摘要：這計畫是研究代替暗物質的理論：「修正牛頓力學」。它包含兩個部分。第一部分，我們希望應用相對論版本「修正牛頓力學」於引力透鏡上。第二部分，我們將研究恒星系統之結構及其被潮汐作用破壞的情況。第一部分主要以觀測數據規範不同模型，而第二部分則依賴電腦模擬。暗物質與「修正牛頓力學」都是為了詮釋天體之加速度與牛頓力學之差異而發明的。「修正牛頓力學」提出當加速度小的時候相互作用比牛頓力學來得強。我們認為在星系尺度上「修正牛頓力學」遠較暗物質成功。「修正牛頓力學」有些自由參數和函數，其中最重要的是小加速度參數和插值函數（連接牛頓範疇和「修正牛頓力學」範疇）。小加速度參數可以極端「修正牛頓力學」範疇的觀測訂定，如螺旋星系的自轉曲線。研究插值函數則要中程「修正牛頓力學」範疇的觀測。我們發現強引力透鏡常常發生在中程「修正牛頓力學」範疇。我們將使用張量－矢量－標量引力理論研究強引力透鏡系統。我們對橢圓星系透鏡有興趣，尤其是有速度測量的。在橢圓星系「質量基本平面」假設下，我們能約束插值函數。我們也對愛因斯坦環感興趣，因為它們提供一個單一尺度方便插值函數在中程「修正牛頓力學」範疇之討論。此外，我們也想研究「修正牛頓力學」的微透鏡和弱透鏡。這部分的一個副產品是橢圓星系的（重子）質光比分佈。恒星系統之結構及其被大物體破壞的情況應有異於牛頓力學。「修正牛頓力學」可視為一種修正引力理論，它的勢能滿足一條修正泊松方程。我們建議發展一個正確包含「修正牛頓力學」的多體程式碼。程式碼含兩部分：勢能解算碼和多體碼。我們將建立若干多方模型，然後詳細研究它們在「修正牛頓力學」潮汐力中遭到破壞的情況。我們想看看「修正牛頓力學」能否解釋我們附近缺乏矮星系的現象。 Abstract: This proposal is a study on the MOdified Newtonian Dynamics (MOND) as an alternative to dark matter. It contains two parts. In the first part, we want to apply relativistic version of MOND to gravitational lensing, and in the second part we want to study the structure of a stellar system and its destruction by tidal interaction. The first one mainly uses observational data to constraint different models, while the second one relies on simulations. Discrepancy between observed acceleration in many astrophysical objects and Newtonian dynamics (or general relativity) invokes different interpretations. Basically, both dark matter dynamics and MOND can be considered as an algorithm to interpret the observational data. MOND proposes that at small acceleration the interaction is stronger than Newtonian dynamics. In our opinion, MOND is far more successful than dark matter in galaxy scales. As in other theories, MOND has some free parameters and functions. The most important ones are the small acceleration parameter and the interpolation function (which connects Newtonian regime and MONDian regime). Small acceleration parameter can be fixed in deep MOND regime (i.e., the acceleration is very small), such as rotation curve of spiral galaxies. To probe the interpolation function, one needs to go to intermediate MOND regime. We find that strong gravitational lensing often happens in intermediate MOND regime. We propose to use TeVeS (Tensor-Vector-Scalar gravity theory, a relativistic version of MOND) to study strong lensing systems. We are interested in elliptical galaxies acting as lenses, in particular, those with dispersion velocity measurement. Under the hypothesis of a mass fundamental plane among elliptical galaxies, we can constraint the interpolation function. We are also keen on Einstein rings as they provide a unique scale for us to discuss those interpolation functions in the intermediate MOND regime. Moreover, we would like to work on microlensing and weak lensing in MOND. A byproduct of this part is the distribution of the (baryonic) mass-to-light ratio of elliptical galaxies. The structure of a stellar system and its destruction during an encounter with a larger object should be different from Newtonian case. MOND can be interpreted as a modified gravity theory where the potential is described by a modified Poisson equation. We propose to develop an N-body code which incorporates MOND correctly. The code will comprise two parts, the potential solver and the N-body part. We would like to construct some models of polytropes and study the detail dynamics of tidal disruption in MOND. We would like to see if MOND can explain the apparent scarcity of dwarf galaxies in our neighbourhood. 研究期間：9908 ~ 10007
