Stable Neutron Star Research Articles

Tight multimessenger constraints on the neutron star equation of state from GW170817 and a forward model for kilonova light-curve synthesis

ABSTRACT We present a rapid analytic framework for predicting kilonova light curves following neutron star (NS) mergers, where the main input parameters are binary-based properties measurable by gravitational wave detectors (chirp mass and mass ratio, orbital inclination) and properties dependent on the nuclear equation of state (tidal deformability, maximum NS mass). This enables synthesis of a kilonova sample for any NS source population, or determination of the observing depth needed to detect a live kilonova given gravitational wave source parameters in low latency. We validate this code, implemented in the public mosfit package, by fitting it to GW170817. A Bayes factor analysis overwhelmingly (B > 1010) favours the inclusion of an additional luminosity source in addition to lanthanide-poor dynamical ejecta during the first day. This is well fit by a shock-heated cocoon model, though differences in the ejecta structure, opacity or nuclear heating rate cannot be ruled out as alternatives. The emission thereafter is dominated by a lanthanide-rich viscous wind. We find the mass ratio of the binary is q = 0.92 ± 0.07 (90 per cent credible interval). We place tight constraints on the maximum stable NS mass, MTOV $=2.17^{+0.08}_{-0.11}$ M⊙. For a uniform prior in tidal deformability, the radius of a 1.4-M⊙ NS is R1.4 ∼ 10.7 km. Re-weighting with a prior based on equations of state that support our credible range in MTOV, we derive a final measurement R1.4 $=11.06^{+1.01}_{-0.98}$ km. Applying our code to the second gravitationally detected NS merger, GW190425, we estimate that an associated kilonova would have been fainter (by ∼0.7 mag at 1 d post-merger) and declined faster than GW170817, underlining the importance of tuning follow-up strategies individually for each GW-detected NS merger.

Equation of state and radial oscillations of neutron stars

We investigate radial oscillations of pure neutron stars and hybrid stars, employing equations of state of nuclear matter from Brueckner-Hartree-Fock theory, and of quark matter from the Dyson-Schwinger quark model, performing a Gibbs construction for the mixed phase in hybrid stars. We calculate the eigenfrequencies and corresponding oscillation functions. Our results for the zero points of the first-order radial oscillation frequencies give the maximum mass of stable neutron stars, consistent with the common criterion $dM/d\rho_c=0$. Possible observations of the radial oscillation frequencies could help to learn more about the equation of state, predict the maximum mass of neutron stars more precisely, and indicate the presence of quark matter.

Neutron stars phenomenology with scalar–tensor inflationary attractors

In this work we shall study the implications of a subclass of E -models cosmological attractors, namely of a -attractors, on hydrodynamically stable slowly rotating neutron stars. Specifically, we shall present the Jordan frame theory of the a -attractors, and by using a conformal transformation we shall derive the Einstein frame theory. We discuss the inflationary context of a -attractors in order to specify the allowed range of values for the free parameters of the model based on the latest cosmic-microwave-background-based Planck 2018 data. Accordingly, using the notation and physical units frequently used in theoretical astrophysics contexts, we shall derive the Tolman–Oppenheimer–Volkoff equations in the Einstein frame. Assuming a piecewise polytropic equation of state, the lowest density part of which shall be chosen to be the WFF1, or APR or the SLy EoS, we numerically solve the Tolman–Oppenheimer–Volkoff equations using a double shooting python-based “LSODA” numerical code. The resulting picture depends on the value of the parameter a characterizing the a -attractors. As we show, for large values of a , which do not produce a viable inflationary era, the M – R graphs are nearly identical to the general relativistic result, and these two are discriminated at large central densities values. Also, for large a -values, the WFF1 equation of state is excluded, due to the GW170817 constraints on the radius of an M ∼ 1 . 6 M ⊙ neutron star, which must be larger than R = 10 . 6 8 − 0 . 04 + 15 km and on the radius corresponding to the maximum mass which must be larger than R = 9 . 6 − 0 . 03 + 0 . 14 km. In addition, the small a cases produce larger masses and radii compared to the general relativistic case and are compatible with the GW170817 constraints on the radii of neutron stars. A notable feature is that as the parameter a decreases, the radii of the static hydrodynamically stable neutron stars increase. Our results indicate deep and not yet completely understood connections between non-minimal inflationary attractors and neutron stars phenomenology in scalar–tensor theory.

