Vortex pinning and the elastic response of neutron-star crusts II. Non-axisymmetric loading and Magnus mountains

Abstract

Pinned superfluid vortices transmit a Magnus force to the neutron-star crust. A non-axisymmetric component of the superfluid-lattice lag can therefore support a persistent mass quadrupole. We calculate the l=m=2 response of self-gravitating, radially stratified spherical stars with SLy4 and BSk21 backgrounds, using a local microscopic pinning cap and a density-dependent Coulomb-lattice shear modulus. For a 1.4 M_sun star at 100 Hz, the equilibrium-compression maxima are epsilon=2.67x10^-9 (SLy4) and 2.44x10^-9 (BSk21). The global quadrupole is strikingly insensitive to the shear prescription: replacing mu=0.01P by the Coulomb profile and strongly varying uncertain edge layers changes the result only at the percent level. The dominant internal sensitivity is instead compressional. A density-resolved compressional kernel increases through the inner crust and steepens close to the crust-core interface, particularly for BSk21, showing that the deep inner crust controls the EoS dependence of the mountain. A fixed-composition calculation is used only as a non-relaxed sensitivity diagnostic, not as the secular prediction. At a common true local velocity benchmark, our fiducial ellipticities remain more than an order of magnitude below the complementary two-component cylindrical calculation of Gangwar & Jones (2026). We argue that the comparison points to the relative superfluid-lattice degree of freedom as the natural next ingredient for a common spherical model. The main result is therefore physical rather than numerical: the Magnus-mountain scale is robust to shear microphysics, while the deep-crust compressional response sets the leading uncertainty of the one-displacement model.