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Keywords: cosmic rays - solar magnetic fields - interplanetary magnetic fields
关键词： 宇宙射线--太阳磁场--行星际磁场

The solar magnetic field is the key to the study of solar physics. It has a period of change for about 11 years. Because of the limited space and ground observations, only the photosphere magnetic field can be measured more accurately. The coronal magnetic field(CMF) above the photosphere is usually obtained by extrapolation with the observed photosphere magnetic field under some theoretical model. For example, the potential field source surface(PFSS) model which is extrapolated from the potential field model in the spherical coordinate system(Schatten et al. 1969; Altschuler & Jr 1969), and the current sheet source surface(CSSS) model which is modified by current sheet model(Zhao & Hoeksema 1995) and so on. According to some results from indirect observation, these two models perform well in describing large-scale and steady-state coronal magnetic fields(Schrijver & Derosa 2003; Zhao et al. 2002), and are also used as the initial input magnetic fields for the study of solar explosive activities(Liu & Hayashi 2006). Even so,
太阳磁场是研究太阳物理学的关键。它的变化周期约为 11 年。由于空间和地面观测的限制，只能对光层磁场进行较精确的测量。光球上方的日冕磁场（CMF）通常是在某种理论模型下，通过与观测到的光球磁场进行外推得到的。例如，由球面坐标系下的势场模型外推而成的势场源面（PFSS）模型（Schatten 等，1969 年；Altschuler & Jr，1969 年），以及由电流片模型修正而成的电流片源面（CSSS）模型（Zhao & Hoeksema，1995 年）等。根据间接观测的一些结果，这两个模型在描述大尺度和稳态日冕磁场方面表现良好（Schrijver & Derosa 2003; Zhao et al.即便如此、
the ability of these two greatly simplified models to describe the CMF for different solar activities and solar cycles is still unknown. Therefore, more direct observations of the CMF are particularly necessary.
这两个被大大简化的模型是否能够描述不同太阳活动和太阳周期的 CMF 仍然是个未知数。因此，对 CMF 进行更直接的观测尤为必要。
The solar photosphere magnetic field is continuously blown out by the solar wind into the interplanetary space to form the interplanetary magnetic field(IMF)(Parker 1958). The measurement of IMF usually focuses on the Lagrange point near the Earth. With the CMF as the boundary, the IMF in the other interplanetary space is obtained by the Parker spiral model. This model has been proved by experiments(Smith & Balogh 1995) and has been used widely. Due to its simplifications and the uncertainty of input CMF, however, there are still big differences between it and the observed results at 1AU. Therefore, more observations of the IMF are also needed.
太阳光层磁场不断被太阳风吹到行星际空间，形成行星际磁场（IMF）（Parker，1958 年）。行星际磁场的测量通常集中在地球附近的拉格朗日点。以 CMF 为边界，其他行星际空间的 IMF 可通过 Parker 螺旋模型获得。该模型已被实验证明（Smith & Balogh，1995 年），并被广泛使用。然而，由于该模型的简化和输入 CMF 的不确定性，它与 1AU 的观测结果之间仍然存在很大差异。因此，还需要对 IMF 进行更多的观测。
Cosmic rays originating outside the solar system usually arrive at the Earth nearly isotropically. In the process, they will be blocked by the Sun or the Moon and casts a shadow on the sky map. The positively charged nuclei are the main components of the cosmic ray. They are deflected by the Lorentz force and can be used as a probe for the magnetic field detection. Therefore, we can use the cosmic ray shadow as a powerful tool to measure the whole solar-terrestrial space magnetic field and its variation(Clark 1957). The Moon shadow is displaced comparing to its optical direction under the influence of the geomagnetic field(GMF). And the displacement has been well studied and also has been used to calibrate the absolute rigidity scale of cosmic rays by extensive air shower arrays(Amenomori et al. 2009; Bartoli et al. 2011).
源自太阳系外的宇宙射线通常以近乎等向的方式到达地球。在此过程中，它们会受到太阳或月球的阻挡，并在天空图上投下阴影。带正电荷的原子核是宇宙射线的主要成分。它们在洛伦兹力的作用下发生偏转，可以用作磁场探测的探针。因此，我们可以利用宇宙射线的阴影作为测量整个日地空间磁场及其变化的有力工具（克拉克，1957 年）。在地磁场（GMF）的影响下，月影与其光学方向相比会发生位移。人们对这种位移进行了深入研究，并通过广泛的空气淋浴阵列来校准宇宙射线的绝对刚度尺度（Amenomori 等人，2009 年；Bartoli 等人，2011 年）。
Because of the complexity of the CMF, the IMF and their variations, the relationships between magnetic fields and features of the Sun shadow, including the deficit, the extension, and the displacement, are still not completely clear. The Tibet AS $\gamma$$\gamma$gamma\gamma collaboration is the first to study the relationship between the IMF and the displacement of the Sun shadow at about 10 TeV . During the second half of the solar cycle 22, they found that the different sector structures of the IMF, including “away” and “toward”, cause the Sun shadow to shift northward and southward respectively(Amenomori et al. 1993, 1996, 2000). In the first half of the solar cycle 24, the ARGO-YBJ collaboration uses the relationship to quantitatively measure the strength of the IMF and its sector structures firstly(Aielli et al. 2011). And then, the Tibet AS $\gamma$$\gamma$gamma\gamma found that the average IMF strength observed by the displacement of the Sun shadow in the north-south direction is about 1.5 times larger than the prediction from the model of magnetic fields(Amenomori et al. 2018). Besides, in terms of the displacement of the Sun shadow in the east-west direction, the Tibet AS $\gamma$$\gamma$gamma\gamma found that the IMF can also deflect the Sun shadow to the eastward, counteracting the influence from the GMF during the solar minimum(Amenomori et al. 2000). But another simulation work from Saeed et al. (2017) pointed out that the westward displacement is obtained by the accumulation of the GMF and the CMF during the maximum in solar cycle 24. Both the displacement of the Sun shadow and the factors affecting it need to be further understood.
由于CMF、IMF及其变化的复杂性，磁场与日影的亏缺、延伸和位移等特征之间的关系还不完全清楚。西藏AS $\gamma$$\gamma$gamma\gamma 合作首次研究了约10 TeV的IMF与日影位移之间的关系。在太阳周期22的后半段，他们发现IMF的不同扇形结构，包括 "离 "和 "向"，分别导致了日影的北移和南移（Amenomori等，1993，1996，2000）。在太阳周期 24 的前半段，ARGO-YBJ 合作首先利用这种关系定量测量了 IMF 的强度及其扇形结构（Aielli 等，2011 年）。随后，西藏AS $\gamma$$\gamma$gamma\gamma 发现，通过南北方向日影位移观测到的平均IMF强度比磁场模型的预测值大1.5倍左右（Amenomori et al.）此外，西藏AS $\gamma$$\gamma$gamma\gamma 发现，在东西方向的日影位移中，IMF也可以使日影向东偏转，抵消太阳黑子最小期间来自GMF的影响（Amenomori等，2000）。但 Saeed 等人（2017 年）的另一项模拟工作指出，日影向西偏移是在太阳周期 24 的最大值期间由 GMF 和 CMF 累积而成的。日影位移及其影响因素都有待进一步了解。

