Stiff Equation Of State Research Articles

Quark star matter in the color-flavor-locked state with a density-dependent quark mass model

The properties of strange quark matter (SQM) and color-flavor-locked (CFL) quark matter are investigated in quark stars (QSs) at zero temperature case within confined-isospin-density-dependent-mass (CIDDM) model. The mass–radius relation of QSs are also studied by considering newly proposed mass–radius constraints in CFL phase. Our results indicate that we can obtain more stable and stiffer equation of state (EOS) by considering CFL phase within CIDDM model at zero temperature. While the GW190814's secondary component with a mass around 2.6 M ⊙ cannot be QSs within CIDDM model in SQM case, it can be well described as QSs by considering CFL phase within CIDDM model in this work. In particular, we further construct a density-dependent pairing energy gap to connect the EOS of SQM and CFL quark matter with constant pairing energy gap Δ, and the results indicate that by extending the paring energy gap to include density dependence, the mass–radius lines within CIDDM model can satisfy most of the mass–radius region constraints in recent pulsar observations.

Induced gravitational waves and baryon asymmetry fluctuations from primordial black hole formation

We consider black hole formation due to the gravitational collapse produced by large density fluctuations during an epoch of reheating with a stiff equation of state and calculate the induced gravitational wave spectrum. By considering the existing bounds on the total energy density of gravitational waves today, we find constraints on the parameter space of this scenario. We also calculate the lepton asymmetry generated by metric perturbations via the chiral gravitational anomaly present in the Standard Model and find that, once the electroweak sphaleron processes have taken place, the large spectrum of scalar perturbations responsible for black hole formation induces a peak in the baryon asymmetry fluctuations on small scales.

An Optical Study of the Black Widow Population

The optical study of the heated substellar companions of black widow (BW) millisecond pulsars (MSPs) provides unique information on the MSP particle and radiation output and on the neutron star mass. Here we present an analysis of optical photometry and spectroscopy of a set of relatively bright BWs, many newly discovered in association with Fermi γ-ray sources. Interpreting the optical data requires sophisticated models of the companion heating. We provide a uniform analysis, selecting the preferred heating model and reporting on the companion masses and radii, the pulsar heating power, and neutron star mass. The substellar companions are substantially degenerate, with average densities 15–30× Solar, but are inflated above their zero temperature radii. We find evidence that the most extreme recycled BW pulsars have both large >0.8M ⊙ accreted mass and low <108G magnetic fields. Examining a set of heavy BWs, we infer that neutron star masses larger than 2.19M ⊙ (1σ confidence) or 2.08M ⊙ (3σ confidence) are required; these bounds exclude all but the stiffest equations of state in standard tabulations.

Effects of a phase transition on two-pion interferometry in heavy ion collisions at $$\sqrt {{s_{{\rm{NN}}}}} = 2.4 - 7.7\,\,{\rm{GeV}}$$

Hanbury-Brown-Twiss (HBT) correlations for charged pions in central Au+Au collisions at $\sqrt{s_\mathrm{NN}}=2.4 - 7.7~\text{GeV}$ (corresponding to beam kinetic energies in the fixed target frame from $E_{\rm{lab}}=1.23~\text{to}~30~\text{GeV/nucleon}$) are calculated using the UrQMD model with different equations of state. The effects of a phase transition at high baryon densities are clearly observed in the HBT parameters that are explored. It is found that the available data on the HBT radii, $R_{O}/R_{S}$ and $R^{2}_{O}-R^{2}_{S}$, in the investigated energy region favors a relatively stiff equation of state at low beam energies which then turns into a soft equation of state at high collision energies consistent with astrophysical constraints on the high density equation of state of QCD. The specific effects of two different phase transition scenarios on the $R_{O}/R_{S}$ and $R^{2}_{O}-R^{2}_{S}$ are investigated. It is found that a phase transition with a significant softening of the equation of state below 4 times nuclear saturation density can be excluded using HBT data. Our results highlight that the pion's $R_{O}/R_{S}$ and $R^{2}_{O}-R^{2}_{S}$ are sensitive to the stiffness of the equation of state, and can be used to constrain and understand the QCD equation of state in the high baryon density region.

