Daiichiro Sugimoto

GRAPE-4: A Massively Parallel Special-Purpose Computer for Collisional N-Body Simulations

In this paper, we describe the architecture and performance of the GRAPE-4 system, a massively parallel special-purpose computer for N-body simulation of gravitational collisional systems. The calculation cost of N-body simulation of collisional self-gravitating system is O(N3). Thus, even with present-day supercomputers, the number of particles one can handle is still around 10,000. In N-body simulations, almost all computing time is spent calculating the force between particles, since the number of interactions is proportional to the square of the number of particles. Computational cost of the rest of the simulation, such as the time integration and the reduction of the result, is generally proportional to the number of particles. The calculation of the force between particles can be greatly accelerated by means of a dedicated special-purpose hardware. We have developed a series of hardware systems, the GRAPE (GRAvity PipE) systems, which perform the force calculation. They are used with a general-purpose host computer which performs the rest of the calculation. The GRAPE-4 system is our newest hardware, completed in 1995 summer. Its peak speed is 1.08 TFLOPS. This speed is achieved by running 1692 pipeline large-scale integrated circuits (LSIs), each providing 640 MFLOPS, in parallel.

Carbon deflagration supernova, an alternative to carbon detonation

As an alternative to the carbon detonation, we present a carbondeflagration supernova model by a full hydrodynamic computation. A deflagration wave, which propagates through the core due to convective heat transport, does not grow into detonation. Though it results in a complete disruption of the star, the difficulty of overproduction of iron peak elements can be avoided if the deflagration is relatively slow.

Evolution of the Stars

Modern theories on the evolution of stars are extended to the phases of helium burning, carbon burning, and later burnings as far as possible, and the theoretical results are compared wth the Hertzsprung-Russell diagrams of star clusters. The topics discussed include nuclear generation and energy loss by neutrinos, quasi-static equilibrium, envelope,core, and surface solutions, stellar models with homogeneous chemical composition, hydrogen burning phase, helium burning phase, advanced phases of nuclear burning, iinal phase toward white dwarfs, and pre-mainsequence contricting phase. (C.E.S.)

A special-purpose N-body machine GRAPE-1

We have designed and built GRAPE-1 (GRAvity PipE 1), a special-purpose computer for astrophysical N-body calculations. It is designed as a back-end processor that calculates the gravitational interaction between particles. All other calculations are performed on a host computer connected to GRAPE-1. For large-N calculations (N⪆104), GRAPE-1 achieves about 100 Mflops-equivalent in one board of size about 40 by 30 cm at the power of 2.5 watt. The pipelined architecture of the GRAPE-1 which is specialized and optimized for the N-body calculation is the key to the high performance. The design and construction of the GRAPE-1 system are discussed.

Electron capture in highly evolved stars

Electron capture involving iron nuclei in contracting iron stars treated as endothermic nuclear reaction

Presupernova models and supernovae

Present status of the theories for presupernova evolution and triggering mechanisms of supernova explosions are summarized and discussed from the standpoint of the theory of stellar structure and evolution. It is not intended to collect every detail of numerical results thus far obtained, but to extract physically clear-cut understanding from complexities of the numerical stellar models. For this purpose the evolution of stellar cores is discussed in a generalized fashion. The following types of the supernova explosions are discussed. The carbon deflagration supernova of intermediate mass star which results in the total disruption of the star. Massive star evolves into a supernova triggered by photo-dissociation of iron nuclei which results in a formation of a neutron star or a black hole depending on its mass. These two are typical types of the sueprnovae. Between them there remains a range of mass for which collapse of the stellar core is triggered by electron captures, which has been recently shown to leave a neutron star despite oxygen deflagration competing with the electron captures. Also discussed are combustion and detonation of helium or carbon which take place in accreting white dwarfs, and the collapse which is triggered by electron-pair creation in very massive stars.

