Quarkyonic Matter Equation of State in Beta-Equilibrium
Tianqi Zhao, James M. Lattimer
备注：
12 pages, 12 figures. Accepted by PRD. Add nud version of quarkyonic EoS in Appendix. Python code of nud version posted on https://github.com/sotzee/quaryonic_eos
Quark matter may appear due to a hadronic-quark transition in the core of a hybrid star. Quarkyonic matter is an approach in which both quarks and nucleons appear as quasi-particles in a crossover transition, and provides an explicit realization of early ideas concerning quark matter (e.g., the MIT bag model). This description has recently been employed by McLerran and Reddy to model chargeless (pure neutron) matter with an approach that has the virtue that the speed of sound rises quickly at a neutron-quark transition so as to satisfy observational constraints on the neutron star maximum mass ($\gtrsim2M_\odot$) and the radius of a $1.4M_\odot$ star ($R_{1.4}\lesssim 13.5$ km). Traditional models involving first-order transitions result in softer pressure-energy density relations that have difficulty satisfying these constraints except with very narrow choices of parameters. We propose a variation of quarkyonic matter involving protons and leptons whose energy can be explicitly minimized to achieve both chemical and beta equilibrium, which cannot be done in the chargeless formulation. Quarkyonic stellar models are able to satisfy observed mass and radius constraints with a wide range of model parameters, avoiding the obligatory fine-tuning of conventional hybrid star models, including requiring the transition density to be very close to the nuclear saturation density. Our formulation fits experimental and theoretical properties of the nuclear symmetry energy and pure neutron matter, and contains as few as three free parameters. This makes it an ideal tool for the study of high-density matter that is an efficient alternative to piecewise polytrope or spectral decomposition methods.
We suggest an extension to isospin asymmetric matter of the quarkyonic model from McLerran and Reddy. This extension allows us to construct the $β$-equilibrium between quarks, nucleons and leptons. The concept of the quarkyonic matter originates from the large number of color limit for which nucleons are the correct degrees of freedom near the Fermi surface -- reflecting the confining forces -- while deep inside the Fermi sea quarks naturally appear. In isospin asymmetric matter, we suggest that this new concept can be implemented within a global isoscalar relation between the shell gaps diffe…
Observable Signatures of a Quarkyonic Phase in Neutron Stars
National Institute of Technology, Rourkela（鲁尔基拉国家理工学院）；University of Coimbra（科英布拉大学）；Institute for Nuclear Theory, University of Washington（华盛顿大学核理论研究所）；Network for Neutrinos, Nuclear Astrophysics, and Symmetries (N3AS), University of California, Berkeley（加州大学伯克利分校中微子、核天体物理与对称性网络（N3AS））；Stony Brook University（石溪大学）
We show that the commonly used criterion for beta equilibrium in neutrino-transparent dense nuclear matter becomes invalid as temperatures rise above 1 MeV. Such temperatures are attained in neutron star mergers. By numerically computing the relevant weak interaction rates we find that the correct criterion for beta equilibrium requires an isospin chemical potential that can be as large as 10-20 MeV, depending on the temperature at which neutrinos become trapped.
We investigate the influence of nucleon superfluidity on the neutrino emissivity of non-equilibrium beta processes. Calculations are performed of the reduction factors for direct and modified Urca processes with three types of nucleon superfluidity in $npe$ matter. The numerical results are given since the analytical solution is impossible. We find that the behavior of the superfluid influence is closely related to the chemical departure from beta equilibrium. For small chemical departure, the superfluid reduction factor almost only depends on the gap but is hardly affected by the departure. W…
The analytic solution is obtained describing kinetic equilibrium of the $β$-processes in the nucleonic plasma with relativistic pairs. The nucleons $(n,p)$ are supposed to be non-relativistic and non-degenerate, while the electrons and positrons are ultra-relativistic due to high temperature $(T>6\cdot 10^9$K), or high density $(ρ>μ10^6$g/cm$^3$), or both, where $μ$ is a number of nucleons per one electron. The consideration is simplified because of the analytic connection of the density with the electron chemical potential in the ultra-relativistic plasma, and Gauss representation of Fermi fu…
The formation of the chemical composition of neutron star envelopes, at high densities is considered. As hot matter is compressed in the process of collapse, which leads to the explosion of a core collapse supernova, the stage of nuclear equilibrium with free neutrino escape, kinetic equilibrium in \b{eta}-processes, and, as a result, the establishment of limited nuclear equilibrium with a fixed number of nuclei takes place. Cold matter is compressed at a fixed number of nuclei whose atomic weight initially does not change and subsequently decreases. A pycnonuclear reaction of the fusion of av…
We find that the abundance of large clusters of nucleons in neutron-rich matter at sub-nuclear density is greatly reduced by finite temperature effects when matter is close to beta-equilibrium. Large nuclei and exotic non-spherical nuclear configurations called pasta, favored in the vicinity of the transition to uniform matter at $T=0$, dissolve at relatively low temperature. For matter close to beta-equilibrium we find that the pasta melting temperature is $T_m^β\simeq 4\pm 1$~MeV for realistic equations of state. The mechanism for pasta dissolution is discussed, and in general $T_m^β$ is sho…
