Fig. 5.1 . The high-speed tail (left) of the Maxwellian distribution of nuclear particle speeds plotted as a function of kinetic energy, E, for protons near the center of the Sun. The P(E) function (right) describes the quantum mechanical probability of two protons overcoming the electrical repulsion between them; it depends on the Gamow energy EG and the relative energy E of the two colliding protons. The function f(E) is the product of the speed and penetration function (center), and it determines the nuclear reaction rate in the core of the Sun.
Fig. 5.2 . Hydrogen nuclei, or protons, are fused together to form helium nuclei within the solar core, providing the Sunís energy. In 1939 the German-born American physicist Hans Bethe (1906?2005) described the detailed sequence of nuclear fusion reactions, called the proton-proton chain. It begins when two protons, here designated by the letter 1H, combine to form the nucleus of a deuterium atom, the deuteron that is denoted by 2D, together with the emission of a positron, denoted by e+, and an electron neutrino, designated by ?e. Another proton collides with the deuteron to make a nuclear isotope of helium, denoted by 3He, and then a nucleus of helium, designated by 4He, is formed by the fusion of two 3He nuclei, returning two protons to the gas. Overall, this chain successively fuses four protons together to make one helium nucleus. Even in the hot, dense core of the Sun, only rare, fast-moving particles are able to take advantage of the tunnel effect and fuse in this way.
Fig. 5.3 . Calculated and measured solar neutrino fluxes have consistently disagreed for several decades. The fluxes are measured in solar neutrino units, abbreviated SNU, which is defined as one neutrino interaction per trillion trillion trillion, or 1036, atoms per second. Measurements from the chlorine neutrino detector (small dots) give an average solar neutrino flux of 2.6 ? 0.2 SNU (lower broken line), well below theoretical calculations (large dots) that predict a flux of 8.5 ? 1.8 SNU (upper broken line) for the Standard Solar Model. Other experiments have also observed a deficit of solar neutrinos, suggesting that either some process prevents neutrinos from being detected or there is an incomplete understanding of the nuclear processes that make the Sun shine.
Fig. 5.4 . Neutrinos from the Sun travel through more than two kilometers of rock, entering the acrylic tank of the Sudbury Neutrino Observatory, which contains 1,000 tons (1 million liters) of heavy water. When one of these neutrinos interacts with a water molecule, it produces a flash of light that is detected by a geodesic array of photo-multiplier tubes. Some 7,800 tons (7.8 million liters) of ordinary water surrounding the acrylic tank blocks radiation from the rock, while the overlying rock blocks energetic particles generated by cosmic rays in our atmosphere. The heavy water is sensitive to all three types of neutrinos.
Fig. 5.5 . The Sun is an incandescent ball of ionized gas powered by the fusion of hydrogen in its core. As shown in this interior cross-section, energy produced by nuclear fusion is transported outward, first by countless absorptions and emissions within the radiative zone, and then by convection. The visible disk of the Sun, called the photosphere, contains dark sunspots, which are Earth-sized regions of intense magnetic fields. A transparent atmosphere envelops the photosphere, including the low-lying chomosphere with its jet-like spicules and the million-degree corona that contains holes with open magnetic fields, the source of the high-speed solar wind. Loops of closed magnetic fields constrain and suspend the hot million-degree gas within coronal loops and cooler material in prominences.
Fig. 5.6 . Underlying convection shapes the photosphere, producing tiny, varying regions called granules. They are places where hot, and therefore bright, material reaches the visible solar disk. The larges granules are about 1400 km across. They are not circular, but angular in shape. This honeycomb pattern of rising (bright) and falling (dark) gas is in constant turmoil, completely changing on time-scales of minutes and never exactly repeating itself. This image was taken with exceptional angular resolution of 0.2 seconds of arc or 150,000 km at the Sun using the National Solar Observatoryís Vacuum Tower Telescope at the Sacramento Peak Observatory. (Courtesy of Thomas R. Rimmele/AURA/NOAO/NSF.)
Fig. 5.7 . The trajectories of sound waves are shown in a cross section of the solar interior. The rays are bent inside the Sun, like light within the lens of an eye, and circle the solar interior in spherical shells called resonant cavities. Each shell is bounded at the top by a large, rapid density drop near the photosphere and bounded at the bottom at an inner turning point where the bending rays undergo total internal refraction, owing to the increase in sound speed with depth inside the Sun.
Fig. 5.8 . The rotation rate inside the Sun, determined by helioseismology using instruments aboard the SOlar and Heliospheric Observatory, or SOHO for short. The outer parts of the Sun exhibit differential rotation, with material at high solar latitudes rotating more slowly than equatorial ones. This differential rotation persists to the bottom of the convective zone at 28.7 percent of the way down to the center of the Sun. The rotation period in days is given at the left axis, and the corresponding angular velocity scale is on the right axis in units of nanoHertz, abbreviated nHz, where 1 nHz = 10-9 Hz, or a billionth, of a cycle per second. A rotation rate of 320 nHz corresponds to a period of about 36 days (solar poles), and a rate of 460 nHz to a period of about 25 days (solar equator). The rotation in the outer parts of the Sun is given at latitudes of zero (solar equator), 30, 45, 60 and 75 degrees. Just below the convective zone, the rotational speed changes markedly, and shearing motions along this interface may be the dynamo source of the Sunís magnetism. There is uniform rotation in the radiative zone, from the base of the convective zone at 0.713 solar radii to about 0.25 solar radii. The sound waves do not reach the central part of the energy-generating core. (Courtesy of Alexander G. Kosovichev/convective zone/Sebastien Couvidat, Rafael GarcŪa and Sylvaine Turck-ChiŤze/radiative zone. SOHO is a project of international cooperation between ESA and NASA.)
Fig. 5.9 . In about eight billion years the Sun will become much brighter (top) and larger (bottom). The time scale has been expanded near the end of the Sunís life to show relatively rapid changes. (Courtesy of I-Juliana Sackmann and Arnold I. Boothroyd.)