Analysis of hyperbolically symmetric fluid configurations in modified Gauss–Bonnet gravity

This paper studies in detail the general physical properties inherent to the static fluid configurations possessing hyperbolic symmetry through the mechanism of modified Gauss–Bonnet gravity (GBG). The energy density of the anisotropic fluid configuration seems to be essentially negative, which indicates that any possible application of these fluid distributions needs severe physical constraints wherein quantum processes become significant. Several exact hyperbolically symmetric solutions with their corresponding generating functions are presented by imposing certain conditions (i.e., conformal flatness, vanishing complexity factor and stiff equation of state) on the fluid variables in the presence of higher-curvature GBG-corrections. Few of the provided stellar solutions exhibit the evolution of hyperbolically symmetric matter configurations whose center of symmetry is surrounded by a vacuum cavity.

Effect of the σ -cut potential on the properties of neutron stars with or without a hyperonic core

Motivated by the recent observation of high-mass pulsars ($M \simeq 2 M_{\odot}$), we employ the $\sigma$-cut potential on the equation of state (EOS) of high-density matter and the properties of neutron stars within the relativistic mean-field (RMF) model using TM1$^{*}$ parameter set. The $\sigma$-cut potential is known to reduce the contributions of the $\sigma$ field, resulting in a stiffer EOS at high densities and hence leading to larger neutron star masses without affecting the properties of nuclear matter at normal saturation density. We also analyzed the effect of the same on pure neutron matter and also on the neutron star matter with and without hyperonic core and compared it with the available theoretical, experimental, and observational data. The corresponding tidal deformability ($\Lambda_{1.4}$) is also calculated. With the choice of meson-hyperon coupling fixed to hypernuclear potentials, we obtain $\approx 10~\%$ increase in mass by employing the $\sigma$-cut potential for $f_{s} = 0.6$. Our results are in good agreement with various experimental constraints and observational data, particularly with the GW170817 data.

Numerical relativity simulations of the neutron star merger GW190425: microphysics and mass ratio effects

ABSTRACT GW190425 was the second gravitational wave (GW) signal compatible with a binary neutron star (BNS) merger detected by the Advanced LIGO and Advanced Virgo detectors. Since no electromagnetic counterpart was identified, whether the associated kilonova was too dim or the localization area too broad is still an open question. We simulate 28 BNS mergers with the chirp mass of GW190425 and mass ratio 1 ≤ q ≤ 1.67, using numerical-relativity simulations with finite-temperature, composition dependent equations of state (EOS) and neutrino radiation. The energy emitted in GWs is $\lesssim 0.083\mathrm{\, M_\odot }c^2$ with peak luminosity of 1.1–$2.4\times ~10^{58}/(1+q)^2\, {\rm {erg \, s^{-1}}}$. Dynamical ejecta and disc mass range between 5 × 10−6–10−3 and 10−5–$0.1 \mathrm{\, M_\odot }$, respectively. Asymmetric mergers, especially with stiff EOSs, unbind more matter and form heavier discs compared to equal mass binaries. The angular momentum of the disc is 8–$10\mathrm{\, M_\odot }~GM_{\rm {disc}}/c$ over three orders of magnitude in Mdisc. While the nucleosynthesis shows no peculiarity, the simulated kilonovae are relatively dim compared with GW170817. For distances compatible with GW190425, AB magnitudes are always dimmer than ∼20 mag for the B, r, and K bands, with brighter kilonovae associated to more asymmetric binaries and stiffer EOSs. We suggest that, even assuming a good coverage of GW190425’s sky location, the kilonova could hardly have been detected by present wide-field surveys and no firm constraints on the binary parameters or EOS can be argued from the lack of the detection.

