太阳活动区低色球层亮点幂律分布时变规律的观测分析
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摘要
太阳耀斑和微耀斑能量的幂律分布是太阳活动的一个典型特点。调查其统计特征和时变规律,对研究太阳能量的传输和耗散以及高层大气的加热机制有重要意义。研究太阳低层大气中能量释放的统计规律及其演化过程,使用二维区域标记算法,在日出(Hinode)卫星上的太阳光学望远镜(Solar Optical Telescope,SOT)对NOAA 10930活动区观测的低色球层Ca Ⅱ Hλ3 968.5单色像资料上,分析表征亮点能量分布的频数特征及其变化规律。在时间跨度为124 h、视场为202″.4×85″.3的时间序列中,共获得2.99×105个亮点,平均每帧图上每平方角分有24.15±6.34个亮点。主要分析结果如下:(1)亮点尺度(L=(L_xL_y)~(1/2))的瞬时分布基本符合幂律分布并满足自相似性;(2)亮点的产生率及其信噪比随着尺度的增加而减小。海量微小尺度亮点持续的发生可能是加热高层大气的一种稳定而可观的能量来源,例如,尺度小于4″的亮点产生的光通量在样本总光通量中占的比例达到53.23%;(3)小尺度亮点的瞬时数密度随着活动区的衰减而降低;(4)亮点集的尺度服从幂律分布,其离散系数σ(ζ)仅为4%。该实测样本尺度的幂指数γ为1.97,低噪声样本(L≤8″)的γ为2.12;(5)但是,在观测时段内,γ并没有收敛。样本集的γ是一个在观测积累中呈锯齿状变化的过程:在平静时段缓慢升高,在活动瞬间突然降低。(6)亮点瞬时子集的γ与其总光通量呈反比。在样本中剔除大尺度(L>8″)个体后,中小尺度亮点仍服从上述规律。太阳活动不仅产生中、大尺度的增亮区域,还对各尺度区间亮点的频数分布产生全局性的影响,引起瞬时γ的降低。
The power-law distribution of the energy of flares and microflares is an important character of solar activities. Investigating its attributes and temporal variations helps to study the transmission of energy and the heating of the solar corona. In this observation,we study the temporal variations of the frequency distribution of low-chromospheric bright points( BPs),and probe the pattern of energy release in low solar atmospheres. We utilize Ca Ⅱ H λ3968. 5 monograms of NOAA AR 10930 acquired by Hinode/SOT and recognize BPs with a two-dimensional region-labelling algorithm. On the time sequence with a time span of124 h and a field-of-view of 202″. 4 × 85″. 3,a sample of 2. 99 × 105 BPs is identified,with a numerical density of 24. 15 ± 6. 34 per square arcminute. The main results are summarized as follows:( 1) The instantaneous frequency distribution of BP's scale( L =(L_xL_y)~(1/2)) virtually observes the power-law and self-similarity.( 2) The value and signal-to-noise ratio of BP's production decrease with the increase of BP' s scale. Numerous smallscale BPs could be a valid source of energy for the heating of upper atmosphere. For instance,BPs with a scale smaller than 4″ share approximately 53. 23% of the sample' s total light flux budget.( 3) As the active region decays,the numerical density of small-scale BPs also decreases.( 4) The distribution of the sample set's scale observes the power-law,with a dispersion index σ( ζ) of 4%. The power-law index γ of the observed and low-noise( L ≤ 8″) samples are respectively 1. 97 and 2. 12.( 5) However,within the observation time,the overall power-law index γ does not converge. The relationship between the power-law index and the time-span of observation is serrated: in quiet times γ gradually increases,while in active moments γ decreases sharply.( 6) The instantaneous γ is reversely proportional to the instantaneous total light flux. Even after filtering largescale BPs( L > 8″),the low-noise sample,which contains only middle-and small-scale BPs,still shows such correlation. This quashes our initial suspicion that the numerical calculation of γ is rigged by the injection of few large BPs into the sample pool; the observed relationship between large events and the dropping of γ is intrinsic. Solar activities not only produces middle and large scale BPs,but also changes the entire pattern of BP's distribution and hence lowers γ.
