GPU與自適應網格於天文物理的應用─超輕玻色子暗物質之星系尺度模擬

Abstract

本論文利用一結合高速顯示卡及自適應網格運算法之程式，進行超 輕玻色子暗物質之星系尺度模擬。此模擬大小為兩百萬秒差距，而最 高解析度達60 秒差距。 模擬結果顯示，此模型產生之暗物質暈的中心均會出現一核心，且 此核心的密度分布可由一孤立子解所描述。而我們發現暈質量以及暈 的比能各自與核心質量有一比例關係。這兩個關係中，暈質量與核心 質量的關係較不穩固，只對經常進行融合的暗物質暈成立。而暈比能 與核心質量的關係對任何暗物質暈都隨時適用。 我們也修改了兩部分程式，以提供更好的效能。第一，自適應網格 運算法的切細條件經過調整，能避免過度切細，同時保證波型被完整 保留。第二，經過計算及實測，找出一較好的薛丁格方程式的動能運 算子，使振幅與相位之誤差降低，並提供較大的時間步長。

Here we study a galaxy formation simulation in the context of extremely-light bosonic dark matter (ELBDM) model using a GPU-accelerated adaptive mesh refinement code. The simulation is in a 2.0Mpc box with resolution up to 60pc, and the boson mass is about 8.1×10^23 eV. Our results suggest that the ELBDM model produces cores with an universal solitonic density profiles at the dark matter halo center at all halo evolution history, and the core mass obeys two scaling relations with halo virial mass (Mcore ∝ Mhalo^(1/3)) and halo specific energy (Mcore ∝ (Ehalo/Mhalo)^(1/2))respectively. We found the Mcore − Mhalo relation is a time-averaged result, valid for the haloes undergoing merger frequently, while the Mcore − (Ehalo/Mhalo) relation generally holds at any time. The core density of any halo is well fitted by a series of soliton solutions with only one parameter. The cores may find an observable evidence to explain dwarf spheroid galaxies. We also did two modifications on the simulation code to optimize the computation efficiency and accuracy. First, the refinement criterion on the wave speed is tuned to avoid over-refinement, and meanwhile it ensures wave patterns are nicely captured. Second, we evaluated the performance of several explicit schemes for the Schrodinger kinetic energy solver, which normally has problems with enhanced wave dispersion and unphysical wave damping. A better scheme is searched and identified.