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太阳活动区光球磁场特征的量化

杨晓华 王栖溪 夏仲飞 包赟 彭代亮 田天 徐龙

杨晓华, 王栖溪, 夏仲飞, 包赟, 彭代亮, 田天, 徐龙. 太阳活动区光球磁场特征的量化[J]. 空间科学学报, 2022, 42(1): 34-43. doi: 10.11728/cjss2022.01.200826076
引用本文: 杨晓华, 王栖溪, 夏仲飞, 包赟, 彭代亮, 田天, 徐龙. 太阳活动区光球磁场特征的量化[J]. 空间科学学报, 2022, 42(1): 34-43. doi: 10.11728/cjss2022.01.200826076
YANG Xiaohua, WANG Qixi, XIA Zhongfei, BAO Yun, PENG Dailiang, TIAN Tian, XU Long. Quantitative Characterization of Photospheric Magnetic Field in Solar Active Regions (in Chinese). Chinese Journal of Space Science,  2022, 42(1): 34-43.  DOI: 10.11728/cjss2022.01.200826076
Citation: YANG Xiaohua, WANG Qixi, XIA Zhongfei, BAO Yun, PENG Dailiang, TIAN Tian, XU Long. Quantitative Characterization of Photospheric Magnetic Field in Solar Active Regions (in Chinese). Chinese Journal of Space Science,  2022, 42(1): 34-43.  DOI: 10.11728/cjss2022.01.200826076

太阳活动区光球磁场特征的量化

doi: 10.11728/cjss2022.01.200826076
基金项目: 国家自然科学基金项目资助(11033001)
详细信息
    作者简介:

    杨晓华:E-mail:yxhua3@163.com

  • 中图分类号: P353

Quantitative Characterization of Photospheric Magnetic Field in Solar Active Regions

  • 摘要:

    为有效解决太阳活动区磁场特征量化问题,对所有SOHO卫星MDI磁图预处理后,分割出日面角45°以内的活动区,分析活动区投影面积变形来源,研究建立Cosine面积校正因子,校正活动区面积,构建具有21个特征参数的活动区磁场特征量化指标体系,通过主成分分析法对量化结果计算累积方差,结合活动区10486爆发X17.2级耀斑时的磁场变化定性分析。结果表明:强梯度极性分隔线权重磁场绝对值之和R、极性分隔线长度LPS、 强梯度极性分隔线长度Lsg和强梯度极性分隔线磁场绝对值之和

    $\phi $

    PSL能够解释活动区磁场结构变化; 磁场通量绝对值总和

    $\phi $

    uns、磁场负通量总和

    $\phi $

    、磁场值代数和

    $\phi $

    tot和磁场绝对值之和的平均值

    $\phi $

    mean能够解释活动区磁场通量变化。

    $\phi $

    PSL为本文新构建特征参数。上述参数可有效监测耀斑爆发前后活动区磁场结构和磁场通量的变化情况,量化结果可作为耀斑、质子事件监测及耀斑预报模型输入,为开展太阳爆发活动监测预警提供技术支撑。

     

  • 图  1  太阳球面面积校正。(a) 表示磁图影像为1024 pixel×1024 pixel (红线),太阳圆盘直径为994 pixel (黄线) ,太阳圆盘半径为497 pixel(绿线),紫色点为日面中心。(b) Rsun 表示太阳半径,$x$表示一个像元的边长,li表示平面图中像元边长所对应的弧长$x$${\theta _i}$表示弧长li对应的日心角,αi${\varphi _i}$表示计算过程中的变量

    Figure  1.  Schematic diagram of solar spherical area correction. (a) Shows that the magnetic image is 1024 pixel×1024 pixel (red line), the diameter of the solar disk is 994 pixel (yellow line), the radius of the solar disk is 497 pixel (green line), and the purple point is the center of the Sun. (b) Rsun denotes the solar radius, $x$ represents the edge length of a pixel, li represents the arc length corresponding to the pixel edge length $x$ in the plane view, ${\theta _i}$ represents the heliocentric angle corresponding to the arc length li, $ {a_i} $ and ${\varphi _i}$ represent the variables in the calculation process

    图  2  活动区10486磁场(a)(b)、黑子群(c)和X射线通量(d)

