arXiv subjects

Junichiro Makino

Publications and source records attributed to Junichiro Makino.

At least 55 records · Page 3Linked to original sources

arXiv2013

Density Independent Smoothed Particle Hydrodynamics for Non-Ideal Equation of State

The smoothed particle hydrodynamics (SPH) method is a useful numerical tool for the study of a variety of astrophysical and planetlogical problems. However, it turned out that the standard SPH algorithm has problems in dealing with hydrodynamical instabilities. This problem is due to the assumption that the local density distribution is differentiable. In order to solve this problem, a new SPH formulation, which does not require the differentiability of the density, have been proposed. This new SPH method improved the treatment of hydrodynamical instabilities. This method, however, is applicable only to the equation of state (EOS) of the ideal gas. In this paper, we describe how to extend the new SPH method to non-ideal EOS. We present the results of various standard numerical tests for non-ideal EOS. Our new method works well for non-ideal EOS. We conclude that our new SPH can handle hydrodynamical instabilities for an arbitrary EOS and that it is an attractive alternative to the standard SPH.

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arXiv2013

The Cosmogrid Simulation: Statistical Properties of Small Dark Matter Halos

We present the results of the "Cosmogrid" cosmological N-body simulation suites based on the concordance LCDM model. The Cosmogrid simulation was performed in a 30Mpc box with 2048^3 particles. The mass of each particle is 1.28x10^5 Msun, which is sufficient to resolve ultra-faint dwarfs. We found that the halo mass function shows good agreement with the Sheth & Tormen fitting function down to ~10^7 Msun. We have analyzed the spherically averaged density profiles of the three most massive halos which are of galaxy group size and contain at least 170 million particles. The slopes of these density profiles become shallower than -1 at the inner most radius. We also find a clear correlation of halo concentration with mass. The mass dependence of the concentration parameter cannot be expressed by a single power law, however a simple model based on the Press-Schechter theory proposed by Navarro et al. gives reasonable agreement with this dependence. The spin parameter does not show a correlation with the halo mass. The probability distribution functions for both concentration and spin are well fitted by the log-normal distribution for halos with the masses larger than ~10^8 Msun. The subhalo abundance depends on the halo mass. Galaxy-sized halos have 50% more subhalos than ~10^{11} Msun halos have.

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arXiv2013

Gamma-ray Signal from Earth-mass Dark Matter Microhalos

Earth-mass dark matter microhalos with size of ~100 AUs are the first structures formed in the universe, if the dark matter of the Universe are made of neutralino. Here, we report the results of ultra-high-resolution simulations of the formation and evolution of these microhalos. We found that microhalos have the central density cusps of the form $ρ\propto r^{-1.5}$, much steeper than the cusps of larger dark halos. The central regions of these microhalos survive the encounters with stars except in very inner region of the galaxy down to the radius of a few hundreds pcs from the galactic center. The annihilation signals from nearest microhalos are observed as gamma-ray point-sources (radius less than 1'), with unusually large proper motions of ~0.2 degree per year. Their surface brightnesses are ~10% of that of the galactic center. Their S/N ratios might be better if they are far from the galactic plane. Luminosities of subhalos are determined only by their mass, and they are more than one order of magnitude luminous than the estimation by Springel et al. (2008): A boost factor can be larger than 1000. Perturbations to the millisecond pulsars by gravitational attractions of nearby earth-mass microhalos can be detected by the observations of Parkes Pulsar Timing Array (PPTA).

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arXiv2013

A Density Independent Formulation of Smoothed Particle Hydrodynamics

The standard formulation of the smoothed particle hydrodynamics (SPH) assumes that the local density distribution is differentiable. This assumption is used to derive the spatial derivatives of other quantities. However, this assumption breaks down at the contact discontinuity. At the contact discontinuity, the density of the low-density side is overestimated while that of the high-density side is underestimated. As a result, the pressure of the low (high) density side is over (under) estimated. Thus, unphysical repulsive force appears at the contact discontinuity, resulting in the effective surface tension. This tension suppresses fluid instabilities. In this paper, we present a new formulation of SPH, which does not require the differentiability of density. Instead of the mass density, we adopt the internal energy density (pressure), and its arbitrary function, which are smoothed quantities at the contact discontinuity, as the volume element used for the kernel integration. We call this new formulation density independent SPH (DISPH). It handles the contact discontinuity without numerical problems. The results of standard tests such as the shock tube, Kelvin-Helmholtz and Rayleigh-Taylor instabilities, point like explosion, and blob tests are all very favorable to DISPH. We conclude that DISPH solved most of known difficulties of the standard SPH, without introducing additional numerical diffusion or breaking the exact force symmetry or energy conservation. Our new SPH includes the formulation proposed by Ritchie & Thomas (2001) as a special case. Our formulation can be extended to handle a non-ideal gas easily.

