Helium as an Indicator of the Neutron-Star Merger Remnant Lifetime and its Potential for Equation of State Constraints

Abstract

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 $\hat{I}»1083.3$ 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, $M_{\mathrm{thres}}$, for which we estimate $M_{\mathrm{thres}}\lesssim 2.93M_{\odot }$. This upper bound on $M_{\mathrm{thres}}$ yields upper limits on the radii and maximum mass of cold, non-rotating NSs, which rule out simultaneously large values for both quantities. In combination with causality arguments, this result implies a maximum NS mass of $M_{\max }\lesssim 2.3M_{\odot }$. The combination of all limits constrains the radii of 1.6 M${}_{\odot }$ NSs to about 12$\pm$1 km for $M_{\max }$ = 2.0 M${}_{\odot }$ and 11.5$\pm$1 km for $M_{\max }$ = 2.15 M${}_{\odot }$. This $\sim 2$ km allowable range then tightens significantly for $M_{\max }$ above $\approx 2.15$ M${}_{\odot }$. 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... [abridged]

36 pages, 22 figures, 3 tables. PRD, in press