「修正牛頓力學」在解釋螺旋星系的平坦旋轉曲線、塔利-費舍爾關係方面都很成功，不過在橢圓星系 的相關研究則寥寥無幾。 「修正牛頓力學」的難 題在於如何疊加不同的質量分布所產生之影響。我們建立橢圓星系質量模型時 只用一種分布就可以。反觀螺旋星系則起碼要兩種分布。我們認為橢圓星系可提供「修正牛頓力學」 一個乾淨的實驗。 橢圓星系的動力物質可以從測量它們的恆星運動或者背景源的引力透鏡影像得知。我們利用球形分布 模型分析橢圓星系引力透鏡和恆星運動的公開數據，計算各橢圓星系的恆星質量。我們的主要目標是 希望以單獨的橢圓星系研究來獲得「修正牛頓力學」的最重要物理量，它的加速度常數。 下一步我們將發展「略變球形」分布模型所需的研究方案。這將是我們第一次能較自由地認真處理質 量分布的問題，這是「修正牛頓力學」一直存在的難題。 我們也計劃探討兩個重要議題：螺旋星系的強引力透鏡與宇宙弱引力透鏡。這對「修正牛頓力學」來 講都可能是重要的主題但卻乏人問津。這兩個議題也將碰到如何疊加質量分布這困難但有趣的老問 題。螺旋星系需要盤加核球，而弱引力透鏡則有多層微擾。 注意：因為字數限制，所以中文版較簡略，請看英文版。 ;As an alternative to Newtonian dynamics at small acceleration regime, MOdified Newtonian Dynamics (MOND) is very competitive against dark matter in elucidating dynamical phenomena related to galaxy-scale objects. MOND has been very successful in interpreting the flat rotation curve and Tully-Fisher relation of spiral galaxies. However, much less attentions have been dedicated to elliptical galaxies. The nonlinearity in MOND leads to the conundrum of how to superpose the influences by different mass distributions. Most of the baryons (a.k.a. “normal matter”) in elliptical galaxies reside in stars, thus we can model an elliptical galaxy as a one component mass distribution. However, for spiral galaxy we need at least two components (a disk and a bulge, and perhaps a gaseous disk as well). We deem that elliptical galaxies provide a clean (or cleaner) experiment for MOND. A large part of the project will be devoted to the dynamics of elliptical galaxies in the framework of MOND. Observationally, the essence of MOND is the luminous mass is the same as the dynamical mass. The dynamical mass of an elliptical galaxy can be measured by its stellar kinematics (velocity dispersion) or by the images of a background source if the galaxy is the gravitational lens. We worked out the formulations for both phenomena for spherical mass distribution. We apply these methods to publicly available data on strong lensing and stellar kinematics of elliptical galaxies, and then obtain stellar mass of each galaxy. Our main goal is to estimate the acceleration constant (the utmost important quantity) in MOND solely from elliptical galaxies. The next step is to go beyond spherical model. We will develop corresponding formulations for slightly deformed spherical distribution. This will enable us, for the first time, to do some detail mass modelling “freely”, which is not easy in MOND. Moreover we will have a handle on the uncertainty of the acceleration constant found by the spherical model. We also want to study two more topics related to the nonlinearity of MOND: strong gravitational lensing by spiral galaxies and cosmological weak gravitational lensing. Both are potentially important for MOND but largely ignored. The difficult and interesting part of both topics is the same old problem on how to sum up the contributions of different mass distributions. For spiral galaxies we need a disk and a bulge (and perhaps a gaseous disk), and for weak lensing we have layers of perturbations.
