In this work, we study the effect of (anti)kaon condensation on the properties of compact stars that develop hypernuclear cores with and without an admixture of $\mathrm{\ensuremath{\Delta}}$-resonances. We work within the covariant density functional theory with the parameters adjusted to $K$-atomic and kaon-nucleon scattering data in the kaonic sector. The density-dependent parameters in the hyperonic sector are adjusted to the data on $\mathrm{\ensuremath{\Lambda}}$ and ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ hypernuclei data. The $\mathrm{\ensuremath{\Delta}}$-resonance couplings are tuned to the data obtained from their scattering off nuclei and heavy-ion collision experiments. We find that (anti)kaon condensate leads to a softening of the equation of state and lower maximum masses of compact stars than in the absence of the condensate. Both the ${K}^{\ensuremath{-}}$ and ${\overline{K}}^{0}$ condensations occur through a second-order phase transition, which implies no mixed-phase formation. For large values of (anti)kaon and $\mathrm{\ensuremath{\Delta}}$-resonance potentials in symmetric nuclear matter, we observe that condensation leads to an extinction of ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-},0}$ hyperons. We also investigate the influence of inclusion of additional hidden-strangeness ${\ensuremath{\sigma}}^{*}$ meson in the functional and find that it leads to a substantial softening of the equation of state and delay in the onset of (anti)kaons.

Massive Δ -resonance admixed hypernuclear stars with antikaon condensations

Recent measurements of neutron star mass from several candidates (PSR $\mathrm{J}1614\ensuremath{-}2230$, PSR $\mathrm{J}0348+0432$, MSP $\mathrm{J}0740+6620$) set the lower bound on the maximum possible mass for this class of compact objects $\ensuremath{\sim}2\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$. Existence of stars with high mass brings the possibility of existence of exotic matter (hyperons, meson condensates) at the core region of the objects. In this work, we investigate the (anti)kaon (${K}^{\ensuremath{-}}$, ${\overline{K}}^{0}$) condensation in $\ensuremath{\beta}$-equilibrated nuclear matter within the framework of covariant density functional theory. The functionals in the kaonic sector are constrained by the experimental studies on ${K}^{\ensuremath{-}}$ atomic, kaon-nucleon scattering data fits. We find that the equation of state softens with the inclusion of (anti)kaon condensates, which lowers the maximum mass of neutron star. In one of the density-independent coupling cases, the ${K}^{\ensuremath{-}}$ condensation is through a first order phase transition type, which produces a $2\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$ neutron star. The first order phase transition results in mixed phase region in the inner core of the stars. While ${\overline{K}}^{0}$ condensation appears via second-order phase transition for all the models we consider here.

Dense matter equation of state of a massive neutron star with antikaon condensation

In this work, we study magnetic field effects on neutron star matter containing the baryon octet and additional heavier spin 3/2 baryons (the $$\varDelta $$
 ’s). We make use of two different relativistic hadronic models that contain an additional vector-isovector self interaction for the mesons: one version of a relativistic mean field (RMF) model and the chiral mean field (CMF) model. We find that both the additional interaction and a strong magnetic field enhance the $$\varDelta $$
 baryon population in dense matter, while decreasing the relative density of hyperons. At the same time that the vector-isovector meson interaction modifies neutron-star masses very little (
 $$<0.1~\mathrm M_{\mathrm{Sun}}$$
 ), it decreases their radii considerably, allowing both models to be in better agreement with observations. Together, these features indicate that magnetic neutron stars are likely to contain $$\varDelta $$
 baryons in their interior.

