The Production of Electron-Capture Elements in Thermonuclear Supernovae: Theory vs. Observations

Abstract: Type Ia supernovae (SNe Ia) explosively destroy carbon-oxygen white dwarfs (WDs) in multiple stellar systems. They produce approximately 50% of the iron-group elements in the Universe, synthesize electron-capture (EC) elements, drive nuclear physics experiments, and underpin high-precision cosmology. To first order, the outcome is governed by nuclear physics, a property often described as stellar amnesia. Recently, this stellar amnesia has begun to be broken by the nearly universal detection of EC elements with JWST. These elements trace high-density burning, largely ruling out the currently popular helium-triggered, sub-Mch detonation models as the dominant channel. Instead, the ubiquitous presence of EC is shifting back the focus to dynamical and secular mergers, and near-Mch explosions similar to the deflagration model W7, but in which the nuclear flame undergoes a deflagration-to-detonation transition. The early deflagration phase is especially important because spherical simulations identify the central WD density, and thus the WD mass, as a key parameter governing the explosion. Here, we present detailed magneto-hydrodynamical simulations. We find that small-scale, pre-existing turbulence expected from the pre-explosion smoldering phase is essential for overcoming the fundamental challenges imposed by the intrinsic 3D physics. This turbulence systematically reduces the production of EC elements by about a factor of two, implying the need for WD central densities closer to those associated with accretion-induced collapse to a neutron star. We also demonstrate the effect of magnetic fields near the saturation field strength and highlight the need for higher-precision EC rates at low Ye.

• The paper shows that pre-existing small-scale turbulence restores near-spherical deflagration burning, while turbulent magnetic fields accelerate mixing and expansion in 3D white-dwarf simulations.
• The simulations find that faster expansion suppresses electron-capture production by roughly a factor of two, requiring central densities about 40% higher than 1D estimates to explain observed stable nickel.
• The results support near-Chandrasekhar-mass Type Ia supernova channels and identify key priorities, including improved electron-capture rates, later-stage explosion modeling, and self-consistent magnetic-field evolution.

Observational motivation

The paper addresses a central diagnostic in Type Ia supernova (SN Ia) research: electron-capture (EC) elements. JWST mid-infrared spectroscopy has now revealed forbidden lines of stable $^{58}$Ni in every one of the roughly dozen SNe Ia with published mid-IR spectra, implying that $>0.04\,M_\odot$ of $^{58}$Ni forms in these events. Because $^{58}$Ni is produced only when the electron fraction $Y_e$ is driven down by electron captures at high density, its presence at low velocities ($<3000\ \mathrm{km\,s^{-1}}$) points to high-density, central burning in near-Chandrasekhar-mass progenitors ($M_{\rm WD} > 1.2\,M_\odot$). This observation largely rules out He-triggered sub-$M_{\rm Ch}$ detonation models as the dominant channel, since their lower burning densities and supersonic detonation fronts suppress EC production.

The authors also analyze late-time [Fe II] 1.644 $\mu$m line widths in SN 2013aa, SN 2017cbv, and SN 2014J out to 500+ days. Sustained line broadening at these epochs requires that positrons from $^{56}$Co decay remain magnetically trapped, supporting initial magnetic fields in the progenitor of order $>0.04\,M_\odot$0 G or higher—well above typical isolated WD fields. The paper therefore embeds its simulations in a context where both high central densities and strong magnetic fields are observationally motivated.

Numerical setup

The simulations use FLASH 4.8 to evolve the early deflagration phase of a $>0.04\,M_\odot$1 C/O WD (central density $>0.04\,M_\odot$2, radius $>0.04\,M_\odot$3 km) on a Cartesian AMR grid with maximum refinement levels of 7–10, corresponding to minimum cell sizes of 10 km down to 1.2 km. The MHD solver is an unsplit staggered-mesh scheme with a hybrid Roe/HLLD Riemann solver and a Helmholtz equation of state. Burning is captured with an advection–diffusion–reaction scheme (sKPP reaction term) at a constant flame speed of 200 km/s; NSE, NSQE, and carbon-burning energy releases are assigned by density. Nucleosynthesis, including EC rates, is performed in post-processing on 7,500–8,500 passive tracer particles.

A key methodological choice is the inclusion of pre-existing turbulence as an initial condition, generated with the BxC toolkit. The turbulence is meant to represent the smoldering (simmering) phase preceding runaway ignition, with diffusion radii $>0.04\,M_\odot$4 of 40–300 km and rms velocities up to $>0.04\,M_\odot$5 km/s. Magnetic fields are initialized either as small-scale turbulent fields (rms up to $>0.04\,M_\odot$6 G) or as large-scale dipoles (up to $>0.04\,M_\odot$7 G at 500 km), spanning sub-percent to several-percent fractions of the equipartition field. The authors acknowledge that the initial field configurations are assumed ab initio rather than grown self-consistently, and that the transition from smoldering to explosive burning remains poorly understood.

