Star Equation Research Articles

Interpreting the cosmic far-infrared background anisotropies using a gas regulator model

Cosmic far-infrared background (CFIRB) is a powerful probe of the history of star formation rate (SFR) and the connection between baryons and dark matter across cosmic time. In this work, we explore to which extent the CFIRB anisotropies can be reproduced by a simple physical framework for galaxy evolution, the gas regulator (bathtub) model. This model is based on continuity equations for gas, stars, and metals, taking into account cosmic gas accretion, star formation, and gas ejection. We model the large-scale galaxy bias and small-scale shot noise self-consistently, and we constrain our model using the CFIRB power spectra measured by Planck. Because of the simplicity of the physical model, the goodness of fit is limited. We compare our model predictions with the observed correlation between CFIRB and gravitational lensing, bolometric infrared luminosity functions, and submillimetre source counts. The strong clustering of CFIRB indicates a large galaxy bias, which corresponds to haloes of mass $10^{12.5} M_\odot$ at z=2, higher than the mass associated with the peak of the star formation efficiency. We also find that the far-infrared luminosities of haloes above $10^{12} M_\odot$ are higher than the expectation from the SFR observed in ultraviolet and optical surveys.

GW170817: Joint Constraint on the Neutron Star Equation of State from Multimessenger Observations

Abstract Gravitational waves detected from the binary neutron star (NS) merger GW170817 constrained the NS equation of state by placing an upper bound on certain parameters, describing the binary’s tidal interactions. We show that the interpretation of the UV/optical/infrared counterpart of GW170817 with kilonova models, combined with new numerical-relativity results, imply a complementary lower bound on the tidal deformability parameter. The joint constraints tentatively rule out both extremely stiff and soft NS equations of state.

Pulsar glitch dynamics

We discuss pulsar glitch dynamics from three different viewpoints: statistical description, neutron star equation of state description and finally an electromagnetic field description. For the latter, the pulsar glitch recovery times are the dissipation time constants of sheet surface currents created in response to the glitch-induced crustal magnetic field disruption. We mathematically derive these glitch time constants (Ohmic time constant and Hall sheet current time constant) from a perturbation analysis of the electromagnetic induction equation. Different crustal channels will carry the sheet surface current and their different electron densities determine the time constants.

Constraints on the equation of state of neutron star matter based on observations

Many calculations of the neutron star (NS) equation of state (EOS) have been performed over the years. Recent observations of NSs have begun to play an important role in finding the realistic EOS. In this paper, we compare mass–radius relations derived from various EOSs with observational data of NSs. In addition, we adjust EOSs to be consistent with observational data from NSs and employ Bayesian statistical analyses to obtain constraints on the EOS. Our results show that the EOS needs to be softened in the medium density region ([Formula: see text]–[Formula: see text], where [Formula: see text] is the saturation density) and to have a rapid change of stiffness around an energy density of [Formula: see text] 650 MeV/fm3.

Neutron star equation of state and uncertainty on the radius determination

The new generation of X-ray telescopes will provide simultaneous measurements of the radius and mass of a number of neutron stars (NSs), potentially constraining their equation of state (EoS). However the use of non-unified EoSs, that are based on different nuclear models for the crust and core, can introduce an uncertainty on the NS radius of the order of the precision expected from these instruments. Two solutions to this problem are presented. First a large number of unified EoSs and second an approximate approach to the NS crust that allows to obtain with a very large precision the relation between the NS mass and radius with no need to use an EoS for the crust. Correlations between the NS radius and nuclear parameters, which are properties of the EoS that can be indirectly measured in laboratory, are discussed. These open the possibility of constraining the NS radius with experiments on Earth. Finally, the appearance of hyperons in the core of NSs is examined. They are included in the EoS models consistently with available measurements on the hyperon properties. Because of the scarcity of these experimental data one can not exclude that hyperons appear at high densities in NSs in spite of the observations of massive NSs.

