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Physics 1002 Chapter 14 Our Star Reading: 14.1-14.3

Our Star  A closer look at the Sun  Structure of the Sun  Nuclear fusion in the Sun  Sun- Earth connection

1

Our Star – The SUN Radius: 6.9  108 m (109 times that of Earth)

Mass: 2  1030 kg

(300,000 times that of Earth) Luminosity:

3.8  1026 watts

2

A Closer Look at the Sun Why does the Sun shine? 

“The sun's rays are the ultimate source of almost every motion which takes place on the surface of the earth. By its heat are produced all winds,...By their vivifying action vegetables are elaborated from inorganic matter, and become, in their turn, the support of animals and of man, and the sources of those great deposits of dynamical efficiency which are laid up for human use in our coal strata.” Treatise on Astronomy, John Herschel 1833



Chemical energy? (e.g. burning wood, coal, ..) Will only last thousands of years 3

If the Sun were made of 2x1030 kg solid COAL … We can measure the amount of energy the Earth receives from the Sun in a year: ~ 5.5x1024 J (For comparison, world total energy consumption in the whole year of 2015 is ~4. x 1020 J.)#  From the size of the Earth, and the distance to the Sun, we can calculate the TOTAL yearly energy output of the Sun: 1.2 x 1034 J  For high grade coal, each kg can produce ~3.75 x 107 J and so the Sun will need to burn 3.2 x1026 kg of coal per year.  And it will last only 6250 years! 

# Key world energy statistics (2017): https://www.iea.org/publications/freepublications/publication/KeyWorld2017.pdf

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Gravitational energy It takes a big rocket to lift the space module above Earth’s surface. On return, this gravitation energy turns into thermal energy when stopped or slow down.



Gravitational energy at work!

Assuming gravitational contraction of the Sun produces its luminosity, it will only last millions of years – NOT ENOUGH! 5



The answer came in 1938 by H.A. Bethe: stars are powered by nuclear reactions involving H and He.

July 2, 1906 – March 6, 2005

NUCLEAR ENERGY! Nuclear Potential Energy (core) Luminosity

~ 10 billion years (for the Sun)

6

Einstein himself explaining: http://www.aip.org/history/einstein/sound/voice1.mp3

“It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing – a somewhat unfamiliar conception for the average mind. Furthermore, the equation E is equal to m csquared, in which energy is put equal to mass, multiplied by the square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa….” 7

Source of Stellar Energy The source of stellar energy is nuclear fusion: the combining of nuclei into heavier ones. (It is different from the nuclear fission of breaking heavier nuclei into lighter ones.)  The amount of energy released is given by the famous Einstein’s equation in physics:



E = mc2 The greater the nuclear binding energy, the more stable the nucleus

8

It Must Be Hot and Dense Enough! Nuclear fusion only occurs at temperatures greater than 10 million K and at a very high density.  Why do we need high temperature? This is because nuclei are made of protons and neutrons. Protons carry positive electrical charges. There is electric repulsion between all nuclei. 

Repulsion

Only when colliding nuclei are moving with high velocities can they overcome the repulsive force and get close enough for nuclear reaction to take place. Thus it must be hot and dense!  But how???? From gravitational contraction! (during star formation) 

9

Sun-like stars: stable energy source for 10 B Years On Earth we can make fusion bombs – but not stable power plants from fusion.  How do stars do it? A one-solar-mass star can have a stable size and structure for 10B years, while giving out steady power.  Fusion requires very high temperature (>10M degrees) and high density (>20x density of iron) and therefore high pressure (>1010 atm). 

Gravity balancing pressure!

Heat energy exploding out

10

Weight of upper layers compresses lower layers

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Stellar Balance: hydrostatic equilibrium Internal pressure Outward

Gravity Inward

At every point, the two forces are equal and opposite: i.e. in equilibrium 12

Gravitational contraction… provided energy that heated the core as the Sun was forming.

Contraction stopped when fusion began replacing the energy radiated into space. 13

How does a star regulate its temperature to stay roughly the same for billions of years? Needs a ‘feedback’ mechanism: that is how a thermostat regulates temperature. You set a temperature. If the actual temperature is too low, it offers more heat. If the temperature is too high, it offers less heat (or turns on cooling).

Stars use the ‘pressure-temperature thermostat’ and rely on the strong temperature dependence of the fusion rate. 14

Heating by Contraction 

When a star contracts, the atoms rush to the centre and gather speed.



When fast atoms collide with each other, they form hot gases. Thus contracting

gases heat up.



This principle has already been used to explain why stars formed from gases contracting under gravity.



Similarly, the reverse is true:

expanding gases cool down. 15

The Pressure-Temperature Thermostat  A feedback mechanism maintains the balance of the system. 

If the core gets hotter, then it will fuse hydrogen faster. More radiation and higher gas pressure will be produced and the core expands. However, the expansion causes the core to cool, and the rate of nuclear reaction to decrease, bringing back the balance of the system.

A star with balanced pressure and temperature

If the core gets hotter, increased pressure causes the core to expand.

The expansion causes the core to cool and density to decrease. Nuclear reaction rate goes down and pressure and temperature become 16 balanced again.

Solar Thermostat

Decline in core temperature causes fusion rate to drop, so core contracts and heats up

Rise in core temperature causes fusion rate to rise, so core expands and cools down 17

What is the Sun’s structure? Solar wind: A flow of charged particles from the surface of the Sun

Corona: Outermost layer of solar atmosphere ~1 million K Chromosphere: Middle layer of solar atmosphere ~ 104–105 K

Photosphere: Visible surface of Sun ~ 6,000 K

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Convection zone: Energy transported upward by rising hot gas ~ 1.5 million K at the bottom. Radiation zone: Energy transported upward by photons

~ 7 to 1.5 million K Core: Energy generated by nuclear fusion

~ 15 million K 19

Structure_Sun.swf

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Modes of Heat Transfer: how does the heat get out from the core?