In addition to the doubts about the Sun shadow’s displacement, the understanding of the deficit of the shadow is also unclear. The Tibet AS $\gamma$$\gamma$gamma\gamma found that the deficit is related to solar activity, and the results at 10 TeV during the solar minimum in solar cycle 23 are more support for CSSS model(Amenomori et al. 2013). The results from IceCube at $50-60\mathrm{TeV}$$50-60\mathrm{TeV}$50-60TeV50-60 \mathrm{TeV} in solar cycle 24 does not show obvious support for certain CMF model(Frederik Tenholt 2019). Furthermore, the ARGO-YBJ and the Tibet AS $\gamma$$\gamma$gamma\gamma reported the observation of the rigidity dependent variation of the Sun shadow(S. Z. Chen 2017; Amenomori et al. 2018). It is not clear which magnetic fields affect the deficit on the one hand, and on the other hand, the magnetic field structure measured by different energies is different. The large high altitude air shower observatory (LHAASO) in the future has a wider range of energy observation, higher sensitivity, and can also give more information about CMF and IMF. Therefore, a deeper understanding of the influences of magnetic fields on the Sun shadow under different rigidity and how to use these characteristics of the Sun shadow to diagnose magnetic fields are quite important and needed. In this work, the precise simulation of the Sun shadow is given to find the answer to the relationships between the Sun shadow and the magnetic fields. On the basis, at multiple energy points, the solar shadow’s expectation for different CMF’ models are given.
除了对日影位移的怀疑，对日影赤字的认识也不清楚。西藏AS $\gamma$$\gamma$gamma\gamma 发现日影赤字与太阳活动有关，而太阳周期23太阳活动最小期10 TeV的结果更支持CSSS模型（Amenomori等，2013）。冰立方在太阳周期24的 $50-60\mathrm{TeV}$$50-60\mathrm{TeV}$50-60TeV50-60 \mathrm{TeV} 的结果并不明显支持某些CMF模型（Frederik Tenholt 2019）。此外，ARGO-YBJ和西藏AS $\gamma$$\gamma$gamma\gamma 报告观测到了日影的刚性变化（S. Z. Chen，2017；Amenomori等，2018）。一方面，哪些磁场会影响赤化并不清楚，另一方面，不同能量测量到的磁场结构也不同。未来的大型高空气流淋浴观测站（LHAASO）观测能量范围更广，灵敏度更高，也能给出更多有关 CMF 和 IMF 的信息。因此，深入了解不同刚度下磁场对日影的影响，以及如何利用日影的这些特征来诊断磁场是相当重要和必要的。在这项工作中，对日影进行了精确模拟，以找到日影与磁场之间关系的答案。在此基础上，在多个能量点上，给出了不同 CMF 模型的日影预期。
The paper is organized as follows. In Section 2, a precise simulation program of the cosmic-ray Sun shadow is developed and tested. The results of the simulation, as well as the discussion about the influences of magnetic fields on the Sun shadow, are present in Section 3. In Section 4, the expectations of different CMF’s models on the Sun shadow under different energies during different solar phases as well as the discussion are shown. A summary of the obtained results is given in Section 5 .
本文的结构如下。第 2 节是宇宙射线日影的精确模拟程序的开发和测试。模拟结果以及磁场对日影影响的讨论见第 3 节。第 4 节展示了不同太阳阶段不同能量下不同 CMF 模型对日影的预期以及讨论。第 5 节总结了所获得的结果。

The large-scale CMF is modelled by extrapolating the observed photosphere magnetogram. And the magnetograms with high measurement accuracy from the Michelson Doppler Imager ${}^1$${}^1$^(1){ }^{1} and the Global Oscillation Network Group ${}^2$${}^2$^(2){ }^{2} are used in 2008 during the solar minimum and 2012 during the solar maximum in solar cycle 24, respectively. The PFSS model (Schatten et al. 1969; Altschuler & Jr 1969) which is built based on the current-free assumption between the photosphere and the source surface is used in this work. The source surface is an arbitrary spherical surface around the Sun. According to same results from Schatten et al. (1969); Lee et al. (2011); Hoeksema (1984), the heights of the source surface are usually at $1.6R_{\odot }$$1.6R_{\odot }$1.6R_(o.)1.6 R_{\odot} or $2.5R_{\odot }$$2.5R_{\odot }$2.5R_(o.)2.5 R_{\odot}. Beyond it, the magnetic field is controlled by the plasma and known as the IMF. Another important model which is built by adding a extra horizontal sheet current is the CSSS model(Zhao & Hoeksema 1995). Except for the source surface, the cusp surface is also involved in controlling the magnetic field. According to the results from M. Schüssler (2006), a typical set of the parameters is selected in this work. Specifically, the height of the cusp surface(Rcp), the source surface(Rss) and the length of horizontal electric currents $l_a$$l_a$l_(a)l_{a} equal to $1.7R_{\odot },10R_{\odot },1R_{\odot }$$1.7R_{\odot },10R_{\odot },1R_{\odot }$1.7R_(o.),10R_(o.),1R_(o.)1.7 R_{\odot}, 10 R_{\odot}, 1 R_{\odot}, respectively.
大尺度 CMF 是通过外推观测到的光球磁图来模拟的。在太阳周期 24 中，分别在 2008 年太阳活动最小期和 2012 年太阳活动最大期使用了迈克尔逊多普勒成像仪 ${}^1$${}^1$^(1){ }^{1} 和全球涛动网络组 ${}^2$${}^2$^(2){ }^{2} 测量精度较高的磁图。本研究采用的 PFSS 模型（Schatten 等，1969 年；Altschuler & Jr，1969 年）是基于光球和源表面之间无电流假设建立的。源面是太阳周围的一个任意球面。根据 Schatten 等人（1969 年）、Lee 等人（2011 年）和 Hoeksema（1984 年）的相同结果，源面的高度通常为 $1.6R_{\odot }$$1.6R_{\odot }$1.6R_(o.)1.6 R_{\odot} 或 $2.5R_{\odot }$$2.5R_{\odot }$2.5R_(o.)2.5 R_{\odot} 。在它之外，磁场由等离子体控制，称为 IMF。另一个重要的模型是 CSSS 模型（Zhao & Hoeksema，1995 年），它是通过增加额外的水平片流而建立的。除了源面，尖面也参与控制磁场。根据 M. Schüssler（2006 年）的研究结果，本研究选择了一组典型的参数。具体来说，尖面高度（Rcp）、源面（Rss）和水平电流长度 $l_a$$l_a$l_(a)l_{a} 分别等于 $1.7R_{\odot },10R_{\odot },1R_{\odot }$$1.7R_{\odot },10R_{\odot },1R_{\odot }$1.7R_(o.),10R_(o.),1R_(o.)1.7 R_{\odot}, 10 R_{\odot}, 1 R_{\odot} 。

