1. Homework Set #6
10/11/17
Due 10/18/17
Chapter 8
Review questions 2 and 13
Problems 3, 5, 9, and 11
Extra Problem
Problem 1. What would the Sun’s lifetime be based only on using up the available fuel (hydrogen) in the proton-proton chain fusion reaction and assuming the luminosity doesn’t change?

2. PHYS-3380 Astronomy

3. PHYS-3380 Astronomy
The Sun 3

4. The Sun’s Energy Source
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The Sun’s Energy Source
The first scientific theories involved chemical reactions or gravitational collapse.
- chemical burning ruled out…it can not account for the Sun’s luminosity
- conversion of gravitational potential energy into heat as the Sun contracts would only keep the Sun shining for 25 million years
late 19th-century geological research indicated the Earth was older than that
Development of nuclear physics led to the correct answer
- the Sun generates energy via nuclear fusion reactions
- Hydrogen is converted into Helium in the Sun’s core
- the mass lost in this conversion is transformed into energy
- the amount of energy is given by Einstein’s equation: E = mc2
- given the Sun’s mass, this will provide enough energy for the Sun to shine for 10 billion years 4

5. PHYS-3380 Astronomy
Striking a Balance
The Sun began as a cloud of gas undergoing gravitational collapse.
- the same heating process, once proposed to power the Sun, did cause the core of the Sun to get hot and dense enough to start nuclear fusion reactions
Once begun, the fusion reactions generated energy which provided an outward pressure.
This pressure perfectly balances the inward force of gravity.
- deep inside the Sun, the pressure is strongest where gravity is strongest
- near the surface, the pressure is weakest where gravity is weakest
This balance is called gravitational equilibrium.
- it causes the Sun’s size to remain stable 5

6. PHYS-3380 Astronomy
One second of output from the Sun (luminosity) would provide power for the human race for the next 500,000 years 6

7. PHYS-3380 Astronomy
Layers of the Sun 7

8. PHYS-3380 Astronomy
Core
T = 1.5 x 107 K; depth = 0 – 0.25 R
Density - up to 150,000 kg/m³ (154 times the density of water on Earth)
Pressure 200 billion times that on the surface of Earth
This is where the Sun’s energy is generated. 8

9. Why does fusion occur in the Sun’s core ?
PHYS-3380 Astronomy
Why does fusion occur in the Sun’s core ?
Nuclear fusion
- a reaction where heavier nuclei are created by combining (fusing) lighter nuclei.
- all nuclei are positively charged
Electromagnetic force causes nuclei to repel each other.
- for fusion to occur, nuclei must be moving fast enough to overcome E- M repulsion
- this requires high temperatures and pressures
When nuclei touch, the nuclear force binds them together 9

10. Energy Generation in the Sun: The Proton-Proton Chain
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Energy Generation in the Sun: The Proton-Proton Chain
Need large proton speed ( high temperature) to overcome Coulomb barrier (electromagnetic repulsion between protons).
T ≥ 107 0K = 10 million 0K
Basic reaction:
4 1H  4He + energy
Sun needs 1038 reactions, transforming 5 million tons of mass into energy every second, to resist its own gravity. 10

11. The Three Step Process p+ n + e+ +  (inverse -decay) n p+ + e- + 
PHYS-3380 Astronomy
The Three Step Process
1H + 1H  2H + e+ + 
- two protons fuse to make deuterium
- one of the protons turns into a neutron and releases energy in the form of a positron and a neutrino
- average time for this step - 1 billion years
neutrino carries up to 0.42 MeV
the positron annihilates with an electron, creating two gamma rays
MeV
Note: In a free state the neutron is unstable with a half-life of about 12 minutes, decaying into a proton, an electron, and an anti-neutrino.
2. 2H + 1H  3He + 
- the deuterium then combines with another proton, releasing a gamma ray and giving a nucleus of helium MeV
- average time for this step - 1 second p+
n + e+ + 
(inverse -decay) n
p+ + e- + 
(-decay) 11