Mixed phase within the multi‐polytrope approach to high‐mass twins

We present a multi‐polytrope approach to describe high‐mass twins fulfilling chiral effective field theory estimations of the neutron star equation of state and test it against the appearance of mixed phases at the hadron–quark interface. In addition, we discuss astrophysical applications of this method and the expected future measurements that will further constrain neutron star matter and the understanding of the quantum chromodynamics phase diagram.

Lense-Thirring precession in ULXs as a possible means to constrain the neutron star equation of state

The presence of neutron stars in at least three ultraluminous X-ray sources is now firmly established and offers an unambiguous view of super-critical accretion. All three systems show long-timescale periods (60-80 days) in the X-rays and/or optical, two of which are known to be super-orbital in nature. Should the flow be classically super critical, i.e. the Eddington limit is reached locally in the disc (implying surface dipole fields that are sub-magnetar in strength), then the large scale-height flow can precess through the Lense-Thirring effect which could provide an explanation for the observed super-orbital periods. By connecting the details of the Lense-Thirring effect with the observed pulsar spin period, we are able to infer the moment-of-inertia and therefore equation-of-state of the neutron star without relying on the inclination of, or distance to the system. We apply our technique to the case of NGC 7793 P13 and demonstrate that stronger magnetic fields imply stiffer equations of state. We discuss the caveats and uncertainties, many of which can be addressed through forthcoming radiative magnetohydrodynamic (RMHD) simulations and their connection to observation.

Equation of State Dependence of Nonlinear Mode-tide Coupling in Coalescing Binary Neutron Stars

Abstract Recently, an instability due to the nonlinear coupling of p-modes to g-modes in tidally deformed neutron stars in coalescing binaries has been studied in some detail. The result is significant because it could influence the inspiral and leave an imprint on the gravitational wave signal that depends on the neutron star equation of state (EOS). Because of its potential importance, the details of the instability should be further elucidated and its sensitivity to the EOS should be investigated. To this end, we carry out a numerical analysis with six representative EOSs for both static and non-static tides. We confirm that the absence of the p-g instability under static tides, as well as its return under non-static tides, is generic across EOSs, and further reveal a new contribution to it that becomes important for moderately high-order p-g pairs (previous studies concentrated on very high order modes), whose associated coupling strength can vary by factors of ∼10–100 depending on the EOS. We find that, for stars with stiffer EOSs and smaller buoyancy frequencies, the instability onsets earlier in the inspiral and the unstable modes grow faster. These results suggest that the instability’s impact on the gravitational wave signal might be sensitive to the neutron star EOS. To fully assess this prospect, future studies will need to investigate its saturation as a function of the EOS and the binary parameters.

Quark-nuclear hybrid star equation of state with excluded volume effects

A two-phase description of the quark-nuclear matter hybrid equation of state that takes into account the effect of excluded volume in both the hadronic and the quark matter phases is introduced. The nuclear phase manifests a reduction of the available volume as density increases, leading to a stiffening of the matter. The quark matter phase displays a reduction of the effective string tension in the confining density functional from available volume contributions. The nuclear equation of state is based upon the relativistic density functional model DD2 with excluded volume. The quark matter is based upon a mean-field modification to the free fermi gas and will be discussed in greater detail. The interactions are decomposed into mean scalar and vector components. The scalar interaction is motivated by a string potential between quarks, whereas the vector interaction potential is motivated by higher order interactions of quarks leading to an increased stiffening at high densities. As an application, we consider matter under compact star constraints of electric neutrality and $\beta$-equilibrium. We obtain mass-radius relations for hybrid stars that form a third family, disconnected from the purely hadronic star branch, and fulfill the $2M_\odot$ constraint.

