Lecture 14: The Sun

Lecture 14: The Sun

1. Solar Composition

   • - the Sun has a surface temperature of about 5700K - we know this from its blackbody peak - at such temperatures all elements are gaseous so the sun must be made of gas - we can obtain the surface composition through spectroscopy
   • Hydrostatic equilibrium
     • - the sun is a gas throughout - pressure increases with temperature  - the sun is in hydrostatic equilibrium, neither expanding nor contracting - at each point in the sun, the force of gravity is balanced by the pressure of the gas - since the weight of overlying material increases as we move inward, the pressure must increase. when the pressure increases, temperature must increase - a simple calculation shows that the centre of the sun must have a temperature of 15 million K, sufficient to support nuclear reactions

2. Energy Generation

   • Old theories
     • 19th century, Lord Kelvin and Hermann von Helmholtz proposed that the sun is power by its gradual collapse, meaning: - collapse releases gravitational energy - Sun would shrink by about 40 meters/year - Sun would be 100 million years old - At the turn of the century, it was realized that the Earth was much older - Earlier theories even suggested that the sun might be powered by something like coal, but the number didn't work out
   • Energy and Power
     • - energy is the ability to do work (J) - power is the rate at which energy is being used or given out (J/s)
   • Einstein's Special Theory of Relativity
     • to calculate energy generation, we use Einstein's special theory of relativity - mass and negery are equivalent: E = mc^2 - this conversion formula describes the amount of energy that is released when we convert matter into energy
   • Nuclear Reactions - fission vs fusion
     • in 1920s, Gamow, Teller and Bethe suggested that the conversion of matter into energy might power the Sun - such conversion is possible through nuclear reactions - fission reactions are those where heavy atomic nuclei are broken down into lighter nuclei - fussion reactions are those where light atomic nuclei come together to form heavier atomic nuclei
     • Fusion in the Sun
       • - the primary source of power in the Sun is the p-p (proton-proton) chain - in the p-p chain, protons collide directly with other protons - to overcome the electromagnetic repulsion, extreme temperatures are required - the centre of the Sun has a temperature of about 15 million K
       • P-P chain reactions
         • p-p chain is a series of 3 nuclear reactions - the first reaction fuses 2 protons to become deuterium and releases a positron and neutrino - the second reaction fuses a proton with deuterium to become helium-3 and releases a game ray - the third reaction fuses 2 helium-3 nuclei to become helium-4 and releases 2 protons
     • Fusion reaction
       • - the strong nuclear force holds the nucleus together - during fusion, as the new nucleus comes together, some of the nuclear energy (called binding energy) is released - when binding energy is released, the resulting nucleus has slightly less mass than before - the missing mass was converted into the binding energy
       • Fusion of 4 H atoms into 1 He atom
         • - the difference in mass of the reactants and product is converted into energy - we can use E = mc^2 to calculate the energy generated from the difference in mass (matter) - to produce the luminosity of the Sun, 600 million tons of H is converted to He every second, with about 4 million tons of matter being converted into energy every second

3. Temperature Regulation

   • - if the centre of the Sun could be heated slightly, the nuclear reactions could occur faster and hence release more heat, so the sun's core would expand and hence cool back to its previous temperature - a hotter core has more nuclear reactions and gives off more heat - when a gas is heated, it expands - the energy produced by the additional fusion reactions causes the core to expand - an expanding gas cools down, so the expanding core cools down - the core then cools back to its previous temperature => hence, the temperature of the Sun stays about the same

4. Energy Transport

   • Photons
     • - in the core, the energy is transported by radiation - the gamma rays from fusion diffuse outward, losing energy in each encounter - in the core, a photon can travel about 0.006 cm before being scattered - in the outer part of the Sun, a photon can travel about 5 cm, on average before being scattered - at each scattering, the photon is just as likely to head back toward the center as out to the surface - this back-forth motion means that on average, it takes 23,000 years for a photon to escape from the core of the Sun
   • Neutrinos
     • unlike photons, neutrinos do not interact with matter so easily. this means that neutrinos can stream out of the sun almost directly
   • Convection
     • - in the outer part of the Sun, convection transports the energy: currents of hot material rise whole cool material sinks - convection is the process where hot gas rises and cool gas sinks: this brings energy to the upper layers of the atmosphere. - in the Sun, this also occurs in the interior: hot gas rises to the surface and cooled gas sinks to the interior

