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11. The Sun
Goals:
1. Examine the characteristic features of the Sun ―
photosphere, chromosphere, corona ― and how they
change with time.
2. Study the activity cycle of the Sun and learn about its
deep interior, where sunlight is generated.
3. Use some hydrodynamics to understand the heating
of the solar chromosphere and corona.
A typical view
of the Sun: a
spherical star
that exhibits
limbdarkening
(brightness
drops towards
the edge) and a
nearly
featureless
disk.
The Sun has increased in size and temperature
since it first formed 4½ billion years ago.
Predicted temporal variations of the Sun’s parameters
from stellar evolutionary models.
Like all stars, the Sun
is in hydrostatic
equilibrium (balance),
otherwise its size
would change very
quickly ! The weight
of each layer in the
Sun is balanced by the
buoyant force exerted
by the pressure
exerted by gas below
it. The pressure comes
from radiation (light)
and the high
temperature of the
gas. The ultimate
power source is
nuclear fusion in the
Sun’s core.
G M ( r )  dr
 dP 
2
r
or
dP  G M ( r ) 

2
dr
r
The core is where hydrogen is converted to helium via the
proton-proton chain, Tcritical = 10 million K.
H1 + H1 → D2 + positron + neutrino
D2 + H1 → He3
He3 + He3 → He4 + 2H1
The proton-proton chain in the 15 million K
Sun’s core simplified.
The source of energy in the Sun’s core is the same as
that which powers an H bomb (hydrogen bomb).
The short-wavelength gamma rays produced in the core
of the Sun gradually diffuse outwards, scattered
(absorbed and re-emitted at slightly lower energies) to
longer wavelengths by interactions with gas atoms and
ions until they eventually emerge at the Sun’s surface
10,000-200,000 years later as visible light photons.
Neutrinos, on
the other hand,
do not interact
with gas atoms
and ions at all,
and reach
Earth 8⅓
minutes later,
detected only
through the
occasional
interactions
they make with
atoms of some
substances.
The Solar Neutrino Problem
The observed flux of neutrinos at Earth is on the
order of ⅓ to ½ the amount predicted by the
Standard Solar Model. Current thinking in
subatomic physics suggests that the electron
neutrinos generated in the Sun’s core are
oscillating between the states of electron, muon,
and tau neutrinos on their way to Earth, so that
detectors on Earth, tuned to detect electron
neutrinos, are missing two thirds of the neutrinos
actually generated by the Sun.
The variation of hydrogen and helium composition with
radius within the Sun.
The heat of the Sun diffuses outwards by simple
radiative transfer in the deep interior, but is
helped by convective eddies over the last 28.6%.
Solar granulation: an indication
of the outer convective region of
the Sun. Shock waves from the
convection zone also heat the
gas in the solar chromosphere
and corona to very high
temperatures.
The active Sun,
displaying
prominences
and flare
activity.
The solar granulation and model (lower).
Models of the Sun’s interior make use of
mathematical relationships describing the
conditions of hydrostatic equilibrium, thermal
equilibrium, radiative equilibrium, and the
general continuity of mass in the Sun in order to
calculate the mass, density, temperature, and
pressure at all points in the solar interior.
The “standard solar model” is well verified by
observation, including helioseismology, which
matches the oscillations seen at the Sun’s surface
with the parameters of seismic waves passing
through the Sun’s outer regions. Neutrinos
detected from the Sun’s core also provide
information about the nuclear reactions
occurring there.
Helioseismology.
The variation of mass and density with radius within the
Sun.
The variation of luminosity and energy generation with
radius within the Sun.
The variation of pressure and temperature with radius
within the Sun.
The variation of pressure/temperature gradient with
radius within the Sun.
Where different portions of spectral lines are formed in
the solar photosphere.
The Sun, Earth to scale, and sunspots.
Bright = Hot
Dark = Cool
White light images of the
Sun showing sunspots, limb
darkening, and the solar
rotation. The orange
“surface” is the solar
photosphere = light sphere.
