Eppur si muove: Shape of topological defects -- and consequent motion -- in active nematics

Topological defects in systems with liquid-crystalline order are crucial in determining their large-scale properties. In active systems, they are known to have properties impossible at equilibrium: for example, $+1\mathrm{/}2$ defects in nematically-ordered systems self-propel. While some previous theoretical descriptions relied on assuming that the defect shape remains unperturbed by activity, we show that this assumption can lead to inconsistent predictions. We compute the shape of $-1\mathrm{/}2$ defects and show that the one of $+1\mathrm{/}2$ is intimately related to their self-propulsion speed. Our analytical predictions are corroborated via numerical simulations of a generic active nematic theory.