Ataru Tanikawa

Phantom-GRAPE: Numerical software library to accelerate collisionless N-body simulation with SIMD instruction set on x86 architecture

Abstract We have developed a numerical software library for collisionless N-body simulations named “Phantom-GRAPE” which highly accelerates force calculations among particles by use of a new SIMD instruction set extension to the x86 architecture, Advanced Vector eXtensions (AVX), an enhanced version of the Streaming SIMD Extensions (SSE). In our library, not only the Newton’s forces, but also central forces with an arbitrary shape f ( r ) , which has a finite cutoff radius r cut (i.e. f ( r ) = 0 at r > r cut ), can be quickly computed. In computing such central forces with an arbitrary force shape f ( r ) , we refer to a pre-calculated look-up table. We also present a new scheme to create the look-up table whose binning is optimal to keep good accuracy in computing forces and whose size is small enough to avoid cache misses. Using an Intel Core i7–2600 processor, we measure the performance of our library for both of the Newton’s forces and the arbitrarily shaped central forces. In the case of Newton’s forces, we achieve 2 × 10 9 interactions per second with one processor core (or 75 GFLOPS if we count 38 operations per interaction), which is 20 times higher than the performance of an implementation without any explicit use of SIMD instructions, and 2 times than that with the SSE instructions. With four processor cores, we obtain the performance of 8 × 10 9 interactions per second (or 300 GFLOPS). In the case of the arbitrarily shaped central forces, we can calculate 1 × 10 9 and 4 × 10 9 interactions per second with one and four processor cores, respectively. The performance with one processor core is 6 times and 2 times higher than those of the implementations without any use of SIMD instructions and with the SSE instructions. These performances depend only weakly on the number of particles, irrespective of the force shape. It is good contrast with the fact that the performance of force calculations accelerated by graphics processing units (GPUs) depends strongly on the number of particles. Substantially weak dependence of the performance on the number of particles is suitable to collisionless N-body simulations, since these simulations are usually performed with sophisticated N-body solvers such as Tree- and TreePM-methods combined with an individual timestep scheme. We conclude that collisionless N-body simulations accelerated with our library have significant advantage over those accelerated by GPUs, especially on massively parallel environments.

The critical mass ratio of double white dwarf binaries for violent merger-induced Type Ia supernova explosions

Mergers of carbon-oxygen (CO) white dwarfs (WDs) are considered as one of the potential progenitors of type Ia supernovae (SNe Ia). Recent hydrodynamical simulations showed that the less massive (secondary) WD violently accretes onto the more massive (primary) one, carbon detonation occurs, the detonation wave propagates through the primary, and the primary finally explodes as a sub-Chandrasekhar mass SN Ia. Such an explosion mechanism is called the violent merger scenario. Based on the smoothed particle hydrodynamics (SPH) simulations of merging CO WDs, we derived more stringent critical mass ratio (qcr) leading to the violent merger scenario than the previous results. We conclude that this difference mainly comes from the differences in the initial condition, synchronously spinning of WDs or not. Using our new results, we estimated the brightness distribution of SNe Ia in the violent merger scenario and compared it with previous studies. We found that our new qcr does not significantly affect the brightness distribution. We present the direct outcome immediately following CO WD mergers for various primary masses and mass ratios. We also discussed the final fate of the central system of the bipolar planetary nebula Henize 2-428, which was recently suggested to be a double CO WD system whose total mass exceeds the Chandrasekhar-limiting mass, merging within the Hubble time. Even considering the uncertainties in the proposed binary parameters, we concluded that the final fate of this system is almost certainly a sub-Chandrasekhar mass SN Ia in the violent merger scenario.

Dynamical evolution of stellar mass black holes in dense stellar clusters: estimate for merger rate of binary black holes originating from globular clusters

We have performed N-body simulations of globular clusters (GCs) in order to estimate a detection rate of mergers of Binary stellar-mass Black Holes (BBHs) by means of gravitational wave (GW) observatories. For our estimate, we have only considered mergers of BBHs which escape from GCs (BBH escapers). BBH escapers merge more quickly than BBHs inside GCs because of their small semi-major axes. N-body simulation can not deal with a GC with the number of stars N ~ 10^6 due to its high calculation cost. We have simulated dynamical evolution of small-N clusters (10^4 <~ N <~ 10^5), and have extrapolated our simulation results to large-N clusters. From our simulation results, we have found the following dependence of BBH properties on N. BBHs escape from a cluster at each two-body relaxation time at a rate proportional to N. Semi-major axes of BBH escapers are inversely proportional to N, if initial mass densities of clusters are fixed. Eccentricities, primary masses, and mass ratios of BBH escapers are independent of N. Using this dependence of BBH properties, we have artificially generated a population of BBH escapers from a GC with N ~ 10^6, and have estimated a detection rate of mergers of BBH escapers by next-generation GW observatories. We have assumed that all the GCs are formed 10 or 12Gyrs ago with their initial numbers of stars N_i=5 x 10^5 -- 2 x 10^6 and their initial stellar mass densities inside their half-mass radii \rho_h,i=6 x 10^3 -- 10^6M_sun pc^-3. Then, the detection rate of BBH escapers is 0.5 -- 20 yr^-1 for a BH retention fraction R_BH=0.5. A few BBH escapers are components of hierarchical triple systems, although we do not consider secular perturbation on such BBH escapers for our estimate. Our simulations have shown that BHs are still inside some of GCs at the present day. These BHs may marginally contribute to BBH detection.

Unexpected formation modes of the first hard binary in core collapse

Abstract The conventional wisdom for the formation of the first hard binary in core collapse is that three-body interactions of single stars form many soft binaries, most of which are quickly destroyed, but eventually one of them survives. We report on direct N-body simulations to test these ideas, for the first time. We find that the assumptions are incorrect in the majority of the cases: (1) quite a few three-body interactions produce a hard binary from scratch; (2) in many cases there are more than three bodies directly and simultaneously involved in the production of the first binary. The main reason for the discrepancies is that the core of a star cluster, at the first deep collapse, contains typically only five or so stars. Therefore, the homogeneous background assumption, which still would be reasonable for, say, 25 stars, utterly breaks down. There have been some speculations in this direction, but we demonstrate this result here explicitly, for the first time.

Does Explosive Nuclear Burning Occur in Tidal Disruption Events of White Dwarfs by Intermediate-mass Black Holes?

We investigate nucleosynthesis in tidal disruption events (TDEs) of white dwarfs (WDs) by intermediate mass black holes (IMBHs). We consider various types of WDs with different masses and compositions by means of 3 dimensional (3D) smoothed particle hydrodynamics (SPH) simulations. We model these WDs with different numbers of SPH particles,

Effects of Hardness of Primordial Binaries on the Evolution of Star Clusters

N

SUCCESSIVE MERGER OF MULTIPLE MASSIVE BLACK HOLES IN A PRIMORDIAL GALAXY

, from a few

High-resolution Hydrodynamic Simulation of Tidal Detonation of a Helium White Dwarf by an Intermediate Mass Black Hole

10^4

Development of a real-time data processing system for a prototype of the Tomo-e Gozen wide field CMOS camera

to a few

Mass-Loss Timescale of Star Clusters in an External Tidal Field. I. Clusters on Circular Orbits

10^7