Mass Limit For Neutron Stars Research Articles

Do we need dense matter equation of state in curved spacetime for neutron stars?

Neutron stars are regarded as natural laboratories for the study of dense strong interaction matter. The equation of state (EoS) of dense matter computed in flat spacetime is used to predict the structure of neutron stars by solving the Tolman-Oppenheimer-Volkoff (TOV) equation. Recently, it has been reported that the curved spacetime effect or specifically gravitational time dilation effect on the EoS of dense matter leads to a significant increase of the maximum mass limit of neutron stars [Phys. Rev. D \textbf{104}, 123005 (2021) and J. Cosmol. Astropart. Phys. 02 (2021) 026]. However, in this work, we show that to study the hydrostatic equilibrium of dense matter within the framework of general relativity and relativistic fluid dynamics, the grand canonical EoS of dense matter, $p(T,\mu)$, should be the same as that computed in flat spacetime, otherwise it is not consistent with local thermodynamic relations and energy-momentum conservation of the fluid. The gravitation influences the pressure $p$ only through enhancing the temperature $T$ and the chemical potential $\mu$, known as Tolman's law and Klein's law. We rewrite the TOV equation as an alternative version so that the grand canonical EoS computed by using field theoretical methods can be used as a direct input. This may provide a tool to study the grand canonical EoS of dense matter via deep learning.

Inverse chameleon mechanism and mass limits for compact stars

As is well known, there are various mass limits for compact stars. For example, the maximum mass for non-rotating white dwarfs is given by the famous Chandrasekhar limit about 1.4 M ☉ (solar masses). Although the mass limit for neutron stars is not so clear to date, one of the widely accepted values is about 2.1 M ☉. Recently, challenges to these mass limits appeared. Motivated by the super-Chandrasekhar mass white dwarfs with masses up to 2.4 ∼ 2.8 M ☉, and compact objects (probably neutron stars) in the mass gap (from 2.5 M ☉ or 3 M ☉ to 5 M ☉) inferred from gravitational waves detected by LIGO/Virgo in the third observing run (O3), we reconsider the mass limits for compact stars in the present work. Without invoking strong magnetic field and/or exotic equation of state (EOS), we try to increase the mass limits for compact stars in modified gravity theory. In this work, we propose an inverse chameleon mechanism, and show that the fifth-force mediated by the scalar field can evade the severe tests on earth, in solar system and universe, but manifest itself in compact stars such as white dwarfs and neutron stars. The mass limits for compact stars in the inverse chameleon mechanism can be easily increased to 3 M ☉, 5 M ☉ or even larger. We argue that the inverse chameleon mechanism might be constrained by the observations of exoplanets orbiting compact stars (such as white dwarfs and neutron stars), and gravitational waves from the last stage of binary compact star coalescence.

Impact of dynamical dark energy on the neutron star equilibrium

We study the density distribution of the minimally-coupled scalar field dark energy inside a neutron star. The dark energy is considered in the hydrodynamical representation as a perfect fluid with three parameters (background density, equation of state, and effective sound speed). The neutron star matter is modeled with three unified equations of state, developed by the Brussels-Montreal group. With the calculated density distribution of the dark energy inside a neutron star (and its dependence on the dark energy parameters) we investigate how its presence impacts the macroscopic characteristics and the value of the mass limit for neutron stars. From this impact we derive the possible constraints on the effective speed of sound of dark energy with the help of maximal known masses of observed neutron stars. In this approach, we have found, that the squared effective speed of sound can not be smaller than ∼ 10−2 in units of squared speed of light.

Neutron and quark stars in f(R) gravity

The realistic compact star models are considered in [Formula: see text] gravity. The main result is that simple modified gravity can be consistent with current observational mass limit of neutron stars, with current data on their masses and radii; also, it simplifies solution of the hyperon problem. The effect of strong magnetic field in [Formula: see text]-gravity is also investigated. The existence of more compact (in comparison with General Relativity) stars with large magnetic fields in central regions is possible. In fact the second branch of stability appears.