    Figure  2.  Magnetic field (a)(b), sunspot (c) and X-ray flux (d) of active region 10486

    图  3  耀斑爆发前后最优特征参数变化趋势

    Figure  3.  Variation trend of the optimal characteristic parameters before and after the flare eruption

    表  1  太阳活动区磁场特征量化指标

    Table  1.   Quantitative index of magnetic field characteristics in solar active region

    特征参数提出或优化算法表达指标描述(均为单个活动区的量化指标)编号
    活动区磁场
    特征量化
    活动区面积Atot $ \displaystyle\sum\nolimits_{p} {{A_{\cos ,t,i}}} $ 计算磁图面积校正后的活动区面积 1
    磁场最大值$\phi $max $\phi $max,t,i 提取活动区中磁场最大值 2
    磁场最小值$\phi $min $\phi $min,t,i 提取活动区中磁场最小值 3
    磁场值代数和$\phi $tot $\displaystyle\sum\nolimits_{p} {{\phi _{t,i}}} $ 活动区中所有正负磁场值的代数和 4
    磁场绝对值和的平均值$\phi $mean ${{\displaystyle\sum\nolimits_{p} {\left| {{\phi _{t,i}}} \right|} } \mathord{\left/ {\vphantom {{\displaystyle\sum\nolimits_{p} {\left| {{\phi _{t,i}}} \right|} } {\displaystyle\sum\nolimits_{p} {{A_{\cos ,t,i}}} }}} \right. } {\displaystyle\sum\nolimits_{p} {{A_{\cos ,t,i}}} }}$ 活动区中所有正负磁场值的绝对值和的平均值 5
    磁场正通量总和$\phi $+ $ \displaystyle\sum\nolimits_{p} {\left( {{\phi _{t,i}} > 0} \right)} $ 活动区中所有正磁场值的代数和 6
    磁场负通量总和$\phi $ $ \displaystyle\sum\nolimits_{p} {\left( {{\phi _{t,i}} < 0} \right)} $ 活动区中所有负磁场值的代数和 7
    磁场通量绝对值总和$\phi $uns $ \displaystyle\sum\nolimits_{p} {\left| {{\phi _{t,i}}} \right|} $ 活动区中所有正负磁场值的绝对值的和 8
    磁场通量不平衡率$\phi $imb $ {{\left| {\left( {{\phi _{ + ,t,i}} - \left| {{\phi _{ - ,t,i}}} \right|} \right)} \right|} \mathord{\left/ {\vphantom {{\left| {\left( {{\phi _{ + ,t,i}} - \left| {{\phi _{ - ,t,i}}} \right|} \right)} \right|} {{\phi _{uns,t,i}}}}} \right. } {{\phi _{uns,t,i}}}} $ 正负磁场通量差值相对于磁通量绝对值总和的变化率 9
    磁场净通量增加率d$\phi $/dt ${\left. {\dfrac{{{\rm{d}}\phi }}{{{\rm{d}}t}}} \right|_{net,t,i}} = {\displaystyle\sum\nolimits_{p} {\left. {\frac{{{\rm{d}}\phi }}{{{\rm{d}}t}}} \right|} _{t,i}} = \dfrac{{\displaystyle\sum\nolimits_{p} {{\phi _{t,i}}} - \displaystyle\sum\nolimits_{p} {{\phi _{t - \Delta t,i}}} }}{{\Delta t}}$ 正负磁场值的代数和在单位时间内变化情况 10
