Post on 13-Jan-2016
transcript
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.
• 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
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
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”
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
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.
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.
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
Solar Structure
Solar Interior
1. Core2. Radiative Interior3. (Tachocline)4. Convection Zone5. Photosphere
Visible Sun
1. Photosphere2. Chromosphere3. Transition Region4. Corona5. (Solar Wind)How do we know?
A star is a self-gravitating mass of gas that radiates energy
Quick overview of the Sun’s properties
Mass pressure temperature heat luminosity
Sun – our closest starGlobal properties:
mass M 1.99 x 1030 kgradius R 6.96 x 108 mluminosity L 3.83 x 1026 W
Sun-Earth mean distance 1 Astronomical Unit (A.U.) = 1.50 x 1011 m
How are these quantities determined?
Distance: Kepler’s 3rd law (P2 / D3) relative scale of solarsystem but not absolute scale; then e.g. radar-ranging to VenusEarlier methods: transit observations; Greek astronomy
Radius: Angular size of Sun + distance
Mass: Orbital motions of planets + distance GM to high precision
θSun
Age of the Sun
Only known indirectly: radioactive dating of rocks;computed evolutionary models of the Sun. ~ 4.6 x 109 years
d
Luminosity: Measure flux (energy per unit time per unit area)at Sun-Earth distance. Useinverse-square law: f = L / (4d2 )( d = 1 A.U. )
solar “constant” ' 1368 W m-2
d1
d2
L
f
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
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
Hydrostatic equilibrium
gdr
dp pressure gravity
mass m(r)
Two differentialequations describing the structure of thesolar interior-- but 3 functionsm(r), p(r), ρ(r)
rONow...
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...
Energy: How does the Sun shine?
Could Sun’s energy source be gravitational energy? -- No.
Total available gravitational energy = G M2 / R
So could sustain present luminosity for time (G M2 / 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
Thermal timescale (Kelvin-Helmholtz timescale)
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
Some simple estimates
Energy transport
Opacity depends on density, temperature and chemical abundances(in solar interior arises mainly due to bound-free absorption)
Note: numerical value is not great, but functional dependence is qualitatively right!
Note2: Opacity is very sensitive to temperature
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
Basic equations:
Composition characterized by abundances X, Y, Z of H, He and the rest
Plus models of convective processes, when temperature gradientsget large enough...
Sources included if templarge enough
Solar Core
Central 25% (175,000 km)Temperature at centre 1.5 x 107 K Temperature at edge 7 x 106 KDensity at centre 150 g cm-3 Density at edge 20 g cm-3
Temperature in core high enough for nuclear reactions. ENERGYp-p chain: 3 step process (above) leads to production of He4 andneutrinos ().Missing neutrinos (not as many detected as thought).Neutrino mass
The Radiative Zone
Extends from 25% to ~70% of the solar radius.Aptly-named: Energy produced in core carried by radiation photon radiationDensity drops: 20 g cm-3 to 0.2 g cm-3
Temperature drops: 7 x 106 K to 2 x 106 K.
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 scalesTemperature 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).
radiative
Temperature
Density
PressureT
(106
K)
15
0
r / R
0 0.5 1.0
convective
r / R0 0.5 1.0
r / R0 0.5 1.0
2
0
150
p
(1016
Nm
-2)
ρ (
103
kg m
-3)
Structure of Sun according to a Standard solar model
0
Hydrogen abundance
Luminosity
Energy generation rate
X
0.7
0.4
r / R
0 0.5 1.0
r / R0 0.5 1.0
r / R0 0.5 1.0
2
0
4
ε (
10-3 J
s-1kg
-1)
L (
1026
W )
The Photosphere
Visible surface of the Sun (100km)
Limb darkening
Photospheric features can be seenin white light. sunspots granules supergranules faculae
Sun rotates differentially at thesurface. (see Lecture 2)Equator ~ 24 daysPoles ~ 30 days.
The Photosphere: SunspotsDark 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 oppositePolarity
Part of the solar cycle (Lecture 2)
The Photosphere: Granules
Convection at solar surface can be seen on many scales.
Smallest is granulation.
Granules ~ 1000 km across
Rising fluid in middleSinking fluid at edge (strong downwards plumes)
Lifetime 20 mins
Supersonic flows (~7 kms-1)
The Photosphere: SupergranulesCan also see larger structuresin convection patterns
(Mesogranules) and Supergranules
Seen in measurements of Dopplerfrequency.
Cover entire Sun
Lifetime: 1-2 days
Flow speeds: ~0.5kms-1
Magnetic flux swept to edgesChromospheric Network.
The Photosphere: FaculaeNot all magnetic fields appear dark at solar surface.
Small concentrations of strongmagnetic field seen at limbappear bright.
Actually win out over sunspotsOver the solar cycle
Sun appears brighter at solar maximum. Important for climate
Different on other stars.
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