R-mode instability of strange stars and observations of neutron stars in LMXBs**Supported by the National Natural Science Foundation of China.

Using a realistic equation of state (EOS) of strange quark matter, namely, the modified bag model, and considering the constraints on the parameters of EOS by the observational mass limit of neutron stars, we investigate the r-mode instability window of strange stars, and find the same result as in the brief study of Haskell, Degenaar and Ho in 2012 that these instability windows are not consistent with the spin frequency and temperature observations of neutron stars in low mass X-ray binaries.

A theory of finite-temperature Bose-Einstein condensates in neutron stars

We investigate the possible occurrence of a Bose-Einstein condensed phase of matter within neutron stars due to the formation of Cooper pairs among the superfluid neutrons. To this end we study the condensation of bosonic particles under the influence of both a short-range contact and a long-range gravitational interaction in the framework of a Hartree-Fock theory. We consider a finite-temperature scenario, generalizing existing approaches, and derive macroscopic and astrophysically relevant quantities like a mass limit for neutron stars.

Beyond the Chandrasekhar limit: Structure and formation of compact stars

The concept of limiting mass, introduced by Chandrasekhar in case of white dwarfs, plays an important role in the formation and stability of compact objects such as neutron stars and black holes. Like white dwarfs, neutron stars have their own mass limit, and a compact configuration would progress from one family to the next, more dense one once a mass limit is crossed. The mass limit of neutron stars depends on the nature of nuclear forces at very high density, which has so far not been determined conclusively. This article reviews how observational determinations of the properties of neutron stars are starting to impose significant constraints on the state of matter at high density.

Neutron stars within the SU(2) parity doublet model

The equation of state of beta-stable and charge neutral nucleonic matter is computed within theSU(2) parity doublet model in mean-field and in the relativistic Hartree approximation. The mass of the chiral partner of the nucleon is assumed to be 1200MeV. The transition to the chiral restored phase turns out to be a smooth crossover in all the cases considered, taking place at a baryon density of just 2ρ0 . The mass-radius relations of compact stars are calculated to constrain the model parameters from the maximum mass limit of neutron stars. It is demonstrated that chiral symmetry starts to be restored, which in this model implies the appearance of the chiral partners of the nucleons, in the center of neutron stars. However, the analysis of the decay width of the assumed chiral partner of the nucleon poses limits on the validity of the present version of the model to describe vacuum properties.

Relativistic finite baryon size effect and the mass limit for neutron stars

We revise our previous calculation of the finite baryon size effect on the mass limit for neutron stars by making the formulation be relativistic. The result is still consistent with the observational data.

Finite volume of baryons and the mass limit for neutron stars

The authors confirm the following idea by numerical calculation; the extended structure of baryons may make the nuclear equation of state stiffer at higher density while keeping the compression modulus for normal nuclear matter around its empirical value K=240 MeV. A model built in this way fits all empirical data for normal nuclear matter and gives a mass limit for neutron stars compatible with observation.

On the maximum mass of a uniformly rotating neutron star

The effect of rapid uniform rotation on the upper mass limit for neutron stars is studied under the assumption that the equation of state is subject to only a minimal set of physical constraints. For given ranges of the energy condition, microstability constraint, and causality constraint, the maximum mass of a uniformly rotating neutron star is about 24-25 percent greater than the corresponding nonrotating maximum mass. The obtained value is compared with that of the maximum mass of uniformly rotating configurations associated with the stiffest of the equations of state proposed for actual neutron-star matter. Rotation increases the upper limit on baryon mass by only about 20 percent, while the limiting moment of inertia is about twice its value for the nonrotating case. Upper limits are also found for the frequency of rotation, the frequency of frame dragging, and the maximum polar and equatorial redshifts. Discarding the causality constraint would allow the upper mass limit to increase by a given value. 16 references.

Must ultrabaric matter be superluminal?

