Implementation of an N-body code in a HP 1000 computer

We describe the implementation of Aarseth's NBODY2 code on a HP 1000 computer. We use the Extended Memory Array (EMA) feature with this code in order to investigate problems that include several hundreds of bodies, but the use of EMA requires some care in order to avoid large increases in computing time. The Vector Instruction Set (VIS) feature, a group of arithmetic subroutines that operates on arrays of floating point numbers and significantly reduces the computing time, turned out to be of little value for this application. We present the computing times demanded by two different problems for a variety of programs, including EMA and VIS. Finally, we present mass loss and mass accretion results for several simulations of galaxy-galaxy encounters performed with our implementation of the NBODY2 code.     

Application of a massively parallel computer to the N-body problem

Parallel processor computers represent a new technology that has recently become available for astronomical applications. We have implemented an N-body code on a TMC Connection Machine CM-2 in order to investigate the advantages of a massively parallel computer over serial machines, including conventional supercomputers. For collisionless problems following N stars, a direct integration code scales as O(N²) on serial machines and on the CM-2 as O(log(N)) for small N and O(N log(N)) for large N. The CM-2 outperforms workstations for N>50 and supercomputers for N>4000.     

Numerical experiments on the efficiency of second-order mixed-variable symplectic integrators for N-body problems

We discuss the efficiency of the so-called mixed-variable symplectic integrators for N-body problems. By performing numerical experiments, we first show that the evolution of the mean error in action-like variables is strongly dependent on the initial configuration of the system. Then we study the effect of changing the stepsize when dealing with problems including close encounters between a particle and a planet. Considering a previous study of the slow encounter between comet P/Oterma and Jupiter, we show that the overall orbital patterns can be reproduced, but this depends on the chosen value of the maximum integration stepsize. Moreover the Jacobi constant in a restricted three-body problem is not conserved anymore when the stepsize is changed frequently: over a 10⁵ year time span, to keep a relative error in this integral of motion of the same order as that given by a Bulirsch-Stoer integrator requires a very small integration stepsize and much more computing time. However, an integration of a sample including 10⁴ particles close to Neptune shows that the distributions of the variation of the elements over one orbital period of the particles obtained by the Bulirsch-Stoer integrator and the symplectic integrator up to a certain integration stepsize are rather similar. Therefore, mixed-variable symplectic integrators are efficient either for N-body problems which do not include close encounters or for statistical investigations on a big sample of particles.     

High-performance direct gravitational N-body simulations on graphics processing units

We present the results of gravitational direct N-body simulations using the commercial graphics processing units (GPU) NVIDIA Quadro FX1400 and GeForce 8800GTX, and compare the results with GRAPE-6Af special purpose hardware. The force evaluation of the N-body problem was implemented in Cg using the GPU directly to speed-up the calculations. The integration of the equations of motions were, running on the host computer, implemented in C using the 4th order predictor–corrector Hermite integrator with block time steps. We find that for a large number of particles (N  10⁴) modern graphics processing units offer an attractive low cost alternative to GRAPE special purpose hardware. A modern GPU continues to give a relatively flat scaling with the number of particles, comparable to that of the GRAPE. The GRAPE is designed to reach double precision, whereas the GPU is intrinsically single-precision. For relatively large time steps, the total energy of the N-body system was conserved better than to one in 10⁶ on the GPU, which is impressive given the single-precision nature of the GPU. For the same time steps, the GRAPE gave somewhat more accurate results, by about an order of magnitude. However, smaller time steps allowed more energy accuracy on the grape, around 10⁻¹¹, whereas for the GPU machine precision saturates around 10⁻⁶ For N  10⁶ the GeForce 8800GTX was about 20 times faster than the host computer. Though still about a factor of a few slower than GRAPE, modern GPUs outperform GRAPE in their low cost, long mean time between failure and the much larger onboard memory; the GRAPE-6Af holds at most 256k particles whereas the GeForce 8800GTX can hold 9 million particles in memory.     

Energetics of a double flare on November 8, 1980

Here we complete an energy balance analysis of a double impulsive hard X-ray flare. From spatial observations, we deduce both flares probably occur in the same loop within the resolution of the data. For the first flare, the energy in the fast electrons (assuming a thick-target model) is comparable to the convective up-flow energy, suggesting that these are related successive modes of energy storage and transfer. The total energy lost through radiation and conduction, 2.0 × 10²⁸ erg, is comparable to the energy in fast electrons 2.5 × 10²⁸ erg. For the second flare, the energy in the fast electrons is more than one order of magnitude greater than the energy of the convective up-flow. Total energy losses are within a factor of two lower than the calculated fast electron energy. We interpret the observations as showing that the first flare occurred in a small loop with fast electrons heating the chromosphere and resulting in chromospheric evaporation increasing the density in the loop. For the second flare most of the heating occurred at the electron acceleration site. The two symmetrical components of the Ca xix resonance line and a high velocity down-flow of 115 km s ^–1 observed at the end of the second hard X-ray burst are consistent with the flare eruption (reconnection) region being high in the flare loop. The estimated altitude of the acceleration site is 5500 km above the photosphere.     