Beyond the source surface, the basic topology of the IMF is an Archimedean spiral. Taking the calculated CMF at Rss as an initial value, the IMF can be calculated by the Parker spiral model(Parker 1958). In this model, the “away” and the “toward” sectors of the IMF can be produced. The radial component of the solar wind velocity we used comes from OMNI observation ${}^3$${}^3$^(3){ }^{3}. Near the Earth, the international geomagnetic reference field- ${12}^4$${12}^4$12^(4)12^{4} is involved to describe the GMF. Within 600 km above the surface of the Earth, the magnetic field which is expanded by the spherical harmonics with the order equals 13 is used. Over 600 km , a dipole field is used.
在源面之外，IMF 的基本拓扑结构是阿基米德螺旋。以 Rss 处计算出的 CMF 为初始值，IMF 可以通过帕克螺旋模型（帕克，1958 年）计算出来。在这个模型中，可以产生 IMF 的 "远离 "和 "朝向 "扇区。我们使用的太阳风速度的径向分量来自 OMNI 观测 ${}^3$${}^3$^(3){ }^{3} 。在地球附近，国际地磁参考场-- ${12}^4$${12}^4$12^(4)12^{4} 被用来描述 GMF。在地球表面以上 600 千米范围内，使用阶次等于 13 的球谐波展开的磁场。超过 600 千米，则使用偶极磁场。

A simulation strategy similar to the Moon shadow(Bartoli et al. 2011) is applied. Firstly, we track the Sun’s position in real time in equatorial coordinates and launch charged particles isotropically in the angular range of ${10}^{\circ }\times {10}^{\circ }$${10}^{\circ }\times {10}^{\circ }$10^(@)xx10^(@)10^{\circ} \times 10^{\circ} around the Sun. The charge of these particles is negative, which will cause the same deflects and the paths with the real cosmic-ray particles in the solar-terrestrial magnetic fields. Then we track the position and the direction of particle motion by the relationship between the momentum change and the position change, as $\mathrm{\Delta }\overrightarrow{p}=\overrightarrow{F}t=q\mathrm{\Delta }\overrightarrow{l}\times \overrightarrow{B}$$\mathrm{\Delta }\overrightarrow{p}=\overrightarrow{F}t=q\mathrm{\Delta }\overrightarrow{l}\times \overrightarrow{B}$Delta vec(p)= vec(F)t=q Delta vec(l)xx vec(B)\Delta \vec{p}=\vec{F} t=q \Delta \vec{l} \times \vec{B}. If it hits the Sun, a missing particle on the Sun shadow is obtained.
我们采用了与月影（Bartoli 等人，2011 年）类似的模拟策略。首先，我们在赤道坐标上实时跟踪太阳的位置，并在 ${10}^{\circ }\times {10}^{\circ }$${10}^{\circ }\times {10}^{\circ }$10^(@)xx10^(@)10^{\circ} \times 10^{\circ} 的角度范围内围绕太阳等向发射带电粒子。这些粒子的电荷为负，在日地磁场中会与真正的宇宙射线粒子产生相同的偏转和路径。然后，我们通过动量变化与位置变化之间的关系（如 $\mathrm{\Delta }\overrightarrow{p}=\overrightarrow{F}t=q\mathrm{\Delta }\overrightarrow{l}\times \overrightarrow{B}$$\mathrm{\Delta }\overrightarrow{p}=\overrightarrow{F}t=q\mathrm{\Delta }\overrightarrow{l}\times \overrightarrow{B}$Delta vec(p)= vec(F)t=q Delta vec(l)xx vec(B)\Delta \vec{p}=\vec{F} t=q \Delta \vec{l} \times \vec{B} ）来跟踪粒子运动的位置和方向。如果它撞上了太阳，就会得到一个在太阳阴影上失踪的粒子。

Specifically, the launch point is set to a point above the atmosphere of the Yangbajing (Tibet, China, $30.11\mathrm{N},90.53$$30.11\mathrm{N},90.53$30.11N,90.5330.11 \mathrm{~N}, 90.53 E, altitude of 4300 m a.s.l.) where most of the observations of the Sun shadow are around here. Because the deflection of the particle in the magnetic field is rigidity dependent, only the proton is used in this work. The energies of particles are $1,3,10,32,100,316$$1,3,10,32,100,316$1,3,10,32,100,3161,3,10,32,100,316 and 1000 TeV , which covered the energy range of the most experiments. About ${10}^7$${10}^7$10^(7)10^{7} particles are thrown from the launch point. The step size of each step in the particle motion is controlled by the deflection angle of antiparticle in the magnetic field, which can help to reduce the errors on the deflection due to the step size. We track the particle one by one if its launched zenith angle is between $0^{\circ }$$0^{\circ }$0^(@)0^{\circ} and ${50}^{\circ }$${50}^{\circ }$50^(@)50^{\circ}. Then we record the motion of particles hitting the Sun and gain the map of the Sun shadow.
具体来说，发射点设定为羊八井（中国西藏， $30.11\mathrm{N},90.53$$30.11\mathrm{N},90.53$30.11N,90.5330.11 \mathrm{~N}, 90.53 东，海拔 4300 米）大气层上方的一点，在这附近观测到的日影大部分都在这里。由于粒子在磁场中的偏转与刚度有关，因此本研究只使用质子。粒子的能量为 $1,3,10,32,100,316$$1,3,10,32,100,316$1,3,10,32,100,3161,3,10,32,100,316 和1000 TeV，涵盖了大多数实验的能量范围。约有 ${10}^7$${10}^7$10^(7)10^{7} 个粒子从发射点抛出。粒子运动的每一步的步长由反粒子在磁场中的偏转角控制，这有助于减少由于步长造成的偏转误差。如果粒子的发射天顶角在 $0^{\circ }$$0^{\circ }$0^(@)0^{\circ} 和 ${50}^{\circ }$${50}^{\circ }$50^(@)50^{\circ} 之间，我们就逐个跟踪。然后，我们记录撞击太阳的粒子的运动，并获得日影图。

