波暗物質模型中的矮星系與自相似解

Dwarf Galaxies and Similarity Solutions in the Wave Dark Matter Scenario

陳姝蓉(Shu-Rong Chen)

指導教授 ： 闕志鴻

國立臺灣大學/理學院/物理學研究所/博士(2022年)

https://doi.org/10.6342/NTU202200549

摘要

波暗物質模型的性質由其粒子質量決定，其預測每個星系的暗物質暈中央存有孤粒子，而核心外的暗物質平均密度分布與傳統冷暗物質相同，在其上有隨時間震盪的顆粒狀結構。本論文包括兩個工作，一是利用Jeans分析法搭配暗物質占多數的矮橢球星系的動力學觀測結果，來估算波暗物質模型的粒子質量；二是推導出波暗物質模型在愛因斯坦-德西特宇宙模型下的自相似解。
在第一部分，我們假設八個矮橢球星系中的恆星的觀測資料皆落在暗物質暈中央的孤立子中，利用Jeans分析方法分析兩組不同的觀測資料\cite{Walker2007}和 \cite{Walker2009b}推估得粒子質量為 $1.18_{-0.24}^{+0.28}\times10^{-22}\eV$ 與 $1.79_{-0.33}^{+0.35}\times10^{-22}\eV~(2\sigma)$ 。利用此分析方法估計的波暗物質粒子質量，對矮橢球星系的動力學觀測資料非常敏感，但對恆星密度分布模型較不敏感。文中亦分析矮橢球星系中不同恆星族群的動力學資料，得到與前述一致的粒子質量。
在第二部分，我們推導出波暗物質在愛因斯坦-德西特宇宙模型下隨時間演化的自相似解。自相似解在慣性座標系裡整體的密度分佈隨時間變寬，但在隨宇宙膨脹的共移座標系下看起來隨時間變窄，而在自相似解的座標系中不隨時間改變。自相似解能量為正，與暗物質暈中心亦具有自相似但能量為負的孤立子不同。自相似解對小擾動相對穩定，而在較大的擾動下會演化成中心帶有孤立子、周圍帶有顆粒狀結構的解，這與宇宙學模擬中見到的暗物質暈非常類似。

關鍵字

波暗物質 ； 矮星系 ； Jeans分析法 ； 自相似解

並列摘要

Wave dark matter ($\psiDM$), characterized by a single parameter, the dark matter particle mass $m_{\psi}$, predicts that in every galaxy there is a central soliton core surrounded by a granular halo. This dissertation includes two major works: (i) using Jeans analysis on dwarf spheroidal galaxies to constrain $m_{\psi}$ and (ii) deriving self-similar solutions of $\psiDM$ halos.

In work (i), we apply Jeans analysis assuming a soliton core profile to the kinematic data of eight classical dSphs so as to constrain $m_{\psi}$, and obtain $m_{\psi}=1.18_{-0.24}^{+0.28}\times10^{-22}\eV$ and $m_{\psi}=1.79_{-0.33}^{+0.35}\times10^{-22}\eV~(2\sigma)$ using the observational data sets of \cite{Walker2007} and \cite{Walker2009b}, respectively. We show that the estimate of $m_{\psi}$ is sensitive to the dSphs kinematic data sets and is robust to various models of stellar density profile. We also consider multiple stellar subpopulations in dSphs and find consistent results.

In work (ii), we identify a class of self-similar, time-dependent solutions, which expand as seen in the inertial frame, contract as observed in the comoving frame, but appear stationary in the self-similar frame. The solutions possess positive energy, in contrast to the negative energy soliton. This solution is found to be relatively stable against small-amplitude perturbations. Such a global solution can evolve into the soliton, where the core radius shrinks faster than $a^{-1/4}$, only when large-amplitude perturbations are applied, and it does so accompanied by the formation of a granular massive halo surrounding the soliton, similar to the results of cosmological simulations.

並列關鍵字

wave dark matter ； dwarf galaxy ； Jeans analysis ； self-similar solution

參考文獻

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