磁緻星是具有極強磁場的中子星，展現出獨特的X射線和無線電波特性。本研究的第一部分針對磁緻星進行了X射線光譜分析。大多數磁緻星的光譜可以用冪定律加黑體輻射進行描述。有趣的是，我們發現冪定律模型的亮度與黑體輻射溫度和黑體輻射面積之間存在關聯，而這種關聯與脈衝星的特性相似，儘管它們的X射線輻射機制不同。這種共同的基本平面表明磁緻星和脈衝星之間存在更深層次的聯繫，強調了對這兩種中子星的磁層輻射特性進一步研究的重要性。
本研究的第二部分聚焦於兩顆磁緻星的無線電波特性，分別是1E 1547.0−5408和XTE J1810−197。結果顯示，1E 1547.0−5408的頻譜在43到95GHz範圍內呈現反轉現象，暗示在數百GHz的頻段存在頻譜峰值。而XTE J1810−197的353GHz光度變化曲線呈下降趨勢，顯示不同頻段之間存在著不同的演化過程。此外，我們從文獻中獲取了其他無線電磁緻星數據，並發現了兩個有趣的特性。首先，在 X 射線爆發期間，無線電的上升時間遠遠長於X射線輻射的上升時間。其次，一些無線電磁緻星的頻譜在幾個GHz和數百GHz之間呈現雙峰結構，這表明在釐米波和次毫米波段存在不同的輻射機制。這些發現為我們深入理解磁緻星無線電的起源以及其與X射線特性之間的關係提供了重要的線索。

Magnetars are neutron stars with exceptionally strong magnetic fields, exhibiting unique X-ray and radio emissions. In Part I, we analyzed the X-ray spectra of magnetars in their quiescent state. Most spectra could be fitted with a power-law plus black body model. Interestingly, we found that the power-law luminosity is related to the black body temperature and black body emission radius, a relationship shared with pulsars despite their different X-ray emission mechanisms. This common fundamental plane suggests a deeper connection between magnetars and pulsars, highlighting the need for further understanding of their magnetospheric emissions.
In Part II, we focused on the radio emission of two magnetars. Observations revealed an inverted spectrum for 1E 1547.0−5408, suggesting a spectral peak in the submm range. The 353 GHz light curve of XTE J1810−197 exhibited a decreasing trend, indicating different evolution processes between frequency bands.Moreover, we discovered two interesting properties of radio magnetars. Firstly, the rise time of radio emission during outbursts was significantly longer than that of X-ray emission. Secondly, some radio magnetars displayed double-peak spectra at a few GHz and a few hundred GHz, indicating distinct emission mechanisms. These findings offer valuable insights into the origin of radio emission and its relationship with X-ray properties.

摘要 i
Abstract ii
I Relations between Non-thermal and Thermal Spectral Parameters in X-
ray of Magnetar 1
1 Introduction 3
1.1 Magnetar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Twisted magnetosphere . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Pulsar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Magnetar-like pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Data 7
2.1 Data selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Chandra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 XMM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.3 Special cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Spectral fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Results 13
3.1 Correlation coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Parameters fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4 Discussion 21
4.1 The common fundamental plane . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2 Possible higher dimensional fundamental plane . . . . . . . . . . . . . . . . . 24
4.3 Notes to three special targets . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5 Summary 31
II High-frequency Radio Spectra of Magnetars 33
1 Introduction 35
1.1 Radio emission from magnetars . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.2 Radio magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2 1E 1547.0−5408 39
2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.1.1 ATCA observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.1.2 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3 XTE J1810−197 43
3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.1 JCMT observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.2 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Discussion 55
4.1 Double-peak spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2 Flux evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5 Summary 63
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