12. The Three Step Process 3. 3He + 3He  4He + 1H + 1H
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The Three Step Process
3. 3He + 3He  4He + 1H + 1H
- the helium-3 nucleus fuses with another helium-3 to form normal helium MeV
- sets free two protons to start the whole process again.
- average time for this step - 1 million years
Total energy  26.7 MeV
Mproton = 1.67 X kg
MHe4(nucleus)= X kg
4(Mproton) - MHe4(nucleus) = 4.74 X kg
E = mc2 = (4.74 X kg)( X 108 m/s)2 = 4.26 X J
(4.26 X J)(1 eV/ X J)=26.7 MeV 12

13. Proton-Proton Chain Animation
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Proton-Proton Chain Animation 13

14. - scattered numerous times - lose energy as they go, heating the gas
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Energy in form of:
Gamma rays
- take one to 10 million years to work their way out from the star's core
- scattered numerous times - lose energy as they go, heating the gas
-eventually emerge from the surface as rays of light and heat.
Positrons
- annihilate with free electrons - produce gamma rays
Energy of motion of particles
- raises temperature of gas
Neutrinos
- almost never interact - escape
- do not contribute to heating
Inside the Sun, about 655 million tons of hydrogen are converted into 650 million tons of helium every second.
In stars heavier than about 2 solar masses, in which the core temperature is more than about 18 million K, the dominant process in which energy is produced by the fusion of hydrogen into helium is a different reaction chain known as the carbon-nitrogen cycle. 14

15. PHYS-3380 Astronomy
The Solar Luminosity
The Sun’s luminosity is stable over the short-term.
However, as more Hydrogen fuses into Helium:
- four H nuclei convert into one He nucleus
- the number of particles in Sun’s core decreases with time
- the Sun’s core will contract, causing it to heat up
- the fusion rate will increase to balance higher gravity
- a new equilibrium is reached for stability at a higher energy output
- the Sun’s luminosity increases with time over the long-term
Models indicate the Sun’s luminosity has increased 30% since it formed 4.6 billion years ago.
- it has gone from 2.9 x 1026 watts to today’s 3.8 x 1026 watts 15

16. Other Helium Production Paths in the Sun
PHYS-3380 Astronomy
Other Helium Production Paths in the Sun
The proton-proton chain is common path to making helium in the Sun, but not the only one. After Step 2 is complete, other reactions can take place -- the PPII chain (31% of the time):
3He + 4He  7Be + 
7Be + e-  7Li + 
7Li + 1H  4He + 4He
Or even the PPIII chain(rare, 0.3% of the time):
7Be + 1H  8B + 
8B  8Be + e+ + 
8Be  4He + 4He 16

17. Energy Production
PHYS-3380 Astronomy
Binding energy due to strong force = on short range, strongest of the 4 known forces: electromagnetic, weak, strong, gravitational
Nuclei are made up of protons and neutrons, but the mass of a nucleus is always less than the sum of the individual masses of the protons and neutrons which constitute it. The difference is a measure of the nuclear binding energy which holds the nucleus together.
Nuclear fusion can produce energy up to the production of iron.
For elements heavier than iron, energy is gained by nuclear fission. 17

18. PHYS-3380 Astronomy
The Neutrino Problem
Neutrinos come to us directly from the core of the Sun, a product of the proton-proton chain.
We have detected them, proving that the theory of nuclear fusion reactions is correct.
But we only detected about 30% - 50% of the neutrinos which were predicted by theoretical models.
- either our understanding of nuclear fusion reactions or our understanding of neutrinos was wrong.
We have since discovered three types (“flavors”)of neutrinos:
- electron (e), muon (), and tau ()
most neutrino detectors can register only electron neutrinos
if neutrinos can change type (“oscillate”) after being created, this would solve the “neutrino problem.”
In Sudbury Neutrino Observatory in Ontario came on line
- capable of detecting all three types
- observations proved neutrino oscillation 18