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arXiv2012

PSDF: Particle Stream Data Format for N-Body Simulations

We present a data format for the output of general N-body simulations, allowing the presence of individual time steps. By specifying a standard, different N-body integrators and different visualization and analysis programs can all share the simulation data, independent of the type of programs used to produce the data. Our Particle Stream Data Format, PSDF, is specified in YAML, based on the same approach as XML but with a simpler syntax. Together with a specification of PSDF, we provide background and motivation, as well as specific examples in a variety of computer languages. We also offer a web site from which these examples can be retrieved, in order to make it easy to augment existing codes in order to give them the option to produce PSDF output.

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arXiv2011

Origin of multiple nuclei in ultraluminous infrared galaxies

Ultraluminous infrared galaxies (ULIRGs) with multiple ($\ge 3$) nuclei are frequently observed. It has been suggested that these nuclei are produced by multiple major mergers of galaxies. The expected rate of such mergers is, however, too low to reproduce the observed number of ULIRGs with multiple nuclei. We have performed high-resolution simulations of the merging of two gas-rich disk galaxies. We found that extremely massive and compact star clusters form from the strongly disturbed gas disks after the first or second encounter between the galaxies. The mass of such clusters reaches $\sim 10^8 M_{\odot}$, and their half-mass radii are $20-30 \rm{pc}$. Since these clusters consist of young stars, they appear to be several bright cores in the galactic central region ($\sim \rm{kpc}$). The peak luminosity of these clusters reaches $\sim 10%$ of the total luminosity of the merging galaxy. These massive and compact clusters are consistent with the characteristics of the observed multiple nuclei in ULIRGs. Multiple mergers are not necessary to explain multiple nuclei in ULIRGs.

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arXiv2011

Unexpected Formation Modes of the First Hard Binary in Core Collapse

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 both assumptions are often incorrect: 1) quite a few three-body interactions produce a hard binary from scratch; 2) and 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.

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arXiv2011

Binary Formation in Planetesimal Disks I. Equal Mass Planetesimals

As to April 2010, 48 TNO (trans-Neptunian Object) binaries have been found. This is about 6% of known TNOs. However, in previous theoretical studies of planetary formation in the TNO region, the effect of binary formation has been neglected. TNO binaries can be formed through a variety of mechanisms, such as three-body process, dynamical friction on two massive bodies, inelastic collisions between two bodies etc. Most of these mechanisms become more effective as the distance from the Sun increases. In this paper, we studied three-body process using direct N-body simulations. We systematically changed the distance from the Sun, the number density of planetesimals, and the radius of the planetesimals and studied the effect of the binaries on the collision rate of planetesimals. In the TNO region, binaries are involved in 1/3 - 1/2 of collisions, and the collision rate is increased by about a factor of a few compared to the theoretical estimate for the direct two-body collisions. Thus, it is possible that the binaries formed through three-body process significantly enhance the collision rate and reduce the growth time scale. In the terrestrial planet region, binaries are less important, because the ratio between the Hill radius and physical size of the planetesimals is relatively small. Although the time scale of our simulations is short, they clearly demonstrated that the accretion process in the TNO region is quite different from that in the terrestrial planet region. Simulations which cover longer time scale are required to obtain more accurate estimate for the accretion enhancement.

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arXiv2011

Particle-Particle Particle-Tree: A Direct-Tree Hybrid Scheme for Collisional N-Body Simulations

In this paper, we present a new hybrid algorithm for the time integration of collisional N-body systems. In this algorithm, gravitational force between two particles is divided into short-range and long-range terms, using a distance-dependent cutoff function. The long-range interaction is calculated using the tree algorithm and integrated with the constant-timestep leapfrog integrator. The short-range term is calculated directly and integrated with the high-order Hermite scheme. We can reduce the calculation cost per orbital period from O(N^2) to O(N log N), without significantly increasing the long-term integration error. The results of our test simulations show that close encounters are integrated accurately. Long-term errors of the total energy shows random-walk behaviour, because it is dominated by the error caused by tree approximation.

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arXiv2011

Shock-induced star cluster formation in colliding galaxies

We studied the formation process of star clusters using high-resolution N-body/smoothed particle hydrodynamcs simulations of colliding galaxies. The total number of particles is 1.2x10^8 for our high resolution run. The gravitational softening is 5 pc and we allow gas to cool down to \sim 10 K. During the first encounter of the collision, a giant filament consists of cold and dense gas found between the progenitors by shock compression. A vigorous starburst took place in the filament, resulting in the formation of star clusters. The mass of these star clusters ranges from 10^{5-8} Msun. These star clusters formed hierarchically: at first small star clusters formed, and then they merged via gravity, resulting in larger star clusters.

