在這項研究中，我們探討18個早型星系的質量密度曲線，希望可以由分析得知這些星系是核狀或尖狀的。我們從最簡單的情形，各向異性參數β=0開始，從Jeans equation和兩個球對稱模型推得預測的速度瀰散度，我們用理論的速度瀰散度擬合觀測的資料，得到最適合的質量密度函數的參數。接著我們由擬合的結果將這些星系分成四類，我們的結果顯示Jaffe model較適合擬合速度瀰散度分佈中心有上升情形的星系，Jaffe model擬合較好的星系的質量分佈可能有尖狀結構。這18個星系的黑洞質量&速度瀰散度關係式也建立了，為log(M_bh/M_sun)=(8.35±0.06)+(4.84±0.02)log(σ/200kms^(-1))，從關係圖可以看出兩個模型皆擬合較差的星系傾向有較大質量的黑洞。

The mass density profiles of 18 early-type galaxies are
investigated in this work, and we hope to know whether these galaxies are core-like or cusp-like from the analysis. We started from the simplest case, those with anisotropy parameter β=0, and derived the predicted velocity dispersion analytically from Jeans equation with two spherically symmetric models. We fitted the observational data with the theoretical velocity dispersion and obtained the best-fit parameter set of the mass density function. Then we grouped the galaxies into four catagories according to the reduced chi-square results. Our results imply that Jaffe model is appropriate to fit galaxies with central rising in the velocity dispersion profile. Galaxies which are Jaffe-model preferred are likely to have cusp structure in the density distribution.
The M_bh-σ relation of our samples was also established, which was log(M_bh/M_sun)=(8.35±0.06)+(4.84±0.02)log(σ/200kms^(-1)). The figure shows that galaxies that can not be fitted well by both models tend to have larger black-hole masses.

致謝 i
中文摘要 ii
Abstract iii
Contents iv
List of Figures vi
List of Tables ix
1 Introduction 1
1.1 The Velocity Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Black-hole-mass & Velocity-dispersion Relation . . . . . . . . . . . . . . 2
1.3 Jeans Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 The Model 6
2.1 Plummer Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Jaffe Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Observational Data and the Fitting Method 14
3.1 The Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 The Chi-square Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.3 The Fitting Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4 Results 19
4.1 Case I The Good Fitting by Both Models . . . . . . . . . . . . . . . . 20
4.2 Case II The Bad Fitting by Both Models . . . . . . . . . . . . . . . . . 30
4.3 Case III The Plummer-model Preferred Fitting . . . . . . . . . . . . . 36
4.4 Case IV The Jaffe-model Preferred Fitting . . . . . . . . . . . . . . . . 36
5 Conclusions and Future Work 48

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