Radio Constraints on Long-Lived Magnetar Remnants in Short Gamma-Ray Bursts

The merger of a neutron star binary may result in the formation of a rapidly-spinning magnetar. The magnetar can potentially survive for seconds or longer as a supramassive neutron star before collapsing to a black hole if, indeed, it collapses at all. During this process, a fraction of the magnetar's rotational energy of ~10^53 erg is transferred via magnetic spin-down to the surrounding ejecta. The resulting interaction between the ejecta and the surrounding circumburst medium powers a >year-long synchrotron radio transient. We present a search for radio emission with the Very Large Array following nine short-duration gamma-ray bursts (GRBs) at rest-frame times of ~1.3-7.6 years after the bursts, focusing on those events which exhibit early-time excess X-ray emission that may signify the presence of magnetars. We place upper limits of <18-32 microJy on the 6.0 GHz radio emission, corresponding to spectral luminosities of <(0.05-8.3)x10^39 erg s^-1. Comparing these limits to the predicted radio emission from a long-lived remnant and incorporating measurements of the circumburst densities from broad-band modeling of short GRB afterglows, we rule out a stable magnetar with an energy of 10^53 erg for half of the events in our sample. A supramassive remnant that injects a lower rotational energy of 10^52 erg is ruled out for a single event, GRB 050724A. This study represents the deepest and most extensive search for long-term radio emission following short GRBs to date, and thus the most stringent limits placed on the physical properties of magnetars associated with short GRBs from radio observations.