1446 Introductory Astronomy II

1. 1446 Introductory Astronomy II Chapter 10B Atomic Nuclei & the Sun’s Interior R. S. Rubins Fall 2011

2. Atoms, Ions and Nuclei 1 • The atom is composed of a tiny central nucleus (containing over 99.9% of the atom’s mass) and surrounding electrons. • The nucleus contains nucleons, which consist of positively charged protonsand electrically neutral neutrons. • Particle masses: m(proton) ≈ m(neutron) ≈ 1840 m(electron). • Atomic diameters: 10–10 to 10– 9 m; • Nuclear diameters: 10–15 to 10–14 m. • Notation for atoms and positively-charged ions • An atom of Fe (for example) is denoted Fe I. • An Fe atom missing one electron is denoted Fe II. • An Fe atom missing 13 electrons is denoted Fe XIV (see the Sun’s corona).

3. Atoms, Ions and Nuclei 2 • The number of protonscontained in a nucleus is its atomic numberZ. • The value of Z determines the chemical speciesof the associated element, which is made up of atoms. • The number of nucleons(protons + neutrons) contained in a nucleus is its mass number A. • Since over 99.9% of an atoms mass is contained in its nucleus, the value of A is approximately the mass of the atom. • Since the volume of the nucleus is less than a trillionth (10–12), that of the atom, its density(mass/volume) is extremely large. • Neutron stars have the density of a nucleus. • A teaspoonful of a neutron star would weigh about a billion tons at the Earth’s surface.

4. Atoms, Ions and Nuclei 3 • Isotopeshave the same value of Z (i.e. are the same element), but different values of A. • Nuclear representation: AXZ, where X is the symbol for the element. • Example: the stable isotopes of oxygen are 15O8, 16O8(the most common), and 17O8. • Some isotopes are1H1 (proton),2H1 , 3He2 , 4He2 (α particle),7Li3 , 12C6 , 14N7 , 16O8 , 20Ne10 , 56Fe26 , 207Pb82 (lead),238U92.

5. Particle Notation

6. Hydrogen Fusion: the Proton Cycle

7. The Proton Cycle: Schematic

8. Proton Cycle Summarized

9. Solar Neutrinos 1 • A neutrino (ν) is extremely difficult to detect, since it has no electric charge, and its mass is extremely small. • Roughly 1038 neutrinos are produced each second in the Sun’s core, about 100 billion (1011) of which per second pass through a horizontal surface on the Earth, the size of a thumb, virtually all of them traversing the Earth undisturbed. • To avoid interference from other radioactive particles, neutrino detectors are buried deep underground. • In the detector built by Raymond Davis at the Homestake Gold Mine in S. Dakota in 1955, and improved in In 1970, using a tank containing 600 tons of C2Cl4, neutrinos were detected by the γ-decay of radioactive 37Ar in the process 0ν0+ 37Cl17 37Ar17 + 0e–1 + γ.

10. Japan’s Super Kamiokande • Deep within a mountain near Tokyo, the Super Kamiokande contains 50,000 tons of purified water and 13,000 light detectors. • While the resolution is very poor, the image of the Sun (taken over 600 days with SK), differs from photos obtained with EM radiations, by being an image of the Sun’s core.

11. Sudbury Neutrino Observatory • The SNO is a sphere of 12m diameter, containing 1000 tons of pure heavy water (deuterium oxide), built in a mine, 6800 ft underground. • It is unique among neutrino detectors in its ability to recognize all three flavors of neutrino, since each flavor interacts differently with matter.

12. Solar Neutrinos 2 • Both the South Dakota and Super Kamiokande found only about 1/3 of the estimated neutrino count. • However, in 2002, the mystery of the “missing” neutrinos was solved. • Theory indicates that, if the neutrino mass were not exactly zero, 4/9 of the electron neutrinos (e) produced in the Sun would have converted to muon neutrinos (μ) and tau neutrinos (τ) by the time they reached the Earth. • Unlike the earlier neutrino detectors, the Sudbury Neutrino Observatory in Canada was able to detect all three flavors of neutrino, thus confirming that neutrinos had mass. • The 2002 Nobel Prize in Physics was shared by Davis and the leader of the Japanese group, Koshiba.

13. Layers of the Sun

14. Approximate Ranges of Interior Layers • Core 0 to 200,000 km or 0 < r < 0.3 RSun. • Radiative zone 200,000 km to 500,000 km or 0.3 RSun < r < 0.7 RSun. • Convective zone 500,000 km to 700,000 km or 0.7 RSun < r < RSun.

15. The Interior Layers of the Sun

16. The Sun’s Core • Only within the core is temperature high enough (~ 107 K) for H fusion to occur at a rate conducive to life on Earth, since a much higher core temperature would appreciably shorten the Sun’s life as a main-sequence star. • The energy provided by nuclear fusion is the source of a star’s luminosity. • Even though the core is neither liquid nor solid, it is about a hundred times denser than water and ten times denser than lead. • 2007 measurements of the very weak vibrations reaching the surface from the Sun’s interior (known as g-mode waves), indicates that the core rotates at an appreciably faster rate than does the surface.

17. The Radiative Zone • Between 200,000 km and 500,000 km, the outward energy flow occurs through the absorption and re-emission of photons, in a process known as radiative transport. • At each stage of its outward journey, the energy is in the form of thermal radiation corresponding to the temperature of the portion of the Sun through which it is passing. • On reaching the photosphere, the original gamma radiation, produced in the Sun’s core, has cooled to thermal radiation at 5800 K, peaking in the visible region. • This outward journey takes hundreds of thousands of years. • By contrast, the neutrinos emitted during nuclear fusion, traveling at close to c, take seconds to reach the Sun’s surface.

18. The Convective Zone • Over the last 200,000 km of its journey, the energy is carried outwards by convection, which is heat transfer occurring through the motion outwards of the hotter interior atoms, ions and electrons. • Convective transport produces the solar granules observed in the photosphere.

19. Hydrostatic Equilibrium • The Sun remains stable because of hydrostatic equilibrium, whereby the inward pressure of gravity(which would cause the star to collapse) is balanced by the outward gas and radiation pressure (which by itself would blow the star apart).

20. The Solar Thermostat The self-regulating(or thermostatic) behavior of the Sun, which ultimately keeps the surface temperature constant, depends on two quite different effects: i. the rate of H fusion in the core is very sensitive to temperature, increasing very rapidly as the temperature increases; ii. expansion of the core causes it to cool, contraction causes warming. Rise in core temperature causesfusion rate to increase increased thermal pressure causes core to expand  expansion causes core to cool causes fusion rate to decrease  decreased thermal pressure causes core to contractcauses a rise in core temperature.

21. Variations of Physical Properties • The luminosity is created by fusion in the core. • Virtually all the mass lies within the inner 450,000 km. • The temperature within the core varies from 10 to 15 million K. • The density decreases continuously from the core to the photosphere.

22. Helioseismology 1 Helioseismology, the study of the Sun’s surface vibrations, using the Doppler effect, is the leading method for studying its interior.

23. Helioseismology 2 • The Doppler effectis used to study the vibrations at the Sun’s surface, caused by waves originating just below the photosphere, which are reflected back up to the surface. • Waves of long wavelength penetrate more deeply into the Sun than those of short wavelength. • The results have fitted the mathematical models used to describe the Sun’s interior. • While vibrations at the Sun’s surface were observed more than thirty years ago, only in 2007 were some very weak vibrations, known as g-mode waves, first detected. • Coming from deep in the Sun, they produce tiny ripples, just a few yards high, at the surface. • In 2008, seismic waves were measured in three nearby stars.