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

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Adjacent type-I and -II proton superconductors in a rotation-powered pulsar are predicted to exist in a metastable state containing macroscopic and quantized flux tubes, respectively. Previous studies show that the type-I and -II regions are coupled magnetically, when macroscopic flux tubes divide dendritically into quantized flux tubes near the type-I–II interface, through a process known as flux branching. The studies assume that the normal-superconducting boundary is sharp, and the quantized flux tubes do not repel mutually. Here, the sharp-interface approximation is refined by accounting for magnetic repulsion. It is found that flux tubes in the same flux tree cluster with a minimum-energy separation two to seven times less than that of isolated flux tubes. Neutron vortices pin and cluster about flux trees. We find that the maximum characteristic wave strain h₀ of the current quadrupole gravitational radiation emitted by a rectilinear array of clustered vortices exceeds by (1+Nv,t)1/2 the strain h₀ ~ 10⁻³²(f/30\, Hz)5/2 (D/1 \, kpc)⁻¹ emitted by uniformly distributed vortices, where Nv,t is the mean number of pinned vortices per flux tree, f is the star’s spin frequency, and D is the star’s distance from Earth. The factor (1 + Nv,t)1/2 brings h₀ close to the sensitivity limit of the current generation of interferometric gravitational wave detectors under certain circumstances, specifically when flux branching forms relatively few (and hence relatively large) flux trees.