9.2 The Solar Interior

Lacking any direct measurements of the Sun’s interior, astronomers must use indirect means to probe the inner workings of our parent star. To accomplish this, they construct mathematical models of the Sun, combining all available observations with theoretical insight into solar physics. The result is the Standard Solar Model, which has gained widespread acceptance among astronomers.

Figure 9.4 Solar Vibration The Sun vibrates in a very complex way as sound waves of many frequencies move through its interior. By observing the motion of the solar surface, scientists can determine the wavelengths and frequencies of the individual waves and thus deduce information about the solar interior not obtainable by other means. The alternating patches of color in this rendering of one particular wave pattern represent gas moving inward (red) and outward (blue). (National Solar Observatory)
Modeling the Structure of the Sun

An important technique for probing the Sun beneath the photosphere emerged in the 1960s, when it was discovered that the surface of the Sun vibrates like a complex set of bells. These vibrations, illustrated in Figure 9.4, are the result of internal pressure ("sound") waves that reflect off the photosphere and repeatedly cross the solar interior. These waves penetrate deep inside the Sun, and analysis of their surface patterns allows scientists to study conditions far below the Sun’s surface. This process is similar to the way in which seismologists study Earth’s interior by observing seismic waves produced by earthquakes. (Sec. 5.4) For this reason, study of solar surface patterns is usually called helioseismology, even though solar pressure waves have nothing whatever to do with solar seismic activity (which doesn’t exist).

The most extensive study of solar vibrations is the ongoing GONG (short for Global Oscillations Network Group) project. By making continuous observations of the Sun from many clear sites around Earth, solar astronomers have obtained uninterrupted high-quality solar data spanning weeks at a time. The Solar and Heliospheric Observatory (SOHO), launched by the European Space Agency in 1995 and now permanently stationed between Earth and the Sun some 1.5 million km from our planet, provides continuous monitoring of the Sun’s surface and atmosphere. Analysis of the data from all these sources provides important detailed information about the temperature, density, rotation, and convective state of the solar interior.

Figure 9.5 Solar Interior Theoretically modeled profiles of density (b) and temperature (c) for the solar interior, presented for perspective in (a). All three parts describe a cross-sectional cut through the center of the Sun.
Figure 9.5 shows the solar density and temperature according to the Standard Solar Model, plotted as functions of distance from the Sun’s center. Notice how the density drops sharply at first, then more slowly near the photosphere. The variation in density is large, ranging from a core value of about 150,000 kg/m3, 20 times the density of iron, to an extremely small photospheric value of 2 10-4 kg/m3, about 10,000 times less dense than air at Earth’s surface. The average density of the Sun (Table 9.1) is 1400 kg/m3, about the same as the density of Jupiter.

As shown in Figure 9.5, the solar temperature also decreases with increasing radius, but not as rapidly as the density. Computer models indicate a central temperature of about 15 million K. The temperature decreases steadily, reaching the observed value of 5800 K at the photosphere.

Energy Transport

The very hot solar interior ensures violent and frequent collisions among gas particles. In and near the core, the extremely high temperatures guarantee that the gas is completely ionized. With no electrons left on atoms to capture photons and move into more excited states, the deep solar interior is quite transparent to radiation. (Sec. 2.6) Only occasionally does a photon scatter off a free electron. The energy produced by nuclear reactions in the core travels outward toward the surface in the form of radiation with relative ease.

As we move outward from the core the temperature falls, and eventually some electrons can remain bound to nuclei. With more and more atoms retaining electrons that can absorb the outgoing radiation, the gas in the interior changes from being relatively transparent to being almost totally opaque. By the outer edge of the radiation zone, 500,000 km from the center, all of the photons produced in the Sun’s core have been absorbed. Not one of them reaches the surface. But what happens to the energy they carry?

That energy is carried to the solar surface by convection—the same basic physical process we saw in our study of Earth’s atmosphere. (Sec. 5.3) Convection can occur whenever cooler material overlies warmer material, and this is just what happens in the outer part of the Sun’s interior. Hot solar gas physically moves outward, while cooler gas above it sinks, creating a characteristic pattern of convection cells. All through the convection zone, energy is transported to the surface by physical motion of the solar gas. Remember that there is no physical movement of material when radiation is the energy-transport mechanism; convection and radiation are fundamentally different ways in which energy can be transported from one place to another.

Figure 9.6 Solar Convection Transport of energy in the Sun’s convection zone. We can visualize this region as a boiling, seething sea of gas. Each convective cell at the top of the convection zone is about 1000 km across. The cells are arranged in tiers, with cells of progressively smaller size at increasing distance from the center. (This is a highly simplified diagram.)
Figure 9.6 is a schematic diagram of the solar convection zone. There is a hierarchy of convection cells, organized in tiers at different depths. The deepest tier, about 200,000 km below the photosphere, is thought to contain cells tens of thousands of kilometers in diameter. Energy is carried upward through a series of progressively smaller cells, stacked one upon another until, at a depth of about 1000 km below the photosphere, the individual cells are about 1000 km across. The top of this uppermost tier of convection is the solar photosphere.

Convection does not proceed into the solar atmosphere. In and above the photosphere, the density is so low that the gas is transparent and radiation once again becomes the mechanism of energy transport. Photons reaching the photosphere escape freely into space.

Evidence for Solar Convection

Figure 9.7 Solar Granulation A photograph of the granulated solar photosphere, taken from the Skylab space station. Typical solar granules are comparable in size to Earth’s continents. The bright portions of the image are regions where hot material is upwelling from below, as shown in Figure 9.6. The dark regions correspond to cooler gas that is sinking back down into the interior. (Palomar Observatory)
In part, our knowledge of solar convection is derived indirectly, from computer models of the solar interior. However, astronomers also have some direct evidence of conditions in the convection zone. Figure 9.7 is a high-resolution photograph of the solar surface. The visible surface is highly mottled with regions of bright and dark gas known as granules. This granulation of the solar surface is a direct reflection of motion in the convection zone. Each bright granule measures about 1000 km across and has a lifetime of between 5 and 10 minutes.

Each granule forms the topmost part of a solar convection cell. Doppler measurements indicate that the bright granules are moving outward with speeds of about 1 km/s, while the dark granules are moving down into the solar interior, exactly as we would expect for the topmost tier of convection in Figure 9.6. (More Precisely 2-3) The brightness variations of the granules result from differences in temperature. The upwelling gas is hotter and therefore (by Stefan’s law) emits more radiation than the cooler downwelling gas. (Sec. 2.4) The adjacent bright and dark gases appear to contrast considerably, but in reality their temperature difference is less than about 500 K.

Careful measurements also reveal a much larger-scale flow beneath the solar surface. Supergranulation is a flow pattern quite similar to granulation except that supergranulation cells measure some 30,000 km across. As with granulation, material upwells at the center of the cells, flows across the surface, then sinks down again at the edges. Scientists believe that supergranules are the imprint on the photosphere of the deepest tier of large convective cells depicted in Figure 9.6.

Concept Check

Describe the two distinct ways in which energy moves outward from the solar core to the photosphere.