Magnetohydrodynamic simulations of binary neutron star mergers in general relativity: Effects of magnetic field orientation on jet launching

Binary neutron star mergers can be sources of gravitational waves coincident with electromagnetic counterpart emission across the spectrum. To solidify their role as multimessenger sources, we present fully 3D, general relativistic, magnetohydrodynamic simulations of highly spinning binary neutrons stars initially on quasicircular orbits that merge and undergo delayed collapse to a black hole. The binaries consist of two identical stars modeled as Γ = 2 polytropes with spin χ NS = 0.36 aligned along the direction of the total orbital angular momentum L. Each star is initially threaded by a dynamical unimportant interior dipole magnetic field. The field is extended into the exterior where a nearly force-free magnetosphere resembles that of a pulsar. The magnetic dipole moment μ is either aligned or perpendicular to L and has the same initial magnitude for each orientation. For comparison, we also impose symmetry across the orbital plane in one case where μ in both stars is aligned along L. We find that the lifetime of the transient hypermassive neutron star remnant, the jet launching time, and the ejecta (which can give rise to a detectable kilonova) are very sensitive to the magnetic field orientation. By contrast, the physical properties of the black hole + disk remnant, such as the mass and spin of the black hole, the accretion rate, and the electromagnetic (Poynting) luminosity, are roughly independent of the initial magnetic field orientation. In addition, we find imposing symmetry across the orbital plane does not play a significant role in the final outcome of the mergers. Our results suggest that, as in the black hole-neutron star merger scenario, an incipient jet emerges only when the seed magnetic field has a sufficiently large-scale poloidal component aligned to the initial orbital angular momentum. The lifetime [Δt ≳ 140(M NS/1.625 M ⊙) ms] and Poynting luminosities [L EM ≃ 1052 erg/s] of the jet, when it forms, are consistent with typical short gamma-ray bursts, as well as with the Blandford-Znajek mechanism for launching jets.

Great Impostors: Extremely Compact, Merging Binary Neutron Stars in the Mass Gap Posing as Binary Black Holes

Can one distinguish a binary black hole undergoing a merger from a binary neutron star if the individual compact companions have masses that fall inside the so-called mass gap of 3-5  M_{⊙}? For neutron stars, achieving such masses typically requires extreme compactness and in this work we present initial data and evolutions of binary neutron stars initially in quasiequilibrium circular orbits having a compactness C=0.336. These are the most compact, nonvacuum, quasiequilibrium binary objects that have been constructed and evolved to date, including boson stars. The compactness achieved is only slightly smaller than the maximum possible imposed by causality, C_{max}=0.355, which requires the sound speed to be less than the speed of light. By comparing the emitted gravitational waveforms from the late inspiral to merger and postmerger phases between such a binary neutron star vs a binary black hole of the same total mass we identify concrete measurements that serve to distinguish them. With that level of compactness, the binary neutron stars exhibit no tidal disruption up until merger, whereupon a prompt collapse is initiated even before a common core forms. Within the accuracy of our simulations the black hole remnants from both binaries exhibit ringdown radiation that is not distinguishable from a perturbed Kerr spacetime. However, their inspiral leads to phase differences of the order of ∼5  rad over an ∼81  km separation (1.7 orbits) while typical neutron stars exhibit phase differences of ≥20  rad. Although a difference of ∼5  rad can be measured by current gravitational wave laser interferometers (e.g., aLIGO/Virgo), uncertainties in the individual masses and spins will likely prevent distinguishing such compact, massive neutron stars from black holes.

