Self-bound Stars Research Articles

Constraining exotic compact stars composed of bosonic and fermionic dark matter with gravitational wave events

ABSTRACTWe investigate neutron star–black hole (NS–BH) merger candidates as a test for compact exotic objects. Using the events GW190814, GW200105, and GW200115 measured by the LIGO-Virgo collaboration, which represent a broad profile of the masses in the NS mass spectrum; we demonstrate the constraining power for the parameter spaces of compact stars consisting of dark matter for future measurements. We consider three possible cases of dark matter stars: self-interacting, purely bosonic or fermionic dark matter stars, stars consisting of a mixture of interacting bosonic and fermionic matter as well as the limiting case of self-bound stars. We find that the scale of those hypothetical objects are dominated by the one of the strong interaction. The presence of fermionic dark matter requires a dark matter particle of the GeV mass scale, while the bosonic dark matter particle mass can be arbitrarily large or small. In the limiting case of a self-bound constant speed of sound parametrization, we find that the vacuum energy of those configurations has to be similar to the one of QCD.

Heavy-quark effects on cold quark matter and self-bound stars

The heavy-quark effects on the equation of state for cold and dense quark matter are obtained from perturbative QCD, yielding observables parametrized only by the renormalization scale. In particular, we investigate the thermodynamics of charm quark matter under the constraints of β equilibrium and electric charge neutrality in a region of densities where perturbative QCD is, in principle, much more reliable. Finally, we analyze the stability of charm stars, which might be realized as a new branch of ultradense hybrid compact stars, and find that such self-bound stars are unstable under radial oscillations.

G -mode oscillations in hybrid stars: A tale of two sounds

We study the principal core g-mode oscillation in hybrid stars containing quark matter and find that they have an unusually large frequency range ($\approx$ 200 - 600 Hz) compared to ordinary neutron stars or self-bound quark stars of the same mass. Theoretical arguments and numerical calculations that trace this effect to the difference in the behaviour of the equilibrium and adiabatic sound speeds in the mixed phase of quarks and nucleons are provided. We propose that the sensitivity of core g-mode oscillations to non-nucleonic matter in neutron stars could be due to the presence of a mixed quark-nucleon phase. Based on our analysis, we conclude that for binary mergers where one or both components may be a hybrid star, the fraction of tidal energy pumped into resonant g-modes in hybrid stars can exceed that of a normal neutron star by a factor of 2-3, although resonance occurs during the last stages of inspiral. A self-bound star, on the other hand, has a much weaker tidal overlap with the g-mode. The cumulative tidal phase error in hybrid stars, $\Delta\phi\cong$ 0.5 rad, is comparable to that from tides in ordinary neutron stars, presenting a challenge in distinguishing between the two cases. However, should the principal g-mode be excited to sufficient amplitude for detection in a post-merger remnant with quark matter in its interior, its frequency would be a possible indication for the existence of non-nucleonic matter in neutron stars.

Distinct classes of compact stars based on geometrically deduced equations of state

We have computed the properties of compact objects like neutron stars based on equation of state (EOS) deduced from a core–envelope model of superdense stars. Such superdense stars have been studied by solving Einstein’s equation based on pseudo-spheroidal and spherically symmetric spacetime geometry. The computed star properties are compared with those obtained based on nuclear matter EOSs. From the mass–radius ([Formula: see text]–[Formula: see text]) relationship obtained here, we are able to classify compact stars in three categories: (i) highly compact self-bound stars that represents exotic matter compositions with radius lying below 9[Formula: see text]km; (ii) normal neutron stars with radius between 9 to 12[Formula: see text]km and (iii) soft matter neutron stars having radius lying between 12 to 20[Formula: see text]km. Other properties such as Keplerian frequency, surface gravity and surface gravitational redshift are also computed for all the three types. This work would be useful for the study of highly compact neutron like stars having exotic matter compositions.