Delta baryons in neutron-star matter under strong magnetic fields

We investigate the properties of anisotropic, spherically symmetric compact stars, especially neutron stars and strange quark stars, made of strongly magnetized matter. The neutron stars are described by SLy equation of state, the strange quark stars by an equation of state based on the MIT Bag model. The stellar models are based on an a priori assumed density dependence of the magnetic field and thus anisotropy. Our study shows that not only the presence of a strong magnetic field and anisotropy, but also the orientation of the magnetic field itself, have an important influence on the physical properties of stars. Two possible magnetic field orientations are considered, a radial orientation, where the local magnetic fields point in the radial direction, and a transverse orientation, where the local magnetic fields are perpendicular to the radial direction. Interestingly, we find that for a transverse orientation of the magnetic field, the stars become more massive with increasing anisotropy and magnetic field strength and increase in size, since the repulsive, effective anisotropic force increases in this case. In the case of a radially orientated magnetic field, however, the masses and radii of the stars decrease with increasing magnetic field strength, because of the decreasing effective anisotropic force. Importantly, we also show that in order to achieve hydrostatic equilibrium configurations of magnetized matter, it is essential to account for both the local anisotropy effects as well as the anisotropy effects caused by a strong magnetic field. Otherwise, hydrostatic equilibrium is not achieved for magnetized stellar models.

Effects of anisotropy on strongly magnetized neutron and strange quark stars in general relativity

Finite-temperature equation of state (EoS) and composition of dense nuclear and hypernuclear matter under conditions characteristic for neutron star binary merger remnants and supernovas are discussed. We consider both the neutrino free-streaming and the trapped regimes which are separated by a temperature of a few MeV. The formalism is based on covariant density functional (CDF) theory for the full baryon octet with density-dependent couplings, suitably adjusted in the hypernuclear sector. The softening of the EoS with the introduction of the hyperons is quantified under various conditions of lepton fractions and temperatures. We find that $\Lambda$, $\Xi^-$, and $\Xi^0$ hyperons appear in the given order with the sharp density increase at zero temperature at the threshold being replaced by an extended increment over a wide density range at high temperatures. The $\Lambda$ hyperon survives in the deep subnuclear regime. The triplet of $\Sigma$s is suppressed in cold hypernuclear matter up to around seven times the nuclear saturation density, but appears in significant fractions at higher temperatures $T\geq 20$ MeV in both supernova and merger remnant matter. We point out that there exists a special isospin degeneracy point where the baryon abundances within each of the three isospin-multiplets are equal to each other as a result of (approximate) isospin symmetry. At that point the charge chemical potential of the system vanishes. We find that under the merger remnant conditions the fractions of electron and $\mu$-on neutrinos are close and are about 1\%, whereas in the supernova case, we find only a significant fraction ($\sim$10\%) of electron neutrinos, given that in this case, the $\mu$-on lepton number is zero.

Equation of state and composition of proto-neutron stars and merger remnants with hyperons

We construct a new equation of state for the baryonic matter under an intense magnetic field within the framework of covariant density functional theory. The composition of matter includes hyperons as well as $ \Delta$-resonances. The extension of the nucleonic functional to the hypernuclear sector is constrained by the experimental data on $\Lambda$ and $\Xi$-hypernuclei. We find that the equation of state stiffens with the inclusion of the magnetic field, which increases the maximum mass of neutron star compared to the non-magnetic case. In addition, the strangeness fraction in the matter is enhanced. Several observables, like the Dirac effective mass, particle abundances, etc show typical oscillatory behavior as a function of the magnetic field and/or density which is traced back to the occupation pattern of Landau levels.

Equation of state of strongly magnetized matter with hyperons and $\Delta$-resonances

We review the covariant density functional approach to the equation of state of the dense nuclear matter in compact stars. The main emphasis is on the hyperonization of the dense matter, and the role played by the $\Delta$-resonances. The implications of hyperonization for the astrophysics of compact stars, including the equation of state, composition, and stellar parameters are examined. The mass-radius relation and tidal deformabilities of static and rapidly rotating (Keplerian) configurations are discussed in some detail. We briefly touch upon some other recent developments involving hyperonization in hot hypernuclear matter at high- and low-densities.

Jia-Jie Li

Papers

Equation of state of strongly magnetized matter with hyperons and $\Delta$-resonances

Hyperonization in compact stars