The Sun is a main sequence star in the center of our solar system. It provides light, heat and other forms of energy to Earth and comprises about 99% of the total mass in the solar system. The Sun’s radius is about 7×105kilometers, approximately 109 times Earth’s radius, see [2] and [3]. Figure 1.1 shows a schematic view of the Sun.
Figure 1.1: Schematic view of the Sun. Source: [5].
Like most other stars, the Sun is made up mostly of atoms of the chemical element hydrogen. About 94% of the atoms are hydrogen, 5.9% helium, and the remaining 0.1%
consist mainly of the elements oxygen, carbon, neon, nitrogen, magnesium, iron and silicon. But hydrogen is the lightest of all elements, and so it accounts for only about 72% of the mass, while helium makes up around 26%.
The inner layers of the Sun, and most of its atmosphere, consist of plasma. Plasma is a partially ionized gas, in which a certain proportion of electrons are free rather than being bound to an atom or a molecule. The degree of this ionization is the proportion of atoms which have lost (or gained) electrons, and is controlled mostly by the temperature.
As the temperature increases, more and more atoms become ionized, and the atoms that are ionized lose more and more electrons. The highest part of the solar atmosphere, called the corona, has a temperature of about 4×106K and is therefore strongly ionized.
The energy of the Sun comes from nuclear fusion reactions that occur deep inside the Sun’s core. As described earlier, most of the atoms inside the Sun are positive ions of the most common form of hydrogen. Thus, most of the Sun consists of single protons and independent electrons. Because nuclei have a positive charge, they tend to repel one another, but the core’s temperature and density are high enough to force nuclei together.
In the most common fusion process in the Sun, the so-called proton-proton chain, the final nucleus after the fusion consists of two protons and two neutrons, a nucleus of the most common form of helium. The mass of this nucleus is slightly less than the mass of the four protons from which it forms. The lost mass is converted into energy. The amount of energy can be calculated from the physicist Albert Einstein’s famous equationE=mc2. In this equation, the symbolE represents the energy,mthe mass that is covered, andc the speed of light. This energy is released in high-energy photons (gamma rays) which are absorbed in only a few millimeters of solar plasma and then re-emitted again in random direction and at slightly lower energy. It takes a long time for radiation to reach the Sun’s surface. Statistically a photon takes between 104and 105years to leave the Sun. At the transparent ”surface” of the photosphere, the photons escape as visible light. Each gamma ray in the Sun’s core is converted into several million visible light photons before escaping into space. The additionally released neutrinos in the core react very rarely with matter, unlike photons, so almost all are able to escape the Sun immediately.
1.1.1 Zones of the Sun
The Sun is generally divided into the core, the radiative zone, the convective zone, the photosphere, and the atmosphere. The heliosphere, which may be considered the tenuous outer atmosphere of the Sun, extends outward past the orbit of Pluto to the heliopause, where it forms a sharp shock front with the interstellar medium, see figure 1.2.
The core extends from the center of the Sun about one-fourth of the way to the surface.
The core has about 2% of the Sun’s volume, but it contains almost half the Sun’s mass.
Its maximum temperature is more than 1.5×107 K and its density reaches 1.5×107mg3, approximately 150 times the density of water on Earth. The high temperature and density of the core result in immense pressure, i.e., about 2×1011 times Earth’s atmospheric pressure at sea level. The core’s pressure supports all the overlying gas, preventing the Sun from collapsing. Almost all the fusion in the Sun takes place in the core.
Surrounding the core is a huge spherical shell, known as the radiative zone. The outer boundary of this zone is 70% of the way to the solar surface. The radiative zone makes up 32% of the Sun’s volume and 48% of its mass. The radiative zone gets its name from the fact that energy travels through it mainly by radiation. Photons emerging from the core pass through stable layers of gas. But they scatter from the dense particles of gas so
Figure 1.2: The tenuous outer atmosphere of the Sun, the solar wind, forms a sharp shock front with the interstellar medium. Source: [6].
Figure 1.3: This figure shows the temperature and density distribution in the outer zones of the Sun. Thex-axis shows the height above the top of the photosphere in km. On the lefty-axis we find the temperature in Kelvin and on the right is the density in gram per cubic centimeter. Source: “The Solar Results From Skylab” on [1].
often that an individual photon takes statistically 105 years to pass through the zone.
The highest level of the solar interior, the convection zone, extends from the radiative zone to the Sun’s surface. This zone consists of the ”boiling” convection cells. It makes up about 66% of the Sun’s volume but only slightly around 2% of its mass. At the top of the zone, the density is near zero, and the temperature is about 6×103K. The convection cells ”boil” to the surface because photons that spread outward from the radiative zone heat them.
