Model Type Ia supernova light curves with the Arnett model—adjust nickel mass and diffusion timescale
Type Ia supernovae are thermonuclear explosions of white dwarfs, producing characteristic light curves powered by radioactive decay. The Arnett (1982) diffusion model provides a remarkably accurate description of the bolometric light curve, capturing the rise to peak, the maximum luminosity, and the exponential decline. These standardizable candles have been instrumental in discovering the accelerating expansion of the universe.
Type Ia explosions synthesize approximately 0.4–0.7 M☉ of ⁵⁶Ni through explosive nuclear burning of carbon and oxygen. This nickel decays to ⁵⁶Co (half-life 6.1 days), which subsequently decays to stable ⁵⁶Fe (half-life 77.1 days). The energy released by these decays powers the supernova's luminosity: ε_Ni ≈ 3.9 × 10¹⁰ erg/s/g and ε_Co ≈ 6.8 × 10⁹ erg/s/g. The light curve's shape reflects this two-stage decay process.
The supernova ejecta is optically thick, so gamma rays and positrons from radioactive decay must diffuse outward before escaping. The diffusion timescale is τ_d ≈ √(κM_ej / v_exp), where κ is the opacity (~0.1 cm²/g), M_ej is the ejecta mass, and v_exp is the expansion velocity. For typical parameters, τ_d ≈ 30 days. The Arnett model describes the luminosity as L(t) ≈ M_Ni × ε(t) × exp(-t²/2τ_d²), where ε(t) is the instantaneous energy generation rate from the decay chain.
The light curve rises as diffusion time decreases (expanding ejecta becomes more transparent) while radioactive heating continues. Peak brightness occurs around t_peak ≈ 19 days, when the diffusion time equals the cobalt decay time. The peak bolometric luminosity is L_peak ≈ 10⁴³ erg/s (absolute magnitude M_B ≈ -19.3), making Type Ia SNe as bright as an entire galaxy for weeks. The rise time and peak depend primarily on nickel mass and ejecta mass.
After peak, the ejecta becomes optically thin and the light curve follows the ⁵⁶Co decay rate: L(t) ∝ exp(-t/τ_Co), where τ_Co = 111.3 days is the mean lifetime. In magnitudes, this appears as a linear decline with slope ~0.98 mag per 100 days. The decline rate Δm₁₅ (magnitude drop in first 15 days after maximum) is a key observable that correlates with peak luminosity via the Phillips relation.
Type Ia SNe are not perfect standard candles—they exhibit a range of peak luminosities. However, Mark Phillips (1993) discovered that brighter SNe decline more slowly. This luminosity-width relation allows standardization: measure Δm₁₅, apply a correction to the absolute magnitude, and use the corrected luminosity for distance measurement. The stretch parameter s (or equivalently x₁) quantifies light curve width: broader light curves have higher nickel masses and reach higher peak luminosities.
Type Ia supernovae are the most important cosmological distance indicators beyond ~100 Mpc. Their high peak luminosity makes them visible to z > 1, and their ~10% luminosity standardization (after Phillips correction) provides precise distance measurements. The 1998 discovery of cosmic acceleration came from measuring Type Ia SNe at z ~ 0.5, revealing that distant SNe are fainter than expected in a decelerating universe—the signature of dark energy.
The diversity in Type Ia light curves reflects variations in progenitor systems and explosion physics. More massive white dwarfs (approaching the Chandrasekhar mass M_Ch ≈ 1.4 M☉) produce more ⁵⁶Ni and brighter explosions. Sub-Chandrasekhar explosions (e.g., double-detonation scenarios) produce less nickel and fainter, faster-declining light curves. Understanding these physical variations is crucial for using Type Ia SNe as precision cosmological probes.