Not as important inside stars

Radiation: At high temperature, all atoms are ionized

Convection: At lower temperature (especially nearer the surface), heavier elements such as Nitrogen, Carbon, Calcium, Iron, and Oxygen are no longer fully ionized and thus can absorb radiation

Scattering of photons radiative zone

convective zone

recombination ionization less-absorptive scattering

more-absorptive scattering

It takes a photon ~1,000,000 yrs to go from the center to the outside! Outer shell electron(s)

photon

electron

ions

heavier atoms 22

Energy gradually leaks out of the radiation zone in the form of randomly bouncing photons.

23

Convection (rising hot gas) takes energy to the surface.

24

Bright blobs on photosphere where hot gas reaches the surface

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Different sizes, different structures Heat transfer mode depends on temperature, thermal and density gradients, and pressure.

< 0.4 M : the whole star is convective  1 M : three zones: core, radiative and convective zones >>1 M : the core is convective and the shell is radiative

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Nuclear Fusion in the Sun

How does nuclear fusion occur in the Sun?

Fission

Fusion

Big nucleus splits into smaller pieces

Small nuclei stick together to make a bigger one

(Nuclear power plants)

(Sun, stars) 27

Sun releases energy by fusing four hydrogen nuclei into one helium nucleus.

High temperatures enable nuclear fusion to happen in the core. 28

Hydrogen Fusion



The proton-proton chain fuses 4 protons into a helium nucleus, producing most of the energy of the Sun.



There are three steps in the p-p chain: 2

H  1 H  3He  

 1

H 1 H  2 H  e   3



He  3He  4He  1H  1H

  29

PPChain.swf

30

Proton–proton chain is how hydrogen fuses into helium in Sun

 Bottleneck, very slow rate: Tunneling + Weak interaction of b + decay (p  n)  On average, a proton in the solar core needs to wait for 9 x 109 years to fuse with another proton.  This is why the life expectancy of the sun is about 10 billion years. 31

~1010 years

~1s

~106 years

Fast step: On average, a deuterium lives only for 1s before fusion with another proton to form helium-3 32

By-product of p-p Cycle:  (中微子 中微子 中微子)) 

Neutrinos are (almost?) massless neutral particles that travel (almost) at the speed of light and thus carry energy.



They interact with matter only very weakly and hence can penetrate matter easily. After production, they leave the star immediately.

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They are common ingredients in cosmic rays. On Earth, there are abundant neutrinos from Sun, known as solar neutrinos.

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Every second 1012 neutrinos pass through you but you don’t notice them at all. 33

Overall H 1 H  2 H  e   2  2 H 1 H  3 He   2

1

+ 3 He  3 He  4 He  1H  1H __________________________________

41H4 He  2e   2ν  2γ The net result is that 4 protons are converted into a helium nucleus and energy-carrying particles.  The energy-carrying particles include: 2 positrons, 2 neutrinos, and 2 gamma ray photons.



34

Mass Balance 4 hydrogen nuclei  6.693  10 -27 kg



-27   1 helium nucleus 6.645 10 kg

________________________________________

difference in mass  0.048  10 -27 kg This mass difference is converted to energy according to Einstein’s equation: 2

- 27



8

E  mc  0.048  10 kg 3  10 m/s



2

 0.43  10-11J 35

Energy Balance 

All main sequence stars fuse hydrogen into helium.



Energy is obtained from a tiny mass difference: one helium nucleus has 0.7% less mass than four hydrogen nuclei.



The “lost” mass is turned into energy by E = mc2, where c is the speed of light.

1 helium

where did you put the mass?

Those photons aren’t for free!

4 hydrogen plus positrons and neutrinos 36

IN 4 protons OUT 4He nucleus 2 gamma rays 2 positrons 2 neutrinos

Total mass is 0.7% lower.

37

Neutrinos created during fusion fly directly through the Sun.

Observations of these solar neutrinos can tell us what’s happening in the core.

38

Solar neutrino problem: Early searches for solar neutrinos failed to find the predicted number.

39

Solar neutrino problem:

More recent observations find the right number of neutrinos, but some have changed form.

Nobel Prize in Physics for 2015 https://www.nobelprize.org/nobel_prizes/physics/laureate s/2015/press.html 40

The Sun–Earth Connection What causes solar activity? Solar activity is like “weather” Sunspots  Solar prominences  Solar flares 



All are related to magnetic fields. 41

Sunspots …

Are cooler than other parts of the Sun’s surface (4,000 K) Are regions with strong magnetic fields

42

Zeeman Effect

We can measure magnetic fields in sunspots by observing the splitting of spectral lines

43

Charged particles spiral along magnetic field lines. 44

Loops of bright gas often connect sunspot pairs. 45

The corona appears bright in X-ray photos in places where magnetic fields trap hot gas.

46

Strong magnetic activity causes solar prominences that erupt high above the Sun’s surface.

47

Magnetic storm causes solar flares that send bursts of X-rays and charged particles into space.

48

How does solar activity affect humans? Coronal mass ejections (huge, balloon-shaped plasma bursts) send bursts of energetic charged particles out through the solar system. A CME recorded by the SOHO satellite in 2000 shows a billion tons of plasma launched two million kilometers off the surface of the sun! The dark area in the middle of the image is from a disk used to block out the light of the sun. The white circle outlines the location of the sun’s surface. Credit: SOHO (NASA/ESA)

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Charged particles streaming from the Sun can disrupt electrical power grids and disable communications satellites. 50...