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With a selected sample of neutron star (NS) equation-of-states (EOSs) that are consistent with the current observations and have a range of maximum masses, we investigate the relations between NS gravitational mass $M_g$ and baryonic mass $M_b$, and the relations between the maximum NS mass supported through uniform rotation ($M_{\rm max}$) and that of nonrotating NSs ($M_{\rm TOV}$). We find that if one intends to apply an EOS-independent quadratic, universal transformation formula ($M_b=M_g+A\times M_{g}^2$) to all EOSs, the best fit $A$ value is 0.080 for non-rotating NSs only and 0.073 when different spin periods are considered. The residual error of the transformation is as large as $\sim0.1M_{\odot}$. For different EOSs, we find that the parameter $A$ for non-rotating NSs is proportional to $R_{1.4}^{-1}$ (where $R_{1.4}$ is NS radius for 1.4$M_\odot$ in unit of km). For a particular EOS, if one adopts the best-fit parameters for different spin periods, the residual error of the transformation is smaller, which is of the order of 0.01$M_\odot$ for the quadratic form and less than 0.01$M_\odot$ for the cubic form ($M_b=M_g+A_1\times M_{g}^2+A_2\times M_{g}^3$). We also find a very tight and general correlation between the normalized mass gain due to spin $\Delta m\equiv(M_{\rm max}-M_{\rm TOV})/M_{\rm TOV}$ and the spin period normalized to the Keplerian period ${\cal P}$, i.e. ${\rm log_{10}}\Delta m = (-2.74\pm0.05){\rm log_{10}}{\cal P}+{\rm log_{10}}(0.20\pm 0.01)$, which is independent of EOS models. Applications of our results to GW170817 is discussed., Comment: 7 pages, 3 figures

From the very first multimessenger event of GW170817, clean robust constraints can be obtained for the tidal deformabilities of the two stars involved in the merger, which provides us unique opportunity to study the equation of states (EOSs) of dense stellar matter. In this contribution, we employ a model from the quark level, describing consistently a nucleon and many-body nucleonic system from a quark potential. We check that our sets of EOSs are consistent with available experimental and observational constraints at both sub-nuclear saturation densities and higher densities. The agreements with ab-initio calculations are also good. Especially, we tune the density dependence of the symmetry energy (characterized by its slope at nuclear saturation $L$) and study its influence on the tidal deformability. The so-called $QMF18$ EOS is named after the case of $L=40~\rm MeV$, and it gives $M_{\rm TOV} =2.08~M_\odot$ and $R= 11.77~\rm km$, $\Lambda=331$ for a $1.4\,M_\odot$ star. The tidal signals are demonstrated to be insensitive to the uncertain crust-core matching, despite the good correlation between the symmetry energy slope and the radius of the star., Comment: 8 pages, 6 figures, Submitted to the AIP Proceedings of the Xiamen-CUSTIPEN Workshop on the EOS of Dense Neutron-Rich Matter in the Era of Gravitational Wave Astronomy, Jan. 3-7, Xiamen, China

We propose the new quark mean-field bag (QMFB) model by incorporating the bag confinement mechanism in the original quark mean-field model. Nuclear matter and neutron star properties are studied with the QMFB model. For the study of the bag effect, we newly fit 12 parameter sets by reproducing the empirical saturation properties of nuclear matter. Quark confinement is found to be mainly demonstrated by the bag after it is included in the model, instead of the confining potential. For nuclear matter, the bag decreases the binding energy and increases the symmetry energy. For neutron star, the bag affects significantly the radius $R$ of a $1.4M_\odot$ star, with the maximum mass only slightly modified. The bag also has a large suppression effect on the well-accepted $R$ vs $L$ dependence, with $L$ the symmetry energy slope at the saturation density., Comment: 8 pages, 5 figures, 2 tables, Phys. Rev. C accepted

