Download 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.
• 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
a
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 Mainsequence 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.
2.
3.
4.
5.
How do we know?
Core
Radiative Interior
(Tachocline)
Convection Zone
Photosphere
Visible Sun
1. Photosphere
2. Chromosphere
3. Transition Region
4. Corona
5. (Solar Wind)
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
radius
R
luminosity L
1.99 x 1030 kg
6.96 x 108 m
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 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
Mass:
θ
Sun
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
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. )
d
L
f
solar “constant” ' 1368 W m-2
Chemical composition of the Sun
d1
d2
Similar to typical composition in the universe:
Hydrogen
~70% by mass
Helium
~30%
Heavier elements ~1-2%
X
Y
Z
O, C, N, Ne, Fe, … in order of abundance
Observational data: solar spectrum, meteorites
Hydrostatic equilibrium
Assumptions
•Sun’s structure is spherically symmetric
~ 10-5
Asphericity
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)
pressure
dp
  g
dr
gravity
Now...
O
r
mass m(r)
So...
But by definition of m(r)
Two
differential
equations
describing the
structure of
the
solar interior
-- but 3
functions
m(r), p(r), ρ(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 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
Thermal timescale (Kelvin-Helmholtz timescale)
Nuclear fusion
Hydrogen  Helium
4 1H
Mass:
4 mH

4He
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:
Sources included if temp
large enough
Composition characterized by abundances X, Y, Z of H, He and the rest
Plus models of convective processes, when temperature gradients
get large enough...
Solar Core
Central 25% (175,000 km)
Temperature at centre 1.5 x 107 K
Density at centre
150 g cm-3
Temperature at edge 7 x 106 K
Density 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 He4 and
neutrinos (n).
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 radiation
Density 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 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).
Structure of Sun
according to a
Standard solar model
Density
ρ (103 kg m-3)
150
Temperature
T (106 K)
15
0
radiative
0
convective
0.5
r / R
1.0
0
0
0.5
r / R
1.0
p (1016 Nm-2)
Pressure
2
0
0
0.5
r / R
1.0
4
L (1026 W )
Luminosity
Hydrogen abundance
0.7
0
X
0
0.5
r / R
1.0
2
0
0.5
r / R
1.0
ε (10-3 J s-1kg-1)
0.4
Energy generation rate
0
0.5
r / R
1.0
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.
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)
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)
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.
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.
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