The Sun

        A: What is the Sun?

  • The Sun is a large (2 x 1030kg) ball of hot gas. It's surface temperature is 5800K.
  • The Sun exhibits limb darkenning: the edges are darker than the center of its disk. This tells us that it gets hotter the deeper we look, since at the center of the disk we are seeing deeper inside than at the edges.
  • We also see absorbtion lines in the Sun's spectrum, telling us that there is cooler atmosphere over the hot visible surface. The lines indicate that the Sun is composed mainly of hydrogen and helium, with about 2% ``metals'' (all other elements). The most common ``metals'' are oxygen, carbon, and nitrogen.
  • The interior must be much hotter than the surface, because energy is flowing outward.
  • Limb darkenning also tells us that the surface isn't solid. At 5800K, most ``metals'' are ionized. At the interior temperatures, even hydrogen and helium are ionized. Hence the Sun is really a plasma ("gas" of charged particles).
  • A hydrostatic equilibrium exists: the outward pressure gradient equals the inward force of gravity.

    B: What powers the Sun?

  • Neither chemical nor gravitational energy can be the Sun's energy source, because neither could have kept it shining for the last 4.5 billion years.
  • Only nuclear reactions provide enough energy to keep the Sun running that long. Also, the Sun is a source of neutrinos, massless particles produced in nuclear reactions.
  • Nuclear fusion in the Sun takes place through the proton-proton chain:
    • 2 x (1H + 1H -> 2D + e+ + neutrino + gamma)
      2 x (e+ + e- -> 2gamma)
      2 x (2D + 1H -> 3He + gamma)
      3He + 3He -> 4He + 1H + 1H + gamma
      ----------------------------------------------------
      41H + 2e- -> 4He + 8gamma + 2 neutrino

    where H is hydrogen, D is deuterium (heavy hydrogen), He is helium, e+ is a positron (positive electron), and gamma is a gamma ray photon.

  • This can only occur at high temperatures (T = 107K). At lower temperatures, the protons (1H) are moving too slowly and so can't make it past the electrostatic barrier (like charges repel).
  • The energy produced (photons and neutrinos) comes from the mass of the original four 1H's, which weigh a little more than the 4He. The difference becomes energy given by E = mc2.
    • Delta m = 6.6943 x 10-27kg - 6.6466 x 10-27kg = 4.8x 10-29kg
      E = 4.8 x 10-29kg x (3 x 108m/s)2 = 4.3 x 10-12 Joules
  • 1 gram of H produces 6.4 x 1011 Joules. A 100 watt lightbulb uses 100 Joules/s, so 1 gram of H could power of lightbulb for 6.4 x 109 seconds = 200 years.
  • The Sun has 2 x 1033 grams of material, most of it hydrogen. Using all of this would give 1.3 x 1045 Joules. The Sun puts out 4 x 1026 Joules/s, so in principle it could last for 3 x 1018 seconds = 1011 years.

    C. Solar Structure and Energy Transport

  • The core of the Sun gets up to 15 x 106K, and the density reaches 150 g/cm3. This is the only part of the Sun hot and dense enough to allow the P-P chain to occur. Since the Sun is opaque, we don't see the core directly. Instead, it's energy has to be processed through the body of the Sun before escaping into space.
  • From the core most of the way to the surface, energy is transported radiatively. Photons are emitted by one ion and absorbed by another. As we move out from the center, the temperature drops. At 2 x 105km below the surface, the temperature reaches 2 x 106K.
  • At this point, convection takes over as the main form of heat transport. Hot packets of material rise up, transfer their energy upwards, and then descend back down as cool packets.
  • The convection ``cells'' (regions in which material cycles) get smaller as we approach the surface. At the bottom they are 30000km across. Near the Sun's surface they are only 1000km across.
  • The visible surface of the Sun is the photosphere. The temperature is 5800K, and the density is 10-7g/cm3. From here, light escapes out into space.
  • The photosphere appears ``grainy'', with individual granules about 1000km across. The centers are bright, while the edges are darker. These are the convection cells.
  • There are spots on the Sun. These are cool areas (4500K) on the surface. They appear dark because they are substantially cooler than the surrounding surface of the Sun. From the Steffan-Boltzman law we have (4500K/5800K)4 = 0.36. Thus, sunspots are only 1/3 as bright as the surrounding photosphere.
  • Sunspots are associated with the Sun's magnetic field. Strong magnetic fields make convection difficult, so heat doesn't get transported to the surface well, and it cools off.
  • The Sun's atmosphere consists of the chromosphere and the corona. These are most easily studied during a total solar eclipse, when the Sun's disk is blocked out.
  • About 500km about the photosphere, the temperature starts increasing rapidly (minimum temperature = 4500K). This turnaround area is the chromosphere.
  • The chromosphere appears as an irregular red region along the edge of the Sun. The colour is from a hydrogen emission line (H-alpha) at 6563Å.
  • There is a transition zone leading up to the corona. The temperature in this region rises up to 106K.
  • The corona is the high temperature limit of the atmosphere. It is very irregular, and glows in the emission lines of highly ionized ``metals''.
  • At 107km above the photosphere, the corona can escape from the Sun and form a ``solar wind'', moving away at 500km/s.
  • Prominences above the strong magnetic fields (spots) on the surface. The solar wind escapes mainly through areas of weak magnetic field. In X-ray photos these weak field areas are called coronal holes.
  • Solar Cycle #23
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