A late-time radio survey of short gamma-ray bursts at z < 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 3σ limits on radio continuum emission of F_ν ≾ 6-20 μJy at the burst positions, or L_ν ≾ (0.6-8.3) × 10²⁸ 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 ≾ (0.6-6.7) × 10⁵² erg (E_ej ≾ (1.8-17.6) ´ 10⁵² erg) for an ejecta mass of 0.03 M_e (0.1 M_e). We present a uniform reanalysis of 27 short GRBs with 5.5-6.0 GHz observations, and find that ≳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 fraction f_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 ≾ 2.23 M 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 ≳ 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.