Comparison among three types of relativistic charged anisotropic fluid spheres for self-bound stars

The number of exact solutions for spherically symmetric anisotropic fluid spheres is derived. And the relativistic model of an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself, such as electrically charged bare strange stars is also investigated. Among the three models, Heintzmann and Durgapal IV, and V permit a simple method that provide bounds on the maximum possible mass of compact electrically charged self-bound stars, and numerically exhibit that the maximum compactness and mass increase in the presence of an electric field and anisotropic pressure. Based on analytic models developed in this work, it has been compared to investigate which one is better than the others; the values of some pertinent physical quantities have been considered by assuming the estimated masses and radii of some well-known potential strange star candidates like Vela X-1, Cen X-3, PSR J1903+327 and EXO 1785-248. This analysis depends on several mathematical assumptions.

Differentially rotating strange star in general relativity

Rapidly and differentially rotating compact stars are believed to be formed in binary neutron star merger events, according to both numerical simulations and the multi-messenger observation of GW170817. The lifetime and evolution of such a differentially rotating star, is tightly related to the observations in the post-merger phase. Various studies on the maximum mass of differentially rotating neutron stars have been done in the past, most of which assume the so-called $j$-const law as the rotation profile inside the star and consider only neutron star equations of state. In this paper, we extend the studies to strange star models, as well as to a new rotation profile model. Significant differences are found between differentially rotating strange stars and neutron stars, with both differential rotation laws. A moderate differential rotation rate for neutron stars is found to be too large for strange stars, resulting in a rapid drop in the maximum mass as the differential rotation degree is increased further from $\hat{A}\sim2.0$, where $\hat{A}$ is a parameter characterizing the differential rotation rate for $j$-const law. As a result the maximum mass of a differentially rotating self-bound star drops below the uniformly rotating mass shedding limit for a reasonable degree of differential rotation. The continuous transition to the toroidal sequence is also found to happen at a much smaller differential rotation rate and angular momentum than for neutron stars. In spite of those differences, $\hat{A}$-insensitive relation between the maximum mass for a given angular momentum is still found to hold, even for the new differential rotation law. Astrophysical consequences of these differences and how to distinguish between strange star and neutron star models with future observations are also discussed.

Compact stars with strongly coupled quark matter in a strong magnetic field

Some time ago we derived from the QCD Lagrangian an equation of state (EOS) for cold quark matter which can be considered an improved version of the MIT bag model EOS. Compared to the latter, our equation of state reaches higher values of the pressure at comparable baryon densities. This feature is due to perturbative corrections and also to nonperturbative effects. Later we applied this EOS to the study of compact stars, discussing the absolute stability of quark matter and computing the mass-radius relation for self-bound (strange) stars. We found maximum masses of the sequences with more than two solar masses, in agreement with recent experimental observations. In the present work we include the magnetic field in the equation of state and study how it changes the stability conditions and the mass-radius curves.

Universality and stationarity of the I-Love relation for self-bound stars

The emergence of the I-Love-Q relations, revealing that the moment of inertia, the tidal Love number (deformability) and the spin-induced quadrupole moment of compact stars are, to high accuracy, interconnected in a universal way disregarding the wide variety of equations of state (EOSs) of dense matter, has attracted much interest recently. However, the physical origin of these relations is still a debatable issue. In the present paper, we focus on the I-Love relation for self-bound stars (SBSs) such as incompressible stars and quark stars. We formulate perturbative expansions for the moment of inertia, the tidal Love number (deformability) and the I-Love relation of SBSs. By comparing the respective I-Love relations of incompressible stars and a specific kind of SBSs, we show analytically that the I-Love relation is, to relevant leading orders in stellar compactness, stationary with respect to changes in the EOS about the incompressible limit. Hence, the universality of the I-Love relation is indeed attributable to the proximity of compact stars to incompressible stars, and the stationarity of the relation as unveiled here. We also discover that the moment of inertia and the tidal deformability of a SBS with finite compressibility are, to leading order in compactness, equal to their counterparts of an incompressible star with an adjusted compactness, thus leading to a novel explanation for the I-Love universal relation.

