A Semi-analytic Criterion for the Spontaneous Initiation of Carbon Detonations in White Dwarfs

Abstract

Despite over forty years of active research, the nature of the white dwarf progenitors of Type Ia supernovae remains unclear. However, in the last decade, various progenitor scenarios have highlighted the need for detonations to be the primary mechanism by which these white dwarfs are consumed, but it is unclear how these detonations are triggered. In this paper we study how detonations are spontaneously initiated due to temperature inhomogeneities, e.g., hotspots, in burning nuclear fuel in a simplified physical scenario. Following the earlier work by Zel'Dovich, we describe the physics of detonation initiation in terms of the comparison between the spontaneous wave speed and the Chapman-Jouguet speed. We develop an analytic expression for the spontaneous wave speed and utilize it to determine a semi-analytic criterion for the minimum size of a hotspot with a linear temperature gradient between a peak and base temperature for which detonations in burning carbonoxygen material can occur. Our results suggest that spontaneous detonations may easily form under a diverse range of conditions, likely allowing a number of progenitor scenarios to initiate detonations that burn up the star.

Numerical Stability of Detonations in White Dwarf Simulations

“…Kushnir et al (2013) argued that many of these simulations featured numerically unstable evolution, ultimately caused by the zone size being significantly larger than the length scale over which detonations form. The detonation length scale can vary widely based on physical conditions (Seitenzahl et al 2009;Garg & Chang 2017) but is generally not larger than 10 km. Kushnir et al argue that this numerically unstable evolution is the primary cause of convergence difficulties.…”

Preparing Nuclear Astrophysics for Exascale

“…Given the size of the domain, the spatial width of a grid zone is 50 kilometers (compare to the radius of the stars, nearly 10,000 kilometers, which is the same order of magnitude as the radius of the Earth -these stars are quite dense). The length scale over which a thermonuclear detonation begins to propagate in this stellar material is not especially well known but is very likely smaller than 10 kilometers ( [30], [31]) and possibly much smaller, so our simulations are unresolved. Worse still, [32] and [33] observe that the thermonuclear fusion process is numerically very unstable at this resolution.…”

Supernovae Ia in 2017: a long time delay from merger/accretion to explosion

“…The same challenges are applicable to the long-MED DD scenario, but the merger is of two WDs due to gravitational waves rather than inside a common envelope. For a recent study of igniting detonation see, e.g., Garg & Chang (2017).…”