Context.
Neutron stars are currently studied with an rising number of electromagnetic and gravitational-wave observations, which will ultimately allow us to constrain the dense matter equation of ...state and understand the physical processes at work within these compact objects. Neutron star global parameters, such as the mass and radius, can be used to obtain the equation of state by directly inverting the Tolman-Oppenheimer-Volkoff equations. Here, we investigate an alternative approach to this procedure.
Aims.
The aim of this work is to study the application of the artificial neural networks guided by the autoencoder architecture as a method for precisely reconstructing the neutron star equation of state, using their observable parameters: masses, radii, and tidal deformabilities. In addition, we study how well the neutron star radius can be reconstructed using only the gravitational-wave observations of tidal deformability, that is, using quantities that are not related in any straightforward way.
Methods.
The application of an artificial neural network in the equation-of-state reconstruction exploits the non-linear potential of this machine learning model. Since each neuron in the network is basically a non-linear function, it is possible to create a complex mapping between the input sets of observations and the output equation-of-state table. Within the supervised training paradigm, we construct a few hidden-layer deep neural networks on a generated data set, consisting of a realistic equation of state for the neutron star crust connected with a piecewise relativistic polytropes dense core, with its parameters representative of state-of-the art realistic equations of state.
Results.
We demonstrate the performance of our machine-learning implementation with respect to the simulated cases with a varying number of observations and measurement uncertainties. Furthermore, we study the impact of the neutron star mass distributions on the results. Finally, we test the reconstruction of the equation of state trained on parametric polytropic training set using the simulated mass–radius and mass–tidal-deformability sequences based on realistic equations of state. Neural networks trained with a limited data set are capable of generalising the mapping between global parameters and equation-of-state input tables for realistic models.
Context. The discovery of a 2 M⊙ neutron star provided a robust constraint for the theory of exotic dense matter, bringing into question the existence of strange baryons in the interiors of neutron ...stars. Although many theories fail to reproduce this observational result, several equations of state containing hyperons are consistent with it. Aims. We study global properties of stars using equations of state containing hyperons, and compare them to those without hyperons to find similarities, differences, and limits that can be compared with the astrophysical observations. Methods. Rotating, axisymmetric, and stationary stellar configurations in general relativity are obtained, and their global parameters are studied. Results. Approximate formulæ describing the behavior of the maximum and minimum stellar mass, compactness, surface redshifts, and moments of inertia as functions of spin frequency are provided. We also study the thin disk accretion and compare the spin-up evolution of stars with different moments of inertia.
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) Λ ∼ − R ( M 1 ) $ \tilde{\Lambda}-R(M_1) $ 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.
The uncertainties in neutron star (NS) radii and crust properties due to our limited knowledge of the equation of state (EOS) are quantitatively analysed. We first demonstrate the importance of a ...unified microscopic description for the different baryonic densities of the star. If the pressure functional is obtained matching a crust and a core EOS based on models with different properties at nuclear matter saturation, the uncertainties can be as large as $\sim 30\%$ for the crust thickness and $4\%$ for the radius. Necessary conditions for causal and thermodynamically consistent matchings between the core and the crust are formulated and their consequences examined. A large set of unified EOS for purely nucleonic matter is obtained based on 24 Skyrme interactions and 9 relativistic mean-field nuclear parametrizations. In addition, for relativistic models 17 EOS including a transition to hyperonic matter at high density are presented. All these EOS have in common the property of describing a $2\;M_\odot$ star and of being causal within stable NS. A span of $\sim 3$ km and $\sim 4$ km is obtained for the radius of, respectively, $1.0\;M_\odot$ and $2.0\;M_\odot$ star. Applying a set of nine further constraints from experiment and ab-initio calculations the uncertainty is reduced to $\sim 1$ km and $2$ km, respectively. These residual uncertainties reflect lack of constraints at large densities and insufficient information on the density dependence of the EOS near the nuclear matter saturation point. The most important parameter to be constrained is shown to be the symmetry energy slope $L$ which exhibits a linear correlation with the stellar radius, particularly for masses $\sim 1.0\;M_\odot$. Potential constraints on $L$, the NS radius and the EOS from observations of thermal states of NS are also discussed. Abriged