    活动区极性分
    隔线特征量化
    强梯度极性分隔线长度Lsg $ \displaystyle\sum\nolimits_{p} {\nabla {\phi _{t,i}} > 50 \times {{10}^{ - 4}} \;{\rm{T}}} $,$ \nabla {\phi _{t,i}} $用三点拉格朗日插值获取,获
    取后选取$ \nabla {\phi _{t,i}} > 50 \times {10^{ - 4}}\;{\rm{T}} $的像元,计算其个数。
    极性分隔线上相邻磁场值差值>50×10–4 T的像元个数总和 11
    极性分隔线长度LPS $ \displaystyle\sum\nolimits_{p} {P \ne 0} $ 极性分隔线上磁场值≠0的像元个数总和 12
    极性分隔线最大磁场梯度$\nabla\phi $max $\nabla\phi $max 极性分隔线上相邻磁场值差值最大的值 13
    极性分隔线平均磁场梯度$\nabla \phi $mean $\nabla\phi $mean 极性分隔线上相邻磁场值差值的平均值 14
    强梯度极性分隔线的梯度权重
    (非势场测量)WLsg
    $ {W_{L\rm{sg}}} = \int {\left( {\nabla \phi z} \right)} {\rm{d}}l $,选取极性分隔线上磁场值>150×10–4 T
    的像元,计算其三点拉格朗日插值,后利用此公式计算WLsgi
    极性分隔线上磁场值>150×10–4 T的像元拉格朗日插值长度积分 15
    修正的WLsg,$W_{L{\rm{sg}}}^* $ $ \displaystyle\sum\nolimits_{p} {{M_{{\rm{PSL}},t,i}} \; \nabla {\phi _{t,i}}} $,$ \nabla {\phi _{t,i}} $用三点拉格朗日插值获取。 极性分隔线上磁场值>150×10–4 T的像元拉格朗日插值磁场值
    积分
    16
    强梯度极性分隔线权重磁场绝对值之和R $ \displaystyle\sum\nolimits_{p} ({{{M}}_{{\rm{PSL,t,i}}}}{{{G}}_{2{\rm{D}}}}) {\phi _{t,i}} $ 强梯度极性分隔线上磁场值乘以高斯权重后绝对值之和 17
    强梯度极性分隔线磁场绝对值之和$\phi $PSL $ \displaystyle\sum\nolimits_{p} {\left| {{\phi _{{\rm{PSL}},t,i}}} \right|} $ 强梯度极性分隔线上磁场值绝对值之和 18
    活动区分类 磁场极性类别(单极/多极) $\phi $imb,t,i ≥ 90%为单极,$\phi $imb,t,i<90%为多极 根据磁场通量不平衡率,分单极或多极 19
    磁场强弱类别(强/弱) $\phi $uns,t,i ≥ 1021Mx为强通量,$\phi $uns,t,i<1021Mx为弱通量 根据磁场通量绝对值总和,分强通量或弱通量 20
    磁场通量演化状态(增加/下降) d$\phi $/dt t,i≥0为磁通量增加,d$\phi $/dt t,i<0为磁通量下降 根据磁场净通量增加率,分磁通量增加或下降 21
     Lsg、$\nabla \phi $max、$\nabla \phi $mean、 $\phi $PSL为本研究中新提出变量;Atot、$\phi $max、$\phi $min、$\phi $tot、$\phi $mean、$\phi $+、$\phi $、$\phi $uns、$\phi $imb、 d$\phi $/dt LPS、 $W_{L{\rm{sg}}}^* $和R 由文献[21]提出;LsgWLsg由文献[18, 19]提出;所有公式中的t, i分别表示t时刻影像的第i个像元; P 为pixel取值范围; G2D为二维高斯平滑。
    下载: 导出CSV

