SOLAR LIFETIME VIA FUSION ENERGY GENERATION

Converting 4 H nuclei into one 4^He nucleus turns about 0.007 (0.7%) of their masses into energy.

  • Typical energy per nuclear reaction is 1 MeV or 1.6 x 10^{-6} erg
  • So number of reactions needed/second = Solar luminosity/Energy per reaction
  • No / sec = 4 x 10^{33} erg/s / 1.6 x 10^{-6} erg = 2.5 x 10^{39}/s
  • Roughly, one proton is used up per reaction and therefore
  • Mass used/sec = m_p x No /sec = (1.67 x 10^{-24} g) x (2.5 x 10^{39}/s) = 4 x 10^{15} g/s
  • Solar lifetime = Solar mass/(Mass used/sec) = (2 x 10^{33} g)/ (4 x 10^{15} g/s)
    = 5 x 10^{17}s = 1.6 x 10{10} years.

    All of these numbers are approximate, the correct value is just under 1.0 x 10^{10} years.

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    THE SOLAR ATMOSPHERE

    PHOTOSPHERE: visible, IR and UV continuum radiation streams out from here.

  • Thickness about 400 km
  • 4500 < T < 5800 K; usually say T_s = 5760 K
  • density between 10^{-5} and 10^{-8} g/cm^3
  • emerging spectrum is continuum (from dense lower layer)
    with superposed absorption lines (from less dense, cooler outer layer)

    CHROMOSPHERE: mostly UV emission line radiation

  • Irregular thickness, averaging 5000 km in SPICULES
  • 4500 < T < 10,000 K (up to 50,000 K in transition zone)
  • density averages around 10^{-10} g/cm^3
  • only visible when photosphere is obscured

    CORONA: mostly X-ray emission

  • Irregular thickness, typically out to 2-3 times Solar radius
  • Average T = 1 x 10^6 K
  • extremely low density
  • only visible when photosphere is obscured or via X-ray telescopes
  • heated via magnetic energy orginating in the convective zone of the sun:
    probably by both magnetohydrodynamic shocks and magnetic reconnection.

    WIND: small amount of matter boiled off CORONA

  • Typical speed, 500 km/s (roughly the Sun's escape velocity)
  • Mostly protons, Helium-4 nuclei (also called alpha particles) and electrons
  • Continually hitting earth's magnetosphere

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    THE SUN'S ATMOSPHERE IS VERY ACTIVE

    Most spectacular are FLARES (very big) and PROMINENCES (big).

  • These can extend to 100,000 km or more into the corona.
  • Typically large amounts of matter following magnetic field lines.
  • The energy is released by changes in magnetic field configurations.

    Big flares yield COSMIC RAYS, charged particles moving close to the speed of light.

  • Mostly protons, then electrons, alpha particles (4^He nuclei) and other nuclei
  • These cosmic rays can penetrate to the earth's atmosphere, yielding
    spectacular auroral displays, power grid failures and disrupt communications.

    CORONAL MASS EJECTIONS (CMEs) involve a great deal of energy too.

  • CMEs are temporary features where matter flows out along open magnetic field lines.
  • These are less explosive than flares, and were unknown until satellites trained
    UV and X-ray telescopes on the sun.

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    The more mundane activity is shown by SUNSPOTS.

  • Measuring them proved that the Sun rotates differentially
    (faster at equator), and is therefore a fluid.
  • Mean sidereal Period for the Sun is about 26 days.
  • The synodic period is a bit longer.
  • Sunspot number fluctuates, reaching a maximum every 11 years.
  • At minima, spots are further from the equator, and get closer during maxima.

  • Magnetic polarities of spots reverse every 11 years so that the
    FULL SOLAR CYCLE is 22 years long.
    I.e., if the N hemisphere leading spots now are N poles,
    the N hemisphere trailing spots are S polls, BUT the S hemisphere leading spots
    now are S poles, and the S hemisphere trailing spots now are N polls,
    BUT 11 years from now the polarities are opposite.

  • Sunspots are dark because they are cooler
    (roughly 4000 K instead of 5760 for the rest of the photsphere).
    This means their fluxes (proportional to T^4) are roughly a quarter as large,
    so they are dark only in comparison to the surrounding bright surface.
  • Sunspots are cooler mostly because their strong magnetic fields
    (typically 300 Gauss vs 1 Gauss in the rest of the photosphere)
    inhibit convection and therefore heat (and radiation) flow.
    The magnetic fields also add a pressure that compensates for the lower thermal pressure in them.

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    MAGNETIC FIELDS are produced only if all of these are present:

  • Differential rotation
  • Fluid (liquid, gas, plasma)
  • with magnetic properties: ionzied H for Sun, metallic H
    for Jupiter and Saturn, molten iron/nickel outer core for Earth.

    We didn't get to this last point in today's lecture and will cover it at the beginning of the next one.