To check the correctness of this simulation program, a Moon shadow simulation for proton primaries which energy is equal to 1 or 5 TeV , and the range of the time covers a complete revolution cycle of moon was done firstly. The results are shown in Figure 1. At 1 TeV , the Moon shadow is extended along the south-north direction because of the large zenith angle and moved to the westward by about 1.41 degrees by the GMF. When energy is increased at 5 TeV , the shadow shows obvious moon’s optical size and a smaller displacement. The deflection angles of particles at 1 TeV are recorded as a distribution in Figure 1. And the particle is deflected by 1.61 degrees on average by the GMF. All results are the same as the results of the Moon shadow(Bartoli et al. 2011), which shows that the correctness of this program.
为了检验该模拟程序的正确性，我们首先对能量等于 1 或 5 TeV 的质子原 子进行了月影模拟，时间范围涵盖月球的一个完整公转周期。结果如图 1 所示。在 1 TeV 时，由于天顶角较大，月影沿南北方向延伸，并在 GMF 的作用下向西移动了约 1.41 度。当能量增加到 5 TeV 时，月影显示出明显的月球光学尺寸，位移较小。图1记录了粒子在1 TeV时的偏转角分布。粒子平均偏转了 1.61 度。所有结果都与月影（Bartoli et al.

${}^1$${}^1$^(1){ }^{1} http://soi.stanford.edu/
${}^2$${}^2$^(2){ }^{2} https://gong.nso.edu/
${}^3$${}^3$^(3){ }^{3} https://omniweb.gsfc.nasa.gov
${}^4$${}^4$^(4){ }^{4} https://www.ngdc.noaa.gov/IAGA/vmod/igrf.html

Figure 1. Counts maps of the simulated Moon shadow and the distribution of particles’ deflection angles at 1 TeV .
图 1.模拟月影的计数图和 1 TeV 下粒子偏转角的分布。

The large-scale CMF, the IMF and the GMF occupy different positions in the solar-terrestrial space and have different directions, strengths, and structures. In order to calculate the influences of every magnetic field on the Sun shadow accurately, each magnetic field is added respectively to the simulation program mentioned above.
大尺度CMF、IMF和GMF在日地空间所处的位置不同，方向、强度和结构也不同。为了准确计算各个磁场对日影的影响，在上述模拟程序中分别加入了各个磁场。

To explore the relationship between the CMF and the Sun shadow, simulated Sun shadows which are influenced only by the PFSS model in 2008 at different energies are shown in Figure 2. The Rss equals to $1.6R_{\odot }$$1.6R_{\odot }$1.6R_(o.)1.6 R_{\odot} in this model. According to the results, at different energies, the Sun shadows don’t show obvious displacement. Also, only a very small expansion occurs in two low-energy Sun shadows. The most obvious feature is the change of counts number of particles.
为探讨 CMF 与日影之间的关系，图 2 显示了 2008 年不同能量下仅受 PFSS 模型影响的模拟日影。在该模型中，Rss 等于 $1.6R_{\odot }$$1.6R_{\odot }$1.6R_(o.)1.6 R_{\odot} 。结果显示，在不同能量下，日影没有出现明显的位移。另外，在两个低能量太阳阴影中也只出现了很小的膨胀。最明显的特征是粒子数的变化。

Figure 2. Counts maps of the simulated Sun shadow in 2008 at $1,10,100\mathrm{TeV}$$1,10,100\mathrm{TeV}$1,10,100TeV1,10,100 \mathrm{TeV}, respectively.
图 2.2008 年分别在 $1,10,100\mathrm{TeV}$$1,10,100\mathrm{TeV}$1,10,100TeV1,10,100 \mathrm{TeV} 处模拟日影的计数图。

Then we use the deficit ratio to describe the change quantitatively. The deficit ratio is defined as the result of the number of particle hitting the Sun with magnetic fields divided by that without magnetic fields. The former represents the ideal negative signals, which describe the change of the number of particles in Figure 2, and the latter represents the background case. The calculated results of the deficit ratios at different energies are shown in Figure 3. With the increase of energy, the deficit ratio influenced by the CMF (open circles) increases firstly, reaches its maximum at 10 TeV and then decreases to $100\mathrm{\%}$$100\mathrm{\%}$100%100 \%.
然后，我们用赤字比来定量描述这一变化。赤字比的定义是有磁场时撞击太阳的粒子数除以无磁场时的粒子数。前者代表理想的负信号，描述图 2 中粒子数量的变化，后者代表背景情况。不同能量下的亏损比计算结果如图 3 所示。随着能量的增加，受CMF影响的亏损比（开圆圈）首先增加，在10 TeV达到最大值，然后减小到 $100\mathrm{\%}$$100\mathrm{\%}$100%100 \% 。
One the other hand, to further determine the origin of the deficit ratio, the results from the individual GMF, IMF and the whole magnetic fields are also compared in Figure 3. Firstly, the GMF (plus signs) does not cause the obvious change of the deficit ratio, which is the same as that in the Moon shadow. The IMF (crosses) can change the deficit ratio a bit which is energy-dependent. Furthermore, the IMF (crosses) superposes the deficit ratio caused by the CMF (open circles), resulting in the total deficit ratio of the sun shadow. By comparing the change trends of the deficit ratios from the whole magnetic field(solid circles) and from the CMF (open circles) with energy, we can conclude that the CMF mainly affects the change of the deficit ratio of the Sun shadow.
另一方面，为了进一步确定赤字率的来源，图 3 还比较了单个 GMF、IMF 和整个磁场的结果。首先，GMF（正号）不会引起赤字率的明显变化，这与月影中的赤字率相同。而 IMF（横线）则会稍稍改变赤字率，这与能量有关。此外，IMF（横线）会叠加 CMF（圆圈）造成的赤字率，形成日影的总赤字率。通过比较整个磁场（实心圆）和 CMF（空心圆）的赤字率随能量的变化趋势，我们可以得出结论：CMF 主要影响日影赤字率的变化。

