Double-Detonation Models for Type Ia Supernovae: Trigger of Detonation in Companion White Dwarfs and Signatures of Companions' Stripped-off Materials

We have studied double-detonation explosions in double-degenerate (DD) systems with different companion white dwarfs (WD) for modeling type Ia supernovae (SNe Ia) by means of high-resolution smoothed particle hydrodynamics (SPH) simulations. We have found that only the primary WDs explode in some of the DD systems, while the explosions of the primary WDs induce the explosions of the companion WDs in the other DD systems. The former case is so-called Dynamically-Driven Double-Degenerate Double-Detonation (D$^6$) explosion, or helium-ignited violent merger explosion. The supernova ejecta of the primary WDs strip materials from the companion WDs, whose mass is $\sim 10^{-3}M_\odot$. The stripped materials contain carbon and oxygen when the companion WDs are carbon-oxygen (CO) WDs with He shells $\lesssim 0.04M_\odot$. Since they contribute to low-velocity ejecta components as observationally interfered for iPTF14atg, D$^6$ explosions can be counterparts of sub-luminous SNe Ia. The stripped materials may contribute to low-velocity C seen in several SNe Ia. In the latter case, the companion WDs explode through He detonation if they are He WDs, and through double-detonation mechanism if they are CO WDs with He shells. We name these explosions "triple" and "quadruple" detonation (TD/QD) explosions after the number of detonations. The QD explosion may be counterparts of luminous SNe Ia, such as SN 1991T and SN 1999aa, since they yield a large amount of $^{56}$Ni, and their He-detonation products contribute to the early emissions accompanying such luminous SNe Ia. On the other hand, the TD explosion may not yield a sufficient amount of $^{56}$Ni to explain luminous SNe Ia.