在這項研究工作中，我們想知道兩顆超大質量黑洞在星系中的演化情形，以及他們是否能在宇宙年齡內形成重力束縛態的雙黑洞系統，由於在此期間黑洞的演化主要受到dynamical friction的影響，所以我們也會探討dynamical friction中的變數以及其他不同的條件如黑洞質量及其初始位置等，我們利用電腦模擬黑洞在星系中的運動並將結果作圖，我們的結果顯示在Hernquist model的星系中黑洞的演化會較其在Plummer model中迅速，在使系統成為束縛態的臨界黑洞質量方面，前者的質量約為後者的十分之一，因此在Hernquist model下較容易形成束縛態的雙黑洞系統。

We study the evolution of two supermassive black holes in the galaxy. We investigate whether two black holes can form a bound binary system within the age of the universe. Since the dynamical friction is the major physical process to determine the early stage of the formation of binary supermassive black holes, we also investigate its variables and other parameters such as the mass and the initial positions of the black holes. We use the simulation to study the behavior of two black holes in the galaxy. The results show that the evolution in the Hernquist model is faster than the one in the Plummer model. The former’s critical black hole mass to become gravitational bound is roughly one tenth of the latter’s. Hence it is easier for the black holes to become a bound binary in the Hernquist model.

1 Introduction 3
2 Theoretical foundations 6
2.1 Galactic potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Dynamical friction . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Simulations and parameters 14
4 Results 16
4.1 Equal mass black holes . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2 Unequal mass black holes . . . . . . . . . . . . . . . . . . . . . . . 22
4.3 Initial radii of the black holes . . . . . . . . . . . . . . . . . . . . . 27
4.4 Different galactic mass . . . . . . . . . . . . . . . . . . . . . . . . . 32
5 Summary and future work 37

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