On the origin of a double, oblique impact on Mars

A double, oblique impact feature north of Olympus Mons provides a unique opportunity to investigate the event that formed it. The sizes of the craters, their ellipticity, shapes of ejecta blankets, separation from each other, and positions relative to each other, all give us information about the event. Coupling this information with an existing model of meteoritic flight through an atmosphere allows us to test several possible scenarios for the event (object type and origin, pre-entry trajectory, atmospheric trajectory, prevailing atmospheric density). We find it highly improbable that the impactor was simply an extra-martian asteroid or comet. We also find that it is unlikely to have been a double-asteroid or a tidally fractured one, but is more likely to have been a Mars-orbiting moonlet whose orbit tidally decayed, and that denser atmospheric conditions than today's may have prevailed when it impacted.     

iVINE – Ionization in the parallel tree/sph code VINE: first results on the observed age-spread around O-stars

We present a three-dimensional, fully parallelized, efficient implementation of ionizing ultraviolet (UV) radiation for smoothed particle hydrodynamics ( sph ) including self-gravity. Our method is based on the sph / tree code vine . We therefore call it iVINE (for Ionization + VINE). This approach allows detailed high-resolution studies of the effects of ionizing radiation from, for example, young massive stars on their turbulent parental molecular clouds. In this paper, we describe the concept and the numerical implementation of the radiative transfer for a plane-parallel geometry and we discuss several test cases demonstrating the efficiency and accuracy of the new method. As a first application, we study the radiatively driven implosion of marginally stable molecular clouds at various distances of a strong UV source and show that they are driven into gravitational collapse. The resulting cores are very compact and dense exactly as it is observed in clustered environments. Our simulations indicate that the time of triggered collapse depends on the distance of the core from the UV source. Clouds closer to the source collapse several 10⁵ yr earlier than more distant clouds. This effect can explain the observed age spread in OB associations where stars closer to the source are found to be younger. We discuss possible uncertainties in the observational derivation of shock front velocities due to early stripping of protostellar envelopes by ionizing radiation.     

Performance tuning of N-body codes on modern microprocessors: I. Direct integration with a hermite scheme on x86_64 architecture

The main performance bottleneck of gravitational N-body codes is the force calculation between two particles. We have succeeded in speeding up this pair-wise force calculation by factors between 2 and 10, depending on the code and the processor on which the code is run. These speed-ups were obtained by writing highly fine-tuned code for x86_64 microprocessors. Any existing N-body code, running on these chips, can easily incorporate our assembly code programs.In the current paper, we present an outline of our overall approach, which we illustrate with one specific example: the use of a Hermite scheme for a direct N² type integration on a single 2.0 GHz Athlon 64 processor, for which we obtain an effective performance of 4.05 Gflops, for double-precision accuracy. In subsequent papers, we will discuss other variations, including the combinations of N log N codes, single-precision implementations, and performance on other microprocessors.     

A fast,exact code for scattered thermal radiation compared with a two-stream approximation

For radiative transfer in plane-parallel emitting, absorbing, and scattering media, the two-stream approximation, and its various modifications or related methods, is probably mathematically the most simple to use. Unfortunately this physical approximation produces errors that are neither analytically known nor controllable. For externally (Sun) driven problems, many error studies exist for reflectivity, transmissivity, and certain defined albedos. A two-stream accuracy study for internally (thermal) driven problems is presented in this paper by comparison with a recently developed “exact” adding/doubling method. The resulting errors in external (or boundary) radiative intensity and flux are usually larger than those for the externally driven problems and vary substantially with the radiative parameters. Error predictions for a specific problem are difficult. An unexpected result was that the exact method is computationally as fast as the two-stream approximation for nonisothermal media. Although the adding/doubling method is mathematically and conceptually more complex, it may be used as a developed code with no essential sacrifice in computing time.     

PICsar: A 2.5D axisymmetric,relativistic, electromagnetic,Particle in Cell code with a radiation absorbing boundary

We present PICsar – a new Particle in Cell code geared towards efficiently simulating the magnetosphere of the aligned rotator. PICsar is a special relativistic, electromagnetic, charge conservative code that can be used to simulate arbitrary electromagnetics problems in axisymmetry. It features stretchable body-fitted coordinates that follow the surface of a sphere, simplifying the application of boundary conditions in the case of the aligned rotator; a radiation absorbing outer boundary, which allows a steady state to be set up dynamically and maintained indefinitely from transient initial conditions; and algorithms for injection of charged particles into the simulation domain. The code is parallelized using MPI and scales well to a large number of processors. We discuss the numerical methods used in PICsar and present tests of the code. In particular, we show that PICsar can accurately and efficiently simulate the magnetosphere of the aligned monopole rotator in the force-free limit. We present simulations of the aligned dipole rotator in a forthcoming paper.     

