Thermonuclear Supernovae

A Type Ia supernova is the thermonuclear disruption of a white dwarf. Unlike a core-collapse event, it involves no massive star and no neutron star; it is a detonation of degenerate carbon and oxygen that leaves nothing behind. The defining observational facts are a spectrum with no hydrogen but a strong silicon absorption line, a light curve powered by radioactivity, and a peak luminosity uniform enough that the small residual scatter can be calibrated away. This lesson sets out the progenitor channels that bring a white dwarf to ignition, the physics of the burning front, the radioactive decay chain that lights the ejecta, and the width-luminosity relation that makes Type Ia supernovae the standardizable candles behind the discovery of cosmic acceleration.

Progenitor channels

A white dwarf in isolation simply cools forever. To explode it must gain mass or merge, and it must be carbon-oxygen: a helium white dwarf is too light to reach ignition, and an oxygen-neon-magnesium white dwarf tends to collapse by electron capture rather than detonate. Two channels dominate the discussion.

• Single-degenerate. The white dwarf accretes hydrogen or helium from a non-degenerate companion — a main-sequence star, subgiant, or red giant — through Roche-lobe overflow. If the accretion rate lies in a narrow window, the accreted hydrogen burns steadily to carbon-oxygen on the surface and the white dwarf grows toward the Chandrasekhar mass. Ignition occurs near $M_{\mathrm{Ch}}$, which naturally explains the uniformity of the explosions: they all detonate at nearly the same mass.
• Double-degenerate. Two white dwarfs in a close binary spiral together through gravitational-wave emission and merge. The combined mass can exceed $M_{\mathrm{Ch}}$, and the disruption of the lighter dwarf onto the heavier one triggers ignition. This channel allows super-Chandrasekhar and sub-Chandrasekhar events and may account for the observed diversity.

The relative importance of the two channels remains unsettled; the near-absence of detected companions and hydrogen in Ia remnants favors double-degenerate mergers for many events, while the tight standardizability points to a common near-Chandrasekhar mass scale.¹

Carbon ignition and the burning front

The white-dwarf interior is degenerate, and degenerate matter is a thermal runaway waiting to happen: its pressure does not depend on temperature, so a rise in temperature raises the reaction rate without raising the pressure that would expand and cool the gas. Compressional heating near the center, or the deep heating of a merger, lifts the temperature until carbon ignites at $T\approx 7\times 10^8\mathrm{K}$. The runaway is explosive because there is no pressure relief valve until the temperature climbs high enough, $\sim 10^9\mathrm{K}$, to lift the electron degeneracy.

The burning front propagates in one of two modes.

The favored models begin as a deflagration and transition to a detonation partway through — the delayed-detonation picture. The initial subsonic burn lets the star expand, lowering the density, so that when the detonation sweeps the outer layers it produces the intermediate-mass elements (silicon, sulfur, calcium) seen in the spectrum alongside the iron-peak core. Roughly half a solar mass of the white dwarf is burned to radioactive nickel-56, and the total energy released, $\sim 10^{44}\mathrm{J}$, exceeds the gravitational binding energy and unbinds the star completely at ejecta speeds of $\sim 10^4\mathrm{km}{\mathrm{s}}^{-1}$.

The radioactive light curve

A Type Ia supernova has no central engine after the explosion. The ejecta expand and would cool adiabatically to invisibility, but they are kept hot by the radioactive decay of the nickel-56 synthesized in the burn. The chain is

both steps electron captures that emit gamma rays. The gamma rays thermalize in the expanding ejecta and are reradiated as the optical display. The peak luminosity is set by the mass of nickel-56 synthesized, through Arnett's rule: the luminosity at maximum equals the instantaneous decay power, because the light-curve rise time matches the effective diffusion time. Since a Chandrasekhar-mass explosion produces a characteristic $\sim 0.6M_{\odot }$ of nickel-56, the peak luminosity is nearly universal, $M_V\approx -19.3$.

After maximum the light curve declines, first on the nickel timescale and then, after a few weeks, on the $77$-day cobalt timescale, which sets the slope of the exponential tail. The two decay constants are visible directly as two slopes in the light curve.

The width-luminosity relation and standardization

Type Ia supernovae are not perfectly identical, but their deviations are correlated. Intrinsically brighter events have broader light curves — they rise and fall more slowly — and fainter events decline faster. This is the Phillips relation, usually parametrized by $\Delta m_{15}$, the magnitude decline in the $15$ days after peak: a larger $\Delta m_{15}$ (faster decline) goes with a fainter peak. Physically, more nickel-56 both brightens the peak and, by raising the ejecta opacity and temperature, lengthens the diffusion time and broadens the curve.

Correcting each light curve by its width — the stretch correction — collapses the family onto a single template. The residual scatter after correction is only about $0.1$–$0.15\mathrm{mag}$, or $\sim 7\%$ in distance. This makes Type Ia supernovae standardizable candles: not standard out of the box, but reducible to a standard by a measured one-parameter correction.

Type Ia as cosmological distance indicators

Because their corrected peak luminosity is known, Type Ia supernovae are visible as standard candles to redshifts beyond $z\approx 1$, far enough to probe the expansion history. Plotting distance modulus against redshift builds the Hubble diagram at cosmological distances, an extension of the local distance ladder. At low redshift the diagram gives the Hubble constant; at high redshift its curvature measures the deceleration or acceleration of the expansion.

In 1998 two teams found that distant Type Ia supernovae were fainter, hence more distant, than a decelerating universe predicts. The observed residual in the Hubble diagram implied that the expansion has been accelerating, driven by a dark-energy component. Type Ia supernovae thus supplied the first direct evidence for cosmic acceleration, the subject of the dark-energy lesson. Their reliability rests on the physics of this lesson: a near-Chandrasekhar mass scale that fixes the nickel yield, and the width-luminosity relation that removes the remaining scatter.

Summary

A Type Ia supernova is the thermonuclear disruption of a carbon-oxygen white dwarf brought to carbon ignition either by accretion toward the Chandrasekhar mass (single-degenerate) or by merger (double-degenerate). Degenerate fuel burns in a runaway because pressure is temperature-independent; a deflagration that transitions to a detonation burns $\sim 0.6M_{\odot }$ to nickel-56 and unbinds the star. The light curve is powered by ${}^{56}\mathrm{Ni}\to {}^{56}\mathrm{Co}\to {}^{56}\mathrm{Fe}$, with the peak luminosity fixed by the nickel mass through Arnett's rule. The Phillips width-luminosity relation reduces the residual scatter to $\sim 7\%$, making these events standardizable candles. Their Hubble diagram, extended past $z\approx 1$, revealed the accelerating expansion and remains a primary probe of dark energy.