Neutron star mergers produce a substantial amount of fast-moving ejecta, expanding outwardly for years after the merger. The interaction of these ejecta with the surrounding medium may produce a weak isotropic radio remnant, detectable in relatively nearby events. We use late-time radio observations of short duration gamma-ray bursts (sGRBs) to constrain this model. Two samples of events were studied: four sGRBs that are possibly in the local (<200 Mpc) universe were selected to constrain the remnant non-thermal emission from the sub-relativistic ejecta, whereas 17 sGRBs at cosmological distances were used to constrain the presence of a proto-magnetar central engine, possibly re-energezing the merger ejecta. We consider the case of GRB~170817A/GW170817, and find that in this case the early radio emission may be quenched by the jet blast-wave. In all cases, for ejecta mass range of M_ej lesssim 10^{-2} (5 * 10^{-2}) M_sun, we can rule out very energetic merger ejecta E_ej gtrsim 5 * 10^{52}(10^{53}) erg, thus excluding the presence of a powerful magnetar as a merger remnant.
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