Figure 3. Comparison of the deficit ratio influenced by the CMF and the GMF, the IMF, and the whole magnetic fields in 2008 at different energies.
图 3.2008 年不同能量下受 CMF 和 GMF、IMF 以及整个磁场影响的赤字率比较。

To explain how the CMF affects the deficit ratio of the Sun shadow in greater detail, the moving trails of particles near the Sun in Figure 4. At 1 TeV , the CMF can deflect the particles at large angles and decrease the value of the deficit ratio because of the low energy. At 10 TeV , the particles with high energy can probe the CMF in lower coronal. And the CMF can be seen easily from the trials because of the small deflection angle and the high energy. Specifically, the magnetic fields along the direction of the $y$$y$yy-axis near two poles and the direction of the $z$$z$zz-axis at other latitudes, which represent some structures of CMF, deflect the particles which are not emitted toward the Sun initially and make them hit the Sun finally. At 100 TeV , the particles can hardly be deflected by the CMF, and all of them hit the Sun. And the corresponding deficit ratio calculated equals to almost $100\mathrm{\%}$$100\mathrm{\%}$100%100 \%.
为了更详细地解释 CMF 如何影响日影的亏辐比，请看图 4 中太阳附近的粒子移动轨迹。在 1 TeV 时，由于能量较低，CMF 可以使粒子发生大角度偏转，从而减小赤字比值。在 10 TeV 时，高能粒子可以探测到日冕下部的 CMF。由于偏转角度小、能量高，从试验中很容易看到CMF。具体来说，两极附近沿 $y$$y$yy 轴方向的磁场和其他纬度沿 $z$$z$zz 轴方向的磁场代表了CMF的一些结构，它们使最初没有发射到太阳的粒子发生偏转，最终撞击到太阳。在100 TeV时，粒子几乎无法被CMF偏转，全部撞向太阳。而计算出的相应亏损比几乎等于 $100\mathrm{\%}$$100\mathrm{\%}$100%100 \% 。

Figure 4. Moving trails of particles near the Sun in PFSS model in the heliocentric earth ecliptic (HEE) coordinates in 2008. The small and the large circles in each panel represent the Sun and the source surface, respectively. The three panels represent the simulated trials which are projected on the $\mathrm{z}-\mathrm{x}$$\mathrm{z}-\mathrm{x}$z-x\mathrm{z}-\mathrm{x} coordinate plane at $1\mathrm{TeV},10\mathrm{TeV}$$1\mathrm{TeV},10\mathrm{TeV}$1TeV,10TeV1 \mathrm{TeV}, 10 \mathrm{TeV} and 100 TeV , respectively.
图 4.2008 年日心地球黄道（HEE）坐标下 PFSS 模型中太阳附近的粒子移动轨迹。每个面板中的小圆圈和大圆圈分别代表太阳和源表面。三个板块分别代表在 $1\mathrm{TeV},10\mathrm{TeV}$$1\mathrm{TeV},10\mathrm{TeV}$1TeV,10TeV1 \mathrm{TeV}, 10 \mathrm{TeV} 和100 TeV下投影在 $\mathrm{z}-\mathrm{x}$$\mathrm{z}-\mathrm{x}$z-x\mathrm{z}-\mathrm{x} 坐标平面上的模拟试验。

According to results in the last section, the influence of the IMF on the Sun shadow’s deficit ratio is weak. At 1 TeV , the corresponding maps of the Sun shadow, which is influenced only by the IMF are shown in the panel (a) in Figure 5. There is no obvious displacement of the centre of the Sun shadow. But the Sun shadow is extended by the IMF and has an asymmetric X shape.
根据上一节的结果，IMF 对日影赤字率的影响是微弱的。在 1 TeV 时，仅受 IMF 影响的日影的相应分布图如图 5 (a) 所示。日影中心没有明显的位移。但日影受 IMF 的影响有所扩大，并呈现出不对称的 X 形。
To comprehend the formation of the Sun shadow, one-year Sun shadow is separated according to the different rotations of the Sun which is recorded by the "Carrington rotations $(\mathrm{CR})$$(\mathrm{CR})$(CR)(\mathrm{CR}) ". We found, for the first time, the Sun shadow is seasonal dependence. In Figure 5, the Sun shadows in three CRs, including CR2068, CR2071, CR2075 which is correspond to the day near the Spring Equinox, the Summer Solstice and the Autumnal Equinox in the northern hemisphere are shown respectively. The Sun shadow in winter is out of the field of view. In different seasons, the Shadows tilt to the left, the middle and the right. The reasons for these results can be traced to the latitude of the
为了理解日影的形成，我们根据 "卡林顿自转 $(\mathrm{CR})$$(\mathrm{CR})$(CR)(\mathrm{CR}) "记录的太阳的不同自转将一年的日影分开。我们首次发现日影与季节有关。图 5 分别显示了北半球春分日、夏至日和秋分日附近三个 CR（包括 CR2068、CR2071 和 CR2075）的日影。冬季的日影在视野之外。在不同季节，日影分别向左侧、中间和右侧倾斜。造成这些结果的原因可以追溯到北半球的纬度。

Yangbajing and the obliquity of the ecliptic. Near Summer Solstice, the angles between the directions of antiparticle emission and the IMF’s equatorial plane are small. The “away/toward” sector of the IMF mainly moves the shadow to the northward/southward and makes the Sun shadow extend in the north-south direction. Near Spring Equinox, angles are large and “away/toward” sector deflects the shadow to the westward/eastward additionally. Near Autumn Equinox, the tilt of the Sun shadow is opposite in the equatorial coordinate system. When Sun shadows of each Carrington rotation are added up, an asymmetric X-shaped Sun shadow is formed. The seasonal dependence of the Sun shadow’s tilts can be seen in the observation(Zhu 2013), which did not mention the phenomenon and its reasons.
阳白经和黄道的纬度。在夏至附近，反粒子发射方向与 IMF 赤道面的夹角很小。IMF的 "离/向 "扇面主要是使日影向北/向南移动，使日影向南北方向延伸。春分附近，倾角较大，"偏离/朝向 "扇面使日影另外向西/向东偏转。秋分附近，日影在赤道坐标系中的倾斜度相反。将每次卡林顿公转的日影加起来，就会形成一个不对称的 X 形日影。日影的倾斜度与季节有关，这在观测资料（Zhu 2013）中可以看到，但该资料并未提及这一现象及其原因。