Kilonovae

The coalescence of double neutron star (NS-NS) and black hole (BH)-NS binaries are prime sources of gravitational waves (GW) for Advanced LIGO/Virgo and future ground-based detectors. Neutron-rich matter released from such events undergoes rapid neutron capture (r-process) nucleosynthesis as it decompresses into space, enriching our universe with rare heavy elements like gold and platinum. Radioactive decay of these unstable nuclei powers a rapidly evolving, approximately isotropic thermal transient known as a "kilonova", which probes the physical conditions during the merger and its aftermath. Here I review the history and physics of kilonovae, leading to the current paradigm of day-timescale emission at optical wavelengths from lanthanide-free components of the ejecta, followed by week-long emission with a spectral peak in the near-infrared (NIR). These theoretical predictions, as compiled in the original version of this review, were largely confirmed by the transient optical/NIR counterpart discovered to the first NS-NS merger, GW170817, discovered by LIGO/Virgo. Using a simple light curve model to illustrate the essential physical processes and their application to GW170817, I then introduce important variations about the standard picture which may be observable in future mergers. These include ∼ hour-long UV precursor emission, powered by the decay of free neutrons in the outermost ejecta layers or shock-heating of the ejecta by a delayed ultra-relativistic outflow; and enhancement of the luminosity from a long-lived central engine, such as an accreting BH or millisecond magnetar. Joint GW and kilonova observations of GW170817 and future events provide a new avenue to constrain the astrophysical origin of the r-process elements and the equation of state of dense nuclear matter.

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.

Identifying Quark Matter in Hybrid Stars through Relativistic Tidal Deformations

We study a specific model of neutron star matter that supports a phase transition to quark matter at high density and examine parameter ranges for consistency with the mass-weighted tidal deformability of Λ ˜ = 300 − 230 + 420 for a mass ratio of q ∈ [ 0.73 , 1.0 ] , as inferred from observations of gravitational waves from the binary neutron star merger event GW170817. By using this observation to restrict the parameter space for the equation of state (EoS) model used throughout this study, we aim to assess the possibility of a potential solution to the masquerade and flavor camouflage problems for hybrid EoS models. Assuming the two stars have the same EoS, in which the Dirac-Brueckner-Hartree Fock (DBHF) nuclear model transitions to the vBag quark model, we see if the parameter space of these hybrid model stars are restricted due to the adherence to the reported Λ 1.4 ∈ 70 , 580 and M m a x ∈ [ 2.01 , 2.16 ] M ⊙ constraints. Upon completion, we find that, while the parameter space for our model does get restricted, it does not ultimately resolve the masquerade and flavor camouflage problems.

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.

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.

A magnetar-powered X-ray transient as the aftermath of a binary neutron-star merger

Mergers of neutron stars are known to be associated with short γ-ray bursts^1-4. If the neutron-star equation of state is sufficiently stiff (that is, the pressure increases sharply as the density increases), at least some such mergers will leave behind a supramassive or even a stable neutron star that spins rapidly with a strong magnetic field^5-8 (that is, a magnetar). Such a magnetar signature may have been observed in the form of the X-ray plateau that follows up to half of observed short γ-ray bursts^9,10. However, it has been expected that some X-ray transients powered by binary neutron-star mergers may not be associated with a short γ-ray burst^11,12. A fast X-ray transient (CDF-S XT1) was recently found to be associated with a faint host galaxy, the redshift of which is unknown¹³. Its X-ray and host-galaxy properties allow several possible explanations including a short γ-ray burst seen off-axis, a low-luminosity γ-ray burst at high redshift, or a tidal disruption event involving an intermediate-mass black hole and a white dwarf¹³. Here we report a second X-ray transient, CDF-S XT2, that is associated with a galaxy at redshift z = 0.738 (ref. ¹⁴). The measured light curve is fully consistent with the X-ray transient being powered by a millisecond magnetar. More intriguingly, CDF-S XT2 lies in the outskirts of its star-forming host galaxy with a moderate offset from the galaxy centre, as short γ-ray bursts often do^15,16. The estimated event-rate density of similar X-ray transients, when corrected to the local value, is consistent with the event-rate density of binary neutron-star mergers that is robustly inferred from the detection of the gravitational-wave event GW170817.

Signatures of Quark-Hadron Phase Transitions in General-Relativistic Neutron-Star Mergers

Merging binaries of neutron-stars are not only strong sources of gravitational waves, but also have the potential of revealing states of matter at densities and temperatures not accessible in laboratories. A crucial and long-standing question in this context is whether quarks are deconfined as a result of the dramatic increase in density and temperature following the merger. We present the first fully general-relativistic simulations of merging neutron-stars including quarks at finite temperatures that can be switched off consistently in the equation of state. Within our approach, we can determine clearly what signatures a quark-hadron phase transition would leave in the gravitational-wave signal. We show that if after the merger the conditions are met for a phase transition to take place at several times nuclear saturation density, they would lead to a postmerger signal considerably different from the one expected from the inspiral, that can only probe the hadronic part of the equations of state, and to an anticipated collapse of the merged object. We also show that the phase transition leads to a very hot and dense quark core that, when it collapses to a black hole, produces a ringdown signal different from the hadronic one. Finally, in analogy with what is done in heavy-ion collisions, we use the evolution of the temperature and density in the merger remnant to illustrate the properties of the phase transition in a QCD phase diagram.