Some new Wyman–Leibovitz–Adler type static relativistic charged anisotropic fluid spheres compatible to self-bound stellar modeling

In this work some families of relativistic anisotropic charged fluid spheres have been obtained by solving the Einstein–Maxwell field equations with a preferred form of one of the metric potentials, and suitable forms of electric charge distribution and pressure anisotropy functions. The resulting equation of state (EOS) of the matter distribution has been obtained. Physical analysis shows that the relativistic stellar structure for the matter distribution considered in this work may reasonably model an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself (e.g., electrically charged bare strange stars). Furthermore these models permit a simple method of systematically fixing bounds on the maximum possible mass of cold compact electrically charged self-bound stars. It has been demonstrated, numerically, that the maximum compactness and mass increase in the presence of an electric field and anisotropic pressures. Based on the analytic models developed in this present work, the values of some relevant physical quantities have been calculated by assuming the estimated masses and radii of some well-known potential strange star candidates like PSR J1614-2230, PSR J1903+327, Vela X-1, and 4U 1820-30.

Well Behaved Charge Analogues of Wyman-Adler Exact Solution for a Self-Bound Star

The exact analytical Wyman-Adler’s relativistic solution describing the interior of a charged spherical strange star candidate is found under the assumption and existence of two parameters K and m. The interior self-bound star matter, pressure, energy density and the adiabatic sound speed are represented in terms of simple algebraic function. The analytic solution depicts a unique static charged configuration of quark matter with radius R~9 km and total mass M~2.5M¬¬⊙. And try to investigate the velocity of sound approximately 1/√3 which is similar to the attitude of SQM (Strange Quark matter). Based on analytic model in the recent work, the applicable values of physical quantities have been calculated by accepting the estimated masses and radii of some well-known strange star candidates like PSR J1903+327, Her X-1, Cen X-3, EXO 1785-248. The equation of state of the charge matter distribution may play a major role in the study of the interior structure of highly compact charge stellar object in astrophysical study.

Some Exact Relativistic Models of Electrically Charged Self-bound Stars

In continuation of recent work done by the present authors (Int. J. Theor. Phys. 2013, doi: 10.1007/s10773-013-1538-y , hereafter paper I) some new exact families of static spherically symmetric perfect fluid solution of Einstein–Maxwell gravitational field equations are presented. These solutions and the corresponding equations of state, presented in parametric form, may be astrophysically significant in constructing relativistic stellar models of electrically charged self-bound stars.

Self-bound interacting QCD matter in compact stars

The quark gluon plasma (QGP) at zero temperature and high baryon number is a system that may be present inside compact stars. It is quite possible that this cold QGP shares some relevant features with the hot QGP observed in heavy ion collisions, being also a strongly interacting system. In a previous work we have derived from the QCD Lagrangian an equation of state (EOS) for the cold QGP, which can be considered an improved version of the MIT bag model EOS. Compared to the latter, our equation of state reaches higher values of the pressure at comparable baryon densities. This feature is due to perturbative corrections and also to non-perturbative effects. Here we apply this EOS to the study of neutron stars, discussing the absolute stability of quark matter and computing the mass-radius relation for self-bound (strange) stars. The maximum masses of the sequences exceed two solar masses, in agreement with the recently measured values of the mass of the pulsar PSR J1614-2230, and the corresponding radii around 10-11 km.

Relativistic Cowling approximation for fluid oscillation modes of color superconducting self-bound stars

AbstractThe investigation of the quasi-normal modes of oscillation of compact stars can reveal much information about their equation of state and internal structure mainly through the analysis of the expected emission of gravitational waves. In this work we study non-radial oscillation modes of strange stars consisting of color superconducting quark matter. We focus on the fundamental and pressure oscillation modes within the frame of the Cowling approximation. We discuss the observable features that may allow a differentiation among hadronic stars, strange stars, and strange stars with color superconductivity.

Equation of state of a dense and magnetized fermion system

The equation of state of a system of fermions in a uniform magnetic field is obtained in terms of the thermodynamic quantities of the theory by using functional methods. It is shown that the breaking of the O(3) rotational symmetry by the magnetic field results in a pressure anisotropy, which leads to the distinction between longitudinal- and transverse-to-the-field pressures. A criterion to find the threshold field at which the asymmetric regime becomes significant is discussed. This threshold magnetic field is shown to be the same as the one required for the pure field contribution to the energy and pressures to be of the same order as the matter contribution. A graphical representation of the field-dependent anisotropic equation of state of the fermion system is given. Estimates of the upper limit for the inner magnetic field in self-bound stars, as well as in gravitationally bound stars with inhomogeneous distributions of mass and magnetic fields, are also found.