The motion of sunspots across the Sun’s disk
indicates that the Sun rotates differentially, that is
the equatorial regions rotate faster than regions
near the poles. Observations indicate a rotational
period of 24½ days at the solar equator and 30
days 60° away from the equator, corresponding to
observed rates from Earth (synodic rates) of ~27
days and ~32 days, respectively.
Differential rotation also occurs in the gaseous
planets Jupiter and Saturn. On the Sun it is
responsible for twisting up the subsurface
toroidal magnetic field.
Nomenclature for sunspot features.
Sunspots are cool
regions (T ~
4500K) of the
photosphere,
where strong
magnetic fields
have restricted
normal
turbulence.
Because they are
cooler than the
surrounding
photosphere (T ~
5800K) they are
less radiative, and
appear dark
through contrast
with the brighter
photosphere.
A complex sunspot group.
The limb darkening of the Sun has a similar
explanation. Our line of sight at the edge of the
solar disk penetrates to shallower, cooler depths
than does the line of sight at disk centre.
The “optical depth” to which we can see into the Sun’s
photosphere (“photon” sphere) is about the same no
matter where we look, but we can see to deeper, hotter
regions near disk centre.
Sunspots, and the sunspot cycle of ~11 years. The
number of spots increases rapidly and declines
slowly during the 11-year sunspot cycle. (Sunspot
number is a curious function that counts 10 for
each spot group, and 1 for each individual spot.)
Sunspot numbers.
Recent sunspot
numbers
Sunspots are
associated with
strong magnetic
regions of the
photosphere, and
cycle through
different latitude
regions during
the 11-year cycle,
beginning near
both poles,
ending near the
equator
(“butterfly”
diagram).
The Butterfly Diagram.
Holland in winter during the Maunder Minimum.
The chromosphere
as seen in the light of
Hα radiation (right)
and at the limb,
where spicules are
visible (below right).
Close-up view of spicules.
In order to understand the heating that occurs in the
Sun’s chromosphere and corona, it is necessary to
consider the situation in terms of hydrodynamics.
Rewrite acceleration as:
d 2 r dv dv dr
dv
accelerati on  2 

v
dt
dt dr dt
dr
The condition for hydrostatic equilibrium is therefore:
dv
dP
M r
v  
G 2
dr
dr
r
where v is the velocity of the flow and ρ is the gas density.
The conservation of mass flow across boundaries
becomes:
4 r v  constant
2
or
d  vr2 
0
dr
At the top of the Sun’s outer convection zone the upwards
motion of the hot, rising gas bubbles and the return flow
of cool gas creates longitudinal (pressure) waves that
propagate outward through the solar photosphere and
into the chromosphere. The wave energy associated with
this outwards flux is the product of the wave energy and
the speed of sound waves in the medium, namely:
FE  12  vw2 vs
where vs is the local sound speed and vw is the velocity
amplitude of the oscillatory wave motion for individual
particles being driven by the convection. Since:
 kT
 kT
vs   P   

 T
 mH
 mH
for fixed γ and μ, it follows that sound speed must
decrease with decreasing temperature in the photosphere.
Initially the longitudinal waves generated near the top of
the solar convection zone travel at subsonic speeds, but
that changes as they near the top of the photosphere
where the sound speed is lower. At that point the
longitudinal waves generated by convection become
supersonic and develop into shock waves. Shock waves
are characterized by a very steep density change over a
short distance, called the shock front. As a shock front
moves through a gas it produces a large amount of
localized heating via collisions. That heating is produced
at the expense of the mechanical energy of the shock, and
is quickly dissipated.
The constant replenishment of rising gas bubbles from
the convection zone produces a constant source of shock
heating in the gases lying above the solar photosphere, i.e.
in the solar chromosphere.
Magnetic fields produce further complications.
Magnetic field lines on the Sun and constraint of ions.
Active (magnetic)
regions in the solar
chromosphere seen in
spectroheliograms
taken in the light of
Ca K radiation.
Bright regions are
called plages or
faculae.
More views of the
chromosphere from Hα
spectroheliograms. A solar
flare is developing at right.
