Mergers of two carbon-oxygen (CO) white dwarfs (WDs) have been considered to be progenitors of Type Ia supernovae (SNe Ia). Based on smoothed particle hydrodynamics (SPH) simulations, previous studies have claimed that mergers of CO WDs lead to SN Ia explosions either in the dynamical merger phase or the stationary rotating merger remnant phase. However, the mass range of CO WDs that lead to SNe Ia has notyet been clearly identified. In the present work, we perform systematic SPH merger simulations for the WD masses ranging from M 0.5  to M 1.1  with higher resolutions than the previous systematic surveys and examine whether or not carbon burning occurs dynamically or quiescently in each phase. We further study the possibility of SNe Ia explosions and estimate the mass range of CO WDs that lead to SNe Ia. We found that when both WDs are massive, i.e., in the mass range of ⩽ ⩽ and the total mass exceeds M 1.38  , they can finally explode in the stationary rotating merger remnant phase. We estimate the contribution of CO WD mergers to the entire SN Ia rate in our galaxy to be of 9%  . Thus, it might be difficult to explain all galactic SNe Ia with CO WD mergers.

We present the basic idea, implementation, measured performance and performance model of FDPS (Framework for developing particle simulators). FDPS is an application-development framework which helps the researchers to develop simulation programs using particle methods for large-scale distributed-memory parallel supercomputers. A particle-based simulation program for distributed-memory parallel computers needs to perform domain decomposition, exchange of particles which are not in the domain of each computing node, and gathering of the particle information in other nodes which are necessary for interaction calculation. Also, even if distributed-memory parallel computers are not used, in order to reduce the amount of computation, algorithms such as Barnes-Hut tree algorithm or Fast Multipole Method should be used in the case of long-range interactions. For short-range interactions, some methods to limit the calculation to neighbor particles are necessary. FDPS provides all of these functions which are necessary for efficient parallel execution of particle-based simulations as "templates", which are independent of the actual data structure of particles and the functional form of the particle-particle interaction. By using FDPS, researchers can write their programs with the amount of work necessary to write a simple, sequential and unoptimized program of O(N 2 ) calculation cost, and yet the program, once compiled with FDPS, will run efficiently on largescale parallel supercomputers. A simple gravitational N -body program can be written in around 120 lines. We report the actual performance of these programs and the performance model. The weak scaling performance is very good, and almost linear speedup was obtained for up to the full system of K computer. The minimum calculation time per timestep is in the range of 30 ms (N = 10 7 ) to 300 ms (N = 10 9 ). These are currently limited by the time for the calculation of the domain decomposition and communication necessary for the interaction calculation. We discuss how we can overcome these bottlenecks.

We perform smoothed particle hydrodynamics (SPH) simulations for merging binary carbon-oxygen (CO) white dwarfs (WDs) with masses of 1.1 and 1.0 M ⊙ , until the merger remnant reaches a dynamically steady state. Using these results, we assess whether the binary could induce a thermonuclear explosion, and whether the explosion could be observed as a type Ia supernova (SN Ia). We investigate three explosion mechanisms: a helium-ignition following the dynamical merger ('helium-ignited violent merger model'), a carbon-ignition ('carbon-ignited violent merger model'), and an explosion following the formation of the Chandrasekhar mass WD ('Chandrasekhar mass model'). An explosion of the helium-ignited violent merger model is possible, while we predict that the resulting SN ejecta are highly asymmetric since its companion star is fully intact at the time of the explosion. The carbonignited violent merger model can also lead to an explosion. However, the envelope of the exploding WD spreads out to ∼ 0.1R ⊙ ; it is much larger than that inferred for SN 2011fe (< 0.1R ⊙ ) while much smaller than that for SN 2014J (∼ 1R ⊙ ). For the particular combination of the WD masses studied in this work, the Chandrasekhar mass model is not successful to lead to an SN Ia explosion. Besides these assessments, we investigate the evolution of unbound materials ejected through the merging process ('merger ejecta'), assuming a case where the SN Ia explosion is not triggered by the heliumor carbon-ignition during the merger. The merger ejecta interact with the surrounding interstellar medium, and form a shell. The shell has a bolometric luminosity of more than 2 × 10 35 erg s −1 lasting for ∼ 2 × 10 4 yr. If this is the case, Milky Way should harbor about 10 such shells at any given time. The detection of the shell(s) therefore can rule out the helium-ignited and carbon-ignited violent merger models as major paths to SN Ia explosions.