The electromagnetic and gravitational-wave radiations of X-ray transient CDF-S XT2

Binary neutron star (NS) mergers may result in remnants of supra-massive or even stable NS, which have been supported indirectly by observed X-ray plateau of some gamma-ray burst (GRB) afterglows. Recently, Xue et al. () discovered an X-ray transient CDF-S XT2 that is powered by a magnetar from merger of double NS via X-ray plateau and following stepper phase. However, the decay slope after the plateau emission is slightly larger than the theoretical value of spin-down in electromagnetic (EM) dominated by losing its rotation energy. In this paper, we assume that the feature of X-ray emission is caused by a supra-massive magnetar central engine for surviving thousands of seconds to collapse into a black hole. Within this scenario, we present the comparisons of the X-ray plateau luminosity, break time, and the parameters of magnetar between CDF-S XT2 and other short GRBs with internal plateau samples. By adopting the collapse time to constrain the equation of state (EOS), we find that three EOSs (GM1, DD2, and DDME2) are consistent with the observational data. On the other hand, if the most released rotation energy of magnetar is dominated by GW radiation, we also constrain the upper limit of ellipticity of NS for given EOS, and its range is [0.32-1.3] × 10−3. Its GW signal cannot be detected by Advanced LIGO or even for more sensitive Einstein Telescope in the future.

A Well Balanced Finite Volume Scheme for General Relativity

In this work we present a novel second order accurate well balanced (WB) finite volume (FV) scheme for the solution of the general relativistic magnetohydrodynamics (GRMHD) equations and the first order CCZ4 formulation (FO-CCZ4) of the Einstein field equations of general relativity, as well as the fully coupled FO-CCZ4 + GRMHD system. These systems of first order hyperbolic PDEs allow to study the dynamics of the matter and the dynamics of the space-time according to the theory of general relativity. The new well balanced finite volume scheme presented here exploits the knowledge of an equilibrium solution of interest when integrating the conservative fluxes, the nonconservative products and the algebraic source terms, and also when performing the piecewise linear data reconstruction. This results in a rather simple modification of the underlying second order FV scheme, which, however, being able to cancel numerical errors committed with respect to the equilibrium component of the numerical solution, substantially improves the accuracy and long-time stability of the numerical scheme when simulating small perturbations of stationary equilibria. In particular, the need for well balanced techniques appears to be more and more crucial as the applications increase their complexity. We close the paper with a series of numerical tests of increasing difficulty, where we study the evolution of small perturbations of accretion problems and stable TOV neutron stars. Our results show that the well balancing significantly improves the long-time stability of the finite volume scheme compared to a standard one.

Magnetic ergostars, jet formation, and gamma-ray bursts: Ergoregions versus horizons

We perform the first fully general relativistic, magnetohydrodynamic simulations of dynamically stable hypermassive neutron stars with and without ergoregions to assess the impact of ergoregions on launching magnetically--driven outflows. The hypermassive neutron stars are modeled by a compressible and causal equation of state and are initially endowed with a dipolar magnetic field extending from the stellar interior into its exterior. We find that, after a few Alfv\'en times, magnetic field lines in the ergostar (star that contains ergoregions) and the normal star have been tightly wound in both cases into a helical funnel within which matter begins to flow outward. The maximum Lorentz factor in the outflow is $\Gamma_L \sim 2.5$, while the force-free parameter holds at $B^2/8\pi\rho_0\lesssim 10$. These values are incompatible with highly relativistic, magnetically-driven outflows (jets) and short $\gamma$-ray bursts. We compare these results with those of a spinning black hole surrounded by a magnetized, massless accretion disk that launches a bona fide jet. Our simulations suggest that the Blandford-Znajek mechanism for launching relativistic jets only operates when a black hole is present, though the Poynting luminosity in all cases is comparable. Therefore, one cannot distinguish a magnetized, accreting black hole from a magnetized hypermassive neutron star in the so-called mass-gap based solely on the value of the observed Poynting luminosity. These results complement our previous studies of supramassive remnants and suggest that it would be challenging for either normal neutron stars or ergostars in a hypermassive state to be the progenitors of short $\gamma$-ray bursts.

What if the neutron star maximum mass is beyond ∼2.3 M⊙?

