⚛️ nuclear theory

Neutron star masses from electron-capture supernovae under equation-of-state uncertainties

This study demonstrates that electron-capture supernovae naturally produce low-mass neutron stars within a narrow gravitational mass range of approximately 1.24–1.265 $M_\odot$ with minimal dependence on the equation of state, suggesting that the even lighter observed neutron stars likely require alternative formation channels such as low-mass iron-core collapse or ultra-stripped supernovae.

Original authors: Vishal Parmar, Domenico Scordino, Ignazio Bombaci

Published 2026-08-25

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Vishal Parmar, Domenico Scordino, Ignazio Bombaci

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Stars are the furnaces of the universe, forging heavy elements in their cores before ending their lives in spectacular explosions. For decades, astronomers have understood two main ways massive stars die. The most common path involves a star building up an iron core until it can no longer support its own weight, collapsing inward to create a neutron star. A second, more delicate path involves stars that are just massive enough to develop cores made of oxygen, neon, and magnesium. In these specific stars, the extreme pressure forces electrons to be captured by atomic nuclei, a process that removes the pressure holding the star up and triggers a collapse. This second path is known as an electron-capture supernova. While both events leave behind a neutron star, the stars that take the electron-capture route are expected to produce the lightest possible neutron stars, making them a unique laboratory for understanding the densest matter in existence.

The question of exactly how light these neutron stars can be has remained difficult to answer because it depends on two complex factors working together. First, the exact chemical makeup of the dying star's core determines when the collapse begins. Second, the internal physics of the resulting neutron star, which is a ball of matter so dense that a single teaspoon would weigh billions of tons, dictates how much of the original star's mass is converted into the final gravitational weight we can observe. Until now, it was unclear whether the uncertainties in the dying star's chemistry or the uncertainties in the physics of dense matter would create a wide range of possible outcomes, or if the process naturally funneled these stars into a very specific, narrow weight class.

A team of researchers has now tackled this problem by combining detailed models of dying stars with a sophisticated statistical approach to the physics of neutron stars. They began by simulating the cores of stars just before they collapse, testing four different realistic mixtures of oxygen, neon, and magnesium. They calculated the precise moment when the star becomes unstable and begins to fall in on itself. Crucially, they did not assume a single, fixed set of rules for how neutron star matter behaves. Instead, they used a vast collection of possible physical models, each consistent with current observations of neutron stars and nuclear physics, to see how the final weight of the star would change under different conditions.

The results reveal a surprisingly tight constraint on the birth weight of these stars. Despite the different chemical recipes of the dying stars, the researchers found that the total amount of matter available to form the neutron star varies very little. When they mapped this matter onto their collection of neutron star models, the final gravitational masses clustered into a narrow window. In the most standard scenario, where no matter is lost during the explosion, the resulting neutron stars weigh between 1.24 and 1.265 times the mass of our Sun. This range is so narrow that the uncertainty in the chemical makeup of the dying star matters far less than the uncertainty in the physics of the neutron star itself. The final weight is primarily controlled by the pressure of matter at densities similar to those found in the center of an atomic nucleus.

This finding has immediate implications for how astronomers identify the origin of the lightest neutron stars they have observed. The study shows that standard electron-capture supernovae cannot easily produce the extremely light neutron stars found in some binary systems, such as the companion to the pulsar PSR J0453+1559, which weighs only about 1.174 solar masses. To reach such a low weight, the explosion would have to eject a massive amount of matter—roughly ten percent of the star's total mass—which current simulations of these explosions do not support. Instead, the researchers suggest that these exceptionally light objects likely originate from a different process, such as the collapse of a very small iron core or a stripped-down star that has lost most of its outer layers before exploding.

The study also highlights how these cosmic objects can serve as tools for probing the fundamental laws of physics. Because the final mass of the neutron star is so sensitive to the pressure of matter at specific densities, a precise measurement of a low-mass neutron star's weight, combined with evidence that it came from an electron-capture supernova, could tell us exactly how stiff or soft the matter inside is. Furthermore, the researchers found that the way these stars distort space and time, a property known as tidal deformability, remains sensitive to the star's size and compactness. This means that when two such stars spiral toward each other and merge, the gravitational waves they emit will carry a signature of their internal structure, offering a way to test the physics of dense matter against the predictions of these models.

Ultimately, the work clarifies that while electron-capture supernovae are a natural factory for low-mass neutron stars, they are not a factory for the lightest ones. The process produces a consistent, restricted range of weights, acting as a cosmic filter that separates the standard low-mass remnants from the extreme outliers. By narrowing down the expected mass range, the study provides a clearer benchmark for astronomers to distinguish between different types of stellar deaths, turning the weight of a neutron star into a precise diagnostic tool for the life and death of stars.

Problem Statement
Electron-capture supernovae (ECSNe) are a theoretically established channel for the formation of low-mass neutron stars, originating from the collapse of strongly electron-degenerate O–Ne–Mg cores in stars near the lower edge of the massive-star regime. However, the precise gravitational mass of the resulting neutron star remnant remains uncertain due to two primary factors: the internal composition of the progenitor core (specifically the relative abundances of Neon and Magnesium) and the Equation of State (EOS) of dense matter. While the threshold density for electron capture is highly sensitive to the O–Ne–Mg mixture, it is unclear how these compositional variations, combined with uncertainties in the neutron-star EOS, propagate to the final observable gravitational mass. Furthermore, recent simulations suggest that low-mass iron-core collapse and ultra-stripped supernovae can also produce very light neutron stars, blurring the observational distinction between formation channels. The paper aims to quantify the minimum remnant mass the ECSN channel can produce and define its plausible mass range when both progenitor-side and remnant-side uncertainties are treated consistently.

