Nonlinearr-Modes in Rapidly Rotating Relativistic Stars

The $r$-mode instability in rotating relativistic stars has been shown recently to have important astrophysical implications, provided that $r$-modes are not saturated at low amplitudes by nonlinear effects or by dissipative mechanisms. Here, we present the first study of nonlinear $r$-modes in isentropic, rapidly rotating relativistic stars, via 3D general-relativistic hydrodynamical evolutions. We find that (1) on dynamical time scales, there is no strong nonlinear coupling of $r$-modes to other modes at amplitudes of order one—the maximum $r$-mode amplitude is of order unity. (2) $r$-modes and inertial modes in isentropic stars are predominantly discrete modes. (3) The kinematical drift associated with $r$-modes appears to be present in our simulations, but confirmation requires more precise initial data.