Pulsational delayed detonation of a bound white dwarf after a failed surface detonation: viability and observational outcome of the channel for Type Ia supernovae

When a near-Chandrasekhar-mass carbon-oxygen white dwarf ignites a weak, off-center thermonuclear deflagration, the burning ash can break out at the surface, sweep around the star, and converge at the antipode; Röpke and Woosley (2006) found that in three dimensions this surface collision fails to reach the conditions needed to initiate a detonation, leaving the star gravitationally bound and entering global pulsations. The open problem, originating with Arnett and Livne (1994), is whether the contraction phase of these pulsations offers a 'second chance' — a second compression that ignites a detonation (the pulsational delayed detonation, or in later terminology pulsating reverse detonation / pulsationally assisted gravitationally confined detonation) — and whether such a detonation yields an explosion consistent with observed Type Ia supernovae. Later three-dimensional simulations have demonstrated that detonation ignition during the pulsation is numerically feasible, but whether the channel occurs in nature and which observed supernova classes, if any, it can reproduce remains unresolved. The most recent dedicated parameter study reports only rough, imperfect agreement with 1991T-like events — an overluminous, slowly declining subclass — and no good match to normal Type Ia supernovae; whether that limited agreement is intrinsic to the channel or instead reflects the restricted parameter coverage and small model sets examined so far is part of what remains to be established.

Background

A Type Ia supernova (SN Ia) is the thermonuclear explosion of a carbon-oxygen white dwarf (WD), a compact stellar remnant supported by electron degeneracy pressure. Such a WD accretes matter from a binary companion until it approaches the Chandrasekhar mass, about 1.4 solar masses, at which point compressional heating ignites runaway carbon fusion. Nuclear burning propagates either as a deflagration — a subsonic flame — or as a detonation, a supersonic combustion wave that consumes the star in about a second and releases roughly $10^{51}$ erg. A pure central deflagration tends to over-produce neutron-rich iron-group isotopes and under-energize the explosion, while a prompt central detonation burns everything at high density; the widely used compromise is the delayed detonation model, in which burning starts as a deflagration, expands the star, and later transitions to a detonation.

Pre-explosion simulations suggest the ignition is not central but asymmetric and off-center. In the gravitationally confined detonation (GCD) scenario (Plewa, Calder and Lamb 2004), a buoyant burning bubble rises, breaks out at the surface, and its ash flows laterally around the star, converging at the point opposite the breakout; the compression there may heat the fuel enough to initiate a detonation that burns inward through the core. Röpke and Woosley (2006) tested this with two- and three-dimensional simulations: they found that a detonation requires temperatures above about $2\times 10^{9}$ K in fuel denser than roughly $3\times 10^{6}$ to $10^{7}$ g cm$^{-3}$, conditions reached only in artificial two-dimensional setups (ignition bubbles centered at radii of 200 km or more), and never in any of their three-dimensional runs, because the energy released by the deflagration expands the star and weakens the collision. They concluded that surface-collision ('gravitationally confined') detonation is unlikely in nature.

Their bound models, however, do not simply die out: a deflagration too weak to unbind the WD leaves it pulsating — expanding, then recontracting under gravity. Arnett and Livne (1994) had proposed that this second contraction can itself trigger a detonation, a scenario they called pulsational delayed detonation. Later authors rediscovered and renamed the same physical idea: the 'pulsating reverse detonation' (PRD) of Bravo and García-Senz, in which the collapsing outer halo forms an accretion shock that confines and heats the unburned core until an inward detonation forms, and the 'pulsationally assisted gravitationally confined detonation' (PA-GCD) of Jordan et al. (2012), in which the recontraction raises the density and temperature of the fuel-ash mixture in the surface collision region until the Zel'dovich gradient mechanism — detonation initiation in a spatial gradient of induction time, possible when the temperature gradient length is comparable to the critical size for spontaneous initiation — launches the detonation. Related milestones: Seitenzahl et al. (2009) achieved the first in-situ gradient-initiated detonation in a whole-star GCD simulation but found the ignition sensitive to numerical resolution; Jordan et al. (2012) then demonstrated, in three full-star three-dimensional simulations, that pulsationally assisted detonations ignite for deflagration energy releases between 38% and 78% of the WD binding energy; and the failed branch, in which no detonation ever forms, produces faint, low-velocity events and a kicked, iron-cored surviving WD, plausibly connected to the Type Iax supernovae, a peculiar class of underluminous, low-velocity thermonuclear transients. Whether the pulsational channel can actually account for observed SNe Ia — the class that anchors the cosmic distance ladder — remains contested: synthetic observables show strong viewing-angle sensitivity, early PRD spectral models were far too red, and the dedicated three-dimensional parameter study of Lach et al. (2022) finds rough agreement only with the overluminous, slowly declining 1991T-like subclass, with normal SNe Ia unexplained.

Problem Statement

After a weak, off-center deflagration in a near-Chandrasekhar-mass carbon-oxygen white dwarf whose ash breakout fails both to unbind the star and to detonate the antipodal surface collision, the gravitationally bound remnant undergoes global pulsations. Determine:

1. Whether, and under what range of deflagration strengths, ignition geometries, and central densities, the contraction phase of these pulsations ignites a thermonuclear detonation (by the Zel'dovich gradient mechanism — detonation initiation in a spatial gradient of induction time — or otherwise) that burns the unburned core. This is resolved by establishing whether a self-sustaining core-burning detonation forms and by bounding the deflagration-strength, ignition-geometry, and central-density range over which it does, across all three axes jointly rather than any one of them alone.

2. Whether such pulsationally triggered explosions — their kinetic energies, $^{56}$Ni and stable-iron-group yields, light curves, spectra, and viewing-angle behavior — are consistent with any observed class of Type Ia supernovae (for example the 1991T-like subclass of overluminous, slowly declining events). This part is required for the configurations in which a detonation is found, and is resolved by determining whether some pulsationally triggered explosion quantitatively reproduces an observed class of Type Ia supernovae, naming that class and the residual mismatch, or by establishing that none does; a merely rough or qualitative correspondence with a single subclass does not resolve this part.

The outcome space is exhaustive: (a) some pulsationally triggered explosion reproduces an observed class of Type Ia supernovae; (b) a detonation ignites but reproduces no observed class, in which case the closest subclass and the remaining discrepancies must be stated, and such partial agreement is not by itself a refutation of the channel; or (c) no pulsationally triggered detonation forms over the examined range, which rules the channel out only within that range, so that within it the star must instead terminate in the failed-detonation outcome — a subluminous, low-velocity transient that leaves a kicked, gravitationally bound white dwarf remnant. Claiming (c) requires stating the examined range explicitly — its parameter bounds and the sampling of ignition geometries and central densities — and the range must span the domain over which detonation ignition has been reported or predicted.

References

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