We examine the nonlinear structure of gravitationally collapsed objects that form in our simulations of wavelike cold dark matter ($psi$DM), described by the Schr{o}dinger-Poisson (SP) equation with a particle mass $sim 10^{-22} {rm eV}$. A distinct
gravitationally self-bound solitonic core is found at the center of every halo, with a profile quite different from cores modeled in the warm or self-interacting dark matter scenarios. Furthermore, we show that each solitonic core is surrounded by an extended halo composed of large fluctuating dark matter granules which modulate the halo density on a scale comparable to the diameter of the solitonic core. The scaling symmetry of the SP equation and the uncertainty principle tightly relate the core mass to the halo specific energy, which, in the context of cosmological structure formation, leads to a simple scaling between core mass ($M_c$) and halo mass ($M_h$), $M_c propto a^{-1/2} M_h^{1/3}$, where $a$ is the cosmic scale factor. We verify this scaling relation by (i) examining the internal structure of a statistical sample of virialized halos that form in our 3D cosmological simulations, and by (ii) merging multiple solitons to create individual virialized objects. Sufficient simulation resolution is achieved by adaptive mesh refinement and graphic processing units acceleration. From this scaling relation, present dwarf satellite galaxies are predicted to have kpc sized cores and a minimum mass of $sim 10^8 {M_odot}$, capable of solving the small-scale controversies in the cold dark matter model. Moreover, galaxies of $2times10^{12} {M_odot}$ at $z=8$ should have massive solitonic cores of $sim 2times10^9 {M_odot}$ within $sim 60 {rm pc}$. Such cores can provide a favorable local environment for funneling the gas that leads to the prompt formation of early stellar spheroids and quasars.
The conventional cold, particle interpretation of dark matter (CDM) still lacks laboratory support and struggles with the basic properties of common dwarf galaxies, which have surprisingly uniform central masses and shallow density profiles. In contr
ast, galaxies predicted by CDM extend to much lower masses, with steeper, singular profiles. This tension motivates cold, wavelike dark matter ($psi$DM) composed of a non-relativistic Bose-Einstein condensate, so the uncertainty principle counters gravity below a Jeans scale. Here we achieve the first cosmological simulations of this quantum state at unprecedentedly high resolution capable of resolving dwarf galaxies, with only one free parameter, $bf{m_B}$, the boson mass. We demonstrate the large scale structure of this $psi$DM simulation is indistinguishable from CDM, as desired, but differs radically inside galaxies. Connected filaments and collapsed haloes form a large interference network, with gravitationally self-bound solitonic cores inside every galaxy surrounded by extended haloes of fluctuating density granules. These results allow us to determine $bf{m_B=(8.1^{+1.6}_{-1.7})times 10^{-23}~eV}$ using stellar phase-space distributions in dwarf spheroidal galaxies. Denser, more massive solitons are predicted for Milky Way sized galaxies, providing a substantial seed to help explain early spheroid formation. Suppression of small structures means the onset of galaxy formation for $psi$DM is substantially delayed relative to CDM, appearing at $bf{zlesssim 13}$ in our simulations.
We present the implementation and performance of a class of directionally unsplit Riemann-solver-based hydrodynamic schemes on Graphic Processing Units (GPU). These schemes, including the MUSCL-Hancock method, a variant of the MUSCL-Hancock method, a
nd the corner-transport-upwind method, are embedded into the adaptive-mesh-refinement (AMR) code GAMER. Furthermore, a hybrid MPI/OpenMP model is investigated, which enables the full exploitation of the computing power in a heterogeneous CPU/GPU cluster and significantly improves the overall performance. Performance benchmarks are conducted on the Dirac GPU cluster at NERSC/LBNL using up to 32 Tesla C2050 GPUs. A single GPU achieves speed-ups of 101(25) and 84(22) for uniform-mesh and AMR simulations, respectively, as compared with the performance using one(four) CPU core(s), and the excellent performance persists in multi-GPU tests. In addition, we make a direct comparison between GAMER and the widely-adopted CPU code Athena (Stone et al. 2008) in adiabatic hydrodynamic tests and demonstrate that, with the same accuracy, GAMER is able to achieve two orders of magnitude performance speed-up.
GAMER is a GPU-accelerated Adaptive-MEsh-Refinement code for astrophysical simulations. In this work, two further extensions of the code are reported. First, we have implemented the MUSCL-Hancock method with the Roes Riemann solver for the hydrodynam
ic evolution, by which the accuracy, overall performance and the GPU versus CPU speed-up factor are improved. Second, we have implemented the out-of-core computation, which utilizes the large storage space of multiple hard disks as the additional run-time virtual memory and permits an extremely large problem to be solved in a relatively small-size GPU cluster. The communication overhead associated with the data transfer between the parallel hard disks and the main memory is carefully reduced by overlapping it with the CPU/GPU computations.
We present the newly developed code, GAMER (GPU-accelerated Adaptive MEsh Refinement code), which has adopted a novel approach to improve the performance of adaptive mesh refinement (AMR) astrophysical simulations by a large factor with the use of th
e graphic processing unit (GPU). The AMR implementation is based on a hierarchy of grid patches with an oct-tree data structure. We adopt a three-dimensional relaxing TVD scheme for the hydrodynamic solver, and a multi-level relaxation scheme for the Poisson solver. Both solvers have been implemented in GPU, by which hundreds of patches can be advanced in parallel. The computational overhead associated with the data transfer between CPU and GPU is carefully reduced by utilizing the capability of asynchronous memory copies in GPU, and the computing time of the ghost-zone values for each patch is made to diminish by overlapping it with the GPU computations. We demonstrate the accuracy of the code by performing several standard test problems in astrophysics. GAMER is a parallel code that can be run in a multi-GPU cluster system. We measure the performance of the code by performing purely-baryonic cosmological simulations in different hardware implementations, in which detailed timing analyses provide comparison between the computations with and without GPU(s) acceleration. Maximum speed-up factors of 12.19 and 10.47 are demonstrated using 1 GPU with 4096^3 effective resolution and 16 GPUs with 8192^3 effective resolution, respectively.
