The main features of the gravitational dynamics of binary neutron star systems are now well established. While the inspiral can be precisely described in the post-Newtonian approximation, fully relativistic magneto-hydrodynamical simulations are required to model the evolution of the merger and post-merger phase. However, the interpretation of the numerical results can often be non-trivial, so that toy models become a very powerful tool. Not only do they simplify the interpretation of the post-merger dynamics, but also allow to gain insights into the physics behind it. In this work, we construct a simple toy model that is capable of reproducing the whole angular momentum evolution of the post-merger remnant, from the merger to the collapse. We validate the model against several fully general-relativistic numerical simulations employing a genetic algorithm, and against additional constraints derived from the spectral properties of the gravitational radiation. As a result, from the remarkably close overlap between the model predictions and the reference simulations within the first milliseconds after the merger, we are able to systematically shed light on the currently open debate regarding the source of the low-frequency peaks of the gravitational wave power spectral density. Additionally, we also present two original relations connecting the angular momentum of the post-merger remnant at merger and collapse to initial properties of the system.
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