The lowest layer of the atmosphere is called the photosphere. The density in the lower part of the photosphere is becoming low enough for the plasma to become transparent at most frequencies of light, so that radiation can escape from the Sun. The photosphere is about 500 km thick. Astronomers often refer to this part as the Sun’s surface, since this is the part where the Sun becomes transparent. The photosphere consists of numerous granules, which are the tops of granulation cells. These granulation cells are caused by convection currents of the plasma within the convection zone and produce magnetic north and south poles all over the surface of the Sun.
The next zone upwards is the chromosphere. As shown in figure 1.3, the coolest layer of the Sun is a temperature minimum region about 500 km above the photosphere, with a temperature of about 4×103K. For reasons not fully understood, the temperature rises after this minimum up to about 104K and is therefore hotter than that of the photosphere.
The most common feature in the chromosphere are spike-shaped structures called spicules.
The density of the chromosphere drops exponentially from 10−7to 10−13mg3, see figure 1.3.
The temperature of the chromosphere is about 2×104K, and the corona is hotter than 5×105K, see figure 1.3. Between the two zones is a region of intermediate temperatures, known as the transition region. This region receives much of its energy from the overlying corona. The transition region is not fixed in space. In models, this region moves up and down in the atmosphere every time a wave from below hits it. The thickness of the transition region is a few hundred to a few thousand kilometers.
For the described structures in the Sun’s atmosphere the magnetic field of the Sun plays an important role. The influence of the magnetic field on the plasma depends on the ratio of the magnetic pressure to the gas pressure. Above the photosphere, the magnetic pressure dominates the gas pressure and thus, we expect magnetic fields to play an important role for the plasma motion in the Sun.
1.1.2 The magnetic field
The magnetic field of the Sun is generated by a physical process called thesolar dynamo.
The big plasma motions in the Sun are the following two.
i) The Sun rotates more rapidly at the equator than at higher latitudes, illustrated in figure 1.4.
ii) The inner parts of the Sun rotate more rapidly than the surface.
These different movements of the plasma cause shear stresses, especially at the tachocline, a transition layer between the radiative zone and the convection zone. Since the Sun is a very good electrical conductor (The ability of the positive and negative charges in a
plasma to move relative to each other makes the plasma electrically conductive.), these shear stresses produce a circular electrical current which, according to Ampere’s law, produce a magnetic field. The detailed mechanism of the solar dynamo is not known, and is the subject of current research, in which simulations like in the chapters 5, 6 and 7 play an important role in order to understand the physical processes in the Sun.
Figure 1.4: The solar cycle. The differences in rotational speed stretch the magnetic field lines. Source: [4].
In the photosphere and below the magnetic pressure is much smaller than the gas pressure (figure 1.3), and the magnetic field is pushed around by the gas. This means that the magnetic field becomes concentrated in the downflow regions at the edges of the convection cells. The typical strength of the Sun’s magnetic field is only about twice that of the Earth’s field. But when the Sun’s magnetic field becomes highly concentrated in these small downflow regions, the field strength is around 103times as great as the typical strength. Above the photosphere the magnetic pressure becomes equal and then larger than the gas pressure, and the magnetic field spreads out. In these regions where the plasma is dominated by the magnetic pressure, the field lines guide ions and electrons into the space above the sunspots. Vibrations, caused by the field being pushed around by convection, are transmitted along the field, with growing amplitude as the gas density drops. All these processes create a variety of features on the Sun’s surface and in its atmosphere, the part that we can see, ranging from relatively cool, dark structures known as sunspots to spectacular eruptions called flares and coronal mass ejections.
An important feature of the solar atmosphere is that the temperature decrease from the core is reversed in the outer atmosphere, see figure 1.3. The heating of the atmo-sphere is only just now becoming understood, using data from modern solar observation satellites, and particularly from the results of numerical modeling. But the above descrip-tion of the Sun implies that the simuladescrip-tion of the entire solar atmosphere is extremely complicated, and involves multiple physical models. Hence, we concentrate on a part of the atmosphere that includes the chromosphere. One of the important energy
carri-ers in the solar atmosphere are convection generated waves from the inner laycarri-ers of the sun. They transport and deposit energy in the overlaying chromospheric and coronal plasmas. The waves interact with complex magnetic fields generated by the plasma, and these interactions affect the qualitative as well as the quantitative features of the energy transfer. One of the most important models for simulating the processes in the solar chromosphere are the so-calledmagneto-hydrodynamic (MHD) equations, together with a gravitational source term.