行星际激波在日球层中的传播：Propagation of Interplanetary Shocks in the Heliosphere （第二部分）

行星际激波在日球层中的传播：Propagation of Interplanetary Shocks in the Heliosphere （第一部分）- Chapter 1: Introduction & Chapter 2: Basics of Magnetohydrodynamics

行星际激波在日球层中的传播：Propagation of Interplanetary Shocks in the Heliosphere （第三部分）- Chapter 4: Analysis methods

行星际激波在日球层中的传播：Propagation of Interplanetary Shocks in the Heliosphere （第四部分）- Chapter 5: Discussion & Chapter 6: Summary and Conclusions

Propagation of Interplanetary Shocks in the Heliosphere
[ Chapter 3 ]

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行星际激波在日球层中的传播：Propagation of Interplanetary Shocks in the Heliosphere （参考文献部分）-CSDN博客

Chapter 3 Solar and heliospheric physics

The Sun is the main source of energy for all lives on the earth as well as the main defining object of the solar system dynamics. Like all other stars, the Sun has both inner complex dynamics and influence on interplanetary space. In this chapter, for the sake of completeness and to explain the origin of these tremendous dynamics, the inner structure of the Sun as well as some important heliospheric activities are briefly discussed.

太阳作为地球上所有生命的主要能量来源，同时也是太阳系动力学的主要决定者。与其他恒星类似，太阳同时具有复杂的内部动力学过程和对行星际空间的深远影响。本章将系统阐述太阳的内部结构及其重要的日球层活动，以完整揭示这些惊人动力学现象的起源机制。

▍3.1 The Sun ▍

Our star, the Sun, is a G2-V type star (Aschwanden, 2014). All stars are in a balance of opposing forces between outward radiation fueled by nuclear fusion and inward pressure dictated by gravitational force. The radiative force is the product of the fusion of hydrogen atoms, which constitutes about 73 %, into helium atoms, which constitute 25 % of the Sun (Basu and Antia, 2007). This process is a thermonuclear reaction via turning a proton into a neutron.

Structurally, the Sun has inner zones and outer zones. The former consists of the core, radiative zone, interface layer (tachocline), and convection zone. The latter consists of the photosphere, the chromosphere, the transition region, and the corona (NASA, 2017) as shown in Figure 3.1.

太阳属于G2-V型主序星（Aschwanden，2014）。所有恒星都维持着两种对立力量的平衡：由核聚变驱动的向外辐射压力与引力作用导致的向内收缩压力。其中，辐射压力源自氢原子（占73%）聚变为氦原子（占25%）的过程（Basu与Antia，2007），这一热核反应本质上是通过质子转化为中子实现的。

从结构上看，太阳可分为内部区域和外部大气。

内部区域包含：核心区、辐射层、差旋层（tachocline）、对流层。

外部大气则由以下层次构成：光球层、色球层、过渡区、日冕层（NASA，2017），具体结构如图3.1所示。

Figure 3.1: The layers of the Sun (Credit: NASA, 2017)

The core of the Sun

The core of the Sun is 25% of the solar radius (Garc´ıa et al., 2007), the density is about 150g/cm3 (Basu et al., 2009) contains 34% of the solar mass even though only 0.8% of the total volume, and it is the hottest part of the Sun that a temperature of 15 million Kelvins (Dr. David H. Hathaway, 2015). This is the zone where the thermonuclear reaction is going. For the radiative zone, it starts from the edge of the core to the interface layer (tachocline), and much of the energy generated in the core is carried away by photons though photons take a million years to reach the next layer due to the dense material of the region (Chemin, 2022).

