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

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]

💡 Research Summary

The authors introduce a novel method to constrain the lifetime of the neutron‑star (NS) merger remnant by exploiting the presence (or absence) of helium in the kilonova ejecta. They focus on the He I λ1083.3 nm transition, which under non‑local thermodynamic equilibrium (NLTE) conditions can produce a prominent P‑Cygni‑type absorption–emission feature in the 800–1200 nm region of the spectrum. Using the 4.4‑day VLT/X‑shooter spectrum of AT2017gfo (the kilonova associated with GW170817), they model the line formation with a detailed collisional‑radiative NLTE code that includes electron‑impact excitation, radiative decay, recombination, and photo‑ionization processes. By varying the helium mass fraction XHe, the electron density ne, and the temperature Te in a homologously expanding ejecta (velocity profile v≈0.19c–0.5c), they find that XHe≈0.01 would generate an optical depth τ≈0.86, producing a clearly detectable absorption trough. The observed spectrum, however, shows no such strong feature, allowing them to place an upper limit of XHe≲0.01 (conservatively XHe≲0.05) in the polar ejecta.

To translate this spectroscopic limit into a constraint on the remnant lifetime, the authors turn to state‑of‑the‑art neutrino‑hydrodynamic simulations of post‑merger remnants. These simulations reveal that the neutrino‑driven wind from a hyper‑massive NS enriches the outflow with helium, and the total helium mass scales roughly linearly with the time the NS survives before collapsing to a black hole (τBH). Their models show that only if τBH is as short as 20–30 ms does the helium mass stay below the spectroscopic bound. Longer lifetimes (≥100 ms) would over‑produce helium, leading to a spectral signature that is not observed. Consequently, the authors argue that the GW170817 remnant collapsed within a few × 10 ms after merger.

A short τBH has immediate implications for the binary’s total gravitational mass Mtot. The collapse time is strongly linked to the threshold binary mass for prompt black‑hole formation, Mthres, which itself depends on the equation of state (EoS). By combining their τBH constraint with the empirical Mthres–Mmax relation (where Mmax is the maximum non‑rotating NS mass), they infer an upper bound Mthres≲2.93 M⊙ and, using causality arguments, a maximum NS mass Mmax≲2.3 M⊙. These limits, together with the previously established lower bound on the NS radius from the kilonova brightness (R≳10.5 km), translate into a narrow allowed range for the radius of a 1.6 M⊙ star: R1.6≈12 ± 1 km if Mmax=2.0 M⊙, and R1.6≈11.5 ± 1 km for Mmax=2.15 M⊙. Radii larger than ~13 km combined with a stiff EoS (high Mmax) are ruled out, eliminating a substantial fraction of contemporary EoS models.

The authors also discuss the broader astrophysical consequences. A rapid collapse favors a black‑hole‑torus central engine for the short gamma‑ray burst GRB 170817A, rather than a long‑lived, highly magnetized NS (magnetar) scenario, which would require a much longer τBH to inject rotational energy into the ejecta—a scenario not supported by the observed afterglow. They acknowledge several sources of uncertainty: the NLTE modeling of the He I line (e.g., line‑blanketing by other r‑process elements), the exact helium yield from neutrino winds (sensitive to neutrino transport and microphysics), and the mapping between τBH and Mthres (dependent on binary mass ratio and EoS). They propose future work to refine atomic data, improve 3‑D neutrino‑radiation‑hydrodynamics simulations, and obtain higher‑quality early‑time spectra of future kilonovae to directly detect or further constrain helium features.

In summary, the paper presents a compelling, observation‑driven pathway from a specific spectral line to stringent constraints on the high‑density nuclear EoS, the maximum mass and radius of neutron stars, and the nature of the central engine in short GRBs. It demonstrates how a modest spectroscopic limit on helium can be leveraged, via sophisticated modeling, to extract profound information about the most extreme matter in the universe.