5. The Solar Interior

   • Solar Seismology
     • - to study the solar interior, we use technique from seismology - disturbances in the Sun creates pressure waves (sound waves) - since these waves propagate through the sun, they can be used to probe the interior of the Sun (like earthquakes here on Earth) - on the surface the waves appear as up and down oscillations of the solar surface - this movement is typically a few km with time scales of 5-10 minutes - the differences between the convective and radiative zones shows up in the surface waves
   • Neutrino Astrophysics
     • Neutrino
       • - neutrinos are tiny, electrically neutral, sub-atomic particles -neutrinos do not often interact with matter (for example, it takes about a light year of lead to stop a neutrino) - therefore, they escape from the Sun in about 2 seconds without interacting with any of the material in the Sun - since they are created in the nuclear reactions in the Sun, they are direct probe of the current conditions at the centre of the Sun  - about 3.5 x 10^16 neutrinos pass through your body each second (even at night)
     • Neutrinos in the Sun
       • - the neutrinos produced by the p-p chain have low energy and are difficult to detect - other nuclear reactions take place in the Sun that produce higher energy neutrinos - these reactions happen so rarely, that they do not contribute appreciably to the total energy output, but they are sensitive to the conditions in the core of the Sun - these reactions involve helium fusion - helium tries to fuse into heavier elements but the conditions are not quite right yet - these fusion reactions produce a higher energy neutrino. detecting these neutrinos requires a lot more effort
     • Homestake Gold Mine
       • 1970 to 1994, Raymond Davis Jr. conducted an experiment to look for solar neutrinos - a tank containing about 100,00 gallons of cleaning fluid was placed nearly a mile underground - some neutrinos may interact with the chlorine in the tank - these neutrinos interact with a chlorine-37 nucleus to produce radioactive Argon - the radioactive Argon can be flushed from the tank and detected - in factm 1 atom of radioactive Argon is produced every 3-4 days which implies that the Sun is giving off a factor of 3-4 less neutrinos than expected
     • Super-Kamiokande
       • - a newer experiment that can detect astrophysical neutrinos - uses 50,000 tons of ultra-pure water - when a neutrino strikes a nucleus, debris from the impact produces blue light which can be detected by 11,146 photomultiplier tubes on the walls - it is sensitive to high energy muon neutrinos from interactions between cosmic rays and the Earth's atmosphere showed that neutrinos have minuscule mass and may oscillate from one type to another - it can also detect the low energy electron neutrinos from the Sun, and finds only 36% of that expected
     • Neutrino oscilation
       • - there are three flavors of neutrinos: electron, muon and tau neutrinos  - the sun produces only electron neutrinos - we might be measuring too few electron neutrinos from the Sun because they changed into other kind of neutrino before reaching the Earth - we can test this using neutrinos created in the Earth's atmosphere when cosmic rays strike - experiments show that the neutrinos oscillate from one flavor to another

6. The Solar Surface

   • - the visible top layer of the convection zone is granulated with areas of upwelling material surrounded by areas of sinking material - hot gas appears brighter, cooler gas appears darker - spectroscopy tells us what elements are present on the surface
   • Sun spots
     • - sun spots are dark spots on the surface of the sun - these are slightly cooler regions so they are dark - sunspots come and go, typically in a few days - these are linked by pairs of magnetic field lines - the strong magnetic field inside a sunspot prevents plasma from entering - the magnetic fieldd can also split spectral lines - this lets us detect and measure the magnetic fields

7. The Solar Atmosphere

   • - the solar atmosphere is very different from a planetary atmosphere
   • Photosphere
     • - is the disk that is visible from earth and space - most of the light comes from this layer
   • Chromosphere
     • - the inner part of the sun's atmosphere - the cooler chromosphere is above the photosphere - very low density, about 10^-4 times as dense as the photosphere ad 10^-8 times as dense as the earth's atmosphere -difficult to see directly as the photosphere is too bright - mostly reddish from the hydrogen-alpha emission
     • Spicules
       • small storms in the chromosphere create filaments known as spicules
   • Corona
     • - outer part of the sun's atmosphere, is above the chromosphere - the chromosphere and corona are very faint compared to the photosphere - this is a very low density, high temperature region - the ionization levels of some gases suggest that the temperature is 3,000,000 K - the temperature rise is not fully understood but magnetic disturbances from the photosphere are thought to be involved

8. Solar Magnetism

   • - the sun has a strong magnetic field and differential rotation - sunspots originate when magnetic field lines are distorted by the sun's differential rotation - differential rotation stretches out the field lines - they eventually form loops
   • Solar cycles
     • - as the magnetic field lines twist around the sun, the sunspots also seem to appear progressively closer to the equator - the sun's magnetic field changes on a 22 year cycle - every 11 years, the magnetic poles flips. in each 11-year-half-cycle, there is a maximum where the number of sunspots is greatest - the solar cycle is not very regular (the time between successive hal-cycles can range between 7-15 years) - even more uncertain is the century-scale solar cycle (historical records 1645-1715 had very few sunspots - reasons uncertain)
   • Magnetic loops
     • - the gas on the surface of the sun is hot enough to be plasma - the magnetic field forces the plasma along field lines - because hot gas cannot enter a sunspot, it remains cooler than the convection cells - hot gas gets trapped inside the magnetic loops instead - sunspots are often associated with active regions of the sun