太阳核心占据太阳半径的25%（García等，2007），其密度高达150g/cm³（Basu等，2009），虽然仅占太阳总体积的0.8%，却包含34%的太阳质量。作为太阳最炽热的区域，核心温度达到1500万开尔文（Hathaway，2015），是持续进行热核反应的区域。在辐射区（从核心边缘延伸至差旋层），核心产生的能量主要通过光子传递，但由于该区域物质密度极高，光子需耗费百万年才能抵达下一层（Chemin，2022）。

Interface Layer

The very next layer, the interface layer (tachocline) is much of our interest because it is believed that the solar magnetic dynamo originates in this very thin layer (Tobias and Weiss, 2007) that magnetic field lines can become stronger due to the changes in the fluid flow velocities crossing this layer. However, recent radio observations of brown dwarf stars show that, despite not having a tachocline layer, they can have similar magnetic strength and activities just like the Sun, which indicates the convection zone may be solely responsible for the solar dynamo (Route, 2016).

差旋层（tachocline）作为核心与对流层的过渡区具有特殊意义。这个极薄的界面层被认为是太阳磁发电机效应的起源地（Tobias与Weiss，2007），因流体速度突变而增强的磁力线在此形成。但最新研究显示，缺乏差旋层的褐矮星同样存在类太阳磁活动（Route，2016），暗示对流层可能独立维持磁发电机效应。

Convection Zone

Next, the convection zone is the outermost layer of the inner zones and it extends about 200,000 km from the depth and the temperature is approximately 2 million Kelvins (Christensen-Dalsgaard et al., 1991), which makes the zone relatively cooler for heavy ions to keep their electrons so that the zone is opaque to the radiation (Ortu˜no-Araujo et al., 2012), which in turn traps the heat and eventually the fluid becomes unstable and start convecting. As a result, this layer is very turbulent (Brummell et al., 1995), which in addition to the rotational motion creates electric currents and magnetic fields, and the gas pressure is much more dominant than the magnetic pressure in this region, and because of this the magnetic field is dragged and twisted by the fluid, which then propagates passing through the photosphere, chromosphere, the transition region up to the corona and creates a multitude of activities on the surface of the Sun called solar activity.

对流层作为太阳内部最外层，延伸约20万公里，温度约200万开尔文（Christensen-Dalsgaard等，1991）。该区域温度使得重离子能束缚电子，导致辐射不透明（Ortuño-Araujo等，2012），进而形成热约束。当流体失稳开始对流时，会产生剧烈湍流（Brummell等，1995）。这种旋转运动不仅生成电流与磁场，还使得气体压力远超过磁压力，导致磁场被流体拖曳扭曲。这些磁结构穿越光球层、色球层、过渡区直达日冕，最终引发各类太阳表面活动现象。

Photosphere

In the photosphere, visible darker areas called sunspots appear due to localized strong magnetic regions, which inhibit some of the heat from reaching the surface and this makes the areas cooler than the other parts of the Sun (Babcock and Babcock, 1955). Because of the mentioned strong magnetic nature, the magnetic field lines around the sunspot often twist and cross, causing a tension of energy that bursts in an explosion called a solar flare (Chakraborty and Basak, 2022).

在光球层中，由于局部强磁场区域的存在，会形成可见的斑——太阳黑子（Babcock父子，1955）。这些磁场阻碍热量传递至表面，使得黑子区域温度显著低于周边。这种强磁场的扭曲特性导致黑子周围磁力线频繁交织，最终引发能量剧烈释放的爆发性事件——太阳耀斑**（Chakraborty与Basak，2022）。

Corona

The corona is the hot and ionized outermost layer of the Sun and it is millions of Kelvins greater than that of the surface of the Sun (Aschwanden, 2006). The solar magnetic field confines much of the coronal plasma, but some of the plasma spread with a supersonic speed into interplanetary space, which is solar wind. The solar magnetic field forms so-called flux tubes. These ropes are tensed by the differential rotation of the Sun. Therefore, store plenty of energy. If a certain configuration appears (X-shape) the magnetic structure reorganizes. Hence, a huge amount of energy is released. The name of this 20 million K-degree flash is a solar flare. It emits plenty of energized protons and other ions in the heliosphere and very often, but not always a huge amount of solar plasma ejects to the IP space. The process is called coronal mass ejections (CME). However, CME could occur without a flare too.