Interacting ud and uds quark matter at finite densities and quark stars

The stability and equation of state of quark matter are studied within both two-flavor and ($2+1$)-flavor Nambu-Jona-Lasinio (NJL) models including the vector interactions. With a free parameter $\ensuremath{\alpha}$, the Lagrangian is constructed by two parts, the original NJL Lagrangian and the Fierz transformation of it, as $\mathcal{L}=(1\ensuremath{-}\ensuremath{\alpha}){\mathcal{L}}_{\mathrm{NJL}}+\ensuremath{\alpha}{\mathcal{L}}_{\text{Fierz}}$. We find that there is a possibility for both $ud$ nonstrange and $uds$ strange matter being absolute stable, depending on the interplay of the confinement with quark vector interaction and the exchange interaction channels. The calculated quark star properties can reconcile with the recently measured masses and radii of PSR $\mathrm{J}0030+0451$ and PSR $\mathrm{J}0740+6620$, as well as the tidal deformability of GW170817. Furthermore, the more strongly interacting quark matter in the nonstrange stars allows a stiffer equation of state and consequently a higher maximum mass ($\ensuremath{\sim}2.7\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$) than the strange ones ($\ensuremath{\sim}2.1\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$). The sound velocities in strange and nonstrange quark star matter are briefly discussed compared to those of neutron star matter.

Slowly rotating neutron star with holographic multiquark core: I-Love-Q relations

Moment of inertia ($I$), rotational (tidal) Love number (${\ensuremath{\lambda}}^{(\mathrm{rot})}$), and quadrupole moment ($Q$) of slowly rotating massive neutron stars (NSs) with holographic multiquarks (MQs) core are computed in comparison to pure MQ stars. The chiral effective theory (CET) stiff equation of state (EoS) is used in the crust of the neutron star. As previously established in earlier work, the dimensionless multipole moments $\overline{I},{\overline{\ensuremath{\lambda}}}^{(\mathrm{rot})}$, and $\overline{Q}$ are found to be independent of the rotation parameters and determined completely by the zeroth-order star profile. Universal ``I-Love-Q'' relations found by Yagi and Yunes [Science 341, 365 (2013); Phys. Rev. D 88, 023009 (2013)] are mostly preserved even in the presence of the MQ core. The tidal deformation parameter ${\overline{\ensuremath{\lambda}}}^{(\mathrm{tid})}$ is also explored in connection with $\overline{I},{\overline{\ensuremath{\lambda}}}^{(\mathrm{rot})},\overline{Q}$, and two kinds of universal I-Love-Q relations are verified. However, the unique kink in the plots of multipoles with respect to mass and compactness of the population of neutron stars can reveal the existence of massive NSs with a MQ core.

Merger of a Neutron Star with a Black Hole: One-family versus Two-families Scenario

Abstract A kilonova (KN) signal is generally expected after a black hole–neutron star merger. The strength of the signal is related to the equation of state of neutron star matter, and it increases with the stiffness of the latter. The recent results obtained by NICER from the analyses of PSR J0740+6620 suggest a rather stiff equation of state, and the expected KN signal is therefore strong, at least if the mass of the black hole does not exceed ∼10 M ⊙, the adimensional spin parameter is not too small, and the orbit is prograde. We compare the predictions obtained by considering equations of state of neutron star matter satisfying the most recent observations and assuming that only one family of compact stars exists with the results predicted in the two-families scenario. In the latter a soft hadronic equation of state produces very compact stellar objects, while a rather stiff quark matter equation of state produces massive strange quark stars, satisfying NICER results. The expected KN signal in the two-families scenario is very weak: in particular, the hadronic star–black hole merger produces a much weaker signal than in the one-family scenario because the hadronic equation of state is very soft. Moreover, according to the only existing simulation, the strange quark star–black hole merger does not produce a KN signal because the amount of mass ejected is negligible. These predictions will be easily tested with the new generation of detectors if black holes with an adimensional spin parameter χ BH ≳ 0.2 or a mass M BH ≲ 4 M ⊙ can be present in the merger.

