A neutron star’s mountains are centimetres tall

On a neutron star, a bump a few centimetres high is already at the limit of what the crust can hold. The mountains that are likely are smaller.

A neutron star packs more than the Sun’s mass into a sphere about twenty kilometres across. The gravity at the surface is about a hundred billion times Earth’s. Under that load the crust, a rigid lattice of nuclei, fails if it is asked to support much relief. Calculations of the breaking strain put the tallest sustainable bump at centimetres, and the bumps a real star is likely to freeze in as it forms are smaller than the theoretical maximum, down toward millimetres and below.

Those bumps matter because a spinning lopsided star radiates gravitational waves. The limits on such waves, from the detectors already in this library, are also limits on how rough a neutron star is allowed to be. The star can be a lighthouse, and another entry says so. It cannot be a landscape.