ABSTRACT By assuming the formation of a black hole soon after the merger event of GW170817, the maximum mass of non-rotating stable neutron star, MTOV ≃ 2.3 M⊙, is proposed by numerical relativity, but there is no solid evidence to rule out MTOV > 2.3 M⊙ from the point of both microphysical and astrophysical views. It is naturally expected that the equation of state (EOS) would become stiffer beyond a specific density to explain massive pulsars. We consider the possibility of EOSs with MTOV > 2.3 M⊙, investigating the stiffness and the transition density in a polytropic model, for two kinds of neutron stars (i.e. gravity-bound and strong-bound stars on surface). Only two parameters are input in both cases: (ρt, γ) for gravity-bound neutron stars, while (ρs, γ) for strong-bound strange stars, with ρt the transition density, ρs the surface density, and γ the polytropic exponent. In the matter of MTOV > 2.3 M⊙ for the maximum mass and 70 ≤ Λ1.4 ≤ 580 for the tidal deformability, it is found that the smallest ρt and γ should be ∼0.50 ρ0 and ∼2.65 for neutron stars, respectively, whereas for strange star, we have γ > 1.40 if ρs > 1.0 ρ0 (ρ0 is the nuclear saturation density). These parametric results could guide further research of the real EOS with any foundation of microphysics if a pulsar mass higher than 2.3 M⊙ is measured in the future, especially for an essential comparison of allowed parameter space between gravity-bound and strong-bound compact stars.

Stringent Search for Precursor Emission in Short GRBs from Fermi/GBM Data and Physical Implications

Abstract We perform a stringent search for precursor emission of short gamma-ray bursts (SGRBs) from the Fermi/GBM data and find 16 precursor events with ≳4.5σ significance. We find that the durations of the main SGRB emission ( ) and the precursor emission ( ), as well as the waiting time ( ) in between, are roughly comparable to each other, with ≈ 2.8 1.2 approximately satisfied for most cases except one significant outlier. We also perform spectral analyses to the precursors and SGRBs, and find that the spectra of precursor emission can be fitted with the blackbody, nonthermal cutoff power law and/or power-law models. We consider several possible models for precursor emission in SGRBs and find that the luminosity and spectral shape may be explained by the the shock breakout or the photospheric radiation of a fireball launched after the merger for thermal precursors, or magnetospheric interaction between two neutron stars prior to the merger for nonthermal precursors. For the fireball photospheric model, a matter-dominated jet is preferred and a constraint on the fireball Lorentz factor can be placed as Γ ∼ 30. For the magnetospheric interaction model, the jet launching mechanism may be constrained. In particular, those events with / ≫ 1 (e.g., GRB191221802) require the formation of a supramassive or stable neutron star after the merger, with the delay time defined by the timescale for an initially baryon-loaded jet to become magnetically dominated and relativistic.

Evidence for quark-matter cores in massive neutron stars

The theory governing the strong nuclear force—quantum chromodynamics—predicts that at sufficiently high energy densities, hadronic nuclear matter undergoes a deconfinement transition to a new phase of quarks and gluons1. Although this has been observed in ultrarelativistic heavy-ion collisions2,3, it is currently an open question whether quark matter exists inside neutron stars4. By combining astrophysical observations and theoretical ab initio calculations in a model-independent way, we find that the inferred properties of matter in the cores of neutron stars with mass corresponding to 1.4 solar masses (M⊙) are compatible with nuclear model calculations. However, the matter in the interior of maximally massive stable neutron stars exhibits characteristics of the deconfined phase, which we interpret as evidence for the presence of quark-matter cores. For the heaviest reliably observed neutron stars5,6 with mass M ≈ 2M⊙, the presence of quark matter is found to be linked to the behaviour of the speed of sound cs in strongly interacting matter. If the conformal bound {c}_{rm{s}}^{2}le 1/3 (ref. 7) is not strongly violated, massive neutron stars are predicted to have sizable quark-matter cores. This finding has important implications for the phenomenology of neutron stars and affects the dynamics of neutron star mergers with at least one sufficiently massive participant.

Universal properties of maximum-mass neutron stars: A new tool to explore superdense matter

I have demonstrated the existence of a tight correlation between the mass, radius, central density, and pressure of maximum-mass neutron stars modeled using diverse baryonic equations of state. A possible explanation for these correlations is provided. Simple analytic forms of such correlations are suggested and compared with observational constraints on the maximum mass of neutron stars and their radii. This gives a valuable tool to constrain maximum pressure and density that could be reached in stable neutron stars, assuming their equation of state is baryonic.

What Constraints on the Neutron Star Maximum Mass Can One Pose from GW170817 Observations?