Magnetohydrodynamic results

The central finding of the hydrodynamic study is that small-scale, pre-existing turbulence is essential for reproducing the near-spherical burning assumed in successful 1D delayed-detonation (DDT) models. Quantitatively:

• Without turbulence, filling factors of burned material within the inner 300 km reach at most $>0.04\,M_\odot$8; large unburned C/O pockets persist throughout the star, and the WD does not pre-expand appreciably, yielding negligible intermediate-mass elements (IME)—in direct conflict with observed pre-maximum spectra.
• Small-scale turbulence ($>0.04\,M_\odot$9 km, $^{58}$0 km/s, simulation turb4b) drags the deflagration into the pockets, raising filling factors toward unity within 800 km by $^{58}$1 s. Nuclear energy generation reaches $^{58}$2 erg (roughly one third of the WD binding energy) by $^{58}$3 s, triggering expansion.
• Larger-scale turbulence ($^{58}$4–300 km) still leaves plumes and pockets; only eddies smaller than the pockets mix efficiently.

Magnetic fields modulate this picture. Turbulent fields below $^{58}$5 of equipartition have minor effects (turb4a vs. turb4b are nearly identical), but a field at $^{58}$6 of equipartition (turb4c) further enhances mixing via Lorentz forces and accelerates burning. Large-scale dipole fields, by contrast, fail to burn the pockets but produce a distinctive squeezing effect: Rayleigh–Taylor growth is inhibited along the dipole axis, and the front overdevelops perpendicular to it, redistributing EC elements asymmetrically without changing total yields.

Consequences for electron-capture production

The EC yields are governed by the duration of high-density burning: as nuclear energy accumulates and the WD expands, densities fall and EC reactions shut off. Because turbulence and turbulent magnetic fields accelerate burning and earlier expansion, they systematically reduce EC element production by about a factor of two relative to spherical models. The paper's headline quantitative conclusion is that 3D effects require a $^{58}$7 increase in the assumed central density $^{58}$8 compared with inferences based on 1D models. Since spherical DDT models infer $^{58}$9–$^{58}$0 (producing 0.01–0.15 $^{58}$1 of $^{58}$2Ni) for observed SNe Ia, the 3D correction pushes required central densities toward the regime approaching accretion-induced collapse to a neutron star. This tightens the constraint on progenitor mass and accretion history, and reinforces the case for near-$^{58}$3 channels—DDT explosions or secular mergers—over sub-$^{58}$4 double detonations.

The paper also notes that $^{58}$5 evolution depends jointly on the nuclear EC rates and the duration of high-density burning, and calls for higher-precision EC rates on iron-group nuclei and on Mn and Cr at low $^{58}$6, at a level commensurate with the $^{58}$7 precision now achievable in mid-IR spectroscopic modeling.

Limitations and open questions

The authors are explicit about several caveats. The simulations cover only the early deflagration phase; while this suffices to fix total EC masses, the final velocity-space distribution of EC elements may be altered by the subsequent Rayleigh–Taylor-dominated deflagration and the detonation phase. Whether the high filling factor in the inner EC region acts as a barrier to inward RT mixing is left unresolved. The parameter grid is narrow—a single progenitor structure at a single central density—and extension to low-density WDs and to densities approaching the accretion-induced-collapse limit is deferred to future work. The growth of the magnetic field during the simulated evolution is observed but not studied in detail, and secular mergers as an alternative high-density channel remain unmodeled. Finally, the constant flame speed of 200 km/s is a simplification adopted to sidestep uncertain sub-grid physics; the authors justify it by tests at 100 km/s showing qualitatively similar behavior, but the dependence of the EC suppression factor on this choice is not fully quantified.

Conclusion

This paper connects JWST-era observations of stable nickel in SNe Ia to 3D MHD simulations of the deflagration phase, showing that physically motivated pre-existing turbulence from the smoldering phase restores the near-spherical burning on which successful 1D DDT models rely, while simultaneously halving EC yields relative to those models. The resulting $^{58}$8 upward revision of inferred central densities, together with evidence for ultra-high magnetic fields from late-time IR line widths, strengthens the case for near-$^{58}$9 progenitors and places new demands on nuclear EC rate measurements. The open questions—final EC distributions through detonation, field growth, and the merger channel—are well defined and tractable with the framework established here.