Figure 5. Counts maps of the Sun shadow influenced only by the IMF. The panel (a), (b), © and(d) refer to the Sun shadow in 2008, CR2068, CR2071 and CR2075, respectively.
图 5.仅受 IMF 影响的日影计数图。图中(a)、(b)、© 和(d)分别为 2008 年、CR2068、CR2071 和 CR2075 的日影。

The quantitative calculation of the north-south deflections of the Sun shadow for different sector structures, including “away” and “toward”, is limited by the specific selection method of the sector structure and it can not be regarded as a common expectation. Therefore, instead of the deflection, the extension of the shadow from the IMF only, other individual and the whole magnetic fields are compared in Figure 6. The RMS of the Sun Shadow’s map, which is projected in the north-south direction is used to calculate the extension quantitatively. In comparison, the effect from the CMF on the extension can be ignored, and the values of the extension are from the RMS of the sun. At low energy, both the GMF and the IMF can expand the Sun shadow. The extension influenced by the GMF mainly comes from the deflection between GMF and particles from the large zenith angle in the east-west direction. Along with the increase of the energy, the extensions from both GMF and IMF gradually decrease. In this process, the extensions from the IMF are more in line with that from the whole magnetic field. Therefore, the IMF dominates the extension of the Sun shadow in the north-south direction.
对不同扇形结构（包括 "偏离 "和 "朝向"）的日影南北偏转的定量计算，受到扇形结构具体选择方法的限制，不能视为共同的预期。因此，图 6 比较的不是偏转，而是日影从 IMF 开始的延伸，以及其他单个磁场和整个磁场的延伸。日影图在南北方向上的投影均方根用于定量计算延伸。相比之下，CMF 对延伸率的影响可以忽略不计，延伸率的数值来自太阳的有效值。在低能量情况下，GMF 和 IMF 都可以扩展日影。受 GMF 影响的延伸主要来自东西向大天顶角产生的 GMF 与粒子之间的偏转。随着能量的增加，GMF 和 IMF 的延伸逐渐减小。在这个过程中，来自 IMF 的延伸与来自整个磁场的延伸更加一致。因此，IMF 主导了日影在南北方向上的延伸。

Figure 6. Comparison of the extension influenced by the CMF and the GMF, the IMF, and the whole magnetic fields in 2008 at different energies.
图 6.2008 年不同能量下受 CMF、GMF、IMF 和整个磁场影响的扩展比较。

In the Moon shadow’s simulation, the GMF along the north direction mainly moves the Moon shadow to the west. In fact, the Sun and the Moon have different orbits in the celestial coordinate system, and the effect from GMF on the Sun shadow also need to investigate thoroughly. The simulated Sun shadow at 1 TeV , which is only influenced by
在月影模拟中，沿北方向的 GMF 主要使月影向西移动。事实上，太阳和月球在天体坐标系中的轨道不同，GMF 对日影的影响也需要深入研究。在 1 TeV 下的模拟日影只受
the GMF and the different effects from the magnetic fields on the displacement in the west-east direction at different energies are shown in Figure 7. From the left panel, the GMF moves the Sun shadow at 1 TeV westward by about ${1.46}^{\circ }$${1.46}^{\circ }$1.46^(@)1.46^{\circ}, which is almost the same as the result of the Moon shadow. And we found the influence caused by the differences between these two orbits can be ignored.
图 7 显示了不同能量下 GMF 和磁场对西东方向位移的不同影响。从左图可以看出，GMF 使 1 TeV 的日影向西移动了约 ${1.46}^{\circ }$${1.46}^{\circ }$1.46^(@)1.46^{\circ} ，这与月影的结果几乎相同。我们发现这两个轨道之间的差异造成的影响可以忽略不计。

Figure 7. Comparison of the displacement in the west-east direction influenced by the CMF and the GMF, the IMF, and the whole magnetic fields in 2008 at different energies.
图 7.2008 年不同能量下受 CMF 和 GMF、IMF 以及整个磁场影响的西-东方向位移比较。

In the right panel, we can see that the displacement of the Sun shadow from the IMF is small. The basic field lines in the IMF which the particle can go through are almost not in the north-south direction in the heliographic coordinate system. But the small obliquity of the ecliptic makes the IMF has the small magnetic field in the north-south direction in the equatorial coordinate system and move the Sun shadow a little in the west-east direction. At 1TeV, the IMF and the GMF move the shadow to the west together, which is the same as the result from Amenomori et al. (2000). Besides, the CMF also have the field lines which have the same direction as the GMF. But, from open circles in the right panel, we can hardly see the effect from the CMF on the displacement of the Sun shadow, even in the solar maximum, which is different from Saeed et al. (2017)'s result. This is because the complexity of the structure of the CMF and the CMF is far away from the Earth. And the total effect from the CMF is expressed as the deficit we have discussed. Because the results of the GMF and the whole magnetic field are almost the same at different energies, we conclude that the GMF mainly affects the displacement of the Sun shadow in the west direction.
在右图中，我们可以看到日影与 IMF 的位移很小。在日球坐标系中，粒子可以穿过的 IMF 基本磁场线几乎不在南北方向上。但黄道的小斜度使得 IMF 在赤道坐标系中具有南北方向的小磁场，并使日影向西东方向稍稍移动。在 1TeV 时，IMF 和 GMF 一起使日影向西移动，这与 Amenomori 等人（2000 年）的结果相同。此外，CMF 也有与 GMF 方向一致的场线。但是，从右图的开圆圈中，我们几乎看不到 CMF 对日影位移的影响，即使在太阳极大期也是如此，这与 Saeed 等人（2017）的结果不同。这是因为CMF结构复杂，而且CMF远离地球。而 CMF 的总效应表现为我们所讨论的赤字。由于在不同的能量下，GMF 和整个磁场的结果几乎相同，因此我们得出结论：GMF 主要影响日影向西的位移。

During solar maximum, the magnetic fields in 2012 are also added to study their influences on the Sun shadow. Based on the results, the conclusions mentioned above still hold. In conclusion, the GMF, the CMF and the IMF are the main reasons for the Sun shadows displacement to the westward, deficit, and extension in the north-south direction, respectively.
在太阳极大期，还加入了 2012 年的磁场，以研究它们对日影的影响。根据研究结果，上述结论仍然成立。总之，GMF、CMF和IMF分别是导致日影向西位移、赤字和向南北方向延伸的主要原因。

