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Register a new userPPPM and TreePM Methods on GRAPE Systems for Cosmological N-body Simulations
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We present Particle-Particle-Particle-Mesh (PPPM) and Tree Particle-Mesh (TreePM) implementations on GRAPE-5 and GRAPE-6A systems, special-purpose hardware accelerators for gravitational many-body simulations. In our PPPM and TreePM implementations on GRAPE, the computational time is significantly reduced compared with the conventional implementations without GRAPE, especially under the strong particle clustering, and almost constant irrespective of the degree of particle clustering. We carry out the survey of two simulation parameters, the PM grid spacing and the opening parameter for the most optimal combination of force accuracy and computational speed. We also describe the parallelization of these implementations on a PC-GRAPE cluster, in which each node has one GRAPE board, and present the optimal configuration of simulation parameters for good parallel scalability.
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Direct $N$-body simulations of star clusters are accurate but expensive, largely due to the numerous $mathcal{O} (N^2)$ pairwise force calculations. To solve the post-million-body problem, it will be necessary to use approximate force solvers, such as tree codes. In this work, we adapt a tree-based, optimized Fast Multipole Method (FMM) to the collisional $N$-body problem. The use of a rotation-accelerated translation operator and an error-controlled cell opening criterion leads to a code that can be tuned to arbitrary accuracy. We demonstrate that our code, Taichi, can be as accurate as direct summation when $N> 10^4$. This opens up the possibility of performing large-$N$, star-by-star simulations of massive stellar clusters, and would permit large parameter space studies that would require years with the current generation of direct summation codes. Using a series of tests and idealized models, we show that Taichi can accurately model collisional effects, such as dynamical friction and the core-collapse time of idealized clusters, producing results in strong agreement with benchmarks from other collisional codes such as NBODY6++GPU or PeTar. Parallelized using OpenMP and AVX, Taichi is demonstrated to be more efficient than other CPU-based direct $N$-body codes for simulating large systems. With future improvements to the handling of close encounters and binary evolution, we clearly demonstrate the potential of an optimized FMM for the modeling of collisional stellar systems, opening the door to accurate simulations of massive globular clusters, super star clusters, and even galactic nuclei.
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(Abridged) We use high resolution cosmological N-body simulations to study the growth of intermediate to supermassive black holes from redshift 49 to zero. We track the growth of black holes from the seeds of population III stars to black holes in the range of 10^3 < M < 10^7 Msun -- not quasars, but rather IMBH to low-mass SMBHs. These lower mass black holes are the primary observable for the Laser Interferometer Space Antenna (LISA). The large-scale dynamics of the black holes are followed accurately within the simulation down to scales of 1 kpc; thereafter, we follow the merger analytically from the last dynamical friction phase to black hole coalescence. We find that the merger rate of these black holes is R~25 per year between 8 < z < 11 and R = 10 per year at z=3. Before the merger occurs the incoming IMBH may be observed with a next generation of X-ray telescopes as a ULX source with a rate of about ~ 3 - 7 per year for 1 < z < 5. We develop an analytic prescription that captures the most important black hole growth mechanisms: galaxy merger-driven gas accretion and black hole coalescence. Using this, we find that SMBH at the center of Milky Way type galaxy was in place with most of its mass by z = 4.7, and most of the growth was driven by gas accretion excited by major mergers. Hundreds of black holes have failed to coalesce with the SMBH by z=0, some with masses of 10000 Msun, orbiting within the dark matter halo with luminosities up to ~ 30000 Lsun. These X-ray sources can easily be observed with Chandra at ~ 100 kpc.
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We use gauge-invariant cosmological perturbation theory to calculate the displacement field that sets the initial conditions for $N$-body simulations. Using first and second-order fully relativistic perturbation theory in the synchronous-comoving gauge, allows us to go beyond the Newtonian predictions and to calculate relativistic corrections to it. We use an Einstein--de Sitter model, including both growing and decaying modes in our solutions. The impact of our results should be assessed through the implementation of the featured displacement in cosmological $N$-body simulations.
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