior structure of the generated remnants have been analysed in detail. The consequences of a potential appearance of a hadron-quark phase transition in the interior region of the produced hypermassive neutron star and the evolution of its underlying matter in the phase diagram of quantum cromo dynamics will be in the focus of this article. It will be shown that the different density/temperature regions of the equation of state can be severely constrained by a measurement of the spectral properties of the emitted post-merger gravitational wave signal from a future binary compact star merger event.

Questions Related to the Equation of State of High-Density Matter

Astronomical data about neutron stars can be combined with laboratory nuclear data to give us a strong base from which to infer the equation of state of cold catalyzed matter beyond nuclear density. However, the nuclear and astrophysical communities are largely distinct; each has their own methods, which means that there is often imperfect communication between the communities regarding caveats about claimed measurements and constraints. Here we present a brief summary from one astronomer’s perspective of relevant observations of neutron stars, with warnings as appropriate, followed by a set of questions that are intended to help enhance the dialog between nuclear physicists and astrophysicists.

Quarkyonic Matter and Neutron Stars

We consider quarkyonic matter to naturally explain the observed properties of neutron stars. We argue that such matter might exist at densities close to that of nuclear matter, and at the onset, the pressure and the sound velocity in quarkyonic matter increase rapidly. In the limit of large number of quark colors N_{c}, this transition is characterized by a discontinuous change in pressure as a function of baryon number density. We make a simple model of quarkyonic matter and show that generically the sound velocity is a nonmonotonic function of density-it reaches a maximum at relatively low density, decreases, and then increases again to its asymptotic value of 1/sqrt[3].

Identifying a First-Order Phase Transition in Neutron-Star Mergers through Gravitational Waves

We identify an observable imprint of a first-order hadron-quark phase transition at supranuclear densities on the gravitational-wave (GW) emission of neutron-star mergers. Specifically, we show that the dominant postmerger GW frequency f_{peak} may exhibit a significant deviation from an empirical relation between f_{peak} and the tidal deformability if a strong first-order phase transition leads to the formation of a gravitationally stable extended quark matter core in the postmerger remnant. A comparison of the GW signatures from a large, representative sample of microphysical, purely hadronic equations of state indicates that this imprint is only observed in those systems which undergo a strong first-order phase transition. Such a shift of the dominant postmerger GW frequency can be revealed by future GW observations, which would provide evidence for the existence of a strong first-order phase transition in the interior of neutron-stars.

Constraining the p-Mode-g-Mode Tidal Instability with GW170817

We analyze the impact of a proposed tidal instability coupling p modes and g modes within neutron stars on GW170817. This nonresonant instability transfers energy from the orbit of the binary to internal modes of the stars, accelerating the gravitational-wave driven inspiral. We model the impact of this instability on the phasing of the gravitational wave signal using three parameters per star: an overall amplitude, a saturation frequency, and a spectral index. Incorporating these additional parameters, we compute the Bayes factor (lnB_{!pg}^{pg}) comparing our p-g model to a standard one. We find that the observed signal is consistent with waveform models that neglect p-g effects, with lnB_{!pg}^{pg}=0.03_{-0.58}^{+0.70} (maximum a posteriori and 90% credible region). By injecting simulated signals that do not include p-g effects and recovering them with the p-g model, we show that there is a ≃50% probability of obtaining similar lnB_{!pg}^{pg} even when p-g effects are absent. We find that the p-g amplitude for 1.4  M_{⊙} neutron stars is constrained to less than a few tenths of the theoretical maximum, with maxima a posteriori near one-tenth this maximum and p-g saturation frequency ∼70  Hz. This suggests that there are less than a few hundred excited modes, assuming they all saturate by wave breaking. For comparison, theoretical upper bounds suggest ≲10^{3} modes saturate by wave breaking. Thus, the measured constraints only rule out extreme values of the p-g parameters. They also imply that the instability dissipates ≲10^{51}  erg over the entire inspiral, i.e., less than a few percent of the energy radiated as gravitational waves.

Bayesian Analysis for Extracting Properties of the Nuclear Equation of State from Observational Data Including Tidal Deformability from GW170817

We develop a Bayesian analysis method for selecting the most probable equation of state under a set of constraints from compact star physics, which now include the tidal deformability from GW170817. We apply this method for the first time to a two-parameter family of hybrid equations of state that is based on realistic models for the hadronic phase (KVORcut02) and the quark matter phase (SFM α ) which produce a third family of hybrid stars in the mass–radius diagram. One parameter ( α ) characterizes the screening of the string tension in the string-flip model of quark matter while the other ( Δ P ) belongs to the mixed phase construction that mimics the thermodynamics of pasta phases and includes the Maxwell construction as a limiting case for Δ P = 0 . We present the corresponding results for compact star properties like mass, radius and tidal deformabilities and use empirical data for them in the newly developed Bayesian analysis method to obtain the probabilities for the model parameters within their considered range.

GW170817: Measurements of Neutron Star Radii and Equation of State

On 17 August 2017, the LIGO and Virgo observatories made the first direct detection of gravitational waves from the coalescence of a neutron star binary system. The detection of this gravitational-wave signal, GW170817, offers a novel opportunity to directly probe the properties of matter at the extreme conditions found in the interior of these stars. The initial, minimal-assumption analysis of the LIGO and Virgo data placed constraints on the tidal effects of the coalescing bodies, which were then translated to constraints on neutron star radii. Here, we expand upon previous analyses by working under the hypothesis that both bodies were neutron stars that are described by the same equation of state and have spins within the range observed in Galactic binary neutron stars. Our analysis employs two methods: the use of equation-of-state-insensitive relations between various macroscopic properties of the neutron stars and the use of an efficient parametrization of the defining function p(ρ) of the equation of state itself. From the LIGO and Virgo data alone and the first method, we measure the two neutron star radii as R_{1}=10.8_{-1.7}^{+2.0}  km for the heavier star and R_{2}=10.7_{-1.5}^{+2.1}  km for the lighter star at the 90% credible level. If we additionally require that the equation of state supports neutron stars with masses larger than 1.97  M_{⊙} as required from electromagnetic observations and employ the equation-of-state parametrization, we further constrain R_{1}=11.9_{-1.4}^{+1.4}  km and R_{2}=11.9_{-1.4}^{+1.4}  km at the 90% credible level. Finally, we obtain constraints on p(ρ) at supranuclear densities, with pressure at twice nuclear saturation density measured at 3.5_{-1.7}^{+2.7}×10^{34}  dyn cm^{-2} at the 90% level.