黑洞在廣義相對論中被認為是無尺度的，意思是兩黑洞的差別只與質量有關。然而 黑洞吸積的物理原理和我們觀察到的現象並不是單純的只跟黑洞質量呈現性關係， 還取決於黑洞的吸積率、黑洞周圍的氣體溫度、黑洞噴流的角度等等。先前的研究 表明，對於次愛丁頓系統(活躍星系核的光度遠低於其愛丁頓極限之系統)，黑洞 的活動只與其質量與吸積率有關。而若我們將樣本限制在低光度活躍星系核這一類 的黑洞，其次毫米光變曲線的特徵時間尺度似乎與質量成線性關係。然而，這樣的 線性關係的證據只基於三個樣本形成的趨勢，是不穩固的。在本論文中，我們將探 討這樣的線性關係是否真的存在。
本論文將呈現六個低光度活躍星系核光變曲線的分析結果。光變觀測的實驗是 使用次毫米波陣列完成的，每個樣本有至少一年以上的觀測跨度。我們藉由將光變 曲線模擬成 damped random walk 模型分析出其特徵時間尺度。我們發現三個樣本 很好的吻合了前述之線性關係，另外兩個樣本不符合線性關係並擁有較大的特徵時 間尺度，這樣較大的時間尺度表明其次毫米光度變化並不是源於黑洞的事件視界尺 度的輻射過程，而是在較大的半徑發生(離黑洞較遠)。除此之外，有一個樣本吻 合線性關係但時間尺度擬合誤差很大。綜合前人之研究，我們可以總結前述之線性 關係是存在的，而樣本吻合線性關係的條件是其光譜能量分佈(SED)在次毫米波 段有達到一個峰值。這樣的線性關係表明有潛在的物理機制使靠近事件視界發射的 次毫米輻射之性質不受其他物理參數影響只與質量有關。

Black holes are believed to be scale-free in general relativity, however, the accretion physics is not simply scaled by mass but also depends on other parameters like accre- tion rate, gas temperature, jet inclination angle, etc. Previous studies show that, for the sub-Eddington system, the black hole behavior can be unified by only depending on black hole mass and accretion rate. For low-luminosity AGNs (LLAGNs), the char- acteristic timescale of submillimeter variability seems to scale by mass. However, the scaling correlation is not robust since it is discovered by evidence which only contains three samples. In this thesis, we would like to verify the existence of this mass scaling correlation.
We present the analysis result of six new light curves of LLAGN, obtained through SMA monitoring observations with a span of at least one year. We identify the characteristic timescale of light curves by modeling them as a damped random walk. We find three of our samples agree with the scaling relationship, while two of our samples show a larger timescale suggests the variability is not associated with the emission process at the event horizon but larger radius. In addition, one sample agrees with the scaling relationship but with poor lower limit be constrain. Combine with the previous study, we conclude that the mass scaling correlation exists for sources which show the SED peak at submillimeter wavelengths, and suggest that the underlying physics emitting submillimeter emission close to the event horizon may be independent of other physical parameters but only related to black hole mass.

Abstract
Acknowledgements
List of Figures
List of Tables
1 Introduction -------------------------------------------------------------1
1.1 Active Galactic Nuclei --------------------------------------------------1
1.1.1 Black Hole accretion --------------------------------------------------2
1.1.2 Low Luminosity AGN -------------------------------------------------3
1.1.3 The Jet --------------------------------------------------------------6
1.2 Emission Mechanisms -------------------------------------------------8
1.2.1 Radiative Transfer and Thermal emission -----------------------------9
1.2.2 Synchrotron Radiation -----------------------------------------------10
1.3 Mass scaling black hole system ---------------------------------------12
1.3.1 Fundamental Plane of Black Hole Accretion --------------------------13
1.3.2 SgrA*, M81* and Hard-state XRBs -----------------------------------14
1.4 Variability of AGN -----------------------------------------------------15
1.4.1 Optical and UV ------------------------------------------------------15
1.4.2 X-ray and near-Infrared ---------------------------------------------16
1.4.3 Radio/Millimeter wavelengths ---------------------------------------18
1.5 This study ------------------------------------------------------------19
1.5.1 Millimeter/Submillimeter long-term variability ------------------------19
1.5.2 LLAGN on tau−M relationship ---------------------------------------20
1.5.3 Linear tau−M correlation --------------------------------------------20
2 Observations and Data Reduction --------------------------------------22
2.1 Theory of Interferometry----------------------------------------------22
2.1.1 Introduction --------------------------------------------------------22
2.1.2 Two Element Interferometer ----------------------------------------23
2.1.3 Spatial Coherence on the sky ---------------------------------------24
2.1.4 Visibility------------------------------------------------------------ 25
2.1.5 Sensitivity ----------------------------------------------------------26
2.2 SMA Data ------------------------------------------------------------26
2.2.1 Observation --------------------------------------------------------26
2.2.2 Calibration & DataReduction ----------------------------------------27
2.2.3 Imaging ------------------------------------------------------------29
2.2.4 Flux measurement --------------------------------------------------31
3 Light Curves -----------------------------------------------------------33
3.1 Archive Data ---------------------------------------------------------33
3.2 The light curves -----------------------------------------------------34
3.3 Uncertainty of Flux Calibration ---------------------------------------36
4 Timescale Analysis ----------------------------------------------------43
4.1 Structure Function ---------------------------------------------------43
4.2 DRW Model ----------------------------------------------------------47
4.2.1 AR(1) and CAR(1) ---------------------------------------------------48
4.2.2 Model Fitting -------------------------------------------------------50
4.2.3 Parameter estimation -----------------------------------------------53
5 Discussion -------------------------------------------------------------61
5.1 Time scales in the Accretion Disk -------------------------------------61
5.2 Black Hole Mass Estimates--------------------------------------------64
5.3 tau−M relationship ---------------------------------------------------65
5.4 Implication -----------------------------------------------------------68
6 Conclusions ------------------------------------------------------------71
A Light Curves of Calibrator-----------------------------------------------73
B Application -------------------------------------------------------------76
B.1 Flux Survey Toward LLAGN at 230GHz---------------------------------76
B.1.1 Sample Selection---------------------------------------------------- 76
B.1.2 Result--------------------------------------------------------------- 77
B.2 What is the Mechanism of Depolarization Behind Low Luminosity AGN? 77
B.2.1 Sample Selection ----------------------------------------------------79
Bibliography---------------------------------------------------------------80

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