These phenomena are the main drivers of space weather and the conditions of the terrestrial cosmic environment (Facsk´o et al., 2022). The solar activity is cyclic, which is called the solar cycle, and it is approximately 11 years (Center/SDO, 2015), see Figure 3.2. Each cycle the magnetic field of the Sun flips, and the periods, in which, the sunspots are the greater in number are called solar maximum and the lower in number are called solar minimum.

日冕作为太阳最外层的高温电离大气，其温度比光球层高出数百万开尔文（Aschwanden，2006）。虽然太阳磁场束缚着大部分日冕等离子体，但仍有部分等离子体以超音速进入行星际空间，形成持续不断的太阳风。日冕中的磁通量管结构因太阳较差自转而不断拉伸，从而储存巨大磁能。当出现特定的X型磁重联构型时，磁场结构会发生重组，瞬间释放出相当于2000万开尔文能量的闪光——即太阳耀斑，并向日球层喷射大量高能粒子。这类事件通常（但非必然）会伴随巨量等离子体抛射进入行星际空间，该过程称为日冕物质抛射（CME）。值得注意的是，CME也可能独立于耀斑单独发生（Facskó等，2022）。

这些爆发活动是空间天气的主要驱动源，直接影响地球空间环境状态。太阳活动呈现约11年的周期性变化（太阳活动周），其全球磁场极性每周期发生一次反转（SDO研究中心，2015），参见图3.2。黑子数最多的时期称为太阳活动极大期，最少的时期则称为极小期。

Figure 3.2: The sunspot cycle over the last several decades (Figure is from Pasachoff et al., 2014; Figure 8)

▍3.2 The Solar Wind and the Interplanetary Magnetic Field ▍

The Sun ejects highly energized and ionized charged particles continuously in all directions, which is the solar wind. The solar wind is a collisionless plasma that consists of equal amounts of protons and electrons with the addition of negligible 3 to 6% helium (Neugebauer, 1981). As a result, the solar wind is a quasi-neutral plasma whose characteristics can be defined by magnetohydrodynamics (MHD). In MHD, Alfvén theorem states that in a fluid with high electric conductivity the magnetic field line is frozen in it and moves along with it (Alfvén, 1942). Since the solar wind is one such fluid the Sun's magnetic field lines are frozen in the flow that they are forced to propagate with the solar wind (Roberts, 2007), forming the interplanetary magnetic field (IMF).

Depending on the origination point whether in the coronal holes or the equatorial belt of the Sun, the solar wind is classified as the fast solar wind with a velocity of 750 km/s and the slow solar wind with a velocity of 400 km/s respectively (Feldman et al., 2005). The coronal holes are areas that appear dark in X-ray images because these areas are much cooler and less dense than other regions (Cranmer, 2009) and the magnetic field around these areas does not loop back down but extends into the interplanetary space (Parker, 1959), so the plasma can easily flow out, creating the fast solar wind. The  holes can appear anywhere on the coronal areas during the solar maximum while they usually appear on northern or southern poles of the sun during the solar minimum (McComas et al., 2003).

3.2 太阳风与行星际磁场

太阳持续向各个方向喷射高能电离带电粒子，这就是太阳风。太阳风是一种无碰撞等离子体，由等量的质子与电子组成，并含有少量（3%-6%）的氦（Neugebauer, 1981）。因此，太阳风是准中性的等离子体，其特性可以用磁流体力学（MHD）来描述。根据MHD中的阿尔芬定理，在高电导率的流体中，磁力线会被冻结并随流体运动（Alfvén, 1942）。由于太阳风正是这种流体，太阳的磁力线被冻结在太阳风中，并被迫随太阳风传播（Roberts, 2007），从而形成行星际磁场（IMF）。

