Type Ia Supernova: Carbon Deflagration Flame Front

Ignition

Progenitor & Flame

Central density ρ_c 2.0×10⁹ g/cm³

Rayleigh–Taylor plumes 14

Time compression 1.0×

DDT trigger density 1.0×10⁷ g/cm³

Flame State

Unignited

Elapsed time

0.00 s

Flame speed

0 km/s

Mass burned

0.000 M☉

Burned fraction

0.0%

Energy released

0.00 foe

⁵⁶Ni yield

0.000 M☉

How it works

A Type Ia supernova ignites a runaway carbon-fusion flame near the centre of a carbon-oxygen white dwarf that has been pushed close to the Chandrasekhar mass (≈1.4 M☉) by accretion. The flame first burns as a subsonic deflagration: hot, buoyant ash is less dense than the fuel ahead of it, so the front is Rayleigh-Taylor unstable and wrinkles into rising plumes that increase its surface area and speed:

Laminar speed:   v_lam(ρ) ≈ v₀ (ρ/ρ₀)^0.8
Turbulent speed: v_RT ≈ v_lam × (1 + 0.15 N_plumes),  capped below 0.3 c_s(ρ)
Sound speed:     c_s(ρ) ≈ c₀ (ρ/ρ₀)^(1/6)   [degenerate electron gas]

If the burning front reaches low enough density (the deflagration-to-detonation transition, DDT — still debated but standard in "delayed-detonation" models), the flame can jump to a supersonic detonation that consumes the rest of the star in a shock-driven burn front near the local sound speed, v_det ≈ 0.8 c_s(ρ).

Material burned at high density reaches nuclear statistical equilibrium and comes out mostly as radioactive ⁵⁶Ni (whose decay chain ⁵⁶Ni→⁵⁶Co→⁵⁶Fe powers the visible light curve); material burned at lower density stalls as intermediate-mass elements (Si, S, Ca). Each burned gram releases roughly Δmc² from fusing to the iron-group peak, so total energy is:

E ≈ Σ e(ρ_local) · m_particle,   e_Ni56 ≈ 9.2×10¹⁷ erg/g,  e_IME ≈ 3×10¹⁷ erg/g
1 foe = 10⁵¹ erg  (typical SN Ia: ~1.3–1.6 foe kinetic, ~0.4–0.8 M☉ of ⁵⁶Ni)

Central density — sets both the local flame speed and the fraction of the star dense enough to burn all the way to ⁵⁶Ni.
RT plumes — more plumes wrinkle the front more, raising the turbulent flame speed and its visible roughness.
DDT trigger density — the ρ ahead of the flame at which it jumps from deflagration to detonation (lower = it must burn more of the star first).

Unburned C/O Burned → ⁵⁶Ni / Fe Detonation shock

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