The Sun and its Spots
Lukas Fried
Integrative Exercise
February 18, 2009
Outline
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Solar structure
Physical conditions in sunspots
Magnetohydrodynamics (MHD)
Solar magnetism and sunspot formation
Larger implications
The Core
 Center to 0.2R☉
 Hot gas at 15 million Kelvin
 No atoms, only nuclei and free
electrons and protons
 Proton-proton (p-p) chain
 1H + 1H → 2D + e+ + νe + 1.44
MeV
 2D + 1H → 3He + γ + 5.49 MeV
 3He + 3He → 4He + 1H + 1H +
12.85 MeV
 Enormous amounts of
liberated energy must escape!
The Radiative Zone
 0.2R☉ to 0.7R☉
 Energy from the core radiates
outward in the form of light
 Photons scattered by electrons,
protons, electron-bare nuclei
 Random walk scattering → 50
million years for energy to escape
completely
 Temperature falls to 1 million K
 Nuclei can now acquire electrons
 Bound electrons absorb and emit
photons
 Gases become opaque; radiation no
longer ideal
The Convection Zone
 0.7R☉ to almost R☉
 Energy transported outward
through convection
 Hot gas at the top of the
radiative zone builds up
 Bubbles (“convection cells”) of
the hot gas rise upwards
 Release energy at the solar
surface, cool, descend
 Convective currents
established as cells rise and
sink in regular patterns
Ideal Gas Law
Fbuoy
ρinside < ρoutside
Fgrav
Gases that are hotter than their surroundings
will be less dense than their surroundings.
Archimedes’ Principle: Buoyant force is the
weight of the substance displaced.
Hotter, less dense gases will be buoyed upward
because the buoyant force exceeds gravity.
Convective heat transfer
The Photosphere
 Outermost ~1000 km, the
visible part
 Visible because of radiating
light
 Small (Texas size) convection
cells called granules
 Granules rise to the surface,
radiate energy, sink
 This is where we see
sunspots
What is a
sunspot?
Let’s get physical.
The sun. Taken Oct. 6, 1894 at Goodsell Observatory, Northfield, Minn.
Umbra
Penumbra
Some Observations
 Wilson effect (Wilson, 1769) – depressions
 Periodic 11-year peak in number (Schwabe, 1843)
 Spörer’s law – drift towards equator
Sunspots are Dark
 Appear dark because they are cooler than the
surrounding photosphere (4200 K vs. 5800 K)
 Cooler objects radiate longer wavelength light, at
lower intensities. Hence, darkness.
Teff* 4 I *
 Stefan’s law
=
Teff
I
 Reason: Sunspots inhibit convection
 Results from their strong magnetic fields
 We’ll get back to this later
Sunspots are Magnetic
 0.4 T (4000 G) fields in and out of umbral centers,
normal to the photosphere, the strongest on the sun
 We know this from Zeeman splitting of spectral lines
B
Magnetic Monopoles? WHAT?!
, so having an isolated sunspot with a magnetic
field of only one polarity seems suspicious
 Solution: Sunspots form in bipolar pairs or groups, with
a preceding and following spot (Hale’s polarity law)
 Magnetic field lines link the two sunspots/groups
 This follows from the formation process
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–
+
–
A Refinement
+
–
+
–
Before, we treated the sun as composed of hot gas
This is not the full picture!
High temperatures → high ionization → plasma
Plasma is a partially ionized gas in which, on
average, there is no net charge. 4th state of matter.
 High ionization → + and – charge move
(somewhat) independently → good electrical
conductivity
 Moving charge generates magnetic fields
 Need to combine fluid dynamics with electricity and
magnetism…
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Magnetohydrodynamics
Behavior of electrically conducting fluids in magnetic fields
Ideal Gas Law
mmu P
r=
kB T
Statement of Continuity
Completely determine dynamics of a
magnetized plasma.
Equation of Motion
Induction Equation
On the order of
vB
l
On the order of
B
4psl 2
But the sun is an excellent conductor!
Therefore, conductivity is large and the right term
drops, leaving:
B evolves with the plasma velocity.
The plasma is literally dragging the magnetic field!
Shearing parallel to field lines does nothing.
Shearing perpendicular to field lines changes
line spacing, and therefore magnetic flux.
Closer lines, higher flux density, stronger net
field.
The Babcock
Model
(or why there are
sunspots)
Babcock Model: Stage 1
S
N
 Sun is initially an
“axisymmetric dipole”
 Magnetic field lines run from
pole to pole along lines of
longitude (“poloidally”)
 ~5G
 Thought to be generated by
electric currents in the
convection zone (dynamo
mechanism)
Babcock Model: Stage 2
 Sun rotates differentially
 w(f) =14.38° - 2.77°sin2 f
 Period of 26 days near equator
vs. 37 near poles
 Diff. rotation shears plasma
perpendicular to field lines
 Lines get distorted & begin to
wrap around equator
 Magnetic fields intensify as
field line spacing decreases
Babcock Model: Stage 3
 3 years have elapsed
 Field lines have been dragged
so that they wrap 5.6 times
around the sun at ±55°
latitude
 Fields are now mostly “toroidal”
 Many sunspots appear on the
surface at mid-latitudes
 Solar maximum
 Flux tubes
r=
mmu P
kB T
Flux Tube Cross Section
Pexternal = Pgas + Pmagnetic
Pgas < Pexternal
ρgas < ρexternal
Flux tube less dense than its
surroundings, so it will feel
“magnetic buoyancy” and rise up
through the convection zone!
Flux Tube Emergence
 Nonuniformities in convection
zone lead to kinking and
twisting of tubes
 More tightly twisted areas
have closer spaced field lines
 Closer spacing = greater flux =
more magnetic buoyancy
 Highly twisted regions rise up
through the convection zone
quickly
 Tube groups erupt out of the
photosphere in vertical Ωshapes
 At the points where the flux
tubes enter, we see…
SUNSPOTS!
Some Answers
 Bipolarity
 Sunspots form in bipolar pairs or groups because they are
fundamentally connected by the magnetic field lines of the
flux tubes that formed them.
 Darkness
 Magnetic pressure allows internal gas pressure to be less
than external gas pressure.
 Lower pressure means either lower density or lower
temperature inside (ideal gas law).
 Less dense plasma would rise more easily (convection aided).
WRONG ANSWER.
 Cooler plasma is less likely to rise up. RIGHT ANSWER.
 Sunspots are cooler than their surroundings. Convection is
inhibited and so radiation is less intense than photosphere.
Babcock Model: Stage 4
 Preceding (p) spots migrate
towards equator
 Follower (f) spots migrate
towards poles
 Fields from bipolar pairs
neutralize and replace weak
poloidal field
 Poloidal field now reversed
 11 years since beginning of
cycle
 Cycle starts over, but with
opposite poloidal polarities
 22-year cycle
Larger Implications
Reconnection → CMEs, space weather, etc.
Aurorae
Terrestrial radiowave propagation & electronics
Earth’s climate? – Maunder minimum & Little Ice
Age
 Economics
 Sunspot-like behavior on other stars?
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Acknowledgements
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Nelson Christensen
Joel Weisberg and Arjendu Pattanayak
Will Mueller
Nick Smith and Cindy Blaha
Brianne Gutmann & Marlea Iiams
Alex Dixon
Any questions?