Matter In Compact Stars Research Articles

Estimating the masses of three neutron stars by twin kilohertz quasi-periodic oscillations and innermost stable circular orbits: constraining equations of state

ABSTRACT We test the magnetohydrodynamics (MHD) model derived by Shi, Zhang and Li by the like-standard deviations of the twin kilohertz (kHz) quasi-periodic oscillation (QPO) frequencies when the modes of the MHD waves in the MHD model are recalculated. A group of approximate equations derived from the MHD equations in the MHD model are proposed. Consequently, the dependence of the twin kHz QPO frequencies on several neutron star (NS) parameters is determined by the approximate equations. Based on the selection criterion that NS parameters corresponding to the minimum like-standard deviation are the most reasonable parameters, the masses of the three NSs in 4U 0614+09, 4U 1636–53 and 4U 1608–52 are estimated as M < 2.60 M⊙, 2.00 M⊙ < M < 2.31 M⊙ and 2.17 M⊙ < M < 2.62 M⊙, respectively. According to these NS masses, some equations of state for the nuclear matter in compact stars can be ruled out.

A mixing interpolation method to mimic pasta phases in compact star matter

We present a new method to interpolate between two matter phases that allows for a description of mixed phases and can be used, e.g., for mimicking transitions between pasta structures occurring in the crust as well as in the inner core of compact stars. This interpolation method is based on assuming switch functions that are used to define a mixture of subphases while fulfilling constraints of thermodynamic stability. The width of the transition depends on a free parameter, the pressure increment relative to the critical pressure of a Maxwell construction. As an example we present a trigonometric function ansatz for the switch function together with a pressure increment during the transition. We note that the resulting mixed phase equation of state bears similarities with the appearance of substitutional compounds in neutron star crusts and with the sequence of transitions between different pasta phases in the hadron-to-quark matter transition. We apply this method to the case of a hadron-to-quark matter transition and test the robustness of the compact star mass twin phenomenon against the appearance of pasta phases modelled in this way.

Sound velocity and tidal deformability in compact stars

The sound velocity $v_s$ and dimensionless tidal deformability $\Lambda$ are analyzed using the pseudo-conformal model we developed before. In contrast to the conclusion obtained in the previous works in the literature, our model with the upper bound of the sound velocity $v_s = 1/\sqrt{3}$, the so-called conformal sound velocity, set in at a { density relevant to compact stars} $\gsim 2 n_0$ where $n_0$ is the normal nuclear matter density, can accommodate {\it all} presently established nuclear matter and compact-star properties including the maximum star-mass constraint $ \simeq 2.3 M_\odot$. This observation is associated with a possible emergence of pseudoconformal structure in compact star matter---in which the trace of energy-momentum tensor is a nearly density-independent nonzero constant---brought in by a topology change at $2.0 \lesssim n_{1/2}/n_0 \lesssim 4.0$ commensurate with a possible change of degrees of freedom from hadrons.

Pseudoconformal equation of state in compact-star matter from topology change and hidden symmetries of QCD

We construct a new effective field theory approach to the equation of state (EoS), dubbed pseudo-confomal model “PCM, for nuclear and compact star matter entirely in terms of effective hadron degrees of freedom. The possible transition at $n\!\sim$(2-4)$n_0$ (where $n_0$ is the normal nuclear matter density) from hadron degrees of freedom to strongly-coupled quark degrees of freedom, giving rise to a soft-to-hard changeover in the EoS that can accommodate the massive stars observed, is effectuated by the topology change at $n_{1/2}\mathrel{\rlap{\lower3pt\hbox{\hskip1pt$∼$}}\raise1pt\hbox{$>$}}2n_0$ from skyrmions to half-skyrmions without involving local order-parameter fields. The mechanism exploits possible emergence of hidden scale and local symmetries of QCD at high density, leading to a precocious “pseudo-conformal sound velocity $v_{\rm~s}^2=1/3$ (in unit of $c=1$) for $n\mathrel{\rlap{\lower3pt\hbox{\hskip1pt$∼$}}\raise1pt\hbox{$>$}}3n_0$. The resulting prediction signals a drastic departure from standard nuclear many-body theory in the density regime involved in the massive stars. We suggest that the tidal deformability implemented in gravitational waves coming from coalescing neutron stars in LIGO/Virgo-type observations could pin down the location of the topology change density $n_{1/2}$.

