Gusakov M E, Chugunov A I
Ioffe Institute, 194021 St. Petersburg, Russia.
Phys Rev Lett. 2020 May 15;124(19):191101. doi: 10.1103/PhysRevLett.124.191101.
We study the equation of state (EOS) of an accreting neutron star crust. Usually, such an EOS is obtained by assuming (implicitly) that the free (unbound) neutrons and nuclei in the inner crust move together. We argue that this assumption violates the condition μ_{n}^{∞}=const, required for hydrostatic (and diffusion) equilibrium of unbound neutrons (μ_{n}^{∞} is the redshifted neutron chemical potential). We construct a new EOS respecting this condition, working in the compressible liquid-drop approximation. We demonstrate that it is close to the catalyzed EOS in most of the inner crust, being very different from EOSs of accreted crust discussed in the literature. In particular, the pressure at the outer-inner crust interface does not coincide with the neutron drip pressure, usually calculated in the literature, and is determined by hydrostatic (and diffusion) equilibrium conditions within the star. We also find an instability at the bottom of the fully accreted crust that transforms nuclei into homogeneous nuclear matter. It guarantees that the structure of the fully accreted crust remains self-similar during accretion.
我们研究了吸积中子星地壳的状态方程（EOS）。通常，这样的状态方程是通过（隐含地）假设内壳层中自由（未束缚）的中子和原子核一起运动而得到的。我们认为这个假设违反了未束缚中子的流体静力学（以及扩散）平衡所需的条件(\mu_{n}^{\infty}=\text{const})（(\mu_{n}^{\infty})是红移后的中子化学势）。我们在可压缩液滴近似下构建了一个符合该条件的新状态方程。我们证明，在大部分内壳层中它与催化状态方程相近，与文献中讨论的吸积地壳的状态方程有很大不同。特别是，外 - 内壳层界面处的压力与通常在文献中计算的中子滴压力不一致，而是由恒星内部的流体静力学（以及扩散）平衡条件决定。我们还发现了完全吸积地壳底部存在一种不稳定性，它会将原子核转变为均匀的核物质。这保证了在吸积过程中完全吸积地壳的结构保持自相似。
