The slow decay of some radio afterglows - a puzzle for the simplest γ-ray burst fireball model

The decay of half of the γ-ray burst (GRB) radio afterglows with long temporal monitoring is significantly slower than at optical frequencies, contrary to what is expected in the simplest fireball model. We investigate four ways to decouple the radio and optical decays: an evolving index of the power-law distribution of the shock-accelerated electrons, the presence of a spectral break between the two domains, a structured outflow, and a long-lived reverse shock contribution to the afterglow emission. For most afterglows, the first scenario cannot accommodate all the properties of the afterglow emission. If the spectral break of the second scenario is the cooling frequency, then observations require that, as the fireball decelerates, the parameter for the minimal electron energy decreases and the magnetic field strength is constant or increases. The latter behaviour seems implausible and is alleviated if the circumburst density increases outwards. In the framework of the third scenario, the optical afterglow arises from a more energetic, narrow outflow core while the radio emission comes from a more extended envelope. This scenario is at best marginally consistent with the general properties of the radio and optical afterglow emissions and requires a total electron energy exceeding equipartition, and thus it does not provide an acceptable solution. In the fourth scenario, it is assumed that the radio afterglow emission arises in the reverse shock propagating in a steady stream of ejecta, which catch up with the decelerating GRB remnant. This scenario can accommodate the properties of the afterglows with slow radio decays and requires that the injected energy is less than or comparable to the initial fireball energy, while other afterglow parameters have reasonable values. We find the reverse-forward shock scenario to be the most viable explanation for the shallow decay observed in some radio afterglows. For a jet, the transition to a semirelativistic motion mitigates the radio decay; however, this scenario would work only when the slower radio decay is observed well after the steeper optical fall-off. A structured outflow with a relativistic core, yielding a fast-decaying optical emission, and a non-relativistic envelope, producing a slowly falling-off radio afterglow, is not a viable solution, as it fails to decouple the radio and optical decays.