The power-law distribution of the energy of flares and microflares is an important character of solar activities. Investigating its attributes and temporal variations helps to study the transmission of energy and the heating of the solar corona. In this observation,we study the temporal variations of the frequency distribution of low-chromospheric bright points( BPs),and probe the pattern of energy release in low solar atmospheres. We utilize Ca Ⅱ H λ3968. 5 monograms of NOAA AR 10930 acquired by Hinode/SOT and recognize BPs with a two-dimensional region-labelling algorithm. On the time sequence with a time span of124 h and a field-of-view of 202″. 4 × 85″. 3,a sample of 2. 99 × 105 BPs is identified,with a numerical density of 24. 15 ± 6. 34 per square arcminute. The main results are summarized as follows:( 1) The instantaneous frequency distribution of BP's scale( L =(L_xL_y)~(1/2)) virtually observes the power-law and self-similarity.( 2) The value and signal-to-noise ratio of BP's production decrease with the increase of BP' s scale. Numerous smallscale BPs could be a valid source of energy for the heating of upper atmosphere. For instance,BPs with a scale smaller than 4″ share approximately 53. 23% of the sample' s total light flux budget.( 3) As the active region decays,the numerical density of small-scale BPs also decreases.( 4) The distribution of the sample set's scale observes the power-law,with a dispersion index σ( ζ) of 4%. The power-law index γ of the observed and low-noise( L ≤ 8″) samples are respectively 1. 97 and 2. 12.( 5) However,within the observation time,the overall power-law index γ does not converge. The relationship between the power-law index and the time-span of observation is serrated: in quiet times γ gradually increases,while in active moments γ decreases sharply.( 6) The instantaneous γ is reversely proportional to the instantaneous total light flux. Even after filtering largescale BPs( L > 8″),the low-noise sample,which contains only middle-and small-scale BPs,still shows such correlation. This quashes our initial suspicion that the numerical calculation of γ is rigged by the injection of few large BPs into the sample pool; the observed relationship between large events and the dropping of γ is intrinsic. Solar activities not only produces middle and large scale BPs,but also changes the entire pattern of BP's distribution and hence lowers γ.
引文
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[38]Kalkofen W.Oscillations in chromospheric network bright points[J].The Astrophysics Journal,1997,486(2):L145-L148.
[39]Bocchialini K,Vial J C,Einaudi G.Statistical analysis of a bright point observed simultaneously in two chromospheric and transition region lines by SUMER[C]//Wilson A,Fifth SOHO workshop:The corona and solar wind near minimum activity,1997,404:211-215.
[40]Pérez-Suárez D,Maclean R C,Doyle J G,et al.The structure and dynamics of a bright point as seen with Hinode,So HO and TRACE[J].Astronomy&Astrophysics,2008,492(2):575-583.
[41]卢小广.统计学教程[M].北京:清华大学出版社,2005:33-36.
[42]Newman M E J.Power laws,Pareto distributions and Zipf's law[J].Contemporary Physics,2005,46(5):323-351.
[2]Lin R P,Schwartz R A,Kane S R,et al.Solar hard X-ray microflares[J].The Astrophysical Journal,1984,283(1):421-425.
[3]Dennis B R.Solar hard X-ray bursts[J].Solar Physics,1985,100(1):465-490.
[4]Bai T.Variability of the occurrence frequency of solar flares as a function of peak hard X-ray rate[J].The Astrophysical Journal,1993,404:805-809.
[5]Crosby N B,Aschwanden M J,Dennis B R.Frequency distributions and correlations of solar Xray flare parameters[J].Solar Physics,1993,143(2):275-299.
[6]Shimojo M,Shibata K.Occurrence rate of microflares in an X-ray bright point within an active region[J].The Astrophysical Journal,1999,516(2):934-938.
[7]Veronig A,Temmer M,Hanslmeier A,et al.Temporal aspects and frequency distributions of solar soft X-ray flares[J].Astronomy&Astrophysics,2002,382(3):1070-1080.
[8]Su Y,Gan W Q,Li Y P.A statistical study of Rhessi flares[J].Solar Physics,2006,238(1):61-72.
[9]Mc Intosh S W,Gurman J B.Nine years of EUV bright points[J].Solar Physics,2005,228(1):285-299.
[10]Alipour N,Safari H.Statistical properties of solar coronal bright points[J].The Astrophysical Journal,2015,807(2):175-183.
[11]Aschwanden M J,Crosby N B,Dimitropoulou M,et al.25 years of self-organized criticality:solar and astrophysics[J].Space Science Reviews,2016,198(1):47-166.
[12]Wheatland M S,Sturrock P A.Avalanche models of solar flares and the distribution of active regions[J].The Astrophysical Journal,1996,471(2):1044-1048.
[13]Wheatland M S.Flare frequency-size distributions for individual active regions[J].The Astrophysical Journal,2000,532(2):1209-1214.
[14]Perrone D,Dendy R O,Furno I,et al.Nonclassical transport and particle-field coupling:from laboratory plasmas to the solar wind[J].Space Science Reviews,2013,178(2):233-270.
[15]Hale G E.Solar magnetism[J].Nature,1935,136(3444):703-705.
[16]Mc Intosh S W,Wang X,Leamon R J,et al.Deciphering solar magnetic activity I:on the relationship between the sunspot cycle and the evolution of small magnetic features[J].The Astrophysical Journal,2014,792(2):12-30.
[17]Rieger E,Kanbach G,Reppin C,et al.A 154-day periodicity in the occurrence of hard solar flares?[J].Nature,1984,312:623-625.
[18]赵明宇,陈军权,刘煜,等.太阳活动峰年和谷年期间黑子群与耀斑的统计分析[J].中国科学:物理学力学天文学,2014,44(1):109-120.Zhao Mingyu,Chen Junquan,Liu Yu,et al.Statistical analysis of sunspot groups and flares for solar maximum and minimum[J].Scientia Sinica:Physica Mechanica Astronomica,2014,44(1):109-120.