Spectral analysis of gravitational waves from binary neutron star merger remnants

In this work we analyze the gravitational wave signal from hypermassive neutron stars formed after the merger of binary neutron star systems, focusing on its spectral features. The gravitational wave signals are extracted from numerical relativity simulations of models already considered by De Pietri et al. [Phys. Rev. D 93, 064047 (2016)], Maione et al. [Classical Quantum Gravity 33, 175009 (2016)], and Feo et al. [Classical Quantum Gravity 34, 034001 (2017)], and allow us to study the effect of the total baryonic mass of such systems (from $2.4{M}_{\ensuremath{\bigodot}}$ to $3{M}_{\ensuremath{\bigodot}}$), the mass ratio (up to $q=0.77$), and the neutron star equation of state, in both equal and highly unequal mass binaries. We use the peaks we find in the gravitational spectrum as an independent test of already published hypotheses of their physical origin and empirical relations linking them with the characteristics of the merging neutron stars. In particular, we highlight the effects of the mass ratio, which in the past was often neglected. We also analyze the temporal evolution of the emission frequencies. Finally, we introduce a modern variant of Prony's method to analyze the gravitational wave postmerger emission as a sum of complex exponentials, trying to overcome some drawbacks of both Fourier spectra and least-squares fitting. Overall, the spectral properties of the postmerger signal observed in our simulation are in agreement with those proposed by other groups. More specifically, we find that the analysis of Bauswein and Stergioulas [Phys. Rev. D 91, 124056 (2015)] is particularly effective for binaries with very low masses or with a small mass ratio and that the mechanical toy model of Takami et al. [Phys. Rev. D 91, 064001 (2015)] provides a comprehensive and accurate description of the early stages of the postmerger.

Searching for X-ray Pulsations from Neutron Stars Using NICER

AbstractThe Neutron Star Interior Composition Explorer (NICER) presents an exciting new capability for exploring the modulation properties of X-ray emitting neutron stars, including large area, low background, extremely precise absolute event time stamps, superb low-energy response and flexible scheduling. The Pulsation Searches and Multiwavelength Coordination working group has designed a 2.5 Ms observing program to search for emission and characterize the modulation properties of about 30 known or suspected neutron star sources across a number of source categories. A key early goal will be to search for pulsations from millisecond pulsars that might exhibit thermal pulsations from the surface suitable for pulse profile modeling to constrain the neutron star equation of state. In addition, we will search for pulsations from transitional millisecond pulsars, isolated neutron stars, low-mass X-ray binaries (LMXBs), accretion-powered millisecond pulsars, central compact objects and other sources. We present our science plan and initial results from the first months of the NICER mission, including the discovery of pulsations from the millisecond pulsar J1231–1411.

Neutron star equation of state and uncertainty on the radius determination

AbstractSimultaneous measurements of the radius and mass of neutron stars (NSs) are expected from the new generation of X-ray telescopes, potentially constraining the NS equation of state (EoS). However using ‘non-unified’ EoSs with the ones for the core and the crust not based on the same nuclear model can introduce an uncertainty on the radius as large as the precision expected from these instruments. I present two solutions to this problem: a large collection of unified EoSs and an approximate and yet precise approach that, with no need of a crust EoS, provides the relation between the NS mass and radius. I discuss correlations between the NS radius and nuclear parameters, possibly allowing to constrain the NS radius with experiments on Earth. Finally, I show that in spite of the observation of massive NSs, one can not exclude that hyperons appear at high densities in NSs due to the scarcity of the available experimental data.

Relativistic Disc Line: A Tool to Constrain Neutron Star Equation of State Models

Relativistic iron K$\alpha$ spectral emission line from the inner disc of a neutron star low-mass X-ray binary (LMXB) was first detected in 2007. This discovery opened up new ways to probe strong gravity and dense matter. The past decade has seen detections of such a line from many neutron star LMXBs, and confirmation of this line from the same source with several X-ray satellites. These have firmly established the new field of relativistic disc line from neutron star systems in only ten years. Fitting the shape of such a line with an appropriate general relativistic model provides the accretion disc inner edge radius to the stellar mass ratio. In this review, we briefly discuss how an accurate measurement of this ratio with a future larger area X-ray instrument can be used to constrain neutron star equation of state models.

