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The structure and dynamics of the Solar Interior

The structure and dynamics of the Solar Interior. Steve Tobias (Leeds). 5th Potsdam Thinkshop, 2007. Solar Observations: A brief history 1. 1223 BC: First Eclipse record. Clay tablet in Ugarit, Babylonia. 8 th C BC. Babylonians systematic record of eclipses.

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The structure and dynamics of the Solar Interior

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  1. The structure and dynamics of the Solar Interior Steve Tobias (Leeds) 5th Potsdam Thinkshop, 2007

  2. Solar Observations: A brief history 1. • 1223 BC: First Eclipse record. Clay tablet in Ugarit, Babylonia. • 8th C BC. Babylonians systematic record of eclipses. • ~800 BC. First sunspot observation • “A dou is seen in the Sun”, Book of changes, China. For more details on Solar history see: http://www.hao.ucar.edu/public/education

  3. a Solar Theory: A brief History 2 • The Aristotelian View • Aristotle (384-322 BC). Earth at centre of Universe • Ptolemy (100-170 AD) • ~200 BC. First calculation of distance to Sun (Aristarchos of Samos) • Got EM/ES = 19 • True value EM/ES=397

  4. Solar Theory: A brief History 3 • 968 AD – First mention of Corona (Diaconus) • “At the fourth hour of the day…darkness covered the Earth and all the bright stars shone forth. And it was possible to see the disk of the Sun, dull and unlit, and a dim feeble glow like a narrow band shining in a circle around the edge of the disk”. • 1128 AD – First Sunspot drawing (John of Worcester) • “…from morning to evening, appeared something like two black circles within the Sun, the one in the upper part being bigger, the one in the lower part smaller”

  5. Solar Theory: A brief History 4 • 1543 Copernicus moves the Sun to the centre, with all planets orbiting in circular orbits • Kepler (1609) Sun at one focus of an ellipse. • Galileo (1610) First telescopic observations of Sunspots

  6. Solar Theory: A brief History 5 • Descartes (1644). Sun but one of many stars, each of which having formed at the centre of a primaeval vortex. • 17th C. Sunspots vanish – Maunder Minimum (see lecture 2). • Origin of Sunspots: Herschel (1738-1822) • Sunspots openings in Sun’s luminous atmosphere, allowing a view of the underlying cooler solar surface. • 1796 – Laplace. Nebular hypothesis. Sun and solar system formed from gravitational collapse of slowly-rotating, diffuse cloud of gas.

  7. Solar Theory: A brief History 6 • 1800 – Herschel discovers infrared radiation. • 1817 – Fraunhofer – solar spectral lines • 1907 – Hale – Zeeman splitting of spectral lines  magnetic fields in sunspots.

  8. The Sun as a star • Sun is a G2 Main-sequence star. • Its activity and structure can be related to that of many other stars “solar-type” stars. • As it has spun-down owing to magnetic braking its magnetic properties have changed. HR-diagram

  9. Solar Structure Solar Interior • Core • Radiative Interior • (Tachocline) • Convection Zone • Photosphere Visible Sun • Photosphere • Chromosphere • Transition Region • Corona • (Solar Wind) How do we know?

  10. Quick overview of the Sun’s properties A star is a self-gravitating mass of gas that radiates energy Mass  pressure  temperature  heat  luminosity Sun – our closest star Global properties: mass M 1.99 x 1030 kg radius R 6.96 x 108 m luminosity L 3.83 x 1026 W Sun-Earth mean distance  1 Astronomical Unit (A.U.) = 1.50 x 1011 m

  11. How are these quantities determined? Distance: Kepler’s 3rd law (P2 / D3)  relative scale of solar system but not absolute scale; then e.g. radar-ranging to Venus Earlier methods: transit observations; Greek astronomy Radius: Angular size of Sun + distance θ Sun Mass: Orbital motions of planets + distance  GM to high precision Age of the Sun Only known indirectly: radioactive dating of rocks; computed evolutionary models of the Sun. ~ 4.6 x 109 years

  12. Luminosity: Measure flux (energy per unit time per unit area) at Sun-Earth distance. Use inverse-square law: f = L / (4pd2 ) ( d = 1 A.U. ) L d f solar “constant”' 1368 W m-2 Chemical composition of the Sun Similar to typical composition in the universe: Hydrogen ~70% by mass X Helium ~30%Y Heavier elements ~1-2%Z O, C, N, Ne, Fe, … in order of abundance Observational data: solar spectrum, meteorites d1 d2

  13. pressure gravity Modelling the Sun's Interior Hydrostatic equilibrium • Assumptions • Sun’s structure is spherically symmetric • Define radial coordinate r -- distance from centre • Sun’s properties change so slowly that can neglect the rate of change • with time of these properties • Start with equation of hydrostatic balance (which is a good approximation) Asphericity ~ 10-5

  14. r O Two differential equations describing the structure of the solar interior -- but 3 functions m(r), p(r), ρ(r) Now... mass m(r) So... But by definition of m(r) In order to make progress, we need to relate the pressure to the density (and temperature and the constution of the gas!) Hence we need to know something about energy...