[19]牛俊,方涵先,翁利斌.太阳活动与热层大气密度的相关性研究[J].空间科学学报,2014,34(1):73-80.Niu Jun,Fang Hanxian,Weng Libin.Correlation between solar activity and thermospheric density[J].Chinese Journal of Space Science,2014,34(1):73-80.
[20]Lu E T,Hamilton R J.Avalanches and the distribution of solar flares[J].The Astrophysical Journal Letters,1991,380(2):L89-L92.
[21]Abramenko V,Yurchyshyn V,Goode P,et al.Statistical distribution of size and lifetime of bright points observed with the new solar telescope[J].The Astrophysical Journal Letters,2010,725(1):L101-L105.
[22]李小波,杨志良,张洪起.基于三维区域标记对太阳活动区低色球层亮点的统计分析[J].北京师范大学学报(理),2016,52(5):542-549.Li Xiaobo,Yang Zhiliang,Zhang Hongqi.Distribution of low-chromospheric brightpoints in a solar active region as observed by region-labeling[J].Journal of Beijing Normal University(Natural Science),2016,52(5):542-549.
[23]冯恒强,曹行健.行星际磁通量绳尺度的幂律谱分布[J].天文研究与技术——国家天文台台刊,2010,7(1):1-7.Feng Hengqiang,Cao Xingjian.Power-law distribution of scale lengths of interplanetary magnetic flux ropes[J].Astronomical Research&Technology——Publications of National Astronomical Observatories of China,2010,7(1):1-7.
[24]Wheatland M S.Evidence for departure from a power-law flare size distribution for a small solar active region[J].The Astrophysical Journal,2010,710(2):1324-1334.
[25]Parker E N.The sun:the ultimate challenge to astrophysics[J].Advances in Space Research,1998,21(1-2):267-274.
[26]Ilonidis S,Zhao J,Kosovichev A.Detection of emerging sunspot regions in the solar interior[J].Science,2011,333(6045):993-996.
[27]Bak P,Tang C,Wiesenfeld K.Self-organized criticality:an explanation of the 1/f noise[J].Physical Review Letters,1987,59(4):381-384.
[28]Albert R,Barabási A L.Statistical mechanics of complex networks[J].Reviews of Modern Physics,2002,74(1):47-97.
[29]Daly E,Porporato A.Effect of different jump distributions on the dynamics of jump processes[J].Physical Review E,2010,81(6):061133-1-061133-10.
[30]Zirin H.The magnetic structure of plagues[C]//Athay R G.Chromospheric fine structure,volume 56 of IAU Symposium.Boston:Reidel,1974:161-175.
[31]Li X B,Yang Z L,Zhang H.Formation of pores associated with the inflow of moving magnetic features[J].The Astrophysical Journal,2015,807(2):160-174.
[32]Hudson H S.Solar flares,microflares,nanoflares,and coronal heating[J].Solar Physics,1991,133(2):357-369.
[33]Tu C Y,Marsch E.MHD structures,waves and turbulence in the solar wind:Observations and theories[J].Space Science Reviews,1995,73(1):1-210.
[34]Suzuki T K,Inutsuka S I.Solar winds driven by nonlinear low-frequency Alfvén waves from the photosphere:Parametric study for fast/slow winds and disappearance of solar winds[J].Journal of Geophysical Research,2006,111(A6):06101.
[35]方锦清,汪小帆,郑志刚,等.一门崭新的交叉科学:网络科学(上)[J].物理学进展,2007,27(3):239-343.Fang Jinqing,Wang Xiaofan,Zheng Zhigang,et al.New interdisciplinary science:networks science[J].Progress in Physics,2007,27(3):239-343.
[36]刘艳霄,杨云飞,林隽.太阳光球磁亮点的识别算法[J].天文研究与技术,2014,11(2):145-150.Liu Yanxiao,Yang Yunfei,Lin Jun.A region-growth algorithm to recognize magnetic bright spots in the solar photosphere[J].Astronomical Research&Technology,2014,11(2):145-150.
[37]Crockett P J,Mathioudakis M,Jess D B,et al.The area distribution of solar magnetic bright points[J].The Astrophysical Journal Letters,2010,722(2):188-193.
[38]Kalkofen W.Oscillations in chromospheric network bright points[J].The Astrophysics Journal,1997,486(2):L145-L148.
[39]Bocchialini K,Vial J C,Einaudi G.Statistical analysis of a bright point observed simultaneously in two chromospheric and transition region lines by SUMER[C]//Wilson A,Fifth SOHO workshop:The corona and solar wind near minimum activity,1997,404:211-215.
[40]Pérez-Suárez D,Maclean R C,Doyle J G,et al.The structure and dynamics of a bright point as seen with Hinode,So HO and TRACE[J].Astronomy&Astrophysics,2008,492(2):575-583.
[41]卢小广.统计学教程[M].北京:清华大学出版社,2005:33-36.
[42]Newman M E J.Power laws,Pareto distributions and Zipf's law[J].Contemporary Physics,2005,46(5):323-351.