Abstract The post-merger product of the first binary neutron star merger event detected in gravitational waves, GW170817, depends on neutron star equation of state (EoS) and is not well determined. We generally discuss the constraints one may pose on the maximum mass of a non-spinning neutron star, M TOV, based on the observations and some EoS-independent universal relations of rapidly spinning neutron stars. If the merger product is a black hole after a brief hypermassive neutron star (HMNS) phase, we derive at the 2σ (1σ) level. The cases for a massive neutron star (MNS), neither a supramassive neutron star (SMNS) nor even a stable neutron star (SNS) are also allowed by the data. We derive for the SMNS case and for the SNS case, at the 2σ (1σ) confidence level. In the MNS cases, we also discuss the constraints on the neutron star parameters (the dipolar magnetic field strength at the surface B p and the ellipticity ϵ) that affect the spin down history, by considering different MNS survival times, e.g., 300 s, 1 day, and 155 days after the merger, as suggested by various observational arguments. We find that once an SMNS is formed, without violating the electromagnetic observational constraints, there always exist a set of ( ) parameters that allow the SMNS to survive for 300 s, 1 day, 155 days, or even longer.

Why the Spacetime Embedding Incompressible Cores of Pulsars Must Be Conformally Flat?

The multi-messenger observations of the merger event in GW170817 did not rule out the possibility that the remnant might be a dynamically stable neutron star with $\mathcal{M}_{rm}\geq 2.69 \,\mathcal{M}_{\odot}.$ Based on this and other recent events, I argue that the universal maximum density hypothesis should be revived. Accordingly, the central densities in the cores of ultra-compact objects must be upper-limited by the critical density number $n_{cr},$ beyond which supradense nuclear matter becomes purely incompressible. Based on the spacetime-matter coupling in GR, it is shown that the topology of spacetime embedding incompressible quantum fluids with $n =n_{cr}$ must be Minkowski flat, which implies that spacetime at the background of ultra-compact objects should be of bimetric type.

On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations

In this paper we propose an extension of the generalized Lagrangian multiplier method (GLM) of Munz et al. [52,30], which was originally conceived for the numerical solution of the Maxwell and MHD equations with divergence-type involutions, to the case of hyperbolic PDE systems with curl-type involutions. The key idea here is to solve an augmented PDE system, in which curl errors propagate away via a Maxwell-type evolution system. The new approach is first presented on a simple model problem, in order to explain the basic ideas. Subsequently, we apply it to a strongly hyperbolic first order reduction of the CCZ4 formulation (FO-CCZ4) of the Einstein field equations of general relativity, which is endowed with 11 curl constraints. Several numerical examples, including the long-time evolution of a stable neutron star in anti-Cowling approximation, are presented in order to show the obtained improvements with respect to the standard formulation without special treatment of the curl involution constraints.The main advantages of the proposed GLM approach are its complete independence of the underlying numerical scheme and grid topology and its easy implementation into existing computer codes. However, this flexibility comes at the price of needing to add for each curl involution one additional 3 vector plus another scalar in the augmented system for homogeneous curl constraints, and even two additional scalars for non-homogeneous curl involutions. For the FO-CCZ4 system with 11 homogeneous curl involutions, this means that additional 44 evolution quantities need to be added.

Stability analysis of neutron stars in Palatini f(R, T) gravity

In this paper, we have studied the stability of neutron stars in the background of Palatini f(R, T) gravity. In this context, the static spherically symmetric geometry is considered which is assumed to be coupled with an isotropic matter configurations. The evolution of the system is considered with the help of Tolman–Oppenheimer–Volkoff equations and conformal transformations. We found the stable configurations of the spherical stars with some constraints.

A Pulsar Wind Nebula Embedded in the Kilonova AT 2017gfo Associated with GW170817/GRB 170817A

Abstract The first detected gravitational wave GW170817 from a binary neutron star merger is associated with an important optical transient AT 2017gfo, which is a direct observation of kilonova. Recent observations suggest that the remnant compact object of the binary neutron star merger associated with GW170817/GRB 170817A may be a stable long-lived magnetized neutron star. In this situation, there would be a pulsar wind nebula (PWN) embedded inside the dynamic ejecta. The PWN emission may be absorbed by the ejecta or leak out of the system. We study the effect of the PWN emission on the observed light curves and radiation spectra. Different from previous works, the absorption and leakage of the PWN emission are all involved in our model, where the absorption of the PWN emission heats up the ejecta and alters its radiation. It is found that the characteristic emission of the embedded PWN quickly evolves. For the multiband and long-term observations of AT 2017gfo, we find that the dynamic ejecta with a PWN emission can fit the observational data very well, especially for the light curves at t ∼ 5 days and those in the late phase. In addition, our model can naturally generate the thermal to nonthermal spectrum evolution of AT 2017gfo. Our fitting result suggests that a PWN is embedded in the AT 2017gfo.

