Magnetic coupling through flux branching of adjacent type-I and -II superconductors in a neutron star

Abstract

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 $\sim 10^{12}(r_1/10^6\mathrm{cm})\mathrm{erg}$ 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 ($\lesssim 10^{27}\mathrm{G}\mathrm{c}{\mathrm{m}}^3$) of recycled pulsars imply $f_1\lesssim 10^{-1.5}$.

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Cited by in corpus (1)

• Flux tube clustering from magnetic coupling of adjacent type-I and -II superconductors in a neutron star: persistent gravitational radiation