Context. Rapidly rotating neutron stars are an ideal laboratory to test models of matter at high densities. In particular, the maximum rotation frequency of a neutron star depends on the equation of ...state and can be used to test models of the interior. However, observations of the spin distribution of rapidly rotating neutron stars show evidence for a lack of stars spinning at frequencies higher than f ≈ 700 Hz, well below the predictions of theoretical equations of state. This has generally been taken as evidence of an additional spin-down torque operating in these systems, and it has been suggested that gravitational wave torques may be operating and be linked to a potentially observable signal. Aims. We aim to determine whether additional spin-down torques (possibly due to gravitational wave emission) are necessary, or if the observed limit of f ≈ 700 Hz could correspond to the Keplerian (mass-shedding) break-up frequency for the observed systems, and is simply a consequence of the currently unknown state of matter at high densities. Methods. Given our ignorance with regard to the true equation of state of matter above nuclear saturation densities, we make a minimal physical assumption and only demand causality, that is, that the speed of sound in the interior of the neutron star should be lower than or equal to the speed of light c. We then connected our causally limited equation of state to a realistic microphysical crustal equation of state for densities below nuclear saturation density. This produced a limiting model that gave the lowest possible maximum frequency, which we compared to observational constraints on neutron star masses and frequencies. We also compared our findings with the constraints on the tidal deformability obtained in the observations of the GW170817 event. Results. We rule out centrifugal breakup as the mechanism preventing pulsars from spinning faster than f ≈ 700 Hz, as the lowest breakup frequency allowed by our causal equation of state is f ≈ 1200 Hz. A low-frequency cutoff, around f ≈ 800 Hz could only be possible when we assume that these systems do not contain neutron stars with masses above M ≈ 2 M⊙. This would have to be due either to selection effects, or possibly to a phase transition in the interior of the neutron star that leads to softening at high densities and a collapse to either a black hole or a hybrid star above M ≈ 2 M⊙. Such a scenario would, however, require a somewhat unrealistically stiff equation of state for hadronic matter, in tension with recent constraints obtained from gravitational wave observations of a neutron star merger.
Context. The existence of 2 M⊙ pulsars puts very strong constraints on the equation of state (EOS) of neutron stars (NSs) with hyperon cores, which can be satisfied only by special models of hadronic ...matter. The radius-mass relation for these models is sufficiently specific that it could be subjected to an observational test with future X-ray observatories. Aims. We want to study the impact of the presence of hyperon cores on the radius-mass relation for NS. We aim to find out how, and for which particular stellar mass range, a specific relation R(M), where M is the gravitational mass, and R is the circumferential radius, is associated with the presence of a hyperon core. Methods. We consider a set of 14 theoretical EOS of dense matter, based on the relativistic mean-field approximation, allowing for the presence of hyperons in NSs. We also discuss a recent EOS based on non-relativistic G-matrix theory yielding NSs with hyperonic cores and M> 2M⊙. We seek correlations between R(M) and the stiffness of the EOS below the hyperon threshold needed to pass the 2 M⊙ test. Results. For NS masses 1.0 <M/M⊙< 1.6, we get R> 13 km, because of a very stiff pre-hyperon segment of the EOS. At nuclear density (n0 = 0.16 fm-3), the pressure is significantly higher than a robust upper bound obtained recently using chiral effective field theory. Conclusions. If massive NSs do have a sizable hyperon core, then according to current models the radii for M = 1.0 − 1.6 M⊙ are necessarily >13 km. If, on the contrary, a NS with a radius R(obs)< 12 km is observed in this mass domain, then sizable hyperon cores in NSs, as we model them now, are ruled out. Future X-ray missions with <5% precision for a simultaneous M and R measurement will have the potential to solve the problem with observations of NSs. Irrespective of this observational test, present EOS allowing for hyperons that fulfill condition Mmax> 2 M⊙ yield a pressure at nuclear density that is too high relative to up-to-date microscopic calculations of this quantity.
•Gravitational wave detected on 09.14.2015 resulted from a merger of two black holes.•Gamma ray burst that could be related with GW150914 was observed by Fermi satellite.•Collapsing massive star and ...a black hole in a close binary could lead to the event.•GRB was powered by a weak neutrino flux produced in the remnant matter.•Low spin and kick velocity of the merged black hole are found in our simulations.
Data from the Fermi Gamma-ray Burst Monitor satellite observatory suggested that the recently discovered gravitational wave source, a pair of two coalescing black holes, was related to a gamma-ray burst. The observed high-energy electromagnetic radiation (above 50 keV) originated from a weak transient source and lasted for about 1 s. Its localization is consistent with the direction to GW150914. We speculate about the possible scenario for the formation of a gamma-ray burst accompanied by the gravitational-wave signal. Our model invokes a tight binary system consisting of a massive star and a black hole which leads to the triggering of a collapse of the star’s nucleus, the formation of a second black hole, and finally to the binary black hole merger. For the most-likely configuration of the binary spin vectors with respect to the orbital angular momentum in the GW150914 event, the recoil speed (kick velocity) acquired by the final black hole through gravitational wave emission is of the order of a few hundred km/s and this might be sufficient to get it closer to the envelope of surrounding material and capture a small fraction of matter from the remnant of the host star. The gamma-ray burst is produced by the accretion of this remnant matter onto the final black hole. The moderate spin of the final black hole suggests that the gamma-ray burst jet is powered by weak neutrino emission rather than the Blandford–Znajek mechanism, and hence explains the low power available for the observed GRB signal.