根据起源位置的不同——无论是来自日冕洞还是太阳赤道带，太阳风可分为速度达750 km/s的快太阳风和约400 km/s的慢太阳风（Feldman等, 2005）。日冕洞在X射线图像中呈现暗区，因为该区域温度更低、密度更稀薄（Cranmer, 2009），且磁场不会回折而是延伸至行星际空间（Parker, 1959），因此等离子体可自由流出形成快太阳风。在太阳活动极大期，日冕洞可能出现在日冕任何区域；而在太阳活动极小期，它们通常出现在太阳两极（McComas等, 2003）。

Figure 3.3: Combined X-ray image of the Sun’s active regions observed from several telescopes. High-energy X-rays from NASA’s Nuclear Spectroscopic Telescope Array (NuSTAR) are shown in blue, low-energy X-rays from Japan’s Hinode spacecraft are green, and extreme ultraviolet light from NASA’s Solar Dynamics Observatory (SDO) is yellow and red (Credit: NASA/JPL-Caltech/GSFC/JAXA, 2015)

The expansion of the solar wind is a radial propagation away from the Sun that it is diluted and cools down on its journey. As seen from some observations the density of the solar wind decreases approximately as r^(-2) while the temperature decrease is less significant about a factor of 20 (Baumjohann and Treumann, 2012). During the expansion of the radial flow, the Sun rotates, which is 27 days on average, and because the magnetic field lines are anchored in the sun, the radial flow looks like an Archimedean spiral called the Parker Spiral. At 1 AU the spiral makes 45° to the Earth-Sun line, see Figure 3.4.

太阳风的膨胀是远离太阳的径向传播，在此过程中逐渐稀释冷却。观测表明，太阳风密度近似按r^(-2)递减，而温度下降较缓，降幅约20倍（Baumjohann和Treumann, 2012）。由于太阳自转（平均周期27天）且磁力线锚定于太阳，径向流会形成阿基米德螺旋线结构（帕克螺旋）。在1天文单位（AU）处，该螺旋与日地连线呈45°夹角，参见图3.4。

Figure 3.4: Schematic representation of the Archimedes spiral structure of the interplan etary magnetic field (Figure is from Bittencourt, 2004; Figure 3)

The solar wind travels throughout the solar system and defines the heliosphere the region in space whose frontier is impeded by the interstellar medium. Consequently, the heliosphere is a giant bubble whose center is the Sun and protects the solar system from interstellar radiations and cosmic rays. The size of the heliosphere is about 121 AU (Cowen, 2013). The solar wind decelerates when it flows outward through the Solar System. At a certain point, the flow becomes subsonic and forms a shock. Its name is termination shock (Jokipii, 2013). Then the flow continues its journey outward and interacts with the interstellar material. It is under debate whether the speed of the Solar System is super- or sub-sonic. A bow shock or bow wave forms before the heliosphere, respectively. Furthermore, due to the interaction, the solar wind becomes turbulent and this region is called heliosheath which is in between the termination shock and the heliopause (Burlaga, 2015).

太阳风在太阳系中传播并定义了日球层——这个空间区域的边界受星际介质阻挡。因此，日球层是一个以太阳为中心的巨型气泡，它保护太阳系免受星际辐射和宇宙射线的侵害。日球层的尺寸约为121天文单位（AU）（Cowen，2013）。当太阳风向外穿过太阳系时会逐渐减速。在某个临界点，太阳风流会变为亚音速并形成激波这个激波被称为终止激波（Jokipii，2013）。随后，太阳风继续向外传播并与星际物质相互作用。目前学界仍在争论系的速度是超音速还是亚音速的问题，这分别会导致在日球层前形成弓激波或弓形波。此外，由于这种相互作用太阳风会变得湍流，这个区域被称为日球鞘，它位于终止激波和日球层顶之间**（Burlaga，2015）。

▍3.3 Interplanetary shocks ▍

The average interplanetary magnetic field strength is around 6 nT at 1 AU (Lowrie and Fichtner, 2020) and considering the average speed of the solar wind, the solar wind is both supersonic and super-Alfvénic, which means it is super-magnetosonic. As a result of this nature of the solar wind, when it collides with celestial objects such as planets, moons, asteroids, and comets or its slow-flowing part, shocks are formed. The main characteristic of shocks that can be found in interplanetary space to interstellar regions is a denser state in contrast to the medium in which they propagate due to the shock formation. Furthermore, if the celestial objects are magnetized, then the shock formations create interesting interaction regions, and their physics looks very exciting.

