The time until black-hole formation in a binary neutron-star (NS) merger contains invaluable information about the nuclear equation of state (EOS) but has thus far been difficult to measure. We propose a new way to constrain the merger remnant’s NS lifetime, which is based on the tendency of the NS-remnant neutrino-driven winds to enrich the ejected material with helium. Based on the He i $\lambda 1083.3\mathrm{nm}$ line, we show that the feature around 800–1200 nm in AT2017gfo at 4.4 days seems inconsistent with a helium mass fraction of $X_{\mathrm{He}}\gtrsim 0.05$ in the polar ejecta. Our recent neutrino-hydrodynamic simulations of merger remnants are only compatible with this limit if the NS remnant collapses within 20–30 ms. Such a short lifetime implies that the total binary mass of GW170817, $M_{\mathrm{tot}}$, lay close to the threshold binary mass for direct gravitational collapse, $M_{\text{thres}}$, for which we estimate $M_{\text{thres}}\lesssim 2.93M_{\odot }$. This upper bound on $M_{\text{thres}}$ yields upper limits on the radii and maximum mass of cold, nonrotating NSs, which rule out simultaneously large values for both quantities. In combination with causality arguments, this result implies a maximum NS mass of $M_{\max }\lesssim 2.3M_{\odot }$. We include an updated constraint yielding lower limits on NS radii from a previous argument that the remnant did not promptly collapse, which is independent of the consideration of the helium content. The combination of all limits constrains the radii of $1.6M_{\odot }$ NSs to about $12\pm 1\mathrm{km}$ for $M_{\max }=2.0M_{\odot }$ and $11.5\pm 1\mathrm{km}$ for $M_{\max }=2.15M_{\odot }$. This $\sim 2\mathrm{km}$ allowable range tightens significantly for $M_{\max }$ above $\approx 2.15M_{\odot }$. This rules out a significant number of current EOS models. The short NS lifetime also implies that a black-hole torus, not a highly magnetized NS, was the central engine powering the relativistic jet of GRB170817A. Our work motivates future developments to further corroborate and improve uncertainties in our chain of arguments regarding non-local-thermodynamic-equilibrium spectral modeling, helium production in merger outflows, and the dependence of the remnant lifetime on the binary mass, with the potential to tighten our constraints from existing data and in particular from future events. This novel method may provide a powerful tool to get a handle on the poorly constrained remnant lifetime, the still debated central engine of short gamma-ray bursts, and the high-density EOS.

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• Equations of state
• Nuclear physics of explosive environments
• Transient & explosive astronomical phenomena
• Neutron stars & pulsars