Gravitational radiation from neutron stars deformed by crustal Hall drift

A precondition for the radio emission of pulsars is the existence of strong, small-scale magnetic field structures (`magnetic spots') in the polar cap region. Their creation can proceed via crustal Hall drift out of two qualitatively and quantitatively different initial magnetic field configurations: a field confined completely to the crust and another which penetrates the whole star. The aim of this study is to explore whether these magnetic structures in the crust can deform the star sufficiently to make it an observable source of gravitational waves. We model the evolution of these field configurations, which can develop, within $\sim 10^4$ -- $10^5$ yr, magnetic spots with local surface field strengths $\sim 10^{14}$ G maintained over $\gtrsim 10^6$ yr. Deformations caused by the magnetic forces are calculated. We show that, under favourable initial conditions, a star undergoing crustal Hall drift can have ellipticity $\epsilon\sim 10^{-6}$, even with sub-magnetar polar field strengths, after $\sim 10^5$ yr. A pulsar rotating at $\sim 10^2$ Hz with such $\epsilon$ is a promising gravitational-wave source candidate. Since such large deformations can be caused only by a particular magnetic field configuration that penetrates the whole star and whose maximum magnetic energy is concentrated in the outer core region, gravitational wave emission observed from radio pulsars can thus inform us about the internal field structures of young neutron stars.