Self-bound CFL stars in binary systems: Are they “hidden” among the black hole candidates?

The identification of black holes is one of the most important tasks of modern astrophysics. Candidates have been selected among binary stars based on a high mass function, and seriously considered when the lower mass limit exceeds ∼3 M� . More recently the absence of (type I) thermonuclear bursts has been advanced as an additional criterion in favor of the black hole interpretation, since the absence of a solid surface naturally precludes the accumulation and ignition of accreting material. We discuss in this Letter the possibility that self-bound stars made of CFL-paired quarks mimic the behavior of at least the low-mass end black holes as a result of: a) higher maximum masses than ordinary neutron stars, b) low steady luminosities due to the bare surface properties, and c) impossibility of generating type I bursts because of the complete absence of normal matter crusts at their surfaces. These features caution against a positive identification of event horizons based on the lack of bursts.

Kaon Condensation in Hyperonic Matter and Structure of Neutron Stars

The effects of kaon condensates on the equation of state (EOS) in hyperonic matter, where hyperons (A, Σ - ) are mixed in the ground state of neutron-star matter, are investigated. In the fully-developed phase of kaon condensation, it is shown that the EOS is much softened due to the s-wave kaon-baryon interactions as well as due to the hyperon-mixing. As a result, the energy of the system has a local minimum, which leads to a metastable self-bound kaon-condensed star in addition to a kaon-condensed star obtained by Maxwell's construction. The lifetime of the metastable state of the kaon-condensed bound star is estimated.

QUARK–DIQUARK MATTER EQUATION OF STATE AND COMPACT STAR STRUCTURE

We present the equation of state (EOS) of quark-diquark matter in the quark mass-density-dependent model. The region of the 2-D parameter space inside which this quark-diquark matter is stable against diquark disassembling and hadronization is determined. Motivated by observational data suggesting a high compactness of some neutron stars (NS) we present models based on the present EOS and compare the results with those obtained with previous works addressing a quark-diquark composition based on the MIT Bag model. We show that very compact self-bound stars (yet having ≥ 1M⊙) are allowed by our EOS even if the diquark itself is unbound.

QUARK–DIQUARK EQUATIONS OF STATE MODELS: THE ROLE OF INTERACTIONS

Recent observational data suggests a high compacticity (the quotient M/R) of some "neutron" stars. Motivated by these works we revisit models based on quark–diquark degrees of freedom and address the question of whether that matter is stable against diquark disassembling and hadronization within the different models. We find that equations of state modeled as effective λϕ4 theories do not generally produce stable self-bound matter and are not suitable for constructing very compact star models, that is the matter would decay into neutron matter. We also discuss some insights obtained by including hard sphere terms in the equation of state to model repulsive interactions. We finally compare the resulting equations of state with previous models and emphasize the role of the boundary conditions at the surface of compact self-bound stars, features of a possible normal crust of the latter and related topics.

From quark stars to hybrid stars

We show the possible existence of compact stars having a surface composed of a mixed phase of quarks and hadrons. This scenario can be realized both for self-bound stars, satisfying the so-called Witten-Bodmer hypothesis, and for gravitationally bound stars. This class of solutions of the Tolman-Oppenheimer-Volkoff equation can be obtained in all the models we discuss, within a physically acceptable range of values of the model parameters.

Fast pulsars, variational bounds, other facets of compact stars

We derive a limit on the rotation period of a gravitationally bound star that is analogous to Ruffini's mass limit for a neutron star. We discuss the impact of gravitational radiation-reaction instabilities. The condition that self-bound stars can rotate faster is derived. The present status of searches for fast pulsars is reviewed. The composition of neutron stars is discussed in the context of nuclear and hypernuclear constraints. The phase transition from hadron to quark phase in the interior of dense neutron stars is discussed properly accounting for the fact that this first order phase transition involves two conserved charges. Hybrid stars are then described.