Three-Dimensional Simulation of Double-Detonations in the Double-Degenerate Model for Type Ia Supernovae and Interaction of Ejecta with a Surviving White Dwarf Companion

We study the hydrodynamics and nucleosynthesis in the double-detonation model of Type Ia supernovae (SNe~Ia) and the interaction between the ejecta and a surviving white dwarf (WD) companion in the double-degenerate scenario. We set up a binary star system with $1.0M_\odot$ and $0.6M_\odot$ carbon-oxygen (CO) WDs, where the primary WD consists of a CO core and helium (He) shell with $0.95$ and $0.05M_\odot$, respectively. We follow the evolution of the binary star system from the initiation of a He detonation, ignition and propagation of a CO detonation, and the interaction of SN ejecta with the companion WD. The companion (or surviving) WD gets a flung-away velocity of $\sim 1700$~km~s$^{-1}$, and captures $^{56}$Ni of $\sim 0.03M_\odot$, and He of $3 \times 10^{-4}M_\odot$. Such He can be detected on the surface of surviving WDs. The SN ejecta contains a `companion-origin stream', and unburned materials stripped from the companion WD ($\sim 3 \cdot 10^{-3}M_\odot$), although the stream compositions would depend on the He shell mass of the companion WD. The ejecta has also a velocity shift of $\sim 1000$~km~s$^{-1}$ due to the binary motion of the exploding primary WD. These features would be prominent in nebular-phase spectra of oxygen emission lines from the unburned materials like SN~2010lp and iPTF14atg, and of blue- or red-shifted Fe-group emission lines from the velocity shift like a part of sub-luminous SNe~Ia. We expect SN~Ia counterparts to the D$^6$ model would leave these fingerprints for SN~Ia observations.