On a temporary confinement of chaotic orbits of four dimensional symplectic mapping: A test on the validity of the synthetic approach

Poincaré maps for Hamiltonian systems with 3 degrees of freedom lead to the study of four dimensional symplectic mappings. As a test for the validity of a synthetic mapping of order 3 using gradient informations, we study the evolution with time of Liapounov Indicators in the case of the four dimensional standard map with chaotic and stable zones. Both Liapounov Indicators show the same behaviour for the real and synthetic mappings. They reveal exploding diffusion phenomena for temporarily confined chaotic orbits. The distribution of the time of explosion fits well with a Poisson law for the real mapping, but not for the synthetic one. However the mean time of explosion is essentially the same in both cases.     

Searching the Sinus Amoris: Using profiles of geological units,impact and volcanic features to characterize a major terrane interface on the Moon

Geochemical profiles of surface units, impact, and volcanic features are studied in detail to determine the underlying structure in an area of extensive mare/highland interface, Sinus Amoris. This study region includes and surrounds the northeastern embayment of Mare Tranquillitatis. The concentrations of two major rock-forming elements (Mg and Al), which were derived from the Apollo 15 orbital geochemical measurements, were used in this study. Mapped units and deposits associated with craters in the northwestern part of the region tend to have correlated low Mg and Al concentrations, indicating the presence of KREEP-enriched basalt. Found along the northeastern rim of Tranquillitatis were areas with correlated high Mg and Al concentration, indicating the presence of troctolite. Distinctive west/east and north/south trends were observed in the concentrations of Mg and Al, and, by implication, in the distribution of major rock components on the surface. Evidence for a systematic geochemical transition in highland or basin-forming units may be observed here in the form of distinctive differences in chemistry in otherwise similar units in the western and eastern portions of the study region.     

Study of a large helical eruptive prominence associated with double CME on 21 April 2001

Here we present a preliminary analysis of a helical eruptive prominence at the east limb of the Sun on 21 April 2001. Unusually this eruption is associated with a double CME. We have tried to study the morphology of the event, energy budget of the prominence and associated CMEs. Our analysis shows that the prominence and first CME started simultaneously from the limb and prominence carries sufficient energy to feed both the CMEs. Moreover, it is also concluded that CMEs are magnetically driven and internally powered.     

Superthermal effect of electrons on nonplanar dust-ion-acoustic solitary waves and double layers in a dusty plasma

The basic features of planar and nonplanar time-dependent dust-ion-acoustic (DIA) solitary waves (SWs) and double layers (DLs) have been studied in an unmagnetized dusty plasma system consisting of positively and negatively charged dust, Boltzmann distributed ions and superthermal electrons (represented by kappa distribution). Using the reductive perturbation technique (RPT) we have derived modified Gardner (MG) equation, which gives information beyond the Korteweg-de Vries (KdV) limits (corresponding to the vanishing of nonlinear coefficient of the KdV equation). It is seen that the properties of nonplanar DIA SWs and DLs are significantly differs as the value of spectral index kappa (κ) changes. The present investigation may have relevance in the study of propagation of DIA waves in space and laboratory plasmas.     

Effects of two temperature electrons on Gardner solitons and double layers in a nonthermal dusty electronegative plasma

Gardner solitons (GSs) and double layers (DLs) of dust ion acoustic (DIA) waves in an electronegative plasma (composed of inertial positive and negative ions, Maxwellian cold electrons, non-thermal hot electrons, and negatively charged static dust) are studied. The reductive perturbation method is employed to derive the Korteweg-de Vries (K-dV), modified K-dV, and standard Gardner equations, which admits solitary wave and DLs solutions for σ around its critical value σ _c (where σ _c is the value of σ corresponding to the vanishing of the nonlinear coefficient of the K-dV equation). The parametric regimes for the existence of the GSs and DLs, are obtained. The basic features of DIA GSs and DLs (associated with negative structure only) are analyzed. It has been found that the characteristics of DIA GSs and DLs, are different from that of the K-dV solitons and mK-dV (mixed K-dV) solitons. The implications of our results to different space and laboratory plasma situations are discussed.     

Three pulsars discovered by FAST in the globular cluster NGC 6517 with a pulsar candidate sifting code based on dispersion measure to signal-to-noise ratio plots

We report the discovery of three new pulsars in the globular cluster(GC) NGC 6517, namely NGC 6517 E, F and G, made with the Five-hundred-meter Aperture Spherical radio Telescope(FAST).The spin periods of NGC 6517 E, F and G are 7.60 ms, 24.89 ms and 51.59 ms, respectively. Their dispersion measures are 183.29, 183.713 and 185.3 pc cm~(-3), respectively, all slightly larger than those of the previously known pulsars in this cluster. The spin period derivatives are at the level of 1×10~(-18) s s~(-1),which suggests these are recycled pulsars. In addition to the discovery of these three new pulsars, we updated the timing solutions of the known isolated pulsars, NGC 6517 A, C and D. The solutions are consistent with those from Lynch et al. but with smaller timing residuals. From the timing solution, NGC6517 A, B(position from Lynch et al.), C, E and F are very close to each other on the sky and only a few arcseconds from the optical core of NGC 6517. With currently published and unpublished discoveries,nine pulsars have been discovered in NGC 651, ranking it 6 thfor GCs with the most known pulsars. The discoveries take advantage of the high sensitivity of FAST and a new algorithm used to check and filter possible candidate signals.