Probing the nuclear equation of state using the neutron star observables within the Bayesian inference approach

The constraint on nuclear matter's equation of state has been a shared goal in nuclear physics and astrophysics. The most difficult one to constrain the equation of state is the constraint on the symmetry energy in nuclear matter. In this study, we adopt a theoretical framework that combines an isospin-dependent parametric equation of state for neutron star cores with a Bayesian inference approach to calculate the posterior probability distribution functions of the parameters of the equation of state in the nuclear matter based on mass and radius data reported by the LIGO/Virgo and NICER Collaborations, and thus constrain both the equation of state in symmetric nuclear matter and the equation of state in non-symmetric nuclear matter. It is found that a stiffer equation of state is supported by the data from the NICER Collaboration, and the improvement in the equation of state is not observed. The 68% credible intervals for the parameters are $L~=~45^{+15}_{-9}$ MeV for the slope, $K_{\mathrm{sym}}$ = $-100_{-110}^{+50}$ MeV for the curvature parameters of the symmetry energy and $J_0~=~-180_{-40}^{+60}$ MeV for the skewness parameter of the equation of state of symmetric nuclear matter. The symmetry energy values at two and three times normal density are, respectively, $E_{\mathrm{sym}}(2\rho_0)~=~48.9_{-16}^{+7.8}$ MeV and $E_{\mathrm{sym}}(3\rho_0)~=~81.8_{-57.2}^{+21.1}$ MeV.

Properties of hot finite nuclei and associated correlations with infinite nuclear matter

This work aims to study the various thermal characteristics of nuclei in view of the saturation and critical behavior of infinite nuclear matter. The free energy of a nucleus is parametrized using the density and temperature-dependent liquid-drop model, and interaction among nucleons is worked out within the effective relativistic mean-field theory (E-RMF). The effective mass (${m}^{*}$) and critical temperature of infinite symmetric nuclear matter (${T}_{c}$) of a given E-RMF parameter force play a seminal role in the estimation of thermal properties. Larger ${m}^{*}$ and ${T}_{c}$ of the E-RMF set estimate larger excitation energy, level density, and limiting temperature $({T}_{l})$ for a given nucleus. The limiting temperature of a nucleus also depends on the behavior of the nuclear gas surrounding the nucleus, making the equation of state (EoS) at subsaturation densities an important input. A stiff EoS in the subsaturation region estimates a higher pressure of the nuclear gas, making it less stable. Since ${T}_{c}$ plays an important part in these calculations, we perform a Pearson correlation statistical study of twenty E-RMF parameter sets, satisfying the relevant constraint on the EoS. Effective mass seems to govern the thermal characteristics of infinite as well as finite nuclear matter in the framework of E-RMF theory.

Hyperbolically symmetric sources in [formula omitted] gravity

This paper studies the static fluid distributions admitting the hyperbolically symmetric structure by extending the work of Herrera et al. (2021) in f(R,T) gravity. The unavailability of the fluid distribution in the region which is close to the center of symmetry has been observed. A vacuum cavity can be used to depict this region around the center. The effective matter density emerges inevitably to be negative and this implies that the conceivable use of such fluids needs transcendental physical conditions when the significant quantum effects are observed. Furthermore, the Tolman mass, as well as an appropriate formulation of the mass function, are particularly computed. Along with this, we evaluated the structure scalars through the orthogonal splitting of the Riemann tensor in this modified gravity. Imposing the conditions of conformal flatness and stiff equation of state, we constructed several models for the less-complex systems. We also evaluated the generating functions to study the fluid distribution in this theory. A general hypothesis to attain precise solutions are also conferred through matter-curvature coupling.

Neutron stars and phase diagram from a double hard-wall

Description of nuclear matter in the core of neutron stars eludes the main tools of investigation of QCD, such as perturbation theory and the lattice formulation of the theory. Recently, the application of the holographic paradigm (both via top-down and bottom-up models) to this task has led to many encouraging results, both qualitatively and quantitatively. We present our approach to the description of neutron star cores, relying on a simple model of the (double) hard-wall type: we discuss results concerning the nature of homogeneous nuclear matter at high density emerging from the model including a quarkyonic phase, the mass-radius relation for neutron stars, as well as the rather stiff equation of state we have found. We show how, despite the very simple model employed, for an appropriate calibration we are able to obtain neutron stars that only slightly fall short of the observational bounds on radius and tidal deformability.

