标题： 中子星物质的统一QMF状态方程：静态和动态性质 显示英文标题

标题： Unified QMF equation of state for neutron star matter: Static and dynamic properties

摘要： 我们基于夸克平均场（QMF）模型构建了一组统一的状态方程，这些方程校准到饱和密度处核对称能斜率的不同值（$L_0$），旨在探索中子星（NSs）的静态性质和动态行为，并建立其内部结构的连贯图景。 我们评估了这些QMF模型在描述质量-半径关系、孤立NSs和X射线暂现源的冷却演化以及不稳定性（例如r模）方面的性能。 与在强子层次上构造的相对论平均场（RMF）模型相比，QMF模型预测了更重的核簇和更大的Wigner-Seitz单元尺寸，而在NS外壳中自由中子气体的密度在两种方法之间大致相似。 对于孤立NSs的冷却，热演化在没有直接Urca（dUrca）过程的情况下对多体模型和对称能斜率都不敏感。 然而，当允许通过dUrca过程快速冷却时，在我们研究中大$L_0$值（例如$L_0 \gtrsim 80$MeV）的情况下，QMF模型预测了更长的热弛豫时间。 QMF和RMF模型都能再现与X射线暂现源（例如KS 1731--260）在壳层冷却阶段观测结果一致的冷却曲线，尽管恒星参数会根据模型和对称能斜率略有变化。 在我们统一的框架内，较大的$L_0$值通常会导致更宽的不稳定性窗口，而增加恒星质量则倾向于抑制不稳定性窗口。 我们还提供了简单的幂律参数化方法，量化了饱和密度下核物质的体积粘度和剪切粘度对对称能斜率的依赖性。 显示英文摘要

摘要： We construct a set of unified equations of state based on the quark mean field (QMF) model, calibrated to different values of nuclear symmetry energy slope at the saturation density ($L_0$), with the aim of exploring both the static properties and dynamical behavior of neutron stars (NSs), and building a coherent picture of their internal structure. We assess the performance of these QMF models in describing the mass-radius relation, the cooling evolution of isolated NSs and X-ray transients, and the instabilities (e.g., the r-mode). In comparison to relativistic mean field (RMF) models formulated at the hadronic level, the QMF model predicts heavier nuclear clusters and larger Wigner-Seitz cell sizes in the NS crust, while the density of the free neutron gas remains largely similar between the two approaches. For the cooling of isolated NSs, the thermal evolution is found to be insensitive to both the many-body model and the symmetry energy slope in the absence of the direct Urca (dUrca) process. However, when rapid cooling via the dUrca process is allowed, in the case of large $L_0$ values (e.g., $L_0 \gtrsim 80$ MeV) in our study, the QMF model predicts a longer thermal relaxation time. Both the QMF and RMF models can reproduce cooling curves consistent with observations of X-ray transients (e.g., KS 1731--260) during their crustal cooling phase, although stellar parameters show slight variations depending on the model and symmetry energy slope. Within our unified framework, a larger $L_0$ value generally results in a wider instability window, while increasing the stellar mass tends to suppress the instability window. We also provide simple power-law parameterizations that quantify the dependence of bulk and shear viscosities on the symmetry energy slope for nuclear matter at saturation density.