3.3 行星际激波

在1天文单位（AU）处，平均行星际磁场强度约为6纳特斯拉（nT）（Lowrie和Fichtner，2020）。考虑到太阳风的平均速度，太阳风既是超音速的，又是超阿尔芬速的，这意味着它是超磁声速的。由于太阳风的这种特性，当它与行星、卫星、小行星和彗星等天体或其低速部分碰撞时，就会形成激波。在行星际空间到星际区域中发现的激波，其主要特征是由于激波形成，它们传播的介质会呈现更致密的状态。此外，如果天体被磁化，那么激波的形成会产生有趣的相互作用区域。

One such fascinating magnetized object is our planet, the Earth. The Earth has its magnetic field, known as the magnetosphere, which originated from its inner core via the dynamo effect (Gilbert, 2003). The Earth's magnetosphere extends 60000 kilometers in the sunward direction while a million kilometers in the anti-sunward direction (Lakhina et al., 2009). Such a big extension is a common characteristic of all the magnetized planets, and as a result of this extension, the cross-section of a planet is increased by a large factor. For example for the Earth, the factor is 150 (Baumjohann and Treumann, 2012).

The magnetic field frozen in the supersonic and super-Alfvénic solar wind plasma cannot enter the magnetosphere, the region where the terrestrial magnetosphere dominates. As a result, a special standing wave, the bow shock forms (Baumjohann and Nakamura, 2007). Consequence of the slowing down of the solar wind plasma, the kinetic energy of some of the particles is converted into thermal energy, which occurs behind the bow shock, and this region is called the magnetosheath. The boundary region between two magnetic field lines is called the magnetopause. Bow shock formation is common to all the planets and celestial objects with or without magnetospheres (Mazelle et al., 2004).

地球就是一个磁化天体。地球拥有自身的磁场，称为磁层，其源于地球内核的发电机效应（Gilbert，2003）。地球磁层向太阳方向延伸60000公里，而背向太阳方向延伸达100万公里（Lakhina等，2009）。这种巨大延伸是所有磁化行星的共同特征，由于这种延伸，行星的横截面积被显著放大。以地球为例，放大因子达150倍（Bumjohann和Treumann，2012）。

冻结在超音速和超阿尔芬速太阳风等离子体中的磁场无法进入磁层——这个地球磁场主导的区域。因此会形成一种特殊的驻波，即弓激波（Baumjohann和Nakamura，2007）。由于太阳风等离子体减速，部分粒子的动能转化为热能，这一过程发生在弓激波后方，该区域称为磁鞘。两条磁力线之间的边界区域称为磁层顶。弓激波的形成对所有具有或不具有磁层的行星和天体都是普遍现象（Mazelle等，2004）。

Figure 3.5: Illustration of the Earth’s magnetosphere and its interaction with the solar wind. (Figure is from Kivelson and Bagenal, 2007; Figure 1)

Figure 3.6: Illustration of a CME event. (Credit: NASA, 2017)

In addition, there are several other shocks, the previously mentioned termination shock, coronal mass ejection (CME) driven shock, and a co-rotating interaction region (CIR) driven shock. When a CME event occurs, it moves faster than the background solar wind flow, resulting in a shock wave. On the created shock waves charged particles accelerate. So usually CMEs are one of the main causes of the solar energetic particles (SEPs) (Cane and Lario, 2006), see Figure 3.6.