Topology change and nuclear symmetry energy in compact-star matter

We show that the cusp-like structure in the nuclear symmetry energy, a consequence of topology change, visible in the skyrmion lattice description of dense matter is extremely robust. It is present in the Skyrme model -- with the pion field only -- and is left unscathed by massive degrees of freedom such as the vector mesons $\rho$ and $\omega$ and also the scalar meson introduced as a dilaton. It leads to the emergence of parity-doubling at the skyrmion-half-skyrmion transition and impacts on the nuclear symmetry energy "wilderness" landscape, weeding out roughly half of the wilderness. It is shown that a pseudo-conformal sound velocity arises at a precocious density at which the cusp is formed. It is suggested that the topology change, being robust, could impact on the tidal deformability observed in gravity waves

Equations of state for astrophysical simulations from generalized relativistic density functionals

Simulations of astrophysical events such as binary neutron star mergers or core-collapse supernovae require detailed information on the properties of compact-star matter at finite temperatures. In this work new general-purpose equations of state are constructed. They are based on generalized relativistic density functionals with density-dependent couplings and include a full set of nuclei. The tables are provided in the CompOSE format. Predictions of thermodynamic quantities and the chemical composition of matter are compared with existing models of similar type along curves of constant entropy per nucleon. The focus is on effects of the employed cluster dissociation mechanism and the density dependence of the symmetry energy. A problem with the extraction of data from equation of state tables is identified.

Exact solution of anisotropic compact stars via mass function

The interest in studying relativistic compact objects play an important role in modern astrophysics with an aim to understand several astrophysical issues. It is therefore natural to ask for internal structure and physical properties of specific classes of compact star for astrophysical observable, and we obtain a class of new relativistic solutions with anisotropic distribution of matter for compact stars. More specifically, stellar models, described by the anisotropic fluid, establish a relation between metric potentials and generating a specific form of mass function are explicitly constructed within the framework of General Relativity. New solutions that can be used to model compact objects which adequately describe compact strange star candidates like SMC X-1, Her X-1 and 4U 1538-52, with observational data taken from Gangopadhyay et al. [1]. As a possible astrophysical application the obtained solution could explain the physics of self-gravitating objects, might be useful for strong-field regimes where data are currently inadequate.

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.

Competition between delta isobars and hyperons and properties of compact stars

The Δ-isobar degrees of freedom are included in the covariant density functional (CDF) theory to study the equation of state (EoS) and composition of dense matter in compact stars. In addition to Δ's we include the full octet of baryons, which allows us to study the interplay between the onset of delta isobars and hyperonic degrees of freedom. Using both the Hartree and Hartree–Fock approximation we find that Δ's appear already at densities slightly above the saturation density of nuclear matter for a wide range of the meson–Δ coupling constants. This delays the appearance of hyperons and significantly affects the gross properties of compact stars. Specifically, Δ's soften the EoS at low densities but stiffen it at high densities. This softening reduces the radius of a canonical 1.4M⊙ star by up to 2 km for a reasonably attractive Δ potential in matter, while the stiffening results in larger maximum masses of compact stars. We conclude that the hypernuclear CDF parametrizations that satisfy the 2M⊙ maximum mass constraint remain valid when Δ isobars are included, with the important consequence that the resulting stellar radii are shifted toward lower values, which is in agreement with the analysis of neutron star radii.

On parametrized cold dense matter equation-of-state inference

Constraining the equation of state of cold dense matter in compact stars is a major science goal for observing programmes being conducted using X-ray, radio, and gravitational wave telescopes. We discuss Bayesian hierarchical inference of parametrised dense matter equations of state. In particular we generalise and examine two inference paradigms from the literature: (i) direct posterior equation of state parameter estimation, conditioned on observations of a set of rotating compact stars; and (ii) indirect parameter estimation, via transformation of an intermediary joint posterior distribution of exterior spacetime parameters (such as gravitational masses and coordinate equatorial radii). We conclude that the former paradigm is not only tractable for large-scale analyses, but is principled and flexible from a Bayesian perspective whilst the latter paradigm is not. The thematic problem of Bayesian prior definition emerges as the crux of the difference between these paradigms. The second paradigm should in general only be considered as an ill-defined approach to the problem of utilising archival posterior constraints on exterior spacetime parameters; we advocate for an alternative approach whereby such information is repurposed as an approximative likelihood function. We also discuss why conditioning on a piecewise-polytropic equation of state model - currently standard in the field of dense matter study - can easily violate conditions required for transformation of a probability density distribution between spaces of exterior (spacetime) and interior (source matter) parameters.

