Maximum Mountains: Crustal Breaking Strain, Shear Modulus and the Largest Sustainable Ellipticity

A neutron-star crust can support a non-axisymmetric deformation, a mountain, only until the strain reaches the breaking strain of the Coulomb lattice. This study combines a density-dependent shear modulus with a breaking strain of 0.10 from molecular-dynamics results to compute the largest ellipticity a crust can sustain as a function of stellar mass. The volume-averaged shear modulus of the inner crust is 1.8e+29 Pa. The maximum ellipticity falls from 6.1e-05 at 1.0 solar masses to 3.3e-06 at 2.1 solar masses, passing through 1.8e-05 at 1.4 solar masses. Those maxima sit one to two orders of magnitude above current gravitational-wave upper limits for known pulsars, so present non-detections do not yet test the breaking-strain picture; they test only whether real mountains approach the crustal maximum. The maximum crustal strain energy, 2.7e+39 J for the canonical star, is also the reservoir against which glitch energy budgets must be compared. This study is simulated and computed from stated assumptions; it is not a measurement.