We study the effects of free space nucleon radius on nuclear matter and neutron stars within the framework of quark mean field model. The nucleon radius is treated self-consistently with this model, where quark confinement is adjusted to fit different values of nucleon radius. Corrections due to center-of-mass motion, quark-pion coupling, and one gluon exchange are included to obtain the nucleon mass in vacuum. The meson coupling constants that describe the behavior of many-body nucleonic system are newly-constructed by reproducing the empirical saturation properties of nuclear matter, including the recent determinations of symmetry energy parameters. Our results show that the nucleon radius in free space have negligible effects on nuclear matter equation of state and neutron star mass-radius relations, which is different from the conclusion drawn in previous studies. We further explore that the sensitivity of star radius on the nucleon radius found in earlier publications is actually from the symmetry energy and its slope., Comment: 6 pages, 4 figures, 2 tables, Phys. Rev. C (2018) accepted

Matter state inside neutron stars is an exciting problem in astrophysics, nuclear physics and particle physics. The equation of state (EOS) of neutron stars plays a crucial role in the present multimessenger astronomy, especially after the event of GW170817. We propose a new neutron star EOS "QMF18" from the quark level, which describes well robust observational constraints from free-space nucleon, nuclear matter saturation, heavy pulsar measurements and the tidal deformability of the very recent GW170817 observation. For this purpose, we employ the quark-mean-field (QMF) model, allowing one to tune the density dependence of the symmetry energy and study effectively its correlations with the Love number and the tidal deformability. We provide tabulated data for the new EOS and compare it with other recent EOSs from various many-body frameworks., Comment: 11 pages, 6 figures, 4 tables, ApJ accepted

Binary neutron star (NS) mergers with their subsequent fast-rotating supramassive magnetars are one attractive interpretation for at least some short gamma-ray bursts (SGRBs), based on the internal plateau commonly observed in the early X-ray afterglow. The rapid decay phase in this scenario signifies the epoch when the star collapses to a black hole after it spins down, and could effectively shed light on the underlying unclear equation of state (EoS) of dense matter. In the present work, we confront the protomagnetar masses of the internal plateau sample from representative EoS models, with the one independently from the observed galactic NS-NS binary, aiming to contribute new compact star EoSs from SGRB observations. For this purpose, we employ various EoSs covering a wide range of maximum mass for both NSs and quark stars (QSs), and in the same time satisfying the recent observational constraints of the two massive pulsars whose masses are precisely measured (around $2 M_{\odot}$). We first illustrate that how well the underlying EoS would reconcile with the current posterior mass distribution, is largely determined by the static maximum mass of that EoS. We then construct 3 new postmerger QS EoSs (PMQS1, PMQS2, PMQS3), respecting fully the observed distribution. We also provide easy-to-use parameterizations for both the EoSs and the corresponding maximum gravitational masses of rotating stars. In addition, we calculate the fractions of postmerger products for each EoS, and discuss potential consequences for the magnetar-powered kilonova model., Comment: 12 pages, 5 figures, 3 tables, ApJ (2017) accepted

The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to include $\Delta$-isobars for the study of dense nuclear matter and neutron stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2 particle. Both the direct and exchange terms of the $\Delta$-isobars' self-energies are evaluated in details. In comparison with the relativistic mean field theory (Hartree approximation), a weaker parameter dependence is found for DDRHF. An early appearance of $\Delta$-isobars is recognized at $\rho_B\sim0.27$fm$^{-3}$, comparable with that of hyperons. Also, we find that the $\Delta$-isobars' softening of the equation of state is found to be mainly due to the reduced Fock contributions from the coupling of the isoscalar mesons, while the pion contributions are found negligibly small. We finally conclude that with typical parameter sets, neutron stars with $\Delta$-isobars in their interiors could be as heavy as the two massive pulsars whose masses are precisely measured, with slightly smaller radii than normal neutron stars., Comment: 13 pages, 7 figures, 5 tables, 4 appendixes, Phys. Rev. C (2016) accepted