Aims. We explore the implications of a strong first-order phase transition region in the dense matter equation of state in the interiors of rotating neutron stars, and the resulting creation of two ...disjoint families of neutron-star configurations (the so-called high-mass twins). Methods. We numerically obtained rotating, axisymmetric, and stationary stellar configurations in the framework of general relativity, and studied their global parameters and stability. Results. The instability induced by the equation of state divides stable neutron star configurations into two disjoint families: neutron stars (second family) and hybrid stars (third family), with an overlapping region in mass, the high-mass twin-star region. These two regions are divided by an instability strip. Its existence has interesting astrophysical consequences for rotating neutron stars. We note that it provides a natural explanation for the rotational frequency cutoff in the observed distribution of neutron star spins, and for the apparent lack of back-bending in pulsar timing. It also straightforwardly enables a substantial energy release in a mini-collapse to another neutron-star configuration (core quake), or to a black hole.
Rapidly rotating neutron stars are promising sources of continuous gravitational wave radiation for the LIGO and Virgo interferometers. The majority of neutron stars in our galaxy have not been ...identified with electromagnetic observations. All-sky searches for isolated neutron stars offer the potential to detect gravitational waves from these unidentified sources. The parameter space of these blind all-sky searches, which also cover a large range of frequencies and frequency derivatives, presents a significant computational challenge. Different methods have been designed to perform these searches within acceptable computational limits. Here we describe the first benchmark in a project to compare the search methods currently available for the detection of unknown isolated neutron stars. The five methods compared here are individually referred to as the PowerFlux, sky Hough, frequency Hough, Einstein@Home, and time domain F-statistic methods. We employ a mock data challenge to compare the ability of each search method to recover signals simulated assuming a standard signal model. We find similar performance among the four quick-look search methods, while the more computationally intensive search method, Einstein@Home, achieves up to a factor of two higher sensitivity. We find that the absence of a second derivative frequency in the search parameter space does not degrade search sensitivity for signals with physically plausible second derivative frequencies. We also report on the parameter estimation accuracy of each search method, and the stability of the sensitivity in frequency and frequency derivative and in the presence of detector noise.
Aims. We calculate Keplerian (mass shedding) configurations of rigidly rotating neutron stars and strange stars with crusts. We check the validity of the empirical formula for Keplerian frequency, ...fK, proposed by Lattimer & Prakash, $f_{\rm K}(M)=C\; (M/M_\odot)^{1/2}(R/10~{\rm km})^{-3/2}$, where M is the (gravitational) mass of the Keplerian configuration, R is the (circumferential) radius of the non-rotating configuration of the same gravitational mass, and $C=1.04~$kHz. Methods. Numerical calculations are performed using precise 2D codes based on the multi-domain spectral methods. We use a representative set of equations of state (EOSs) of neutron stars and quark stars. Results. We show that the empirical formula for $f_{\rm K}(M)$ holds within a few percent for neutron stars with realistic EOSs, provided $0.5~M_\odot<M<0.9~M_{\rm max}^{\rm stat}$, where $M_{\rm max}^{\rm stat}$ is the maximum allowable mass of non-rotating neutron stars for an EOS, and $C=C_{\rm NS}=1.08~$kHz. Similar precision is obtained for strange stars with $0.5~M_\odot<M<0.9~M_{\rm max}^{\rm stat}$. For maximal crust masses we obtain $C_{\rm SS}=1.15$ kHz, and the value of CSS is not very sensitive to the crust mass. All our Cs are significantly larger than the analytic value from the relativistic Roche model, $C_{\rm Roche}=1.00$ kHz. For $0.5~M_\odot<M<0.9~M_{\rm max}^{\rm stat}$, the equatorial radius of the Keplerian configuration of mass M, $R_{\rm K}(M)$, is, to a very good approximation, proportional to the radius of the non-rotating star of the same mass, $R_{\rm K}(M)=a\;R(M)$, with $a_{\rm NS}\approx a_{\rm SS} \approx 1.44$. The value of aSS is very weakly dependent on the mass of the crust of the strange star. Both a values are smaller than the analytic value $a_{\rm Roche}=1.5$ from the relativistic Roche model.
PDF
