中子星中相邻I型与II型超导体通过通量分支实现的磁耦合
Magnetic coupling through flux branching of adjacent type-I and -II superconductors in a neutron star
AI总结：
本研究揭示中子星内核I型与外核II型质子超导体通过通量分支磁耦合，推导耦合能公式，解释再循环脉冲星低磁矩对内核半径比的约束。
摘要：
中子星的内核和外核被认为分别含有I型和II型质子超导体。I型超导体处于中间态，由宏观的无通量区域和含通量区域组成，而II型超导体除了微观的量子化通量管外均为无通量状态。本文中我们证明，当宏观通量管以树突状细分为量子化通量管时，内核与外核会发生磁耦合，这一现象被称为通量分支。一个重要的推论是，将一根量子化通量管从其母体宏观通量管上分离需要高达约$10^{12} (r_1/10^6 \rm{cm}) \rm{erg}$的能量，其中$r_1$是宏观通量管的长度。我们将正常态-超导态边界近似为锐边界，计算了由通量分支导致的量子化通量管与宏观通量管之间的磁耦合能，该能量是$f_1$的函数，$f_1$为I型内核半径与II型外核半径的比值。强耦合会延缓II型超导体中的磁场衰减。对于一个仅含有I型质子超导体和极向通量的理想化内核，在不存在双极扩散和抗磁屏蔽的情况下，再循环脉冲星的低磁矩（$\rm{\boldsymbol{\boldsymbol{<}}} \boldsymbol{\boldsymbol{\tilde{}}} 10^{27} \rm{G \rm{cm^3}}$）意味着$f_1 \rm{\boldsymbol{\boldsymbol{<}}} \boldsymbol{\boldsymbol{\tilde{}}} 10^{-1.5}$。
英文摘要：
The inner and outer cores of neutron stars are believed to contain type-I and -II proton superconductors, respectively. The type-I superconductor exists in an intermediate state, comprising macroscopic flux-free and flux-containing regions, while the type-II superconductor is flux-free, except for microscopic, quantized flux tubes. Here, we show that the inner and outer cores are coupled magnetically, when the macroscopic flux tubes subdivide dendritically into quantized flux tubes, a phenomenon called flux branching. An important implication is that up to $\sim 10^{12} (r_1/10^6 \, {\rm cm}) \, {\rm erg}$ of energy are required to separate a quantized flux tube from its progenitor macroscopic flux tube, where $r_1$ is the length of the macroscopic flux tube. Approximating the normal-superconducting boundary as sharp, we calculate the magnetic coupling energy between a quantized and macroscopic flux tube due to flux branching as a function of, $f_1$, the radius of the type-I inner core divided by the radius of the type-II outer core. Strong coupling delays magnetic field decay in the type-II superconductor. For an idealised inner core containing only a type-I proton superconductor and poloidal flux, and in the absence of ambipolar diffusion and diamagnetic screening, the low magnetic moments ($\lesssim 10^{27} \, {\rm G \, cm^3}$) of recycled pulsars imply $f_1 \lesssim 10^{-1.5}$.
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