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Lecture 13

Lecture 13. Review: Static Stellar structure equations. Hydrostatic equilibrium:. Equation of state:. Mass conservation:. Energy generation:. Polytrope. or. Radiation. Convection. The Solar model. In this way we can build up a model of the interior structure of the Sun

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Lecture 13

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  1. Lecture 13

  2. Review: Static Stellar structure equations • Hydrostatic equilibrium: • Equation of state: • Mass conservation: • Energy generation: • Polytrope • or • Radiation • Convection

  3. The Solar model • In this way we can build up a model of the interior structure of the Sun • In general the differential equations are solved numerically • Instead of assuming a polytrope, choose the temperature gradient depending on the mode of energy transport • Boundary conditions: • in the simplest case, r, P and T =0 at r=R • M,L=0 at r=0

  4. Convection zones in the Sun • For the solar model we can plot dlnP/dlnT as a function of radius. Where this is >2.5, radiation is the most effective form of energy transport.

  5. The Solar interior • The interior can be divided into three regions: • Core: site of nuclear reactions • The radiative zone • The convective zone

  6. Abundance distribution • H is depleted in the core, where He is produced • is an intermediate species in the pp chain. It is most abundant at the top of the H-burning region, where the temperature is lower. • Abundances are homogeneous within the convective zone, since the plasma is effectively mixed

  7. The solar model: evolution • As the abundances in the core change, the nuclear reaction rates change accordingly, and the luminosity, temperature and radius of the star are affected.

  8. Energy production • Although nuclear reaction rates are higher where the temperature is higher, most of the energy is not produced at the centre of the Sun, because: • The amount of mass in a shell at radius r is • i.e. there is more mass per unit volume at large radius (assuming constant density) • The mass fraction of hydrogen (X) at the centre has been depleted due to fusion, and the rate equations depend on X2.

  9. Recall: Proton-proton chain • The net reactions are: • PPI • PPII • PPIII

  10. Direct observations of the core: neutrinos • One type of neutrino detector on Earth uses an isotope of chlorine, which will (rarely) interact with a neutrino to produce a radioactive isotope of argon. • This reaction requires the neutrino to have an energy of 0.814 MeV or more, and can only detect neutrinos from the “side-reactions” in the PP chain: • PPII • PPIII • The Homestake detector contains ~400,000 L of cleaning fluid • 2x1030 atoms of Cl isotope • Detect one Argon atom every 2-3 days.

  11. Direct observations of the core: neutrinos • More recently, the GALLEX (also SAGE) experiments uses 30 tons of natural gallium in a 100 ton aqueous gallium chloride solution to detect neutrinos via: • This is sensitive to lower neutrino energies (0.233 MeV) and can detect neutrinos from the main branch of the PP chain

  12. The Solar neutrino problem • Both the Homestake and GALLEX experiments detected fewer neutrinos (by a factor 2-3) than were expected from the PP-chain reactions. This problem existed for about 30 years. • The solution to the problem was suggested by results from the Super-Kamiokande detector in Japan • Results showed that electron neutrinos produced in the upper atmosphere can change into tau- or muon-neutrinos • This means neutrinos must have some mass and can therefore oscillate between flavours.

  13. The Solar neutrino problem… solved • The Sudbury Neutrino Observatory uses heavy water, and was able to directly detect the flux of all types of neutrinos from the Sun. • The results are now completely consistent with the standard solar model.

  14. Break

  15. age Increasing mass The main sequence • The atmospheres of most stars are mostly hydrogen, X=0.7. • The fraction of metals varies from Z~0 to Z~0.03 • Because of the relative slow burning of hydrogen, the structure of the star changes only slowly with time. • In general, the central temperature is higher for more massive stars • Thus, low mass stars will be dominated by the pp-chain • Higher mass stars undergo the CNO cycle • Central density is actually lower for more massive stars.

  16. The main sequence • Assuming hydrogen-burning reactions in the core, we can construct a theoretical relation between L, T and M • Stars undergoing hydrogen burning lie along the main sequence • For low-mass stars, <0.08MSun, central temperatures are not high enough to allow nuclear fusion • At very high masses, M>90 MSun, the stars become unstable: thermal oscillations in the core coupled with extreme temperature sensitivity of the nuclear reactions means an equilibrium is never attained.

  17. Main sequence lifetimes • At the lower end of the main sequence, • Such low-mass stars are entirely convective, so all the hydrogen (70% by mass) is available for fusion. What is the lifetime of such a star? • At the upper end of the main sequence, • Only the central ~10% of the mass is available for hydrogen fusion, because the star is not fully convective. What is the lifetime of such a star?

  18. Stellar lifetimes • From observations of the cosmic microwave background, we know the Big Bang occurred about 13.7 billion years ago • Galaxies have been observed at a time when the Universe was less than 1 billion years old. Thus stars have been forming for at least ~13 billion years

  19. Main sequence lifetimes • Bluer (hotter) stars must be very young, formed within the last 0.01% of the age of the Universe • On the other hand, some of the reddest (coolest) stars may have been formed shortly after the Big Bang, and would still be around. • The stars lying off the main sequence are not explained by the hydrogen-burning model: something else must be going on…

  20. The Solar Atmosphere • The solar atmosphere extends thousands of km above the photosphere (from which the optical radiation is emitted) • It is of much lower density and higher temperature than the photosphere T~106 K T~25000K T~5770 K Core T~107 K

  21. The extended solar spectrum • While the solar radiation is similar to a blackbody prediction at optical wavelengths, there is excess radiation at very short wavelengths. • This light is also highly variable.

  22. The chromosphere • UV (30.4 nm) images reveal the chromosphere • Can sometimes see large prominences rising high above the surface of the Sun. • At the north and south poles of the Sun, less EUV light is emitted - these regions often end up looking dark in the pictures, giving rise to the term coronal holes. • These are low density regions extending above the surface where the solar magnetic field opens up HeI emission

  23. The X-ray sun • The X-rays we see all come from the corona. • The corona is a very stormy place, constantly changing and erupting. Movie from http://www.lmsal.com/SXT/sxt_movie.html

  24. Sunspots • Dark (cool) regions of the photosphere • Number of spots changes on a 11 year cycle • Concentrations of magnetic field lines

  25. The Sun’s magnetic field • By studying sunspots we can learn about the nature of the Sun’s magnetic field • Switches polarity every 11 years

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