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arXiv2011

A Natural Symmetrization for the Plummer Potential

We propose a symmetrized form of the softened gravitational potential which is a natural extension of the Plummer potential. The gravitational potential at the position of particle i (x_i,y_i,z_i), induced by particle j at (x_j,y_j,z_j), is given by: phi_ij = -G m_j/|r_ij^2+e_i^2+e_j^2|^1/2, where G is the gravitational constant, m_j is the mass of particle j, r_ij = |(x_i-x_j)^2+(y_i-y_j)^2+(z_i-z_j)^2|^1/2 and e_i and e_j are the gravitational softening lengths of particles i and j, respectively. This form is formally an extension of the Newtonian potential to five dimensions. The derivative of this equation in the x,y, and z directions correspond to the gravitational accelerations in these directions and these are always symmetric between two particles. When one applies this potential to a group of particles with different softening lengths, as is the case with a tree code, an averaged gravitational softening length for the group can be used. We find that the most suitable averaged softening length for a group of particles is = sum_j^N m_j e_j^2 / M, where M = sum_j^N m_j and N are the mass and number of all particles in the group, respectively. The leading error related to the softening length is O(sum_j r_j d(e_j^2)/r_ij^3), where r_j is the distance between particle j and the center of mass of the group and d(e_j^2) = e_j^2 - . Using this averaged gravitational softening length with the tree method, one can use a single tree to evaluate the gravitational forces for a system of particles with a wide variety of gravitational softening lengths. Consequently, this will reduce the calculation cost of the gravitational force for such a system with different softenings without the need for complicated forms of softening. We present the result of simple numerical tests. We found that our modification of the Plummer potential works well.

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arXiv2011

High Performance Gravitational N-body Simulations on a Planet-wide Distributed Supercomputer

We report on the performance of our cold-dark matter cosmological N-body simulation which was carried out concurrently using supercomputers across the globe. We ran simulations on 60 to 750 cores distributed over a variety of supercomputers in Amsterdam (the Netherlands, Europe), in Tokyo (Japan, Asia), Edinburgh (UK, Europe) and Espoo (Finland, Europe). Regardless the network latency of 0.32 seconds and the communication over 30.000 km of optical network cable we are able to achieve about 87% of the performance compared to an equal number of cores on a single supercomputer. We argue that using widely distributed supercomputers in order to acquire more compute power is technically feasible, and that the largest obstacle is introduced by local scheduling and reservation policies.

cs.DC↗

arXiv2010

Eccentric evolution of SMBH binaries

In recent numerical simulations \citep{matsubayashi07,lockmann08}, it has been found that the eccentricity of supermassive black hole(SMBH) - intermediate black hole(IMBH) binaries grows toward unity through interactions with stellar background. This increase of eccentricity reduces the merging timescale of the binary through the gravitational radiation to the value well below the Hubble Time. It also gives the theoretical explanation of the existence of eccentric binary such as that in OJ287 \citep{lehto96, valtonen08}. In self-consistent N-body simulations, this increase of eccentricity is always observed. On the other hand, the result of scattering experiment between SMBH binaries and field stars \citep{quinlan96} indicated no increase of eccentricity. This discrepancy leaves the high eccentricity of the SMBH binaries in $N$-body simulations unexplained. Here we present a stellar-dynamical mechanism that drives the increase of the eccentricity of an SMBH binary with large mass ratio. There are two key processes involved. The first one is the Kozai mechanism under non-axisymmetric potential, which effectively randomizes the angular momenta of surrounding stars. The other is the selective ejection of stars with prograde orbits. Through these two mechanisms, field stars extract the orbital angular momentum of the SMBH binary. Our proposed mechanism causes the increase in the eccentricity of most of SMBH binaries, resulting in the rapid merger through gravitational wave radiation. Our result has given a definite solution to the "last-parsec problem".

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arXiv2010

The origin of S-stars and a young stellar disk: distribution of debris stars of a sinking star cluster

Within the distance of 1 pc from the Galactic center (GC), more than 100 young massive stars have been found. The massive stars at 0.1-1 pc from the GC are located in one or two disks, while those within 0.1 pc from the GC, S-stars, have an isotropic distribution. How these stars are formed is not well understood, especially for S-stars. Here we propose that a young star cluster with an intermediate-mass black hole (IMBH) can form both the disks and S-stars. We performed a fully self-consistent $N$-body simulation of a star cluster near the GC. Stars escaped from the tidally disrupted star cluster were carried to the GC due to an 1:1 mean motion resonance with the IMBH formed in the cluster. In the final phase of the evolution, the eccentricity of the IMBH becomes very high. In this phase, stars carried by the 1:1 resonance with the IMBH were dropped from the resonance and their orbits are randomized by a chaotic Kozai mechanism. The mass function of these carried stars is extremely top-heavy within 10". The surface density distributions of young massive stars has a slope of -1.5 within 10" from the GC. The distribution of stars in the most central region is isotropic. These characteristics agree well with those of stars observed within 10" from the GC.