Merging strangeon stars

The state of supranuclear matter in compact stars remains puzzling, and it is argued that pulsars could be strangeon stars. What would happen if binary strangeon stars merge? This kind of merger could result in the formation of a hyper-massive strangeon star, accompanied by bursts of gravitational waves and electromagnetic radiation (and even a strangeon kilonova explained in the paper). The tidal polarizability of binary strangeon stars is different from that of binary neutron stars, because a strangeon star is self-bound on the surface by the fundamental strong force while a neutron star by the gravity, and their equations of state are different. Our calculation shows that the tidal polarizability of merging binary strangeon stars is favored by GW170817. Three kinds of kilonovae (i.e., of neutron, quark and strangeon) are discussed, and the light curve of the kilonova AT 2017 gfo following GW170817 could be explained by considering the decaying strangeon nuggets and remnant star spin-down. Additionally, the energy ejected to the fireball around the nascent remnant strangeon star, being manifested as a gamma-ray burst, is calculated. It is found that, after a prompt burst, an X-ray plateau could follow in a timescale of 102 − 103 s. Certainly, the results could be tested also by further observational synergies between gravitational wave detectors (e.g., Advanced LIGO) and X-ray telescopes (e.g., the Chinese HXMT satellite and eXTP mission), and especially if the detected gravitational wave form is checked by peculiar equations of state provided by the numerical relativistical simulation.

Revisiting the equation of state of hybrid stars in the Dyson-Schwinger equation approach to QCD

We investigate the equation of state(EoS) and the effect of the hadron-quark phase transition of strong interaction matter in compact stars. The hadron matter is described with the relativistic mean field theory,and the quark matter is described with the Dyson-Schwinger equation approach of QCD. The complete EoS of the hybrid star matter is constructed with not only the Gibbs construction but also the 3-window interpolation. The mass-radius relation of hybrid stars is also investigated. We find that, although the EoSs of both the hadron matter with hyperon and $\Delta$-baryon and the quark matter are generally softer than that of the nucleon matter, the 3-window interpolation construction may provide an EoS stiff enough for a hybrid star with mass exceeding 2$M_{\odot}^{}$ and, in turn, solve the so called "hyperon puzzle".

Strange matter in compact stars

We discuss possible scenarios for the existence of strange matter in compact stars. The appearance of hyperons leads to a hyperon puzzle in ab-initio approaches based on effective baryon-baryon potentials but is not a severe problem in relativistic mean field models. In general, the puzzle can be resolved in a natural way if hadronic matter gets stiffened at supersaturation densities, an effect based on the quark Pauli quenching between hadrons. We explain the conflict between the necessity to implement dynamical chiral symmetry breaking into a model description and the conditions for the appearance of absolutely stable strange quark matter that require both, approximately masslessness of quarks and a mechanism of confinement. The role of strangeness in compact stars (hadronic or quark matter realizations) remains unsettled. It is not excluded that strangeness plays no role in compact stars at all. To answer the question whether the case of absolutely stable strange quark matter can be excluded on theoretical grounds requires an understanding of dense matter that we have not yet reached.

Dense and hot matter in compact stars and heavy-ion collisions

We discuss the effect of exotic particles in neutron star matter and the corresponding impact on gross properties of neutron stars within effective models for the strong interaction. Particularly, for the quark-hadron parity-doublet model, we show results for compact star properties and discuss the phase structure of the model and its possible relevance for heavy-ion collision phenomenology.

Compact star matter: EoS with new scaling law

In this paper, we present a simple discussion on the properties of compact stars using an EoS obtained in effective field theory anchored on scale and hidden-local symmetric Lagrangian endowed with topology change and a unequivocal prediction on the deformation of the compact star, that could be measured in gravitational waves. The objective is not to offer a superior or improved EoS for compact stars but to confront with a forthcoming astrophysical observable, the given model formulated in what is considered to be consistent with the premise of quantum chromodynamics (QCD). The model so obtained is found to satisfactorily describe the observation of a two-solar mass neutron star [P. B. Demorest et al., Nature 467 (2010) 1081, J. Antoniadis et al., Science 340 (2013) 1233232] with a minimum number of parameters. Specifically, the observable we are considering in this paper is the tidal deformability parameter [Formula: see text] (equivalently the Love number [Formula: see text]), which affects gravitational wave forms at the late period of inspiral stage. The forthcoming aLIGO and aVirgo observations of gravitational waves from binary neutron star system will provide a valuable guidance for arriving at a better understanding of highly compressed baryonic matter.

