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Variability is one of the most important observational features of quasars, and it is still not clear that the different quasars show different characteristic variability patterns. The optical variability of quasar is very complex, and optical variability has the non-linear characteristic of complex system. In this paper, the approximate entropy method is employed to analyze the complexities of variability in the Sloan digital sky survey (SDSS) stripe 82 quasars. Firstly, in order to show that the approximate entropy method has the effective ability to distinguish the different types of time sequences, the approximate entropy of periodic sequence, noise sequence, chaotic sequence and their mixed sequences are calculated by using the analog signals. The approximate entropy method proves to be an effective method to identify different types of time sequences. Then, we present the approximate entropy of optical variability of spectroscopically-confirmed quasars from the SDSS data release 7 spectroscopic catalog, and their complexities are analyzed. The results show that the maximum approximate entropy of quasars’ optical variability is only 0.58. The complexity of quasars’ optical variability is between the complexities of periodic sequence and white noise sequence. For nearly half of the samples, the complexities of their optical variability are basically consistent with the complexity of chaotic sequence. Quasars’ optical variability is neither completely periodic nor completely stochastic.
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Keywords:
- quasars /
- variability /
- approximate entropy /
- complexity
[1] Fan J H, Zhang Y W, Qian B C, Tao J, Liu Y, Hua T X 2009 Astrophys. J. Suppl. Ser. 181 466
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Google Scholar
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Google Scholar
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Hao B L 2001 Physics 30 466
Google Scholar
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Google Scholar
[20] 金宁德, 董芳, 赵舒 2007 物理学报 56 0720
Jin N D, Dong F, Zhao S 2007 Acta. Phys. Sin. 56 0720
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
Tang J, Liu X Q, Fu M X 2018 Journal of Shaanxi University of Technology (Natural Science Edition)
33 87 Google Scholar
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图 1 典型时间序列
Figure 1. Typical time series
图 2 典型时间序列的近似熵
Figure 2. The approximate entropy of typical time series
图 3 SDSS J012228.72-001332.0的光变曲线
Figure 3. Light curve of SDSS J012228.72-001332.0
图 4 SDSS J012228.72-001332.0的近似熵
Figure 4. The approximate entropy of SDSS J012228.72-001332.0
图 5 SDSS类星体的近似熵分布
Figure 5. Approximate entropy distribution of SDSS quasars
表 1 SDSS类星体的近似熵
Table 1. Approximate entropy of SDSS quasars
近似熵值 0—0.1 0.1—0.2 0.2—0.3 0.3—0.4 0.4—0.5 0.5—0.6 波段 总样本数 样本数 百分数/% 样本数 百分数/% 样本数 百分数/% 样本数 百分数/% 样本数 百分数/% 样本数 百分数/% i 6465 39 0.60 365 5.65 1848 28.58 3106 48.04 1077 16.66 30 0.47 r 6547 40 0. 61 438 6.69 1898 28.99 3131 47.82 1003 15.32 37 0.57 g 6439 34 0.53 374 5.81 1794 27.86 3153 48.97 1033 16.04 51 0.79 z 6373 40 0.63 203 3.19 1438 22.56 3223 50.57 1400 21.97 69 1.08 u 6092 27 0.44 190 3.12 1503 24.67 3117 51.17 1214 19.93 41 0.67 
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[1] Fan J H, Zhang Y W, Qian B C, Tao J, Liu Y, Hua T X 2009 Astrophys. J. Suppl. Ser. 181 466
Google Scholar
[2] 黄克谅 2005 类星体与活动星系核 (北京: 科学出版社) 第3页
Huang K L 2005 Quasars and Active Galactic Nucleus (Beijing: Science Press) p3 (in Chinese)
[3] Kawaguchi T, Mineshige S, Umemura M 2002 Astrophys. J. 504 671
[4] MacLeod C L, ŽIvezić C S, Kochanek S, Kozłowski B, Kelly E, Bullock A, Kimball B, Sesar D, Westman K B 2010 Astrophys. J. 721 1014
Google Scholar
[5] Kasliwal P V, Vogeley S M, Richards T G 2015 Mon. Not. R. Astron. Soc. 451 4328
Google Scholar
[6] Guo H X, Wang J X, Cai Z Y, Sun M Y 2017 Astrophys. J. 847 132
Google Scholar
[7] Harko T, Leung C S, Mocanu G 2014 European Physical Journal C 74 2900
Google Scholar
[8] Charisi M, Bartos I, Haiman Z, Price-Whelan A M, Márka S 2015 Mon. Not. R. Astron. Soc. 45 4
[9] D'Orazio D J, Haiman Z, Schiminovich D 2015 Nature 525 351
Google Scholar
[10] Bhatta G, Zola S, Stawarz Ł, Ostrowski M, Winiarski M, Ogłoza W, Dróżdż M, Siwak M, Liakos A, et al 2016 Astrophys. J. 832 47
Google Scholar
[11] Carrasco L, Dultzinhacyan D, Cruzgonzalez I 1985 Nature 314 146
Google Scholar
[12] Kidger M, Takalo L, Sillanpää A 1992 Astron. Asrtophys. 264 32
[13] Valtonen M J, Lehto H J, Sillanpää A, Nilsson K, Mikkola S, Hudec R, Basta M, Teräsranta H, Haque S, Rampadarath H 2006 Astrophys. J. 646 34
[14] Misra R, Harikrishnan K P, Ambika G, Kembhavia A K 2006 Advances in Space Research 643 1114
[15] Harikrishnan K P, Misra R, Ambika G 2011 Research in Astron. Astrophys. 11 71
Google Scholar
[16] Emmanoulopoulos D 2007 Ph. D. Dissertation (Heidelber: Ruperto-Carola University of Heidelberg)
[17] 唐洁 2014 物理学报 63 049701
Google Scholar
Tang J 2014 Acta. Phys. Sin. 63 049701
Google Scholar
[18] 郝柏林 2001 物理 30 466
Google Scholar
Hao B L 2001 Physics 30 466
Google Scholar
[19] Pincus S M, Huang W M 1992 Commun. Statist-Theory Meth. 21 3061
Google Scholar
[20] 金宁德, 董芳, 赵舒 2007 物理学报 56 0720
Jin N D, Dong F, Zhao S 2007 Acta. Phys. Sin. 56 0720
[21] Lempel A, Ziv J 1976 IEEE Trans. on Inf. Theory 22 75
Google Scholar
[22] 郭家梁, 钟宁, 马小萌, 张明辉, 周海燕 2016 物理学报 65 190501
Google Scholar
Guo J L, Zhong N, Ma X M, Zhang M H, Zhou H Y 2016 Acta. Phys. Sin. 65 190501
Google Scholar
[23] Pettitt A N, Stephens M A 1977 Technometrics 19 205
Google Scholar
[24] Hughes P A, Aller H D, Aller M F 1992 Astrophys. J. 396 469
Google Scholar
[25] Scargle J D 1982 Astrophys. J. 263 835
Google Scholar
[26] 唐洁, 刘晓琴, 傅明星 2018 陕西理工大学学报(自然科学版) 33 87
Google Scholar
Tang J, Liu X Q, Fu M X 2018 Journal of Shaanxi University of Technology (Natural Science Edition)
33 87 Google Scholar
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