Numerical simulation of tidal evolution of a viscoelastic body modelled with a mass-spring network

Abstract

We use a damped mass-spring model within an N-body code to simulate the tidal evolution of the spin and orbit of a self-gravitating viscoelastic spherical body moving around a point-mass perturber. The damped mass-spring model represents a Kelvin-Voigt viscoelastic solid. We measure the tidal quality function (the dynamical Love number k2 divided by the tidal quality factor Q) from the numerically computed tidal drift of the semimajor axis of the binary. The shape of k2/Q, as a function of the principal tidal frequency, reproduces the kink shape predicted by Efroimsky for the tidal response of near-spherical homogeneous viscoelastic rotators. We demonstrate that we can directly simulate the tidal evolution of spinning viscoelastic objects. In future, the mass-spring N-body model can be generalized to inhomogeneous and/or non-spherical bodies.