We report a first case study of the phase diagram of 2+1 flavor strongly interacting matter in $β-$equilibrium, using the Polyakov$-$Nambu$-$Jona-Lasinio model. Physical characteristics of relevant thermodynamic observables have been discussed. A comparative analysis with the corresponding observables in the Nambu-Jona-Lasinio model is presented. We find distinct differences between the models in terms of a number of thermodynamic quantities like the speed of sound, specific heat, various number densities as well as entropy. The present study is expected to give us a better insight into the ro…
After an introduction to the QCD phase diagram, the nuclear equations of state, and neutron star mergers, I discuss three projects related to transport and nuclear matter in neutron star mergers. The first is the nature of beta equilibrium in the portion of a merger that is transparent to neutrinos. We calculate the weak interaction (Urca) rates and find that the beta equilibrium condition needs to be modified by adding an additional chemical potential, which changes slightly the particle content in neutrino-transparent beta equilibrium. Secondly, we calculate the bulk viscosity in neutrino-tr…
We present an analytic formulation for the equilibrium gas density profile of early-type galaxies that explicitly includes the contribution of stars in the gravitational potential. We build a realistic model for an isolated elliptical galaxy and explore the equilibrium gas configurations as a function of multiple parameters. For an assumed central gas temperature k_B*T_0=0.6 keV, we find that neglecting the gravitational effects of stars, which can contribute substantially in the innermost regions, leads to an underestimate of the enclosed baryonic gas mass by up to ~65% at the effective radiu…
This thesis aims to study how amending certain astrophysical observable of quark stars due to presence of magnetic field. To do this we need to obtain Equation of State (EOS) and consider the stability of Strange Quark Matter (made up of quarks u, d and s) cold dense and magnetized in stellar equilibrium (beta equilibrium, conservation of the baryonic number and charge neutrality). We will work using the phenomenological MIT Bag model. The stability of the Magnetized Strange Quark Matter (MSQM) is studied taking into account the variation of parameters from the model: s quark mass, baryonic de…
General relativity guarantees a unique one-to-one correspondence between static observables of neutron stars (NSs) accessible by multi-messenger astronomy, such as mass-radius or tidal deformability, and the equation of state (EoS) of beta equilibrated matter. It is well known that these static properties are not enough to discern conventional NSs from hybrid stars. However, if one assumes that hadrons present in the neutron star core are only neutrons and protons, the lepton fraction is in principle determined unequivocally by the condition of chemical equilibrium. Using a simple analytical m…
As another step towards understanding the long-term evolution of the magnetic field in neutron stars, we provide the first simulations of ambipolar diffusion in a spherical star. Restricting ourselves to axial symmetry, we consider a charged-particle fluid of protons and electrons carrying the magnetic flux through a motionless, uniform background of neutrons that exerts a collisional drag force on the former. We also ignore the possible impact of beta decays, proton superconductivity, and neutron superfluidity. All initial magnetic field configurations considered are found to evolve on the an…
Parametric equations of state (EoSs) provide an important tool for systematically studying EoS effects in neutron star merger simulations. In this work, we perform a numerical validation of the M*-framework for parametrically calculating finite-temperature EoS tables. The framework, introduced in Raithel et al. (2019), provides a model for generically extending any cold, beta-equilibrium EoS to finite-temperatures and arbitrary electron fractions. In this work, we perform numerical evolutions of a binary neutron star merger with the SFHo finite-temperature EoS, as well as with the M*-approxima…
When a rotating neutron star loses angular momentum, the progressive reduction of the centrifugal force makes it contract. This perturbs each fluid element, raising the local pressure and originating deviations from beta equilibrium, inducing reactions that release heat (rotochemical heating). This effect has previously been studied by Fernández & Reisenegger (2005) for non-superfluid neutron stars and by Petrovich & Reisenegger (2010) for superfluid millisecond pulsars. Both studies found that pulsars reach a quasi-steady state in which the compression driving the matter out of beta equilibri…
Neutron stars contain the strongest magnetic fields known in the Universe. In this paper, I discuss briefly how these magnetic fields are inferred from observations, as well as the evidence for their time-evolution. I show how these extremely strong fields are actually weak in terms of their effects on the stellar structure, as is also the case for magnetic stars on the upper main sequence and magnetic white dwarfs, which have similar total magnetic fluxes. I propose a scenario in which a stable hydromagnetic equilibrium (containing a poloidal and a toroidal field component) is established soo…
