Breaking Strain of Neutron Star Crust and Gravitational Waves

Mountains on rapidly rotating neutron stars efficiently radiate gravitational waves. The maximum possible size of these mountains depends on the breaking strain of the neutron star crust. With multimillion ion molecular dynamics simulations of Coulomb solids representing the crust, we show that the breaking strain of pure single crystals is very large and that impurities, defects, and grain boundaries only modestly reduce the breaking strain to around 0.1. Because of the collective behavior of the ions during failure found in our simulations, the neutron star crust is likely very strong and can support mountains large enough so that their gravitational wave radiation could limit the spin periods of some stars and might be detectable in large-scale interferometers. Furthermore, our microscopic modeling of neutron star crust material can help analyze mechanisms relevant in magnetar giant flares and microflares.

Figure 1

Shear stress versus strain for perfect and defective bcc and fcc single crystals containing about $2\times {10}^6$ ions for different shear systems—as given by the crystallographic orientation of the shear plane and the direction of the applied stress [17]—is shown. In addition a polycrystalline sample containing $12.8\times {10}^6$ ions and 8 randomly oriented grains with an average grain diameter of 3962 fm is shown. Results were obtained at a strain rate of $4\times {10}^{-7}c/\mathrm{fm}$.

Figure 2

Polycrystalline sample with $12.8\times {10}^6$ ions consisting of 8 differently oriented grains with an average grain diameter of 3961 fm at strains of 0.0, 0.05, 0.1, and 0.15. Upper panel: The radial distribution functions at different shear states exhibit the characteristic peaks of the bcc structure for strains up to 0.1. At 0.15 strain some degree of amorphization might be possible. Lower panel: At 0.0 strain the eight different grains are shown in different colors. At strains of 0.05, 0.1, and 0.15 the dark gray (red) color indicates plastic deformation, i.e., deviations of the ions away from an ideally uniformly sheared bcc lattice in the range of 0 to 2 times the nearest neighbor distance. Note that the top and bottom layers are frozen and moved to impose the shear.