Active regions
on the Sun
are associated
with sunspot
zones, which
are 5° to ~30°
away from
the Sun’s
equator.
Prominences
associated with
sunspots
protrude into
the solar corona.
Their “feet” rest
on active
sunspots.
Solar prominences seen on the limb.
Features of the solar
corona can be seen
in X-rays (right) or
radio images
(below), which
isolate hot regions,
even when gas
density is low.
The Babcock mechanism as a qualitative
explanation for the solar cycle of activity.
The Babcock
mechanism
(part 2) as a
qualitative
explanation
for the solar
cycle of
activity.
The solar corona. Its extent varies with the
sunspot cycle (largest during sunspot maximum).
Solar corona showing coronal holes.
The magnetic
Sun.
The active Sun,
displaying
prominences
and a time
sequence of a
flare
developing.
Solar flare debris injected into the solar wind, eventually
to reach Earth a few days later.
The auroral zone on Earth lies within 20° to 30°
of Earth’s magnetic poles.
Displays of the aurora borealis.
Noctilucent clouds, perhaps an indicator of solar
activity but more likely of climate change.
Astronomical Terminology
Photosphere = light sphere. The region (disk) of the Sun
from which light appears to originate. It also
constitutes the solar atmosphere.
Chromosphere = coloured sphere. The region lying
above the solar photosphere containing spicules
where the temperature increases with height.
Corona = crown. The outermost region of hot gases
surrounding the Sun where temperatures reach 12 million K, and where the solar wind originates.
Sunspot cycle. The interval of ~11 years over which
sunspot numbers increase and wane.
Proton-proton chain. The sequence of nuclear reactions
in which hydrogen nuclei (protons) interact and
are fused to become helium nuclei (α particles),
with the release of energy.
Convection zone. The upper 29% of the Sun where
energy is carried by convective bubbles of hot gas.
Astronomical Terminology (continued)
Granulation. The mottled structure of the photosphere
caused by hot bubbles of gas at the Sun’s surface.
Spicule. A spikey jet of hot gas from the solar
chromosphere erupting into the solar corona.
Prominence. Huge gaseous eruptions of arching clouds
of ionized particles streaming between sunspots of
opposite polarity through the corona.
Filament. The dark projection of a prominence viewed
against the Sun’s surface in monochromatic light.
Sunspot. A region of cool gas (T ≈ 4500K) in the
surrounding solar photosphere (T ≈ 5800 K)
appearing as a dark penumbral region, often with
a surrounding gray penumbra, that is the site of
strong magnetic field.
Floculli, Plages. Light and dark markings in the solar
chromosphere seen in monochromatic images of
the Sun.
Astronomical Terminology (continued)
Maunder Minimum. A period of ~60 years in the late
1600s and early 1700s when sunspot numbers were
at an unusual low and northern hemisphere
winters were unusually cold. Possibly related to
Spörer minima at earlier epochs when sunspot
activity may also have been low.
Optical Depth. How far into the Sun’s photosphere we
can see before the gas becomes completely opaque.
Neutrino. A nearly massless nuclear particle that travels
at nearly the speed of light and is produced during
the production of a deuteron through a collision of
two protons.
Solar Wind. The stream of ionized and neutral gas
particles away from the Sun.
Aurora Borealis = Northern Lights. Radiation produced
in Earth’s upper atmosphere by the streaming of
charged particles towards the magnetic poles.
Sample Questions
10. In the proton-proton chain process, the mass
of four protons is slightly greater than the mass
of a helium nucleus. Explain what happens to this
difference in mass.
Answer. The difference in mass is accounted for
by the energy released in the process in the form
of gamma rays, neutrinos, and positrons.
14. The Sun has a radius equal to about 2.3 light
seconds. Explain why a gamma ray produced in
the Sun’s core does not emerge from the Sun’s
surface 2.3 seconds later.
Answer. The ionized gas near the Sun’s core is
opaque to gamma rays and absorbs the photons
before they can travel very far. The light is reemitted as photons of slightly lower energy in
random directions, repeating the absorption and
re-emission process a multitude of times before
the light eventually emerges at the Sun’s surface.