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.

Tidal Love numbers of neutron stars in f(R) gravity

The recent detection of gravitational waves from a neutron star merger was a significant step towards constraining the nuclear matter equation of state by using the tidal Love numbers (TLNs) of the merging neutron stars. Measuring or constraining the neutron star TLNs allows us in principle to exclude or constraint many equations of state. This approach, however, has the drawback that many modified theories of gravity could produce deviations from General Relativity similar to the deviations coming from the uncertainties in the equation of state. The first and the most natural step in resolving the mentioned problem is to quantify the effects on the TLNs from the modifications of General Relativity. With this motivation in mind, in the present paper we calculate the TLNs of (non-rotating) neutron stars in R 2 -gravity. More precisely, by solving numerically the perturbation equations, we calculate explicitly the polar and the axial l = 2 TLNs for three characteristic realistic equations of state and compare the results to General Relativity. Our results show that while the polar TLNs are slightly influenced by the R 2 modification of General Relativity, the axial TLNs can be several times larger (in terms of the absolute value) compared to the general relativistic case.

Two Novel Approaches to the Hadron-Quark Mixed Phase in Compact Stars

First-order phase transitions, such as the liquid-gas transition, proceed via formation of structures, such as bubbles and droplets. In strongly interacting compact star matter, at the crust-core transition but also the hadron-quark transition in the core, these structures form different shapes dubbed “pasta phases”. We describe two methods to obtain one-parameter families of hybrid equations of state (EoS) substituting the Maxwell construction that mimic the thermodynamic behaviour of pasta phase in between a low-density hadron and a high-density quark matter phase without explicitly computing geometrical structures. Both methods reproduce the Maxwell construction as a limiting case. The first method replaces the behaviour of pressure against chemical potential in a finite region around the critical pressure of the Maxwell construction by a polynomial interpolation. The second method uses extrapolations of the hadronic and quark matter EoS beyond the Maxwell point to define a mixing of both with weight functions bounded by finite limits around the Maxwell point. We apply both methods to the case of a hybrid EoS with a strong first order transition that entails the formation of a third family of compact stars and the corresponding mass twin phenomenon. For both models, we investigate the robustness of this phenomenon against variation of the single parameter: the pressure increment at the critical chemical potential that quantifies the deviation from the Maxwell construction. We also show sets of results for compact star observables other than mass and radius, namely the moment of inertia and the baryon mass.

Neutron Star Tidal Deformabilities Constrained by Nuclear Theory and Experiment

We confront observational data from gravitational wave event GW170817 with microscopic modeling of the cold neutron star equation of state. We develop and employ a Bayesian statistical framework that enables us to implement constraints on the equation of state from laboratory measurements of nuclei and state-of-the-art chiral effective field theory methods. The energy density functionals constructed from the posterior probability distributions are then used to compute consistently the neutron star equation of state from the outer crust to the inner core, assuming a composition consisting of protons, neutrons, electrons, and muons. In contrast to previous studies, we find that the 95% credibility range of predicted neutron star tidal deformabilities (136<Λ<519) for a 1.4 solar-mass neutron star is already consistent with the upper bound deduced from observations of the GW170817 event. However, we find that lower bounds on the neutron star tidal deformability will very strongly constrain microscopic models of the dense matter equation of state. We also demonstrate a strong correlation between the neutron star tidal deformability and the pressure of beta-equilibrated matter at twice saturation density.