Scale-invariant hidden local symmetry, topology change, and dense baryonic matter

When scale symmetry is implemented into hidden local symmetry in low-energy strong interactions to arrive at a scale-invariant hidden local symmetric (HLS) theory, the scalar $f_0(500)$ may be interpreted as pseudo-Nambu-Goldstone (pNG) boson, i.e., dilaton, of spontaneously broken scale invariance, joining the pseudo-scalar pNG bosons $\pi$ and the matter fields $V=(\rho,\omega)$ as relevant degrees of freedom. Implementing the skyrmion-half-skyrmion transition predicted at large $N_c$ in QCD at a density roughly twice the nuclear matter density found in the crystal simulation of dense skyrmion matter, we determine the intrinsically density-dependent (IDD) "bare parameters" of the scale-invariant HLS Lagrangian matched to QCD at a matching scale $\Lambda_M$. The resulting effective Lagrangian, with the parameters scaling with the density of the system, is applied to nuclear matter and dense baryonic matter relevant to massive compact stars by means of the double-decimation renormalization-group $V_{lowk}$ formalism. We satisfactorily post-dict the properties of normal nuclear matter and more significantly {\it predict} the EoS of dense compact-star matter that quantitatively accounts for the presently available data coming from both the terrestrial and space laboratories. We interpret the resulting structure of compact-star matter as revealing how the combination of hidden-scale symmetry and hidden local symmetry manifests itself in compressed baryonic matter.

Scalar pseudo-Nambu-Goldstone boson in nuclei and dense nuclear matter

The notion that the scalar listed as $f_0 (500)$ in the particle data booklet is a pseudo-Nambu-Goldstone (NG) boson of spontaneously broken scale symmetry, explicitly broken by a small departure from an infrared fixed point, is explored in nuclear dynamics. That notion which puts the scalar -- that we shall identify as a "dilaton" -- on the same footing as the pseudo-scalar pseudo-NG bosons, i.e., octet $\pi$, while providing a simple explanation for the $\Delta I=1/2$ rule for kaon decay, generalizes the standard chiral perturbation theory (S$\chi$PT) to "scale chiral perturbation theory," denoted $\chi$PT$_\sigma$, with {\it one infrared mass scale for both symmetries}, with the $\sigma$ figuring as a chiral singlet NG mode in non-strange sector. Applied to nuclear dynamics, it is seen to provide possible answers to various hitherto unclarified nuclear phenomena such as the success of one-boson-exchange potentials (OBEP), the large cancellation of strongly attractive scalar potential by strongly repulsive vector potential in relativistic mean field theory of nuclear systems and in-medium QCD sum rules, the interplay of the dilaton and the vector meson $\omega$ in dense skyrmion matter, the BPS skyrmion structure of nuclei accounting for small binding energies of medium-heavy nuclei, and the suppression of hyperon degrees of freedom in compact-star matter.

Dark compact planets

We investigate compact objects formed by dark matter admixed with ordinary matter made of neutron-star matter and white-dwarf material. We consider non-self annihilating dark matter with an equation of state given by an interacting Fermi gas. We find new stable solutions, dark compact planets, with Earth-like masses and radii from a few Km to few hundred Km for weakly interacting dark matter which are stabilized by the mutual presence of dark matter and compact star matter. For the strongly interacting dark matter case, we obtain dark compact planets with Jupiter-like masses and radii of few hundred Km. These objects could be detected by observing exoplanets with unusually small radii. Moreover, we find that the recently observed $2\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$ pulsars set limits on the amount of dark matter inside neutron stars which is, at most, $1{0}^{\ensuremath{-}6}\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$.

Elastic properties of polycrystalline dense matter

Abstract Elastic properties of the solid regions of neutron star crusts and white dwarfs play an important role in theories of stellar oscillations. Matter in compact stars is presumably polycrystalline and, since the elastic properties of single crystals of such matter are very anisotropic, it is necessary to relate elastic properties of the polycrystal to those of a single crystal. We calculate the effective shear modulus of polycrystalline matter with randomly oriented crystallites using a self-consistent theory that has been very successful in applications to terrestrial materials and show that previous calculations overestimate the shear modulus by approximately 28 per cent.

Nucleating quark droplets in the core of magnetars

To assess the possibility of homogeneous nucleation of quark matter in magnetars, we investigate the formation of chirally symmetric droplets in a cold and dense environment in the presence of an external magnetic field. As a framework, we use the one-loop effective potential of the two-flavor quark-meson model. Within the thin-wall approximation, we extract all relevant nucleation parameters and provide an estimate for the typical time scales for the chiral phase conversion in magnetized compact star matter. We show how the critical chemical potential, critical radius, correlation length and surface tension are affected, and how their combination to define the nucleation time seems to allow for nucleation of quark droplets in magnetar matter even for not so small values of the surface tension.