Sub-horizon perturbations under the extreme initial condition of the axion model are investigated, where initial axion angles start near the potential maximum. This work focuses on a few new features found in the extreme axion model but absent in the free-particle model. A particularly novel new feature is the spectral excess relative to the CDM model in some wave number range, where the excess may be so large that landscapes of high-redshift universe beyond z = 10 can be significantly altered. For axions of particle mass 10 −22 eV, this range of wave number corresponds to first galaxies of few times 10 9 − 10 10 M⊙. We demonstrate that sub-horizon perturbations are accurately described by Mathieu's equation and subject to parametric instability, which explains this novel feature. Actually the axion model is not a special one; perturbations in a wide range of scalar field models can share the similar characteristic.

Using cosmological particle hydrodynamical simulations and uniform ultraviolet backgrounds, we compare Lyman-α forest flux spectra predicted by the conventional cold dark matter (CDM) model, the free-particle wave dark matter (FPψDM) model and extreme-axion wave dark matter (EAψDM) models of different initial axion field angles against the BOSS Lyman-α forest absorption spectra with a fixed boson mass m b ∼ 10 −22 eV. We recover results reported previously (Iršič et al. 2017b;Armengaud et al. 2017) that the CDM model agrees better with the BOSS data than the FPψDM model by a large margin, and we find the difference of total χ 2 's is 120 for 420 data bins. These previous results demand a larger boson mass by a factor > 10 to be consistent with the date and are in tension with the favoured value determined from local satellite galaxies. We however find that such tension is removed as some EAψDM models predict Lyman-α flux spectra agreeing better with the BOSS data than the CDM model, and the difference of total χ 2 's can be as large as 24 for the same bin number. This finding arises with no surprise since EAψDM models have unique spectral shapes with spectral bumps in excess of the CDM power near the small-scale cutoff typical of ψDM linear matter power spectra as well as more extended cutoffs than FPψDM (Zhang & Chiueh 2017a,b).

Linear perturbations of the wave dark matter, or ψ dark matter (ψDM), of particle mass ∼ 10 −22 eV in the radiation-dominant era are analyzed, and the matter power spectrum at the photonmatter equality is obtained. We identify four phases of evolution for ψDM perturbations, where the dynamics can be vastly different from the counterparts of cold dark matter (CDM). While in late stages after mass oscillation long-wave ψDM perturbations are almost identical to CDM perturbations, some subtle differences remain, let alone intermediate-to-short waves that bear no resemblance with those of CDM throughout the whole evolutionary history. The dissimilarity is due to quantum mechanical effects which lead to severe mode suppression. We also discuss the axion model with a cosine field potential. The power spectrum of axion models are generally almost identical to those of ψDM, but in the extreme case when the initial axion angle is near the field potential top, this axion model predict a power excess over a range of wave number and a higher spectral cutoff than ψDM as if ψDM had a higher particle mass.

We present the implementation and performance of a class of directionally unsplit Riemannsolver-based hydrodynamic schemes on Graphic Processing Units (GPU). These schemes, including the MUSCL-Hancock method, a variant of the MUSCL-Hancock method, and 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 in adiabatic hydrodynamic tests and demonstrate that, with the same accuracy, GAMER is able to achieve two orders of magnitude performance speed-up.Subject headings: adaptive-mesh-refinement-graphic-processing-unit-hybrid MPI/OpenMPhydrodynamics-methods: numerical Schive et al. (2010a) present a parallel GPU-accelerated adaptive-mesh-refinement (AMR) code named GAMER (GPU-accelerated Adaptive-MEsh-Refinement), which is dedicated to high-performance and highresolution astrophysical simulations. The AMR implementation is based on constructing a hierarchy of