New Constraints on Radii and Tidal Deformabilities of Neutron Stars from GW170817

We explore in a parameterized manner a very large range of physically plausible equations of state (EOSs) for compact stars for matter that is either purely hadronic or that exhibits a phase transition. In particular, we produce two classes of EOSs with and without phase transitions, each containing one million EOSs. We then impose constraints on the maximum mass (M<2.16  M_{⊙}) and on the dimensionless tidal deformability (Λ[over ˜]<800) deduced from GW170817, together with recent suggestions of lower limits on Λ[over ˜]. Exploiting more than 10^{9} equilibrium models for each class of EOSs, we produce distribution functions of all the stellar properties and determine, among other quantities, the radius that is statistically most probable for any value of the stellar mass. In this way, we deduce that the radius of a purely hadronic neutron star with a representative mass of 1.4  M_{⊙} is constrained to be 12.00<R_{1.4}/km<13.45 at a 2σ confidence level, with a most likely value of R[over ¯]_{1.4}=12.39  km; similarly, the smallest dimensionless tidal deformability is Λ[over ˜]_{1.4}>375, again at a 2σ level. On the other hand, because EOSs with a phase transition allow for very compact stars on the so-called "twin-star" branch, small radii are possible with such EOSs although not probable, i.e., 8.53<R_{1.4}/km<13.74 and R[over ¯]_{1.4}=13.06  km at a 2σ level, with Λ[over ˜]_{1.4}>35.5 at a 3σ level. Finally, since these EOSs exhibit upper limits on Λ[over ˜], the detection of a binary with a total mass of 3.4  M_{⊙} and Λ[over ˜]_{1.7}>461 can rule out twin-star solutions.

From hadrons to quarks in neutron stars: a review

In recent years our understanding of neutron stars has advanced remarkably, thanks to research converging from many directions. The importance of understanding neutron star behavior and structure has been underlined by the recent direct detection of gravitational radiation from merging neutron stars. The clean identification of several heavy neutron stars, of order two solar masses, challenges our current understanding of how dense matter can be sufficiently stiff to support such a mass against gravitational collapse. Programs underway to determine simultaneously the mass and radius of neutron stars will continue to constrain and inform theories of neutron star interiors. At the same time, an emerging understanding in quantum chromodynamics (QCD) of how nuclear matter can evolve into deconfined quark matter at high baryon densities is leading to advances in understanding the equation of state of the matter under the extreme conditions in neutron star interiors. We review here the equation of state of matter in neutron stars from the solid crust through the liquid nuclear matter interior to the quark regime at higher densities. We focus in detail on the question of how quark matter appears in neutron stars, and how it affects the equation of state. After discussing the crust and liquid nuclear matter in the core we briefly review aspects of microscopic quark physics relevant to neutron stars, and quark models of dense matter based on the Nambu-Jona-Lasinio framework, in which gluonic processes are replaced by effective quark interactions. We turn then to describing equations of state useful for interpretation of both electromagnetic and gravitational observations, reviewing the emerging picture of hadron-quark continuity in which hadronic matter turns relatively smoothly, with at most only a weak first order transition, into quark matter with increasing density. We review construction of unified equations of state that interpolate between the reasonably well understood nuclear matter regime at low densities and the quark matter regime at higher densities. The utility of such interpolations is driven by the present inability to calculate the dense matter equation of state in QCD from first principles. As we review, the parameters of effective quark models-which have direct relevance to the more general structure of the QCD phase diagram of dense and hot matter-are constrained by neutron star mass and radii measurements, in particular favoring large repulsive density-density and attractive diquark pairing interactions. We describe the structure of neutron stars constructed from the unified equations of states with crossover. Lastly we present the current equations of state-called 'QHC18' for quark-hadron crossover-in a parametrized form practical for neutron star modeling.

Gravitational-Wave Constraints on the Neutron-Star-Matter Equation of State

The detection of gravitational waves originating from a neutron-star merger, GW170817, by the LIGO and Virgo Collaborations has recently provided new stringent limits on the tidal deformabilities of the stars involved in the collision. Combining this measurement with the existence of two-solar-mass stars, we generate a generic family of neutron-star-matter equations of state (EOSs) that interpolate between state-of-the-art theoretical results at low and high baryon density. Comparing the results to ones obtained without the tidal-deformability constraint, we witness a dramatic reduction in the family of allowed EOSs. Based on our analysis, we conclude that the maximal radius of a 1.4-solar-mass neutron star is 13.6 km, and that the smallest allowed tidal deformability of a similar-mass star is Λ(1.4  M_{⊙})=120.