Non-linear r modes in neutron stars:: a hydrodynamical limitation on r-mode amplitudes

Previously, we found that large-amplitude r modes could decay catastrophically due to non-linear hydrodynamic effects. In this paper, we found the particular coupling mechanism responsible for this catastrophic decay, and identified the fluid modes involved. We find that for a neutron star described by a polytropic equation of state with polytropic index Gamma = 2, the coupling strength of the particular three-mode interaction causing the decay is strong enough that the usual picture of the r-mode instability with a flow pattern dominated by that of an r mode can only be valid for the dimensionless r-mode amplitude less than O(10(-2)).