  15. Thermal timescale (Kelvin-Helmholtz timescale) Energy: How does the Sun shine? Could Sun’s energy source be gravitational energy? -- No. Total available gravitational energy = G M2 / R So could sustain present luminosity for time (G M2 / R ) / L  107 yrs By virial theorem, thermal time (if Sun were shining by cooling down) Is the same to within a factor 2. Neither can explain how Sun has shone for > 109 yrs

  16. Nuclear fusion Hydrogen  Helium 4 1H 4He Mass: 4 mH 3.97 mH E = m c2  energy production (0.03 mH) c2 i.e. fraction 0.007 of mass converted to energy This could power sun for tnuc ~ 0.007 M  c2 / L   1011 yr Note tdyn << tK-H << tnuc We’ll come back to this later

  17. Some simple estimates

  18. Energy transport Opacity depends on density, temperature and chemical abundances (in solar interior arises mainly due to bound-free absorption)

  19. Note: numerical value is not great, but functional dependence is qualitatively right! Note2: Opacity is very sensitive to temperature

  20. That’s it really...except • At some stage the temperature gradients may become large enough that the energy can not be carried by radiation (and convection sets in) • Energy production (fusion) can only take place if the temperature is high enough. • Where these occurs depends on the mass, age (etc) of the star

  21. Sources included if temp large enough Numerical modelling of the Sun's Interior Basic equations: Composition characterized by abundances X, Y, Z of H, He and the rest Plus models of convective processes, when temperature gradients get large enough...

  22. Solar Core Central 25% (175,000 km) Temperature at centre 1.5 x 107 K Temperature at edge 7 x 106 K Density at centre 150 g cm-3Density at edge 20 g cm-3 Temperature in core high enough for nuclear reactions. ENERGY p-p chain: 3 step process (above) leads to production of He4and neutrinos (n). Missing neutrinos (not as many detected as thought).Neutrino mass

  23. The Radiative Zone Extends from 25% to ~70% of the solar radius. Aptly-named: Energy produced in core carried by radiation photon radiation Density drops: 20 g cm-3 to 0.2 g cm-3 Temperature drops: 7 x 106 K to 2 x 106 K.

  24. The Convection Zone Extends from: 70% of the solar radius to visible surface. Radiation less efficient as heavier ions not fully ionised (e.g. C, N, O, Ca, Fe). Fluid becomes unstable to convection (which adiabatically mixes the fluid). Highly turbulent. Motion on large range of scales Temperature drops: from 2 x 106 K to 5,700 K. Density drops exponentially to 2 x 10-7 g cm-3 Convection visible at the surface (photosphere) as granules and supergranules (see later).

  25. 0 0.5 1.0 r / R 1.0 1.0 0 0 0.5 0.5 r / R r / R Structure of Sun according to a Standard solar model Density 150 ρ (103 kg m-3) Temperature 15 0 radiative convective T (106 K) Pressure 2 0 p (1016 Nm-2) 0

  26. 0 0.5 1.0 r / R 1.0 1.0 0 0 0.5 0.5 r / R r / R 4 Luminosity L (1026 W ) Hydrogen abundance 0.7 0 X 2 Energy generation rate 0.4 ε (10-3 J s-1kg-1)

  27. The Photosphere Visible surface of the Sun (100km) Limb darkening Photospheric features can be seen in white light. sunspots granules supergranules faculae Sun rotates differentially at the surface. (see Lecture 2) Equator ~ 24 days Poles ~ 30 days.

  28. The Photosphere: Sunspots Dark spots on Sun (Galileo) cooler than surroundings ~3700K. Last for several days (large ones for weeks) Sites of strong magnetic field (~3000G) Dark central umbra (strong B) Filamentary penumbra. (inhibit convection) Arise in pairs with opposite Polarity Part of the solar cycle (Lecture 2)

  29. The Photosphere: Granules Convection at solar surface can be seen on many scales. Smallest is granulation. Granules ~ 1000 km across Rising fluid in middle Sinking fluid at edge (strong downwards plumes) Lifetime 20 mins Supersonic flows (~7 kms-1)

  30. The Photosphere: Supergranules Can also see larger structures in convection patterns (Mesogranules) and Supergranules Seen in measurements of Doppler frequency. Cover entire Sun Lifetime: 1-2 days Flow speeds: ~0.5kms-1 Magnetic flux swept to edges Chromospheric Network.

  31. The Photosphere: Faculae Not all magnetic fields appear dark at solar surface. Small concentrations of strong magnetic field seen at limb appear bright. Actually win out over sunspots Over the solar cycle Sun appears brighter at solar maximum. Important for climate Different on other stars.

  32. So in summary... • The solar interior conditions are determined largely theoretically. • Can be checked to a certain extent using helioseismology. • The solar interior determines all the dynamics of the Sun-Earth system, by providing all the energy. • The activity of the Sun is all generated by the magnetic field which is generated by a hydromagnetic dynamo located in the solar interior. • With thanks to HAO, JCD, MJT

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