Compressibility of quark matter under strong magnetic field in the NJL model

The compressibility of magnetized quark matter is investigated in the SU(2) NJL model. The increases of the chemical potential and the temperature can reduce the compressibility, and lead to the much stiffer equation of state. The variation of the compressibility with the magnetic field will depend on the phase region. Due to the anisotropic structure, the compressibility is different in the directions parallel and perpendicular to the field. The discontinuity of longitudinal compressibility with the chemical potential and the temperature captures the signature of a first-order chiral phase transition and the crossover at high temperature. Moreover, the magnetic-field-and-temperature running coupling would have an important effect on the position of the phase transition. Under the lowest landau level approximation at zero temperature, the longitudinal compressibility has a direct inverse proportional relation to the magnetic field strength and the chemical potential square as ${\ensuremath{\kappa}}_{\mathrm{LLL},\ensuremath{\chi}}^{\ensuremath{\parallel}}\ensuremath{\propto}1/(eB{\ensuremath{\mu}}^{2})$.

Black-hole–Neutron-star Mergers Are Unlikely Multimessenger Sources

Abstract The promise by the LIGO/Virgo/Kagra (LVK) collaboration to detect black-hole–neutron-star (BH–NS) mergers via gravitational wave (GW) emission has recently been fulfilled with the detection of GW200105 and GW200115. Mergers of BH–NS binaries are particularly exciting for their multimessenger potential since GW detection can be followed by an electromagnetic (EM) counterpart (kilonova, gamma-ray burst, afterglow) that can reveal important information on the equation of state (EOS) of NSs and the nature of the BH spin. This can happen whenever the NS does not directly plunge into the BH, but rather is tidally disrupted, leaving behind debris to accrete. We carry out a statistical study of the binary stars that evolve to form a BH–NS binary and compute the rate of merger events that can be followed by an EM counterpart. We find that ≳50% of the mergers can lead to an EM counterpart only in the case where BHs are born highly spinning (χ BH ≳ 0.7), while this fraction does not exceed about 30% for stiff NS EOSs and a few percent for soft NS EOSs for low-spinning BHs (χ BH ≲ 0.2), suggesting that a high rate of EM counterparts of BH–NS would provide support for high natal BH spins. However, the possibilities that BHs are born with near-maximal spins and that NS internal structure is described by a stiff EOS are disfavored by current LVK constraints. Considering that these values only represent an upper limit to observe an EM counterpart due to current observational limitations, such as brightness sensitivity and sky localization, BH–NS mergers are unlikely multimessenger sources.

Effects of the Nuclear Equation of State on Type I X-Ray Bursts: Interpretation of the X-Ray Bursts from GS 1826–24

Abstract Type I X-ray bursts are thermonuclear explosions on the neutron star (NS) surface caused by mass accretion from a companion star. Observations of X-ray bursts provide valuable information on X-ray binary systems, e.g., binary parameters, the chemical composition of accreted matter, and the nuclear equation of state (EOS). There have been several theoretical studies to constrain the physics of X-ray bursters. However, they have mainly focused on the burning layers above the solid crust of the NS, which brings up issues of the treatment of NS gravitational and internal energy. In this study, focusing on the microphysics inside NSs, we calculate a series of X-ray bursts using a general-relativistic stellar-evolution code with several NS EOSs. We compare the X-ray-burst models with the burst parameters of a clocked burster associated with GS 1826–24. We find a monotonic correlation between the NS radius and the light-curve profile. A larger radius shows a higher recurrence time and a large peak luminosity. In contrast, the dependence of light curves on the NS mass becomes more complicated, where neutrino cooling suppresses the efficiency of nuclear ignition. We also constrain the EOS and mass of GS 1826–24, i.e., stiffer EOSs, corresponding to larger NS radii, are not preferred due to a too-high peak luminosity. The EOS and the cooling and heating of NSs are important to discuss the theoretical and observational properties of X-ray bursts.