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arXiv2010

FAST: A Fully Asynchronous Split Time-Integrator for Self-Gravitating Fluid

We describe a new algorithm for the integration of self-gravitating fluid systems using SPH method. We split the Hamiltonian of a self-gravitating fluid system to the gravitational potential and others (kinetic and internal energies) and use different time-steps for their integrations. The time integration is done in the way similar to that used in the mixed variable or multiple stepsize symplectic schemes. We performed three test calculations. One was the spherical collapse and the other was an explosion. We also performed a realistic test, in which the initial model was taken from a simulation of merging galaxies. In all test calculations, we found that the number of time-steps for gravitational interaction were reduced by nearly an order of magnitude when we adopted our integration method. In the case of the realistic test, in which the dark matter potential dominates the total system, the total calculation time was significantly reduced. Simulation results were almost the same with those of simulations with the ordinary individual time-step method. Our new method achieves good performance without sacrificing the accuracy of the time integration.

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arXiv2010

Simulating the universe on an intercontinental grid of supercomputers

Understanding the universe is hampered by the elusiveness of its most common constituent, cold dark matter. Almost impossible to observe, dark matter can be studied effectively by means of simulation and there is probably no other research field where simulation has led to so much progress in the last decade. Cosmological N-body simulations are an essential tool for evolving density perturbations in the nonlinear regime. Simulating the formation of large-scale structures in the universe, however, is still a challenge due to the enormous dynamic range in spatial and temporal coordinates, and due to the enormous computer resources required. The dynamic range is generally dealt with by the hybridization of numerical techniques. We deal with the computational requirements by connecting two supercomputers via an optical network and make them operate as a single machine. This is challenging, if only for the fact that the supercomputers of our choice are separated by half the planet, as one is located in Amsterdam and the other is in Tokyo. The co-scheduling of the two computers and the 'gridification' of the code enables us to achieve a 90% efficiency for this distributed intercontinental supercomputer.

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arXiv2009

GreeM : Massively Parallel TreePM Code for Large Cosmological N-body Simulations

In this paper, we describe the implementation and performance of GreeM, a massively parallel TreePM code for large-scale cosmological N-body simulations. GreeM uses a recursive multi-section algorithm for domain decomposition. The size of the domains are adjusted so that the total calculation time of the force becomes the same for all processes. The loss of performance due to non-optimal load balancing is around 4%, even for more than 10^3 CPU cores. GreeM runs efficiently on PC clusters and massively-parallel computers such as a Cray XT4. The measured calculation speed on Cray XT4 is 5 \times 10^4 particles per second per CPU core, for the case of an opening angle of θ=0.5, if the number of particles per CPU core is larger than 10^6.

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arXiv2009

Triplets of supermassive black holes: Astrophysics, Gravitational Waves and Detection

Supermassive black holes (SMBHs) found in the centers of many galaxies have been recognized to play a fundamental active role in the cosmological structure formation process. In hierarchical formation scenarios, SMBHs are expected to form binaries following the merger of their host galaxies. If these binaries do not coalesce before the merger with a third galaxy, the formation of a black hole triple system is possible. Numerical simulations of the dynamics of triples within galaxy cores exhibit phases of very high eccentricity (as high as $e \sim 0.99$). During these phases, intense bursts of gravitational radiation can be emitted at orbital periapsis. This produces a gravitational wave signal at frequencies substantially higher than the orbital frequency. The likelihood of detection of these bursts with pulsar timing and the Laser Interferometer Space Antenna ({\it LISA}) is estimated using several population models of SMBHs with masses $\gtrsim 10^7 {\rm M_\odot}$. Assuming a fraction of binaries $\ge 0.1$ in triple system, we find that few to few dozens of these bursts will produce residuals $>1$ ns, within the sensitivity range of forthcoming pulsar timing arrays (PTAs). However, most of such bursts will be washed out in the underlying confusion noise produced by all the other 'standard' SMBH binaries emitting in the same frequency window. A detailed data analysis study would be required to assess resolvability of such sources. Implementing a basic resolvability criterion, we find that the chance of catching a resolvable burst at a one nanosecond precision level is 2-50%, depending on the adopted SMBH evolution model. On the other hand, the probability of detecting bursts produced by massive binaries (masses $\gtrsim 10^7\msun$) with {\it LISA} is negligible.

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