Merger of binary globular clusters : case of unequal masses

Merger process of binary globular cluster is discussed for a pair of unequal-mass components. We calculated the case of mass ratio 1∶0.5 by means of anN-body code with 6144 particles in total. We have found the followings. The mass exchange between the components takes place through the Roche-lobe overflow. In the early stages, however, the dynamical evolution is mainly governed by escape of particles from the system. As the particles escape carrying angular momentum with them, the separation between the component cluster shrinks. The time-scale of this shrinkage depends upon the size of the clusters. When a critical separation is reached, the orbital angular momentum is transferred unstably to the spins of the component clusters. This is the process of the synchronization instability which was found in a previous study on binary cluster of equal masses. As a result the component clusters merge into a single cluster. The structures of the mergers are quite similar among different cases except for the central cores which retain their initial central concentrations. In particular, the ellipticity and the rotation curve are quite close each other among models of different initial radii and of different mass ratios.

Why Stars Become Red Giants

The evolution of stars to red giants is revisited in order to promote a better understanding of the behavior of stars on the H-R diagram by separating the essential nonlinear characteristics of stellar structure from detailed effects of input physics such as chemical compositions, opacity, convection criterion, etc. It is shown that the red giant and dwarf structures are clearly discriminated in terms of the variation through the stellar interior of the ratio, W, between the mass interior to the relevant shell and the mass contained in the pressure scale height at the shell (≡ GM/4πr4P). For the simplest structures of dwarfs such as main-sequence stars, W increases monotonically from zero at the center to the greatest value at the surface. In later stages of evolution such as the red giants, W evolves to have a local extremum near the hydrogen-burning shell. Such a change in the distribution of W is a consequence of the increase in the ratio, Θ, of thermal and/or Fermi energy (P/ρ) between the core center and the envelope. In fact there exists a lower bound to Θ that is required by a red giant structure. During stellar evolution, the increase in Θ is brought about by the gravitational contraction of the core and by the fact that shell burning prevents the envelope from following the core contraction. Structures with an extremum of W correspond to an envelope of the condensed type, the properties of which are strongly regulated by the polytropic index N and the ratio, V [= (GMr/r)/(P/ρ)], between the local gravitational potential to the thermal energy in the lower envelope. A large polytropic index N 3 makes the envelope expanded, particularly when V N + 1 is realized in the lower envelope. On the basis of such an understanding, we are able to analyze the effects of input physics on the excursion of the star to a red giant. A key role is played by the gradients of the opacity and of the mean molecular weight. The stellar radius can be larger if the opacity is increasing outward to make N larger than 3. A moderate gradient in the mean molecular weight also allows the value of N to come into the range of 3-5, which is appropriate for V N + 1 to be realized in the bottom of the envelope, while a steep gradient yields too large a value of N. The so-called peculiar evolution of the SN 1987A progenitor, Sk -69°202, can be understood in such a context. In particular, a constraint is derived for the mechanism of the extra mixing that is responsible for the final red-to-blue excursion of the star.

On the numerical stability of computations of stellar evolution

Numerical stability in computations of stellar evolution taking into account hydrostatic equilibrium and thermal processes

Rapidly Rotating Polytropes and Concave Hamburger Equilibrium

Rotating poly tropes have equilibrium figures of concave hamburger shape, which bifurcates from Maclaurin-spheroid-like figures and continues into toroids. However, two existing numerical computations of the concave hamburgers are quantitatively in contradiction to each other. Reasons for this contradiction are found to lie in the wrong treatments: One of their methods was applied for deformations too strong to be treated within its limit of applicability so that their boundary condition failed in its convergence of the series and in its analytic continuation into the complex plane. A modified method of numerical computation is developed which can not only avoid such problems but is still reasonably efficient. With this method we have recomputed sequences of rotating poly tropes. We have found the following. When the polytropic index N is greater than 0.02, the sequence of the Maclaurin-spheroid-like figures terminates by mass shedding from the equator. When N < 0.02, on the other hand, it continues into a sequence of the concave hamburgers. Contrary to the earlier computation, the Maclaurin spheroids are shown to be the limiting configuration to N = O. Some details are also discussed concerning the bifurcation to the concave hamburgers.