Neutron Star Stability in Light of the Neutron Decay Anomaly.

A recent proposal suggests that experimental discrepancies on the lifetime of neutrons can be resolved if neutrons decay to dark matter. At the same time it has been demonstrated that such a decay mode would soften the nuclear equation of the state resulting in neutron stars with a maximum mass much below currently observed ones. In this Letter, we demonstrate that appropriate dark matter-baryon interactions can accommodate neutron stars with mass above two solar masses. We compare this stabilization mechanism to one based on dark matter self-interactions, finding that it is less sensitive to the details of the nuclear equation of state. We present a simple microscopic model realization of this mechanism.

Asymmetric dark stars and neutron star stability

We consider gravitationally bound states of asymmetric dark matter (ADM stars), and the impact of ADM capture on the stability of neutron stars. We derive and interpret the equation of state for ADM with both attractive and repulsive interactions, and solve the Tolman-Oppenheimer-Volkoff equations to find equilibrium sequences and maximum masses of ADM stars. Gravitational wave searches can utilize our solutions to model exotic compact objects (ECOs). Our results for attractive interactions differ substantially from those in the literature, where fermionic ADM with attractive self-interactions was employed to destabilize neutron stars more effectively than non-interacting fermionic ADM. By contrast, we argue that fermionic ADM with an attractive force is no more effective in destabilizing neutron stars than fermionic ADM with no self-interactions.

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 bursts1-4. 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 field5-8 (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 bursts9,10. 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 burst11,12. 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 do15,16. 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.

Deeply bound dibaryon is incompatible with neutron stars and supernovae

We study the effect of a dibaryon, S, in the mass range 1860 MeV < m_S < 2054 MeV, which is heavy enough not to disturb the stability of nuclei and light enough to possibly be cosmologically metastable. Such a deeply bound state can act as a baryon sink in regions of high baryon density and temperature. We find that the ambient conditions encountered inside a newly born neutron star are likely to sustain a sufficient population of hyperons to ensure that a population of S dibaryons can equilibrate in less than a few seconds. This would be catastrophic for the stability of neutron stars and the observation of neutrino emission from the proto-neutron star of Supernova 1987A over ~ O(10)s. A deeply bound dibaryon is therefore incompatible with the observed supernova explosion, unless the cross section for S production is severely suppressed.

Tidal deformability and other global parameters of compact stars with strong phase transitions

Context. Using parametric equations of state (relativistic polytropes and a simple quark bag model) to model dense-matter phase transitions, we study global, measurable astrophysical parameters of compact stars such as their allowed radii and tidal deformabilities. We also investigate the influence of stiffness of matter before the onset of the phase transitions on the parameters of the possible exotic dense phase. Aims. The aim of our study is to compare the parameter space of the dense matter equation of state permitting phase transitions to a sub-space compatible with current observational constraints such as the maximum observable mass, tidal deformabilities of neutron star mergers, radii of configurations before the onset of the phase transition, and to give predictions for future observations. Methods. We studied solutions of the Tolman-Oppenheimer-Volkoff equations for a flexible set of parametric equations of state, constructed using a realistic description of neutron-star crust (up to the nuclear saturation density), and relativistic polytropes connected by a density-jump phase transition to a simple bag model description of deconfined quark matter. Results. In order to be consistent with recent observations of massive neutron stars, a compact star with a strong high-mass phase transition cannot have a radius smaller than 12 km in the range of masses 1.2 − 1.6 M⊙. We also compare tidal deformabilities of stars with weak and strong phase transitions with the results of the GW170817 neutron star merger. Specifically, we study characteristic phase transition features in the Λ1 − Λ2 relation, and estimate the deviations of our results from the approximate formulæ for Λ∼ − R (M1) and Λ-compactness proposed in the literature. We find constraints on the hybrid equations of state to produce stable neutron stars on the twin branch. For the exemplary equations of state most of the high-mass twins occur for the minimum values of the density jump λ = 1.33 − 1.54; corresponding values of the square of the speed of sound are α = 0.7 − 0.37. We compare results with observations of gravitational waves and with the theoretical causal limit and find that the minimum radius of a twin branch is between 9.5 and 10.5 km, and depends on the phase transition baryon density. For these solutions the phase transition occurs below 0.56 fm−3.