A Late-time Radio Survey of Short Gamma-ray Bursts atz < 0.5: New Constraints on the Remnants of Neutron-star Mergers

Massive, rapidly spinning magnetar remnants produced as a result of binary neutron-star (BNS) mergers may deposit a fraction of their energy into the surrounding kilonova ejecta, powering a synchrotron radio signal from the interaction of the ejecta with the circumburst medium. Here, we present 6.0 GHz Very Large Array (VLA) observations of nine, low-redshift short gamma-ray bursts (GRBs; z < 0.5) on rest-frame timescales of 2.4-13.9 yr following the bursts. We place 3 sigma limits on radio continuum emission of F-nu less than or similar to 6-20 mu Jy at the burst positions, or L-nu less than or similar to (0.6-8.3) x 10(28) erg s(-1) Hz(-1). Comparing these limits with new light-curve modeling that properly incorporates relativistic effects, we obtain limits on the energy deposited into the ejecta of E-ej less than or similar to (0.6-6.7) x 10(52) erg (E-ej less than or similar to (1.8-17.6) x 10(52) erg) for an ejecta mass of 0.03 M-circle dot(0.1M(circle dot)). We present a uniform reanalysis of 27 short GRBs with 5.5-6.0 GHz observations, and find that greater than or similar to 50% of short GRBs did not form stable magnetar remnants in their mergers. Assuming short GRBs are produced by BNS mergers drawn from the Galactic BNS population plus an additional component of high-mass GW194025-like mergers in a fractionf(GW190425)of cases, we place constraints on the maximum mass of a nonrotating neutron star (NS; Tolman-Oppenheimer-Volkoff mass; M-TOV), finding M-TOV less than or similar to 2.23 M-circle dot for f(GW190425) = 0.4; this limit increases for larger values of f(GW190425). The detection (or lack thereof) of radio remnants in untargeted surveys such as the VLA Sky Survey (VLASS) could provide more stringent constraints on the fraction of mergers that produce stable remnants. If greater than or similar to 30-300 radio remnants are discovered in VLASS, this suggests that short GRBs are a biased population of BNS mergers in terms of the stability of the remnants they produce.