Uncertainties and robustness of the ignition process in type Ia supernovae

It is widely accepted that the onset of the explosive carbon burning in the core of a CO WD triggers the ignition of a SN Ia. The features of the ignition are among the few free parameters of the SN Ia explosion theory. We explore the role for the ignition process of two different issues: firstly, the ignition is studied in WD models coming from different accretion histories. Secondly, we estimate how a different reaction rate for C-burning can affect the ignition. Two-dimensional hydrodynamical simulations of temperature perturbations in the WD core (“bubbles”) are performed with the FLASH code. In order to evaluate the impact of the C-burning reaction rate on the WD model, the evolution code FLASH_THE_TORTOISE from Lesaffre et al. (2006) is used. In different WD models a key role is played by the different gravitational acceleration in the progenitor’s core. As a consequence, the ignition is disfavored at a large distance from the WD center in models with a larger central density, resulting from the evolution of initially more massive progenitors. Changes in the C reaction rate at T < 5e8 K slightly influence the ignition density in the WD core, while the ignition temperature is almost unaffected. Recent measurements of new resonances in the C-burning reaction rate (Spillane et al. 2007) do not affect the core conditions of the WD significantly. This simple analysis, performed on the features of the temperature perturbations in the WD core, should be extended in the framework of the state-of-the-art numerical tools for studying the turbulent convection and ignition in the WD core. Future measurements of the C-burning reactions cross section at low energy, though certainly useful, are not expected to affect dramatically our current understanding of the ignition process.

💡 Research Summary

This paper investigates two major sources of uncertainty in the ignition of Type Ia supernovae (SNe Ia): the pre‑explosion white dwarf (WD) structure resulting from different accretion histories, and the nuclear reaction rate of carbon‑carbon (C+C) burning. Using the evolutionary code FLASH_THE_TORTOISE (Lesaffre et al. 2006), the authors construct several WD models that differ in central density (ρ_c) and temperature (T_c) because of variations in the initial mass of the progenitor and the rate at which mass is accumulated. Higher‑mass progenitors produce WDs with larger ρ_c, which in turn yields a stronger gravitational acceleration (g) in the core.

The second part of the study employs the FLASH hydrodynamics code to perform two‑dimensional simulations of localized temperature perturbations—referred to as “bubbles”—embedded in the WD core. Each bubble is initialized with a radius of roughly 10 m and a temperature excess of ~10⁸ K relative to the surrounding plasma. The simulations follow the competition between buoyant rise, conductive cooling, and nuclear energy release over timescales of ~0.1 s. The key finding is that the magnitude of g controls whether a bubble can survive long enough to trigger runaway carbon burning. In models with high g (i.e., high ρ_c), bubbles rise rapidly, experience limited mixing with fresh fuel, and are quenched by thermal diffusion before the nuclear heating can dominate. Consequently, ignition is strongly suppressed at distances greater than ~50 km from the WD centre in these dense models. Conversely, in lower‑g models, bubbles ascend more slowly, allowing sufficient fuel mixing and heating, which makes off‑centre ignition more plausible.

To assess the impact of nuclear physics uncertainties, the authors modify the C+C reaction rate in two ways. First, they impose a ±10 % variation in the rate for temperatures below 5 × 10⁸ K, a regime relevant to the pre‑ignition simmering phase. Second, they incorporate the recent resonance measurements reported by Spillane et al. (2007), which increase the rate by roughly 30 % in the same temperature range. The altered rates are fed back into the WD evolutionary calculations to determine new ignition conditions. The results show that a higher reaction rate lowers the critical central density for ignition by only 2–3 %, while the ignition temperature remains essentially unchanged. Thus, even the most recent experimental refinements of the C+C cross‑section have a negligible effect on the overall ignition picture.

Overall, the study concludes that (1) the gravitational profile of the WD core, set by its accretion history, is the dominant factor governing the fate of temperature perturbations and therefore the location of ignition; (2) present uncertainties in the low‑energy C+C cross‑section do not substantially modify the core conditions at which runaway burning begins; and (3) future work should incorporate three‑dimensional turbulent convection and multi‑bubble interactions using state‑of‑the‑art numerical tools to refine the ignition model. Such advances are essential for improving the predictive power of SNe Ia as standardizable candles in cosmology.