the sun internal structure of the sun nuclear fusion –protons, neutrons, electrons, neutrinos...
TRANSCRIPT
The Sun• Internal structure of the Sun
• Nuclear fusion– Protons, neutrons, electrons, neutrinos– Fusion reactions– Lifetime of the Sun
• Transport of energy in the sun– Radiation versus convection
• The atmosphere of the Sun
Demos: 8B10.35, 4B20.10
The Sun
The Sun
The Sun
Properties of the Sun
• Mass = 21030 kg
• Radius = 696,000 km
• Luminosity = 3.81026 W
• Age = 4.6 billion years
• Surface temperature = 5,800 K
• Composition: 70% H, 28% He, 2% other
Properties of the Sun
Could chemical reactions power the Sun?
years000,80s103W104
J10 Lifetime
J10 availableenergy Total
10kg107.1
kg102 atomsNumber
J10eV10 atomper Energy
1226
39
39
5727
30
18
L
ET
NEE
M
MN
E
tot
atomtot
H
sun
atom
But the Sun is about 4.6 billion years old.
Could gravitational contraction power the Sun?
yearsmillion 30s10W104
J104 Lifetime
J104 energy nalGravitatio
1526
41
412
L
ET
R
GME
grav
grav
Better, but still off by a factor of 100.
Nuclear burning
Nuclear burningElementary particles
• Protons (orange) – found in nuclei, positive charge
• Neutrons (blue) – found in nuclei, no charge
• Electrons (e-) – orbit nuclei, negative charge
• Photons () – particles of light (gamma-rays)
• Positrons (+) – anti-matter electrons, positive charge (e+ in book)
• Neutrinos () – `ghost particles’, no charge, can easily pass through normal matter
Convert proton to neutron
• To convert a proton to a neutron
• A positron (+) and a neutrino () must be produced and released
Make nuclei out of protons and neutrons
1H = normal hydrogen nucleus = proton2H = deuterium hydrogen nucleus (unstable)
= proton plus neutron (in heavy water)3He = light helium nucleus (unstable(
= two protons plus one neutron4He = normal helium nucleus
= two protons plus two neutrons
Nuclear burning
Nuclear burning4(1H) He4 + energy + 2 neutrinos
MH = 1.67310-27 kg MHe = 6.64510-27 kg
J103.4McE
kg108.44122
F
2941
HeH
MMM
Rate of fusion reactions is:
/s109J104.3
J/s108.3 3712-
26
FE
L
Our Sun converts 4 109 kg of matter into energy each second.
Nuclear burning
J104
10J103.4
445
5712 H
Ftot
NEE
Total energy available is:
years108s103J/s104
J10 101826
45
L
ET tot
Lifetime is:
Internal Structure of the Sun
We want to make a model of the Sun, what do we need to know?
Gas in the Sun is in hydrostatic equilibrium
Fish in water are in hydrostatic equilibrium
Transport of energy through the radiative zone
Photons produced via fusion scatter many times in the Sun’s dense interior - a “random walk”.
Random WalkIn one dimension, a random walk can be thought of as tossing a coin: if heads then go left, if tails then go right.
Coin tosses follow the binomial distribution. For large numbers of tosses, the distribution becomes the `normal’ distribution.
The average total distance traveled for n steps of length l is: nlL
Random WalkThe same formula holds in 2 and 3 dimensions.
For the Sun, the average distance between collisions is about l = 1 mm. Photons travel at the speed of light, so the time between collisions is
t = l/c = 10-3 m /(3108 m/s) = 3 10-12 s
The radius of the Sun is L = 7108 m. The average number of collisions before a photon escapes is
n = (L/l)2 = (7108 m/ 10-3 m)2 = 5 1023
The average photon stays in the Sun for a time
T = tn = (3 10-12 s)(5 1023) = 1.5 1012 s = 50,000 years
A more accurate estimate gives 120,000 years
Q: A drunken pirate takes a 0.2 m randomly oriented step each second. He starts at the center of a small island of radius 20 m. On average, how long will it take before he steps into the ocean?
1. 20 sec
2. 100 sec
3. 1000 sec
4. 10,000 sec
5. 100,000 sec
Internal Structure of the Sun
Convective zone
Do the following transport energy by convection or radiation?
