We explore the effects of the deflagration to detonation transition ( DDT ) density on the production of ^ { 56 } { Ni } in thermonuclear supernova explosions ( type Ia supernovae ) .
Within the DDT paradigm , the transition density sets the amount of expansion during the deflagration phase of the explosion and therefore the amount of nuclear statistical equilibrium ( NSE ) material produced .
We employ a theoretical framework for a well-controlled statistical study of two-dimensional simulations of thermonuclear supernovae with randomized initial conditions that can , with a particular choice of transition density , produce a similar average and range of ^ { 56 } { Ni } masses to those inferred from observations .
Within this framework , we utilize a more realistic “ simmered ” white dwarf progenitor model with a flame model and energetics scheme to calculate the amount of ^ { 56 } { Ni } and NSE material synthesized for a suite of simulated explosions in which the transition density is varied in the range 1–3 \times 10 ^ { 7 } g cm ^ { -3 } .
We find a quadratic dependence of the NSE yield on the log of the transition density , which is determined by the competition between plume rise and stellar expansion .
By considering the effect of metallicity on the transition density , we find the NSE yield decreases by 0.055 \pm 0.004 ~ { } M _ { \odot } for a 1 ~ { } Z _ { \odot } increase in metallicity evaluated about solar metallicity .
For the same change in metallicity , this result translates to a 0.067 \pm 0.004 ~ { } M _ { \odot } decrease in the ^ { 56 } { Ni } yield , slightly stronger than that due to the variation in electron fraction from the initial composition .
Observations testing the dependence of the yield on metallicity remain somewhat ambiguous , but the dependence we find is comparable to that inferred from some studies .