臺灣博碩士論文加值系統

重力透鏡可分為強重力透鏡與弱重力透鏡。
強重力透鏡可將銀河系光源變形成多銀河系影像或巨弧影像，而弱重力透鏡產生微弱的變形。
而這篇論文主要是探討這兩種不同的情況。強重力透鏡在這篇論文主要是比較巨大的銀河弧的數量在標準宇宙模型與觀測之間的差異。我們發現標準宇宙模型依然與觀測結果相當符合。而此結果驗證了標準宇宙模型有很高的準確度。而弱重力透鏡在本論文中，是應用於星系團質量的測量，我們發現在標準的質量度量法會得到很高的不準確度，主因為銀河系本身的橢圓性質，與其他物質在測量銀河系間的投影效應。而此不準確度會影響質量函數的測量，進而
影響觀測與宇宙模型間的差異。而我們定量了質量測量的不準確度，因此我們可以將理論的質量函數作一個修正，與未來觀測的質量函數作結合。

Gravitational lensing can be largely divided into two categories: strong lensing and weak lensing. The strong lensing deforms a source galaxy to multiple images or
giant arcs, whereas weak lensing produces tangentially weakly distorted source galaxy images. This dissertation addresses these two issues. On the strong lensing, the observed far greater number of giant arcs than that
predicted by the CDM cosmology has been a long-standing puzzle. We adopt high-resolution cosmological simulations to assess this problem, and show in a quantitative
way that this issue can be resolved by inclusion of high redshift source galaxies. Our CDM results reveal a much higher giant-arc probability galaxies are preferentially magnifed by the foreground lenses with a surprisingly high
e ciency explains why previous theoretical works stantially under-estimated the giant-arc number density. In the previous works, the source galaxies were assumed to
be mostly around z = 1, an assumption commonly adopted in weak lensing studies. In addition, although the lens mergers have been found to yield enhanced lensing cross-
sections, we nd that merely 5% of giant arcs are associated with merging lenses. Our results support not only the CDM cosmology but also the long-standing anticipation that galaxy clusters, mostly formed below z = 1, are powerful gravitational telescopes for probing the high-redshift proto-galaxies. On the weak lensing, mass determination of galaxy clusters has been its inapplication in probing the large scale structure formation. Albeit being a powerful technique, the uncertainty in the weak-lensing mass determination has recently been recognized as a potential problem. The uncertainty arises from the projection e
ect, as the systematic error, and the intrinsic galaxy ellipticity as the noise.We adopt the -statistics to investigate the issue of mass uncertainty measured
by weak lensing. Our results show quite a large uncertainty (δ≧50%) in weak-lensing mass determination. Even after we clean the samples by removing obviously detectable contaminant clusters around the target cluster, the mass uncertainty re-mains about 40%. Taking advantage of the -statistics, we however nd the mass
uncertainty is clearly seen to decrease with a decreasing radius, within which the cluster mass is measured. We thus propose an alternative weak lensing mass estima-
tor M1000. Such an mass estimator reduces the mass uncertainty by a factor about 2 compared with that of M200. In addition, we nd that the weak-lensing mass de-
termination can be bias-free, i.e., no systematic mass error, when the zeta statistics is adopted. This nice feature is in great contrast to the mass determination via the convergence; where over-estimation of cluster mass seems to be the norm.

Contents
Abstract iii
List of Figures viii
List of Tables xii
1 Introduction 1
1.1 High Redshift Arcs by Strong Lensing . . . . . . . . . . . . . . . . . . 3
1.2 Halo Mass Estimation through Weak Lensing . . . . . . . . . . . . . 5
1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Method 8
2.1 Basic Relations of Gravitational Lensing . . . . . . . . . . . . . . . . 8
2.2 Multiple Images From Gravitational Lensing . . . . . . . . . . . . . . 13
2.3 Multiple Images Distortion . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Strong Lensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 Weak Lensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.6 Multiple Lens Plane Theorem . . . . . . . . . . . . . . . . . . . . . . 22
3 Strong-Lensing on High-Redshift Galaxies 26
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Arc Statistics and Comparisons with Observations . . . . . . . . . . . 28
3.3.1 Arc Probability . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.2 Arc Number Density . . . . . . . . . . . . . . . . . . . . . . . 30
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4 HOW WELL CAN WEAK LENSING MEASURE THE MASS OF
GALAXY CLUSTERS? 38
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2.1 Particles N-Body Simulation & Weak Lensing Simulation . . . 39
4.2.2 Cluster Catalog . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3.1 - Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3.2 Adding Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3.3 Mass and Redshift Ranges of Weak Lenses . . . . . . . . . . . 43
4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4.1 Raw Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.4.2 Clean Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.4.3 Moments of Mass Probability Function . . . . . . . . . . . . . 47
4.4.4 Radial Mass Error Pro le . . . . . . . . . . . . . . . . . . . . 48
4.4.5 Alternative Weak-Lensing Mass Estimators? . . . . . . . . . . 48
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5 Conclusion 61
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