1. A gas oven
2. A microwave
3. A heat lamp
4. An electric radiator
Internal Structure of the Sun
• Equation of hydrostatic equilibrium
• Equation of mass continuity
• Equation of state
• Equations of energy production and transport
2
)()(
r
rrGM
dr
dP
)(4 2 rrdr
dM
pm
rkTrrP
)()(
)(
... ...,)( ...,)( dr
dTrPrL rad
Internal Structure of the Sun
How do we know?
Core temperature 15,600,000 K, density 150 water
Surface temperature 5800 K, average density 1.4 water
How can we check if
fusion really powers the
Sun
Test fusion hypothesis by looking for neutrinos
Neutrinos are only produced in nuclear reactions.
Ray Davis shared the 2002 Nobel prize in Physics for originally detecting neutrinos from the Sun.
The Solar Neutrino Problem
Neutrinos are detected, but only at 1/3 the rate expected.
Solution - Neutrinos change ‘flavor’ as they transit from sun to Earth, from electron neutrinos, to tau () and muon (μ) neutrinos:
e
We see oscillations
on the surface of the Sun
• The surface of the Sun vibrates up and down in oscillations which can go deep through the Sun.
• We can observe these oscillations from Earth by looking at the Doppler shifts of different pieces of the Sun.
Helioseismology is a way to probe the Sun’s interior using the Sun’s own vibrations.
Waves inside the Sun
The pattern of waves on the surface is determined by the conditions deep inside the Sun.
What direct observational evidence supports the model of thermonuclear
reactions in the Sun’s core?
1. Neutrinos
2. Gamma rays
3. Sun spot counts
4. WMD inspections
The Sun’s Atmosphere
• Photosphere - the 5800 K layer we see.
• Chromosphere – a thin layer, a few 1000 km thick, at a temperature of about 10,000 K. Can be seen during solar eclipse.
• Corona – Outermost layer, 1,000,000 km thick, at a temperature of about 1,000,000 K.
Outer layers of sun
1 = photosphere, 2 = chromosphere, 3 = corona
Why the outer layers of the Sun’s atmosphere are hotter is a puzzle.
Photosphere
Chromosphere
Corona
Corona
Limb darkening
Limb darkening
Sun spots are about 4000 K (2000 K cooler than solar surface) and have magnetic fields up 1000 the normal solar magnetic field. They can be as large as 50,000 km and last for many months.
Sunspots are low temperature regions in the photosphere
Particles spiral around magnetic field lines
Magnetic field
Motion of charged particle (electron, proton, nucleus)
The large magnetic fields in sunspots decrease the flow of heat via convection causing the sunspot to become cool.
Sunspots are low temperature regions in the photosphere
Sunspot cycle
Sunspots can be used to measure the rotation of the Sun
Near the equator the Sun rotates once in 25 days.
The poles rotate more slowly, about once every 36 days.
Sunspot cycle
Each 11 years, the Sun’s magnetic field changes direction. Overall cycle is 22 years.
Granulation
Which statement is not correct?
1. The solar coronal temperature is about 106 K.
2. Sunspots are very cool and dark, with temperatures of about 300 K.
3. The Sun’s core has a temperature about 107 K.
4. The chromosphere is hotter than the photosphere.
Solar magnetic fields also create other phenomena
• Prominences
• Flares
• Solar wind
• Coronal mass ejections
Particles spiral around magnetic field lines
Magnetic field
Motion of charged particle (electron, proton, nucleus)
Particles, that we see, get trapped along magnetic field lines, that we don’t see, stretching out from the Sun.
Bc
vqF
Prominences -Cooler than photosphere.
Solar flares -Hotter, up to 40,000,000 K
More energetic
Coronal mass ejections -eruption of gas, can reach Earth and affect aurora, satellites
Movie
Aurora
Review Questions
1. How long could the Sun continue to burn H at its current luminosity?
2. What is produced in the fusion of H to He?
3. If the radius of the Sun were doubled, how much longer would it take photons produced in the Sun’s core to escape?
4. What is the connection between sunspots and the Sun’s magnetic field?
5. What is the sunspot cycle?