19. Interior Zones T < 8 x 106 K; depth = 0.25 – 0.86 R
PHYS-3380 Astronomy
Interior Zones
T < 8 x 106 K; depth = 0.25 – 0.86 R
Energy is transported through the interior.
The interior is divided into two zones:
- Radiation Zone - energy is transported outward by photons
- Convection Zone - energy is convected outward by rising hot gas and falling cool gas
Boundary between them is at:
T = 2 x 106 K; depth = 0.70 R 19

20. Methods of Energy Transport
PHYS-3380 Astronomy
Methods of Energy Transport
Radiation Zone
- energy travels as photons of light, which continually collide with particles
- always changing direction (random walk), photons can change wavelengths
- this is called radiative diffusion
This is a slow process!
It takes about 1 million years for energy to travel from the core to the surface. 20

21. Energy Transport Convection zone
PHYS-3380 Astronomy
Energy Transport
Convection zone
- photons arriving at bottom of convection zone are absorbed instead of scattered by matter
- the bottom of the zone is heated - hot gas rises to the top
- cooler gas sinks to the bottom
energy is brought to the surface via bulk motions of matter – convection
Convection motions are visible at the surface as granules

22. Energy Transport Convection zone
- photons arriving at bottom of convection zone are absorbed instead of scattered by matter as in the radiation zone
- the bottom of the zone is heated - hot gas rises to the top
- cooler gas sinks to the bottom
energy is brought to the surface via bulk motions of matter – convection
Convection motions are visible at the surface as granules

23. Photosphere T = 5,800 K; depth = 400 km
PHYS-3380 Astronomy
Photosphere
T = 5,800 K; depth = 400 km
This is the yellow “surface” that we see. 23

24. Photospheric Features
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Photospheric Features
Sunspots: dark spots on the surface where the temperature is cooler.
Regions of strong magnetic fields - suppress convection from below
Sunspots occur in pairs - magnetic fields loop from one sunspot to a neighboring sunspot
Granulation: the tops of convection cells seen “bubbling” on the Solar surface 24

25. PHYS-3380 Astronomy
A sunspot is cooler than the rest of the Sun’s surface and looks darker. They last anywhere from hours to months.
Close up of a sunspot 25

26. PHYS-3380 Astronomy
Sunspots and the Sun’s surface can change very quickly - this movie covers half an hour. 26

27. Solar Activity The photosphere of the Sun is covered with sunspots.
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Solar Activity
The photosphere of the Sun is covered with sunspots.
Sunspots are not constant; they appear and disappear.
They do so in a cycle.
It repeats every 11 yrs.
- Sun’s magnetic field switches polarity every 11 yrs
- so the entire cycle repeats every 22 yrs 27

28. PHYS-3380 Astronomy
11-Year Solar Cycle

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Sunspot Cycle 29

30. Sunspot Number Two official sunspot numbers in common use:
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Sunspot Number
Two official sunspot numbers in common use:
Daily Boulder Sunspot Number - computed by the NOAA Space Environment Center using a formula devised by Rudolph Wolf in 1848:
R=k (10g+s)
g is the number of sunspot groups on the solar disk, s is the total number
of individual spots in all the groups; and k is a variable scaling factor (usually <1) that accounts for observing conditions and the type of telescope (binoculars, space telescopes, etc.). Scientists combine data from lots of observatories -- each with its own k factor -- to arrive at a daily value.
The Boulder number usually about 25% higher than the second official index, the International Sunspot Number, published daily by the Sunspot Index Data Center in Belgium. Both calculated from the same basic formula, but they incorporate data from different observatories.

31. The Latest Sunspot Number Plot and Prediction
PHYS-3380 Astronomy
The Latest Sunspot Number Plot and Prediction