    表  2  磁场特征量化结果主成分分析结果

    Table  2.   Results of principal component analysis of quantitative results of magnetic field characteristics

    特征参数初始特征值提取的平方和载入值
    合计方差/(%)累积 /(%)合计方差 /(%)累积 /(%)
    极性分隔线权重磁场值的和R 8.049 38.327 38.327 8.049 38.327 38.327
    磁场通量绝对值总和$\phi $uns 3.404 16.208 54.535 3.404 16.208 54.535
    极性分隔线长度LPS 1.782 8.488 63.023 1.782 8.488 63.023
    磁场负通量总和$\phi $- 1.360 6.479 69.501 1.360 6.479 69.501
    磁场值代数和$\phi $tot 1.113 5.302 74.803 1.113 5.302 74.803
    磁场最小值$\phi $min 0.985 4.693 79.496 0.985 4.693 79.496
    强梯度极性分隔线长度Lsg 0.889 4.234 83.729 0.889 4.234 83.729
    强梯度极性分隔线磁场绝对值之和$\phi $PSL 0.800 3.812 87.541 0.800 3.812 87.541
    磁场绝对值之和平均值$\phi $mean 0.562 2.678 90.219 0.562 2.678 90.219
    极性分隔线最大磁场梯度$\nabla \phi $max 0.501 2.387 92.606
    磁场强弱类别(强/弱) 0.454 2.164 94.770
    修正的WLsg($W_{ L{\rm{sg}}}^* $) 0.370 1.763 96.533
    磁场净通量增加率d$\phi $/dt 0.271 1.289 97.822
    强梯度极性分隔线梯度权重WLsg 0.180 0.857 98.679
    磁场通量不平衡率$\phi $imb 0.135 0.641 99.320
    磁场极性类别(单极/多极) 0.088 0.421 99.741
    磁场正通量总和$\phi $+ 0.034 0.163 99.903
    磁场最大值$\phi $max 0.020 0.096 100.000
    磁场通量演化状态(增加/下降) 0.000 0.000 100.000
    极性分隔线平均磁场梯度$\nabla \phi $mean 0.000 0.000 100.000
    面积Atot 0.000 0.000 100.000
    下载: 导出CSV

    表  3  2003年10月28日活动区10486磁场特征参数量化结果

    Table  3.   Quantitative results of characteristic parameters of magnetic field in 10486 active area on 28 October 2003

    特征参数08:00 UT09:36 UT11:12 UT12:48 UT14:24 UT08:00-11:12 UT(增加率)
    活动区面积Atot / pixel 1576.05 1588.32 1596.42 1597.98 1621.87 1.29%
    磁场最大值$\phi $max / (×10–4)T 314.97 368.60 468.80 542.06 385.04 48.84%
    磁场最小值$\phi $min / (×10–4)T –247.11 –206.13 –301.62 –491.54 –545.70 22.06%
    磁场值代数和$\phi $tot / (×10–4)T 4283.35 7262.43 8284.17 6309.44 4197.62 93.40%
    磁场绝对值和的平均值$\phi $mean / (×10–4)T 5.58 7.25 11.63 6.94 9.54 108.42%
    磁场正通量总和$\phi $+ / (×10–4)T 6542.03 9385.23 13428.10 8700.38 9836.09 105.26%
    磁场负通量总和$\phi $ / (×10–4)T –2258.68 –2122.80 –5143.94 –2390.94 –5638.47 127.74%
    磁场通量绝对值总和$\phi $uns / (×10–4)T 8800.72 11508.03 18572.04 11091.32 15474.56 111.03%
    磁场通量不平衡率$\phi $imb 0.49 0.63 0.45 0.57 0.27 –8.16%、–164.69%
    磁场净通量增加率d$\phi $/dt 14.66 –25.52 16.51 1.32 –25.11 09:36-11:12 UT
    强梯度极性分隔线长度Lsg / pixel 0.00 0.00 7.00 0.00 0.00
    极性分隔线长度LPS / pixel 6.00 12.00 52.00 14.00 15.00 766.67%
    极性分隔线最大磁场梯度$\nabla \phi $max / (×10–4)T 0.00 0.00 319.35 0.00 0.00
    极性分隔线平均磁场梯度$\nabla \phi $mean / (×10–4)T 0.00 0.00 28.85 0.00 0.00
    强梯度极性分隔线的梯度权重WLsg/ pixel 0.00 0.00 319.35 0.00 0.00
    修正的WLsg,$W_{L{\rm{sg}}}^* $/ pixel 0.00 0.00 663.44 0.00 0.00
    极性分隔线权重磁场值之和R / (×10–4)T 1317.16 3163.26 13262.56 3569.14 4297.99 906.91%
    强梯度极性分隔线磁场绝对/ (×10–4)T
    值之和$\phi $PSL / (×10–4)T
    0.00 0.00 855.14 0.00 0.00
    磁场极性类别(单极/多极) 多极 多极 多极 多极 多极
    磁场强弱类别(强/弱)
    磁场通量演化状态(增加/下降) 增加 下降 增加 增加 下降
     表中灰色部分表示耀斑爆发前后磁场特征值变化较大的特征参数。
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-08-26
  • 录用日期:  2020-08-26
  • 修回日期:  2021-06-29
  • 网络出版日期:  2022-05-25

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