From the last section, we have already known that the Sun shadow’s deficit and the extension in the north-south direction are the results of the influences of the CMF and the IMF, respectively. Due to the continuity between the CMF and the IMF, the CMF also affects the extension in the north-south direction indirectly. In this section, a Sun shadow which is deflected by the whole solar-terrestrial magnetic field is simulated. We calculate the deficit and the extension of the Sun shadow to expect the difference of the Sun shadow under different coronal large-scale magnetic field’s models and different parameters.
从上一节中，我们已经知道，日影的赤度和南北方向的延伸分别是 CMF 和 IMF 影响的结果。由于 CMF 和 IMF 之间的连续性，CMF 也会间接影响南北方向的延伸。本节模拟了受整个日地磁场偏转的日影。我们计算了日影的亏损和延伸，以预测不同日冕大尺度磁场模型和不同参数下日影的差异。

The parameters of the PFSS and the CSSS model we mentioned above are only tested before solar cycle 24, and firstly, we make some simple comparisons between the magnetic fields near the Earth which come from the observation and that from models predictions to evaluate the correctness of parameters and models in solar cycle 24. The results are shown in Figure 8. $B_x$$B_x$B_(x)B_{x} components of the field are compared for CR2070 during the solar minimum and CR2123 during the solar maximum, respectively.
上面提到的 PFSS 和 CSSS 模型的参数只在太阳周期 24 之前进行测试，我们首先将观测到的地球附近磁场与模型预测的磁场进行简单比较，以评估太阳周期 24 中参数和模型的正确性。结果如图 8 所示。 $B_x$$B_x$B_(x)B_{x} 分别比较了太阳极小期的CR2070和太阳极大期的CR2123的磁场成分。

And the corresponding ${\chi }^2$${\chi }^2$chi^(2)\chi^{2} test is also used to quantitative comparison:
而相应的 ${\chi }^2$${\chi }^2$chi^(2)\chi^{2} 检验也用于定量比较：

Figure 8. Comparisons between the measurement and the model calculation of the IMF at 1AU under different models and parameters. The large solid circles represent the measurements of the field component $B_x$$B_x$B_(x)B_{x} using the OMNI observational data. The error bars along the y-axis indicate the RMS of the $B_x$$B_x$B_(x)B_{x}.
图 8.不同模型和参数下 1AU 的 IMF 测量值与模型计算值的比较。大实心圆圈表示利用 OMNI 观测数据测量的场分量 $B_x$$B_x$B_(x)B_{x} 。沿 y 轴的误差条表示 $B_x$$B_x$B_(x)B_{x} 的有效值。
where $B_y$$B_y$B_(y)B_{y} components for the models and for the observation are included additionally. The $\sigma$$\sigma$sigma\sigma is the RMS of the observed $B_x$$B_x$B_(x)B_{x} and $B_y$$B_y$B_(y)B_{y}. The results are summarized in Table 1.
其中，模型和观测数据的 $B_y$$B_y$B_(y)B_{y} 分量另外包括在内。 $\sigma$$\sigma$sigma\sigma 是观测值 $B_x$$B_x$B_(x)B_{x} 和 $B_y$$B_y$B_(y)B_{y} 的均方根。结果汇总于表 1。

Table 1. ${\chi }^2$${\chi }^2$chi^(2)\chi^{2} test between the measurement and the model calculation of the IMF’s $B_x$$B_x$B_(x)B_{x} and $B_y$$B_y$B_(y)B_{y} components near the Earth.
表 1.近地 IMF 的 $B_x$$B_x$B_(x)B_{x} 和 $B_y$$B_y$B_(y)B_{y} 分量的测量值与模型计算值之间的 ${\chi }^2$${\chi }^2$chi^(2)\chi^{2} 检验。

According to the results in Figure 8 and Table 1, in CR2070, the height of the source surface should be lower than $2.5R_{\odot }$$2.5R_{\odot }$2.5R_(o.)2.5 R_{\odot} for the PFSS model because of higher possibility. For the CSSS model, the values of $B_x$$B_x$B_(x)B_{x} vary sharply as time goes by due to the current sheet involved. According the p-value, the CSSS is better than the PFSS model. In CR2123, there is a big difference between model and observation. Just the PFSS model whose Rss equals to $2.5R_{\odot }$$2.5R_{\odot }$2.5R_(o.)2.5 R_{\odot} have a slightly higher possibility. The correlations between the IMF from the PFSS and the observations are also shown in Figure 9. Both for CR2070 and CR2123, correlation coefficients are about 0.7 and the regression coefficients equal to 1.37 and 1.87 , respectively. Therefore, the calculated Bx of IMF at 1 AU is obviously underestimated, and the level of this underestimation is even greater for CR2123.
根据图 8 和表 1 的结果，在 CR2070 中，由于 PFSS 模型的可能性较高，源面高度应低于 $2.5R_{\odot }$$2.5R_{\odot }$2.5R_(o.)2.5 R_{\odot} 。对于 CSSS 模型，由于涉及电流片， $B_x$$B_x$B_(x)B_{x} 的值随着时间的推移而急剧变化。从 p 值来看，CSSS 模型优于 PFSS 模型。在 CR2123 中，模型与观测结果之间存在很大差异。只有 Rss 等于 $2.5R_{\odot }$$2.5R_{\odot }$2.5R_(o.)2.5 R_{\odot} 的 PFSS 模型的可能性略高。图 9 还显示了 PFSS 的 IMF 与观测数据之间的相关性。CR2070 和 CR2123 的相关系数约为 0.7，回归系数分别为 1.37 和 1.87。因此，计算得到的 IMF 在 1 AU 处的 Bx 值明显被低估了，而 CR2123 的低估程度更大。

Figure 9. Comparisons between the observed and the calculated Bx of the IMF at 1AU using PFSS model with lower source surface for CR2070 and PFSS model with higher source surface for CR2123. The dashed and the solid black line are the standard and current trend lines, respectively.
图 9.在 1AU 处使用源面较低的 PFSS 模式（CR2070）和源面较高的 PFSS 模式（CR2123）观测和计算的 IMF Bx 的比较。黑色虚线和实线分别为标准趋势线和当前趋势线。

Because the comparisons of magnetic fields mentioned above are very limited, the extensions and the deficit ratios of Sun shadows which carries the integral information of the whole magnetic fields, are calculated at different energies to explore further. The results are shown in Figure 10.
由于上述磁场的比较非常有限，因此我们计算了不同能量下太阳影子的延伸率和缺失率，以进一步探索整个磁场的整体信息。结果如图 10 所示。

