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We study the hydrodynamics and nucleosynthesis in the double-detonation modelof Type Ia supernovae (SNe~Ia) and the interaction between the ejecta and asurviving white dwarf (WD) companion in the double-degenerate scenario. We setup 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 binarystar system from the initiation of a He detonation, ignition and propagation ofa CO detonation, and the interaction of SN ejecta with the companion WD. Thecompanion (or surviving) WD gets a flung-away velocity of $\sim1700$~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 survivingWDs. The SN ejecta contains a `companion-origin stream', and unburned materialsstripped from the companion WD ($\sim 3 \cdot 10^{-3}M_\odot$), although thestream compositions would depend on the He shell mass of the companion WD. Theejecta has also a velocity shift of $\sim 1000$~km~s$^{-1}$ due to the binarymotion of the exploding primary WD. These features would be prominent innebular-phase spectra of oxygen emission lines from the unburned materials likeSN~2010lp and iPTF14atg, and of blue- or red-shifted Fe-group emission linesfrom the velocity shift like a part of sub-luminous SNe~Ia. We expect SN~Iacounterparts to the D$^6$ model would leave these fingerprints for SN~Iaobservations.

astrophysical journal/the astrophysical journal

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