Capturing the Fire: Flame Energetics and Neutronization for Type Ia Supernova Simulations

Abstract

We develop and calibrate a realistic model flame for hydrodynamical simulations of deflagrations in white dwarf (Type Ia) supernovae. Our flame model builds on the advection-diffusion-reaction model of Khokhlov and includes electron screening and Coulomb corrections to the equation of state in a self-consistent way. We calibrate this model flame-its energetics and timescales for energy release and neutronization-with self-heating reaction network calculations that include both these Coulomb effects and up-to-date weak interactions. The burned material evolves post-flame due to both weak interactions and hydrodynamic changes in density and temperature. We develop a scheme to follow the evolution, including neutronization, of the NSE state subsequent to the passage of the flame front. As a result, our model flame is suitable for deflagration simulations over a wide range of initial central densities and can track the temperature and electron fraction of the burned material through the explosion and into the expansion of the ejecta.

STUDY OF THE DETONATION PHASE IN THE GRAVITATIONALLY CONFINED DETONATION MODEL OF TYPE Ia SUPERNOVAE

“…Additionally, energy losses (through neutrino emission) and changes in the electron mole fraction Y e due to weak interactions (electron and positron decays and captures) are incorporated by convolving the temperature-and density-dependent NSE distributions with all relevant weak reactions. Additional details concerning the nuclear physics and the numerical lookup scheme is presented in Calder et al (2007), Townsley et al (2007), and Seitenzahl et al (2009).…”

“…In particular, we evolve the φ 1 variable using the carbon fusion rate N A σ v CF of Caughlan & Fowler (1988), according toẊ C = −ρX 2 C N A σ v CF /A C for mass density ρ and atomic mass of carbon A C . The relationship between φ 1 and the mass fraction of carbon X C is that presented in Calder et al (2007), X C = (1−φ 1 )X 0 C , where X 0 C is the initial mass fraction of 12 C in the WD, which is taken to be 0.5 in the present case.…”

“…The evolution of Y e and the abundances of nuclei along this trajectory have been calculated using a nuclear reaction network initialized with the initial composition of the WD material in the simulation, equal mass fractions of 12 C and 16 O. The network code used for the integrations is a version of the network used in Calder et al (2007) expanded to 443 nuclear species (see Table 2). The thermonuclear reaction rates are taken from an expanded version (H. Schatz 2005, private communication) of the rate compilation REACLIB (Thielemann et al 1986;Rauscher & Thielemann 2000).…”

“…We have also included the temperature-dependent nuclear partition functions provided by Rauscher & Thielemann (2000), both in the determination of the rates of inverse reactions and in our determination of NSE abundance patterns. Electron screening of thermonuclear reaction rates is incorporated, adopting the relations for weak screening and strong screening provided by Wallace et al (1982; for additional details see the Appendix of Calder et al 2007). Contributions from weak reactions are included using the rates provided by Langanke & Martínez-Pinedo (2001).…”

“…The NSE composition corresponding to the same density and neutron excess for each temperature along the rarefaction part of the trajectory is also shown for comparison (dashed lines). The NSE mass fractions were determined with the NSE solver described in Calder et al (2007) and Seitenzahl et al (2009), which uses the same nuclear physics as the reaction network code. Figure 14 illustrates the degree to which adopting an NSE state at a particular "freeze-out temperature" is a poor approximation to the final freeze-out abundances.…”