Figure 10. Comparisons of the Sun shadow’s extensions and deficit ratios under different CMF’s models and parameters at different energies in 2008 and 2012, respectively. For the extension in 2012, additional negative values are used for easy viewing.
图 10.2008 年和 2012 年，在不同能量下，不同 CMF 模型和参数下的日影延伸率和赤字率比较。为便于查看，2012 年的延伸率使用了额外的负值。

In 2008, below 10 TeV , differences caused by models and parameters are obvious by comparing the extension and the deficit ratio. For the extension, the PFSS model with the lower height of the source surface and the CSSS will increase the extension of the Sun shadow. Besides, at 10 TeV , the deficit ratio calculated by the $\mathrm{PFSS}(\mathrm{Rss}=2.5R_{\odot })$$\mathrm{PFSS}\left(\mathrm{Rss}=2.5R_{\odot }\right)$PFSS(Rss=2.5R_(o.))\operatorname{PFSS}\left(\operatorname{Rss}=2.5 R_{\odot}\right) is obviously larger than that calculated by the $\mathrm{CSSS}\left(10R_{\odot }\right)$$\mathrm{CSSS}\left(10R_{\odot }\right)$CSSS(10R_(o.))\operatorname{CSSS}\left(10 R_{\odot}\right). And when Rss are decreased at $1.6R_{\odot }$$1.6R_{\odot }$1.6R_(o.)1.6 R_{\odot}, the deficit ratio from the PFSS are the same as that from CSSS $\left(10R_{\odot }\right)$$\left(10R_{\odot }\right)$(10R_(o.))\left(10 R_{\odot}\right) which Amenomori et al. (2013) tend to support. The difference between these two results may come from different magnetograms or the influence of the cosmic-ray composition.
2008 年，在 10 TeV 以下，通过比较延伸率和赤字率，可以明显看出模型和参数造成的差异。在延伸率方面，源面高度较低的 PFSS 模型和 CSSS 会增加日影的延伸率。此外，在 10 TeV 下， $\mathrm{PFSS}(\mathrm{Rss}=2.5R_{\odot })$$\mathrm{PFSS}\left(\mathrm{Rss}=2.5R_{\odot }\right)$PFSS(Rss=2.5R_(o.))\operatorname{PFSS}\left(\operatorname{Rss}=2.5 R_{\odot}\right) 计算出的赤字率明显大于 $\mathrm{CSSS}\left(10R_{\odot }\right)$$\mathrm{CSSS}\left(10R_{\odot }\right)$CSSS(10R_(o.))\operatorname{CSSS}\left(10 R_{\odot}\right) 计算出的赤字率。而当 Rss 下降到 $1.6R_{\odot }$$1.6R_{\odot }$1.6R_(o.)1.6 R_{\odot} 时，PFSS 计算出的赤字率与 CSSS $\left(10R_{\odot }\right)$$\left(10R_{\odot }\right)$(10R_(o.))\left(10 R_{\odot}\right) 计算出的赤字率相同，这也是 Amenomori 等（2013）倾向于支持的。这两个结果之间的差异可能来自不同的磁图或宇宙射线成分的影响。
In 2012, differences between the results from models and parameters can also be seen at the extension and the deficit ratio below 10 TeV . But the influence from the different Rss, which represent different magnetic field structures, in the PFSS model cannot be found by the deficit ratio in 2012. Moreover, these expected results depend on the models and their limited accuracy a lot, especially in the solar maximum. Therefore, the energy range of the Sun shadow, which can be used to study the magnetic fields will be expanded to a higher level in the observation.
2012 年，在 10 TeV 以下的扩展和亏损率上也可以看到模型和参数结果之间的差异。但是，PFSS 模型中代表不同磁场结构的不同 Rss 所产生的影响，在 2012 年的赤字率中无法找到。此外，这些预期结果在很大程度上取决于模型及其有限的精度，尤其是在太阳极大期。因此，在观测中，可用于研究磁场的太阳阴影能量范围将扩大到更高水平。

Through the simulation, we found that the CMF, the IMF and the GMF mainly affect the deficit ratio, the extension of the Sun shadow in the north-south direction, and displacement in the west direction, respectively. Furthermore, we calculated and discussed the influence of the energy dependence of the deficit ratio on the measurement of the different structures of the CMF. And we also explain and expect the seasonal dependence of the extension of the Sun shadow. In addition to the GMF, the IMF is also confirmed again in this work to be responsible for the east-west displacement of the Sun shadow.
通过模拟，我们发现 CMF、IMF 和 GMF 分别主要影响赤字率、日影在南北方向上的延伸和在西方向上的位移。此外，我们还计算并讨论了赤字率的能量依赖性对 CMF 不同结构测量的影响。我们还解释并预测了日影延伸的季节依赖性。除 GMF 外，本研究还再次证实 IMF 也是造成日影东西位移的原因。
Base on these, the influences of different models and parameters on the deficit ratio and the extension of the Sun shadow at different energies are compared and discussed. From these expectations, we found that the effect of the Rss in the PFSS model on the deficit ratio and the extension of the Sun shadow is related. And the change of the Rss brings a big impact both on the deficit ratio and the extension in the solar minimum below 10 TeV , which affects the understanding of the magnetic fields directly. In the future, more observation data and the corresponding simulation are expected to learn more about the CMF and the IMF.
在此基础上，比较和讨论了不同能量下不同模型和参数对赤字率和日影延伸的影响。根据这些预期，我们发现 PFSS 模型中的 Rss 对赤字率和日影延伸的影响是相关的。而 Rss 的变化对 10 TeV 以下太阳最低点的赤字率和延伸都有很大影响，这直接影响到对磁场的理解。未来，更多的观测数据和相应的模拟有望进一步了解CMF和IMF。

This work is supported by the National Key R&D Program of China (No. 2018YFA0404201) and the Natural Sciences Foundation of China (No. 11575203 and No. 11775153). We also acknowledge opened calculation programs of magnetic field models which are provided by the solar soft ware, Xuepu Zhao and J. Todd Hoeksema.
这项工作得到了国家重点研发计划（编号：2018YFA0404201）和中国自然科学基金（编号：11575203和11775153）的支持。我们还感谢由太阳软件、赵学普和 J. Todd Hoeksema 提供的磁场模型计算程序。

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