Simultaneous Constraints on the Mass and Radius of Aql X–1 from Quiescence and X-Ray Burst Observations

Abstract The measurement of neutron star mass and radius is one of the most direct ways to distinguish between various dense matter equations of state. The mass and radius of accreting neutron stars hosted in low-mass X-ray binaries can be constrained by several methods, including photospheric radius expansion from type I X-ray bursts and from quiescent spectra. In this paper, we apply for the first time these two methods simultaneously to constrain the mass and radius of Aql X–1. The quiescent spectra from Chandra and XMM-Newton, and photospheric radius expansion bursts from RXTE are used. The determination of the mass and radius of Aql X–1 is also used to verify the consistency between the two methods and to narrow down the uncertainties of the neutron star mass and radius. It is found that the distance to Aql X–1 should be in the range of 4.0–5.75 kpc, based on the overlapping confidence regions between photospheric radius expansion burst and quiescent spectra methods. In addition, we show that the mass and radius determined for the compact star in Aql X–1 are compatible with strange star equations of state and conventional neutron star models.

Hypernuclei and massive neutron stars

(Abridged) The recent measurement of the mass of two $2\, M_\odot$ pulsars has raised the question whether such large masses allow for the existence of exotic degrees of freedom, such as hyperons, inside neutron stars. In the present work we will investigate how the existing hypernuclei properties may constrain the neutron star equation of state and confront the neutron star maximum masses obtained with equations of state calibrated to hypernuclei properties with the astrophysical $2\,M_\odot$ constraint. The study is performed using a relativistic mean field approach to describe both the hypernuclei and the neutron star equations of state. A set of five models consistent with $2\,M_\odot$ for a purely nucleonic composition are employed. The $\Lambda$-meson couplings are determined for all the models considered. Hyperonic stars with the complete baryonic octet are studied, restricting the coupling of the $\Sigma$ and $\Xi$ hyperons to the $\omega-$, $\rho-$ and $\sigma-$mesons due to the lack of experimental data, and maximum star masses calculated for unified equations of state. We conclude that the currently available hypernuclei experimental data and the lack of constraints on the asymmetric equation of state of nuclear matter at high densities do not allow to further constrain the neutron star matter equation of state using the recent $2\, M_\odot$ observations. It is also shown that the $\Lambda$ potential in symmetric nuclear matter takes a value $\sim 30-32$ MeV at saturation for the $g_{\omega \Lambda}$ coupling given by the SU(6) symmetry, close to values generally used in the literature. However, the $\Lambda$ potential in $\Lambda$ matter varies between -16 and -8 MeV taking for vector mesons couplings the SU(6) values, at variance with generally employed values between $-1$ and $-5$ MeV.

Coherent-State Approach for Majorana Representation**Supported by the National Fundamental Research Program of China under Grant No. 2013CBA01502, the National Natural Science Foundation of China under Grant Nos. 11575027, 11475146, and 11405008, the Fundamental Research Funds for the Central Universities under Grant No. 2017FZA3005, and the Plan for Scientific and Technological Development of Jilin Province under Grant No. 20160520173JH

By representing a quantum state and its evolution with the Majorana stars on the Bloch sphere, the Majorana representation provides us an intuitive way to study a physical system with SU(2) symmetry. In this work, based on coherent states, we propose a method to establish the generalization of Majorana representation for a general symmetry. By choosing a generalized coherent state as a reference state, we give a more general Majorana representation for both finite and infinite systems and the corresponding star equations are given. Using this method, we study the squeezed vacuum states for three different symmetries, Heisenberg–Weyl, SU(2) and SU(1,1), and express the effect of squeezing parameter on the distribution of stars. Furthermore, we also study the dynamical evolution of stars for an initial coherent state driven by a nonlinear Hamiltonian, and find that at a special time point, the stars are distributed on two orthogonal large circles.

Twin stars within the SU(3) chiral quark-meson model

We present new stable solutions of the Tolman Oppenheimer Volkoff equations for quark stars using a quark matter equation of state based on the SU(3) Quark-Meson model that exhibits the onset of the chiral phase transition. These new solutions appear as two stable branches in the mass-radius relation allowing for so called twin stars, i.e. two stable quark star solutions with the same mass, but distinctly different radii. We find solutions which are compatible with causality, the stability conditions of dense matter, the astrophysical constraints of the rotation of the millisecond pulsar PSR J1748-2446ad and the 2$M_{\odot}$ pulsar mass constraint.

