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

Albert Sneppen, Oliver Just+10 more|arXiv (Cornell University)|Nov 5, 2024

Geophysics and Gravity MeasurementsEarth and Planetary Sciences3 citations

TL;DR

This paper proposes using helium emission in kilonova spectra—specifically the He i λ1083.3 nm line—as a probe of the neutron-star merger remnant's lifetime. By analyzing AT2017gfo’s spectrum, the authors constrain the remnant’s lifetime to ≤30 ms, implying a total binary mass near the threshold for direct black hole collapse (M_thres ≲ 2.93 M⊙), which in turn limits the neutron-star equation of state to a maximum mass of M_max ≲ 2.3 M⊙ and a radius of 1.6 M⊙ stars to ~12 ± 1 km.

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, $M_\mathrm{ m tot}$, 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]

Motivation & Objective

• To develop a new method for constraining the lifetime of neutron-star merger remnants using helium enrichment in ejecta.
• To link the observed absence of helium in AT2017gfo’s spectrum to constraints on the remnant’s survival time.
• To derive bounds on the nuclear equation of state (EoS) using the remnant lifetime and binary mass threshold for black hole formation.
• To assess the implications for the central engine of GRB170817A, particularly whether it was a black hole-torus or magnetar.

Proposed method

• Analyzing the He i λ1083.3 nm spectral feature in the optical/infrared spectrum of AT2017gfo at 4.4 days post-merger.
• Using neutrino-hydrodynamic simulations of neutron-star merger remnants to predict helium mass fraction (X_He) in polar ejecta as a function of remnant lifetime.
• Applying spectral modeling to infer the upper limit on X_He in the ejecta, assuming non-LTE conditions and idealized ejecta geometry.
• Mapping the inferred X_He limit to a maximum remnant lifetime of 20–30 ms, based on simulated X_He(τ_BH) relations.
• Deriving the threshold total binary mass M_thres from the remnant lifetime, using EoS-dependent simulations.
• Combining M_thres constraints with causality and mass-radius relations to bound M_max and R_1.6, using the inverse relationship between R_1.6 and M_max.

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 Sneppen et al. [ 66 ] ) and P Cygni features for various helium abundances computed using the model described in Sect. II . Given a

Experimental results

Research questions

• RQ1 Can helium emission in kilonova spectra be used to infer the lifetime of a neutron-star merger remnant?
• RQ2 What is the upper limit on the helium mass fraction in the polar ejecta of AT2017gfo, and what does it imply for the remnant's survival time?
• RQ3 How does the remnant lifetime constrain the threshold total binary mass M_thres for direct black hole collapse?
• RQ4 What are the resulting bounds on the neutron-star equation of state, particularly M_max and R_1.6, given M_thres ≲ 2.93 M⊙?
• RQ5 What does the remnant lifetime imply about the central engine powering GRB170817A—was it a black hole-torus or a magnetar?

Key findings

• The He i λ1083.3 nm feature in AT2017gfo at 4.4 days is inconsistent with a helium mass fraction X_He ≳ 0.05 in the polar ejecta.
• Neutrino-hydrodynamic simulations are only compatible with this X_He limit if the neutron-star remnant collapses within 20–30 ms.
• This implies a threshold total binary mass for direct black hole collapse of M_thres ≲ 2.93 M⊙ for GW170817.
• The upper bound on M_thres leads to a maximum neutron-star mass of M_max ≲ 2.3 M⊙ when combined with causality constraints.
• For M_max = 2.0 M⊙, the radius of a 1.6 M⊙ neutron star is constrained to R_1.6 = 12 ± 1 km, and for M_max = 2.15 M⊙, R_1.6 = 11.5 ± 1 km.
• A remnant lifetime of ~20 ms implies that GRB170817A was powered by a black hole-torus central engine, not a magnetar.

Figure 2: The fraction of helium in each ionisation 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 have their