We examine the question of whether or not special relativity requires that the pressure must be less than the energy density of matter. To do this, we study a model of matter consisting of a classical one-dimensional lattice of point particles interacting via a potential satisfying the three-dimensional Klein-Gordon equation. Despite the fact that for this model the pressure $p$ can exceed the energy density $\ensuremath{\rho}{c}^{2}$, giving rise to an adiabatic sound speed ${c}_{s}={(\frac{\mathrm{dp}}{d\ensuremath{\rho}})}^{\frac{1}{2}}gc$, and in the low-frequency limit to a group velocity $\frac{d\ensuremath{\omega}}{\mathrm{dk}}gc$ and phase velocity $\frac{\ensuremath{\omega}}{k}gc$, for this type of lattice model, the formally calculated speed ${c}_{s}$ is not a signal speed and we find that the true signal propagation speed ${v}_{\mathrm{signal}}lc$. Thus special relativity alone does not guarantee that $pl\ensuremath{\rho}{c}^{2}$. We briefly discuss other constraints on $p(\ensuremath{\rho})$, none of which seem sufficiently rigorous to rule out the possibility that $pg\ensuremath{\rho}{c}^{2}$ at high densities. The significance of the present result for the upper mass limit of neutron stars and the existence of black holes is also considered.

The upper mass limit for neutron stars including differential rotation

We show that any significant amount of differential rotation initially present in a neutron star will be damped out within a few days. Consequently, differential rotation need not be considered in determining the upper mass limit for neutron stars. We determine this limit with the fewest possible assumptions. Without rotation the mass may not exceed 8 M/sub sun/Rigid body rotation may increase the mass by no more than 30% according to calculations by others. Thus we find the upper mass limit including rotation to be 11 M/sub sun/Our limit requires no assumptions about the equation of state above a density of 2 x 10/sup 14/ g cm/sup -3/. We can think of no plausible way in which this limit would be violated other than the breakdown of general relativity. If one is willing to accept dP/drho< or =1 as a constraint imposed by causality on static equations of state, the upper mass limit would be reduced to 7 M/sub sun)/s)/sup -3/(B/10/sup 12/ gauss)/sup 3/2/ (R/sub asterisk6/ cm)/sup 9/2/(m/Zm/sub e/)/sup 1/2/ ergs s/sup -1/. This luminosity is sufficient to explain radio pulsars if the beam energy can be converted to radio radiation with reasonably high efficiency, but is insufficient to explainmore » pulsed ..gamma..-ray emission from the Crab and other pulsars. In these numerical estimates, we assume that the closed magnetosphere extends to the light cylinder. We also investigate the rotation rate of the plasma, and show that on the open-field lines of the aligned rotator, the beam current induces a twist to the field lines such that an observer at infinity sees the plasma as nonrotating. We apply these results and point out the necessity of including the effects of field-line curvature in a realistic model.« less

Neutron Star Matter and Neutron Star Models

Various methods to study the ground state of neutron star matter are compared and the corresponding neutron star models are contrasted with each other. In the low density region ρ &lt; 1014gr cm-3 the nuclear gas is treated here by means of a Thomas Fermi method and the nuclei are described by the droplet model of Myers and Swiatecki. For ρ &gt; 1014 gr cm-3 both standard Brueckner theory with more realistic interaction (one-boson-exchange) potentials and the semiphenomenological theory of Fermi liquids (together with the standard Reid softcore potential) are applied to neutron star matter. It is shown that while the high mass limit of neutron stars is hardly affected, some properties of lowmass neutron stars such as their binding depend sensitively on these refinements. Various tentative (but unreliable) extensions of the equation of state into high density regime ρ &gt; 1015 gr cm-3 are investigated and it is shown that the mass limit for heavy neutron stars lies around 2.5 solar masses. It is further shown that a third family of stable (hyperon) stars is not forbidden by general relativistic arguments if there is a phase transition at high densities.

The Effects of Nuclear Forces on the Maximum Mass Limit of Neutron Stars

The original models of neutron stars must be improved by including effects of nuclear interaction. This paper compares the models reached by various groups, and presents an improved model by the Kyoto group. The maximum mass varies between 0.2 M⊙ and 3 M⊙ in the various models. The Vγ model is recommended for use in the absence of further information on the equation of state at high densities.