Methodology
The authors employ a two-stage computational framework to map progenitor properties to remnant masses:

Progenitor Modeling (White-Dwarf-like Cores): The study models cold, unmagnetized, zero-temperature O–Ne–Mg cores as two-component plasmas embedded in a degenerate electron gas. Four representative compositions are analyzed to probe sensitivity:
- 100% $^{20}$ Ne
- 90% $^{20}$ Ne + 10% $^{24}$ Mg
- 50% $^{20}$ Ne + 50% $^{24}$ Mg
- 65% $^{16}$ O + 35% $^{20}$ Ne
  The electron-capture (EC) threshold is determined by finding the pressure where the Gibbs free energy per baryon of the parent composition equals that of the daughter composition. This yields the threshold gravitational mass ( $M^*_{WD}$ ) and the corresponding threshold baryon number ( $N^*_B$ ) for each composition.
Remnant Modeling (Unified Neutron-Star EOS): The authors utilize a Bayesian ensemble of unified crust–core EOSs derived from Relativistic Mean-Field (RMF) theory (Parmar & Bombaci 2026). This ensemble satisfies constraints from nuclear physics (saturation properties, symmetry energy, giant monopole resonances), chiral effective field theory, and astrophysical observations (NICER mass-radius measurements, GW170817 tidal deformability, and the $2M_\odot$ mass limit).
Mapping Procedure: The baryon number of the collapsing progenitor core ( $N^*_B$ ) is mapped to the neutron-star remnant. The study assumes approximate conservation of baryon number ( $N_{B,NS} = N_{B,WD}$ ) as a baseline, while also exploring scenarios with small ( $0.01\text{--}0.02 M_\odot$ ) and extreme ( $0.10 M_\odot$ ) baryonic mass losses ( $\Delta M_B$ ) to account for ejecta mass. The final gravitational mass ( $M_{NS}$ ) is determined by solving the Tolman–Oppenheimer–Volkoff equations for the unified EOS that matches the progenitor's baryon number.

Key Contributions and Results

Narrow Remnant-Mass Window: Despite significant variations in the EC threshold density (which can vary by nearly 50% depending on the Mg fraction), the resulting threshold baryon number of the collapsing core varies only weakly (by less than 1%). Consequently, the ECSN channel produces a narrow window of remnant gravitational masses.
Baseline Mass Range: In the no-loss case ( $\Delta M_B = 0$ ), standard ECSNe yield remnant neutron stars with gravitational masses in the range of 1.24–1.265 $M_\odot$ . The spread within this range is small, driven primarily by EOS uncertainties rather than progenitor composition.
Impact of Mass Loss: Small baryonic mass losses of $0.01\text{--}0.02 M_\odot$ shift this range modestly downward. However, to reach the extremely low mass of the companion in PSR J0453+1559 ( $1.174 M_\odot$ ), an extreme mass loss of $\sim 0.10 M_\odot$ would be required. The authors note that current ECSN simulations do not favor such large mass losses, as these explosions are intrinsically weak with low ejecta masses.
EOS Sensitivity: The residual uncertainty in the remnant mass is controlled mainly by the pressure of nuclear matter around the saturation density ( $n_0$ ), rather than by high-density core properties. The remnant mass correlates strongly with the symmetry energy slope parameter ( $L$ ) and the symmetry energy curvature ( $K_{sym}$ ).
Comparison with Observations:
- Systems like PSR J0737–3039B ( $1.249 M_\odot$ ) and PSR J1946+2052B ( $1.248 M_\odot$ ) fall directly within the predicted no-loss ECSN range.
- PSR J1756–2251 ( $1.230 M_\odot$ ) is compatible if a small mass loss ( $\sim 0.02 M_\odot$ ) is assumed.
- The companion in PSR J0453+1559 ( $1.174 M_\odot$ ) is likely not a standard ECSN remnant, as it requires unphysically large mass loss within this framework.
- Remnants significantly above $\sim 1.27 M_\odot$ (e.g., PSR J1946+2052B at $1.284 M_\odot$ ) are disfavored as standard ECSN products under the current EOS ensemble.

Significance and Claims
The paper claims that while ECSNe are a natural formation channel for low-mass neutron stars, they are restricted to a specific, narrow mass range ( $\approx 1.24\text{--}1.265 M_\odot$ ). The authors conclude that the lightest observed neutron stars (specifically those below $\sim 1.20 M_\odot$ ) likely require alternative formation channels, such as low-mass iron-core collapse or ultra-stripped supernovae, rather than standard ECSN progenitors.

Furthermore, the study establishes that low-mass double neutron star systems can serve as a joint probe of stellar evolution and dense matter physics. Because the remnant mass is tightly constrained by the progenitor's baryon number, a precisely measured low-mass neutron star with independent evidence of an ECSN origin (e.g., low kick, low eccentricity) could provide a direct astrophysical constraint on the pressure of matter near nuclear saturation density. Conversely, improved constraints on the EOS would sharpen the predicted mass window for ECSN remnants, aiding in the identification of their formation channels.

More like this