The gross structure of compact stars composed of pion superfluid quark matter is investigated in the frame of Nambu-Jona-Lasinio model. Under the Pauli-Villars regularization scheme, the uncertainty of the thermodynamic functions for inhomogeneous states is cured, and the LOFF state appeared in the hard cutoff scheme is removed from the phase diagram of pion superfluid. Different from the unpaired quark matter and color superconductor, the strongly coupled pion superfluid in the state close to the BCS limit is a possible candidate of compact stars with mass $M\simeq 3M_{\odot }$ and radius $R\simeq 14$ km.
Magnetic field effect on pion superfluid phase transition is investigated in frame of a Pauli-Villars regularized NJL model. Instead of directly dealing with charged pion condensate, we apply the Goldstone's theorem (massless Goldstone boson $π^+$) to determine the onset of pion superfluid phase, and obtain the phase diagram in magnetic field, temperature, isospin and baryon chemical potential space. At weak magnetic field, it is analytically proved that the critical isospin chemical potential of pion superfluid phase transition is equal to the mass of $π^+$ meson in magnetic field. The pion s…
Pion superfluid phase transition under external magnetic field including the inverse magnetic catalysis (IMC) effect is investigated by the Pauli-Villars regularized NJL model. Based on the Goldstone's theorem, we apply the massless Goldstone boson ($π^+$ meson) to determine the onset of pion superfluid phase. The inverse magnetic catalysis effect is introduced by the magnetic field dependent coupling $G(eB)$, which is a decreasing function of magnetic field. At fixed temperature and baryon chemical potential, the critical isospin chemical potential for pion superfluid phase transition includi…
Speed of sound and trace anomaly in a unified treatment of the two-color diquark superfluid, the pion-condensed high-isospin matter, and the 2SC quark matter
We analyze the evolution of hydrodynamic fluctuations for QCD matter below $T_c$ in the chiral limit, where the pions (the Goldstone modes) must be treated as additional non-abelian superfluid degrees of freedom, reflecting the broken $SU_L(2) \times SU_R(2)$ symmetry of the theory. In the presence of a finite pion mass $m_π$, the hydrodynamic theory is ordinary hydrodynamics at long distances, and superfluid-like at short distances. The presence of the superfluid degrees of freedom then gives specific contributions to the bulk viscosity, the shear viscosity, and diffusion coefficients of the …
The chiral and pion superfluidity phase transitions are studied within NJL model. The model parameters are fitted by pion mass and decay constant together with recent isospin density from lattice QCD. The dense and cold QCD matter suffered the first order chiral phase transition during the quark chemical potential increase. Based on the studies of phase structures, the equation of states~(EoS) of dense QCD matter are calculated with the conditions of $β$ equilibrium and electric charge neutrality. Take the EoS as input, the mass-radius relation of neutron stars are predicted, which is consiste…
With the isovector coupling constants adjusted to reproduce the physical pion mass and lattice QCD results in baryon-free quark matter, we have carried out rigourous calculations for the pion condensate in the 3-flavor Nambu-Jona-Lasinio model, and studied the 3-dimensional QCD phase diagram. With the increasing isospin chemical potential $μ_I$, we have observed two nonzero solutions of the pion condensate at finite baryon chemical potentials $μ_B$, representing respectively the pion superfluid phase and the Sarma phase, and their appearance and disappearance correspond to a second-order (firs…
We investigate hadron spectra in 2-color QCD using lattice simulation with $N_{f}=2$ at low temperature and finite density in which there appears not only the hadronic phase but also the superfluid phase. We first calculate the pion and rho meson spectrum, which is well-known from previous works. The spectral ordering of these mesons flips around the quark chemical potential $μ=m^{0}_π/2$ ($m^{0}_π$: the pion mass at $μ=0$), where the phase transition between the hadronic and superfluid phases occurs. For $μ\gtrsim m^{0}_π/2$, the effective mass for the pion linearly increases while the one fo…
Spin effects in superfluidity, neutron matter and neutron stars
Frankfurt Institute for Advanced Studies（法兰克福高等研究所）；Institute of Theoretical Physics, University of Wrocław（弗罗茨瓦夫大学理论物理研究所）；Columbia Astrophysics Laboratory, Columbia University（哥伦比亚大学天体物理学实验室）
