Early emission from type Ia supernovae

A unique feature of deflagration-to-detonation (DDT) white dwarf explosion models of SNe of type Ia is the presence of a strong shock wave propagating through the outer envelope. We consider the early emission expected in such models, which is produced by the expanding shock-heated outer part of the ejecta and precedes the emission driven by radioactive decay. We expand on earlier analyses by considering the modification of the pre-detonation density profile by the weak-shocks generated during the deflagration phase, the time evolution of the opacity, and the deviation of the post-shock equation of state from that obtained for radiation pressure domination. A simple analytic model is presented and shown to provide an acceptable approximation to the results of 1D numerical DDT simulations. Our analysis predicts a thousand second long UV/optical flash with a luminosity of ~1 to 3*1e39 erg/s. Lower luminosity corresponds to faster (turbulent) deflagration velocity. The predicted luminosity of the UV flash is an order of magnitude lower than that of earlier estimates, and is expected to be strongly suppressed at times longer than an hour due to the deviation from pure radiation domination.

💡 Research Summary

This paper investigates the early emission that precedes the radioactive‑decay powered light curve in Type Ia supernovae (SNe Ia) undergoing a deflagration‑to‑detonation transition (DDT). In DDT models a strong shock wave is generated when the detonation front reaches the low‑density outer layers of the white dwarf (WD). The shock then propagates through the envelope, heating the outermost shells, which subsequently expand, cool, and radiate. The authors extend previous analytic treatments by incorporating three effects that had been neglected: (1) the modification of the pre‑detonation density profile by weak shocks produced during the deflagration phase, (2) the time‑dependent opacity caused by recombination as the photospheric temperature drops toward the recombination temperature, and (3) the deviation of the post‑shock equation of state (EOS) from pure radiation‑pressure domination, i.e., the increasing importance of gas pressure in the outer, low‑density layers.

Using a power‑law density profile ρ∝δⁿ with n≈3 and a self‑similar shock propagation law v∝ρ⁻ᵝ (β≈0.19), the authors adopt the analytic framework of Rabinak & Waxman (2010) to derive expressions for the bolometric luminosity L(t) and effective temperature T_eff(t). For fully ionized material (constant opacity κ≈0.2 cm² g⁻¹) they obtain L≈3.2×10³⁹ erg s⁻¹ t⁻⁰·³¹ and T_eff≈3.5 eV t⁻⁰·⁴⁷. When the temperature approaches the recombination threshold, the opacity drops, and the luminosity evolution changes: for He envelopes L≈3.1×10³⁹ erg s⁻¹ t⁻⁰·⁰², T_eff≈1.5 eV t⁻⁰·³⁸; for C/O envelopes L≈4.4×10³⁹ erg s⁻¹ t⁰·⁰⁷, T_eff≈1.6 eV t⁻⁰·³⁵.

A crucial new quantity is t_drop, the time at which the radiation‑to‑gas pressure ratio η falls to unity. By equating the post‑shock radiation pressure (aT⁴/3) to the ideal‑gas pressure (ρkT/μm_p) and using the self‑similar expansion, the authors find η_sh≈10³ E₅₁^{3/4} (μ/2) ρ₀^{0.53} R₈.₅^{0.84} (M/1.4 M_⊙)^{0.47}. Solving for η=1 yields t_drop≈(3–5)×10³ s (≈1 hour), depending on composition and opacity. After t_drop the luminosity is suppressed by a factor ∼η^{1/3}–η^{4/3}, causing a rapid decline that makes the flash essentially invisible beyond an hour.

To test the analytic model, the authors perform one‑dimensional DDT hydrodynamic simulations that include realistic nuclear energy release, shock acceleration, and radiative diffusion. The simulated velocity and pressure profiles match the self‑similar predictions, and the calculated light curves reproduce the analytic L(t) and T_eff(t) before t_drop. The simulations confirm that the outer layers become gas‑pressure dominated at densities ≲5×10⁵ g cm⁻³, consistent with the derived t_drop.

The main result is that DDT SNe Ia should exhibit a short UV/optical flash lasting ∼10³ seconds with a peak luminosity of 1–3×10³⁹ erg s⁻¹. This is an order of magnitude fainter than earlier estimates that ignored the EOS transition and opacity evolution. The flash is expected to be strongly suppressed after ≈1 hour, providing a distinctive, time‑limited observational signature of the DDT mechanism. Detecting such a flash would require rapid, high‑cadence UV observations of nearby SNe Ia, and its absence could constrain the prevalence of DDT versus pure deflagration or delayed‑detonation scenarios. The paper demonstrates that incorporating weak‑shock pre‑conditioning, recombination‑driven opacity changes, and realistic EOS effects is essential for accurate predictions of early supernova emission.