Similarly to the shocks caused by CMEs, When the fast-moving solar wind flow catches the slow-moving solar wind flow, the so-called co-rotating interaction region is formed, and if the pressure gradient gets sufficiently large and the speed difference surpasses the local speed shocks can arise (Heber et al., 1999), Figure 3.7.

此外还存在其他几种激波，前文提到的终止激波、日冕物质抛射（CME）驱动的激波，以及共转相互作用区（CIR）波。当CME事件发生时，其运动速度超过背景太阳风流速，从而产生激波。在这些激波上，带电粒子被加速。因此CME通常是太阳高能粒子（SEPs）的主要来源之一（Cane和Lario，2006），参见图3.6。

与CME产生的激波类似，当快速运动的太阳风流追上慢速太阳风流时，会形成所谓的共转相互作用区；若压力梯度足够大且速度差超过当地声速，就可能产生激波（Heber等，1999），图3.7。

Figure 3.7: Co-rotating interaction region. (Figure is from David Burgess, 2017)

3.3.1 Classifications of Interplanetary (IP) shocks

Figure 3.8: Categorizations of IP shocks. N, T, B, and V denote number density, the proton temperature, the magnitude of the magnetic field, and speed respectively. (Figure is from WIND MFI Team Science, 2001)

Armed with the above shock definitions and categorizations knowledge, now we can finally be able to classify IP shocks. The IP shocks can be classified based on their travel directions concerning the solar wind frame of reference. If the shock is moving away from its driver, here the Sun is referred but drivers can be detailed such as ICMEs, CIRs, etc, the shock is called forward shock (FS), and if it is moving toward its driver, it is called reverse shock (RS). Adding the previous definitions of fast and slow shocks, IP shocks are usually categorized as fast forward (FF), fast reverse (FR), slow forward (SF) and slow reverse (SR) shocks (Berdichevsky et al., 2000), see Figure 3.8.

基于上述激波定义和分类知识，我们现在终于能够对行星际激波（IP shocks）进行分类。行星际激波可根据其相对于太阳风参考系的传播方向进行分类。若激波远离其驱动源（此处指太阳，但驱动源可具体分为ICMEs、CIRs等），则称为前向激波（FS）；若激波朝向其驱动源传播，则称为反向激波（RS）结合先前对快慢激波的定义，行星际激波通常被分类为快前向（FF）、快反向（FR）、慢前向（SF）和慢反向（SR）激波（Berdichevsky等，2000），参见图3.8。

As you can see from Figure 3.8, the solar wind plasma parameters – number density N, the proton temperature T, the magnitude of the magnetic field B, and the bulk speed V parameters increase dramatically from upstream (unshocked) to downstream (shocked) regions in fast forward (FF) shocks while the parameters except for the bulk speed decrease in fast reverse (FR) shocks [1]. In the case of slow forward (SF) shocks, the parameters except for the magnitude of the magnetic field increase from upstream to downstream whereas in the case of slow reverse (SR) shocks, the number density N and the proton temperature T decrease while the magnitude of magnetic field B and the bulk speed V increase [2].

Within 1 AU, the most frequent IP shocks are fast forward (FF) shocks (Richter et al., 1985).

[1] In a sense of the reverse upstream to downstream in fast reverse (FR) shocks, the parameters except for the bulk speed increase from reversed upstream to downstream

[2] Again in the sense of the reversed upstream to downstream in slow reverse (SR) shocks, the number density N and the proton temperature T increase while the magnitude of magnetic field B and the bulk speed V decrease

如图3.8所示，在快前向（FF）激波中，太阳风等离子体参数——数密度N、质子温度T、磁场强度B和整体速度V从上游（未受扰）到下游（受扰）区域显著增加；而在快反向（FR）激波中，除整体速度外其他参数均下降 [1]。对于慢前向（SF）激波，除磁场强度外其他参数均随上游至下游方向增加；而对于慢反向（SR）激波，数密度N和质子温度T下降，而磁场强度B和整体速度V上升[2]。