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 $\,k_2\,$ divided by the tidal quality factor $\,Q\,$) from the numerically computed tidal drift of the semimajor axis of the binary. The shape of $\,k_2/Q\,$, as a function of the principal tidal frequency, reproduces the kink shape predicted by Efroimsky (2012a; CeMDA 112$\,:\,$283) 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 generalised to inhomogeneous and/or non-spherical bodies.