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 $λ1083.3$ 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, $M_\mathrm{\rm tot}$, lay close to the threshold binary mass for direct gravitational collapse, $M_\mathrm{thres}$, for which we estimate $M_{\mathrm{thres}}\lesssim 2.93 M_\odot$. 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 $M_\mathrm{max}\lesssim2.3 M_\odot$. The combination of all limits constrains the radii of 1.6 M$_\odot$ NSs to about 12$\pm$1 km for $M_\mathrm{max}$ = 2.0 M$_\odot$ and 11.5$\pm$1 km for $M_\mathrm{max}$ = 2.15 M$_\odot$. This $\sim2$ km allowable range then tightens significantly for $M_\mathrm{max}$ above $\approx2.15$ 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]

Figures (22)

• Figure 1: VLT/X-shooter spectrum of AT2017gfo 4.4 days post-merger with a blackbody continuum overlaid ($T_{\rm BB}=3200$ K from the best-fit blackbody compilation in Sneppen2024) and P Cygni features for various helium abundances computed using the model described in Sect. \ref{['sec:observed_helium_constraints']}. Given a sufficient helium abundance, $X_{\rm He} \sim 0.01$, a sizeable absorption feature will be produced in the region 800--1000 nm. The other spectral features in the spectrum have been tentatively linked to Y ii (600--800 nm) and La iii, Ce iii, Te iii (1200--1600 nm, 2000 nm).
• Figure 2: The fraction of helium in each ionization state (top panel), the fraction of helium in the 1s2s $^3$S state (middle panel) and the helium density required to produce the observed feature (red line, bottom panel) as a function of photospheric electron density. All other parameters are set to their standard values, as described in App. \ref{['app:ionisation-eq']}. In the lower panel, dotted and dash-dotted lines show $n_e$ as a function of $n_{\mathrm{He}}$ given various assumed $X_{\mathrm{He}}$ and adopting a mean mass number, $A=100$, and the same mean charge as helium for all other species. While the unphysical regime where $n_e$ is smaller than the electron density solely contributed by helium is shown with the gray shading. The electron densities expected near the photosphere (indicated with shaded orange region, $n_e \approx 6 \times 10^{6}$--$10^{8}\ {\rm cm}^{-3}$, see App. \ref{['sec:electron-density']}) predict He ii should constitute a major ionization state and thus a sizeable population will be in 1s2s $^3$S. This implies i) a small density of helium, $n_{\mathrm{He}} \sim 10^5$--$10^{6}$ cm$^{-3}$, would be sufficient to produce the observed feature, and ii) such electron density cannot solely be explained from the electrons contributed by helium ions, but require contributions from other ions. In the top panel, we also show the Sr ii fraction computed using recombination rates from Banerjee2025Singh2025 with a dashed black line, which suggests Sr ii may be a subdominant species at $n_e\approx10^{7} {\rm cm}^{-3}$.
• Figure 3: Selected contours of the helium mass fraction as a function of electron fraction, $Y_e$, and entropy, $s$, for parametrized outflow conditions (as in Lippuner2015) and expansion timescales typical of dynamical ejecta ($\tau_{\mathrm{exp}}=$1 ms; solid lines) and post-merger ejecta ($\tau_{\mathrm{exp}}=$10 ms; dotted lines). The nucleosynthesis calculations are from Gross2023 except that the nuclear network is started at 8 GK instead of 6 GK to account for quasi-statistical equilibrium corrections Meyer1998Hix.Thielemann:1999a. Starting at 6 GK would result in an artificially steep transition to large $X_{\mathrm{He}}$ (see Fig. 3 of Perego2022 for comparison). The absence of a helium feature in AT2017gfo rules out a significant fraction of the ejecta to have $Y_e \gtrsim 0.45$ and $s \gtrsim40 \,k_B \, {\rm baryon^{-1}}$.
• Figure 4: Factors $F_{1/2/3}$ of Eqs. (\ref{['eq:F1']})--(\ref{['eq:F3']}) (three panels from left) entering the estimate of the electron fraction resulting in neutrino winds, $Y_e^{\rm eq,abs}$ (cf. Eq. (\ref{['eq:yeeq']})), as well as $Y_e^{\rm eq,abs}$ itself (right panel) for all hydrodynamic simulation models in which the NS remnant survives longer than 10 ms. All quantities are measured at a radius of 500 km. Solid lines are obtained using quantites averaged across the entire sphere, while dashed lines use quantities averaged only within $30^\circ$ from the north pole, thus more appropriately probing the conditions in the polar wind. Lines are plotted only until BH formation, because neutrino winds launched from the BH-torus systems are significantly less massive.
• Figure 5: Snapshots from two numerical simulations in which the NS remnants are short lived (model "sym-n1-a6-short" with $\tau_{\mathrm{BH}}=10$ ms; top row) and long lived ("sym-n1-a6" with $\tau_{\mathrm{BH}}=122$ ms; bottom row) at three characteristic times after merger illustrating the launch of early, fast outflows (left column) and late, slow outflows (middle column) as well as the final ejecta configuration in velocity space (right column), where $Y_e, \rho$, and $v_r$ are the electron fraction (measured before onset of the r-process), mass density, and radial velocity, respectively, and $\tilde{\rho}_{\mathrm{He}}=\mathrm{d}M_{\mathrm{He}}/\mathrm{d}\beta_r/\mathrm{d}\Omega = \rho X_{\mathrm{He}}\beta_r^2(c t)^3$ is the final helium density in dimensionless velocity space (with $\beta_r=r/(ct)$ and solid-angle element $\mathrm{d}\Omega$) rescaled by $\beta_r^2$ to enhance visibility for outflows with strong density decline. Being a stronger source of neutrinos than a BH-torus remnant, the NS remnant produces a far more massive and extended helium-rich, high-$Y_e$ ejecta component at early times, while the late BH-torus outflows are inefficient helium sources in both cases.