Incompressibility and symmetry energy of a neutron star

We trace a systematic and consistent method to precisely numerate the magnitude range for various structural and isospin compositional properties of the neutron star. Incompressibility, symmetry energy, slope parameter, and curvature of a neutron star are investigated using the relativistic energy density functional within the framework of coherent density fluctuation model. The analytical expression for the energy density functional of the neutron star matter is motivated from the Br\"uckner functional and acquired by the polynomial fitting of the saturation curves for three different relativistic mean-field parameter sets (NL3, G3, and IU-FSU). The modified functional is folded with the neutron star's density-dependent weight function to calculate the numerical values for incompressibility and symmetry energy using the coherent density fluctuation model. The NL3 parameter set, being the stiffest equation of state, has a higher magnitude of all the properties compared to the other two parameter sets.

Impact of the PSR J0740+6620 radius constraint on the properties of high-density matter

X-ray pulse profile modeling of PSR J0740+6620, the most massive known pulsar, with data from the NICER and XMM-Newton observatories recently led to a measurement of its radius. We investigate this measurement's implications for the neutron star equation of state (EoS), employing a nonparametric EoS model based on Gaussian processes and combining information from other x-ray, radio and gravitational-wave observations of neutron stars. Our analysis mildly disfavors EoSs that support a disconnected hybrid star branch in the mass-radius relation, a proxy for strong phase transitions, with a Bayes factor of $6.9$. For such EoSs, the transition mass from the hadronic to the hybrid branch is constrained to lie outside ($1,2$) $M_{\odot}$. We also find that the conformal sound-speed bound is violated inside neutron star cores, which implies that the core matter is strongly interacting. The squared sound speed reaches a maximum of $0.75^{+0.25}_{-0.24}\, c^2$ at $3.60^{+2.25}_{-1.89}$ times nuclear saturation density at 90% credibility. Since all but the gravitational-wave observations prefer a relatively stiff EoS, PSR J0740+6620's central density is only $3.57^{+1.3}_{-1.3}$ times nuclear saturation, limiting the density range probed by observations of cold, nonrotating neutron stars in $\beta$-equilibrium.

Kilonova Emission from Black Hole–Neutron Star Mergers. II. Luminosity Function and Implications for Target-of-opportunity Observations of Gravitational-wave Triggers and Blind Searches

Abstract We present detailed simulations of the kilonova and gamma-ray burst (GRB) afterglow and kilonova luminosity function from black hole–neutron star (BH–NS) mergers, and discuss the detectability of an electromagnetic (EM) counterpart in connection with gravitational wave (GW) detections, GW-triggered target-of-opportunity observations, and time-domain blind searches. The predicted absolute magnitude of BH–NS kilonovae at 0.5 days after the merger falls in the range [−10, −15.5]. The simulated luminosity function contains potential information on the viewing-angle distribution of the anisotropic kilonova emission. We simulate the GW detection rates, detectable distances, and signal duration for future networks of 2nd/2.5th/3rd generation GW detectors. BH–NSs tend to produce brighter kilonovae and afterglows if the BH has a higher aligned spin, and a less massive NS with a stiffer equation of state. The detectability of kilonovae is especially sensitive to the BH spin. If BHs typically have low spins, the BH–NS EM counterparts are hard to discover. For 2nd generation GW detector networks, a limiting magnitude of m limit ∼ 23–24 mag is required to detect kilonovae even if high BH spin is assumed. Thus, a plausible explanation for the lack of BH–NS-associated kilonova detection during LIGO/Virgo O3 is that either there is no EM counterpart (plunging events) or the current follow-ups are too shallow. These observations still have the chance to detect the on-axis jet afterglow associated with a short GRB or an orphan afterglow. Follow-up observations can detect possible associated short GRB afterglows, from which kilonova signatures may be studied. For time-domain observations, a high-cadence search in redder filters is recommended to detect more BH–NS-associated kilonovae and afterglows.