We studied thermal evolution of isolated neutron stars (NSs) including the pion condensation core, with an emphasis on the stiffness of equation of state (EOS). Many temperature observations can be explained by the minimal cooling scenario which excludes the fast neutrino cooling process. However, several NSs are cold enough to require it. The most crucial problem for NS cooling theory is whether the nucleon direct Urca (DU) process is open. The DU process is forbidden if the nucleon symmetry energy is significantly low. Hence, another fast cooling process is required in such an EOS. As the ca…
Viscosity of neutron star matter and $r$-modes in rotating pulsars
我们研究了中子星物质的粘性和旋转中子星中的$r$模不稳定性。从各种过程的剪切和体积粘度的贡献计算与帐户在介质中修改的核子-核子相互作用。软化的π介子模式和π介子凝聚的可能性包括在内。核子配对被并入。在剪切粘度中，我们包括轻子的贡献计算帐户的朗道阻尼的光子交换，核子的贡献所描述的介质修改的一个π介子交换，和其他条款，如新的声子的贡献在1 S $_0$超流中子相，和中微子项在中微子不透明区域。核子剪切粘滞系数对密度的依赖相当温和，并证明比轻子项小得多。在对体粘滞系数有贡献的项中，由于π介子软化，介质修正的Urca反应项具有最强的密度依赖性。贡献的体积粘度所产生的其他反应引起的带电弱电流。在考虑介质内效应的情况下，计算了在中微子透明区由带电和中性弱流引起的辐射体粘滞系数。对于质量为$\ge 1.8 M_{\odot}$的恒星，计算出的$r$模稳定性的频率边界被证明高于所有旋转年轻恒星的频率。为了解释X射线双星中老恒星快速旋转的稳定性，我们提出了一种新的有效机制，如果角速度超过临界值，则该机制与具有有限动量的玻色子激发的低模凝聚体的出现和/或与恒星某些部分的非均匀π/K介子凝聚体的增强相关联。
Direct Urca neutrino radiation from superfluid baryonic matter
致密恒星中的致密物质通过直接Urca过程n -> p + e + nu和p + e -> n + nu通过中微子发射有效冷却。在配对相变温度Tc以下，这些过程被抑制-在渐近低温下呈指数关系。我们计算的发射率的Urca过程在一个循环的温度T < Tc，在重子配对的情况下，在1 S 0分波。在0.1 < T/Tc < 1的温度范围内，Urca过程被线性抑制，而不是指数抑制。在此温度范围内，电荷电流库珀对断裂过程占Urca总发射率的50%。
We study the quiescent luminosities of accreting neutron stars by a new mechanism as neutrino heating for additional deep crustal heating, where the neutrino heating is produced by charged pions decay from the nuclear collisions on the surface of neutron star during its active accretion. For low mass neutron star($\lesssim1.4~M_{\odot}$), as the neutrino heating is little($\lesssim1$ MeV per accreted nucleon) or there would be no neutrino heating, the quiescent luminsoity will be not affected or slightly affected. While for massive neutron star ($\gtrsim2~M_{\odot}$), the quiescent luminosity …
Superfluid neutron matter is a key ingredient in the composition of neutron stars. The physics of the inner crust is largely dependent on that of its $S$-wave neutron superfluid which has made its presence known through pulsar glitches and modifications on the neutron star cooling. Moreover, with recent gravitational-wave observations of neutron star mergers, the need for an equation of state for the matter of these compact stars is further accentuated and a model-independent treatment of neutron superfluidity is important. \textit{Ab initio} techniques developed for finite systems can be guid…
According to perturbation theory predictions, QCD matter in the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential is expected to be in a superfluid Bardeen-Cooper-Schrieffer (BCS) phase of $u$ and $\bar{d}$ Cooper pairs. It is also expected, on symmetry grounds, that such phase connects via an analytical crossover to the phase with Bose-Einstein condensation (BEC) of charged pions at $μ_\text{I}\geq m_π/2$. With lattice results, showing some indications that the deconfinement crossover also smoothly penetrates the BEC phase, the conjecture was made that the for…
Neutron stars or pulsars are very rapidly rotating compact stars with extremely high density. One of the unsolved long-standing problems of these enigmatic celestial bodies is the origin of pulsars' glitches, i.e., the sudden rapid deceleration in the rotation speed of neutron stars. Although many glitch events have been reported, there is no consensus on the microscopic mechanism responsible for them. One of the important characterizations of the glitches is the scaling law $P(E) \sim E^{-α}$ of the probability distribution for a glitch with energy $E$. Here, we reanalyse the accumulated up-t…
Our bimetric spacetime model of glitching pulsars is applied to the remnant of GW170817. Accordingly, pulsars are born with embryonic incompressible superconducting gluon-quark superfluid cores (SuSu-matter) that are embedded in Minkowski spacetime, whereas the ambient compressible and dissipative media (CDM) are imbedded in curved spacetime. As pulsars cool down, the equilibrium between both spacetime is altered, thereby triggering the well-observed glitch phenomena. Based thereon and assuming all neutron stars (NSs) to be born with the same initial mass of $M_{NS}(t=0) \approx 1.25\,\mathcal…
Pion and kaon structural properties provide insights into the emergence of mass within the Standard Model and attendant modulations by the Higgs boson. Novel expressions of these effects, in impact parameter space and in mass and pressure profiles, are exposed via $π$ and $K$ generalised parton distributions, built using the overlap representation from light-front wave functions constrained by one-dimensional valence distribution functions that describe available data. Notably, e.g. $K$ pressure profiles are spatially more compact than $π$ profiles and both achieve near-core pressures of simil…