Upper limit set by causality on the tidal deformability of a neutron star

A principal goal of gravitational-wave astronomy is to constrain the neutron star equation of state (EOS) by measuring the tidal deformability of neutron stars. The tidally induced departure of the waveform from that of point-particle (or spinless binary black hole (BBH)) increases with the stiffness of the EOS. We show that causality (the requirement that the speed of sound is less than the speed of light for a perfect fluid satisfying a one-parameter equation of state) places an upper bound on tidal deformability as a function of mass. Like the upper mass limit, the limit on deformabity is obtained by using an EOS with $v_{sound} = c$ for high densities and matching to a low density (candidate) EOS at a matching density of order nuclear saturation density. We use these results and those of [B.D. Lackey et al., Phys. Rev. D 89, 043009 (2014)] to estimate the resulting upper limit on the gravitational-wave phase shift of a black hole-neutron star (BHNS) binary relative to a BBH. Even for assumptions weak enough to allow an maximum mass of $4\ M_\odot$ (a match at nuclear saturation density to an unusually stiff low-density candidate EOS), the upper limit on dimensionless tidal deformability is stringent. It leads to a still more stringent estimated upper limit on the maximum tidally induced phase shift prior to merger. We comment in an appendix on the relation between causality, the condition $v_{sound} < c$, and the condition $dp/d\epsilon < 1$ for the effective EOS governing the equilibrium star.

Neutron stars in screened modified gravity: Chameleon versus dilaton

We consider the scalar field profile around relativistic compact objects such as neutron stars for a range of modified gravity models with screening mechanisms of the chameleon and Damour-Polyakov types. We focus primarily on inverse power law chameleons and the environmentally dependent dilaton as examples of both mechanisms. We discuss the modified Tolman-Oppenheimer-Volkoff equation and then implement a relaxation algorithm to solve for the scalar profiles numerically. We find that chameleons and dilatons behave in a similar manner and that there is a large degeneracy between the modified gravity parameters and the neutron star equation of state. This is exemplified by the modifications to the mass-radius relationship for a variety of model parameters.

Measuring neutron star tidal deformability with Advanced LIGO: A Bayesian analysis of neutron star-black hole binary observations

The pioneering discovery of gravitational waves (GWs) by Advanced LIGO has ushered us into an era of observational GW astrophysics. Compact binaries remain the primary target sources for GW observation, of which neutron star-black hole (NSBH) binaries form an important subset. GWs from NSBH sources carry signatures of (a) the tidal distortion of the neutron star by its companion black hole during inspiral, and (b) its potential tidal disruption near merger. In this paper, we present a Bayesian study of the measurability of neutron star tidal deformability ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}\ensuremath{\propto}(R/M{)}_{\mathrm{NS}}^{5}$ using observation(s) of inspiral-merger GW signals from disruptive NSBH coalescences, taking into account the crucial effect of black hole spins. First, we find that if nontidal templates are used to estimate source parameters for an NSBH signal, the bias introduced in the estimation of nontidal physical parameters will only be significant for loud signals with signal-to-noise ratios greater than $\ensuremath{\simeq}30$. For similarly loud signals, we also find that we can begin to put interesting constraints on ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}$ (factor of 1--2) with individual observations. Next, we study how a population of realistic NSBH detections will improve our measurement of neutron star tidal deformability. For an astrophysically likely population of disruptive NSBH coalescences, we find that 20--35 events are sufficient to constrain ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}$ within $\ifmmode\pm\else\textpm\fi{}25%--50%$, depending on the neutron star equation of state. For these calculations we assume that LIGO will detect black holes with masses within the astrophysical mass gap. In case the mass gap remains preserved in NSBHs detected by LIGO, we estimate that approximately 25% additional detections will furnish comparable ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}$ measurement accuracy. In both cases, we find that it is the loudest 5--10 events that provide most of the tidal information, and not the combination of tens of low-SNR events, thereby facilitating targeted numerical-GR follow-ups of NSBHs. We find these results encouraging, and recommend that an effort to measure ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}$ be planned for upcoming NSBH observations with the LIGO-Virgo instruments.