1. The Sun – A typical Star The only star in the solar system
Diameter: 100  that of Earth
Mass: 300,000  that of Earth
Density: 0.3  that of Earth (comparable to the Jovians)
Rotation period = 24.9 days (equator), 29.8 days (poles)
Temperature of visible surface = 5800 K (about 10,000º F)
Composition: Mostly hydrogen, 9% helium, traces of other elements
We begin the study of the stars with the one we know best.
Other stars are so far away that until about 15 years ago no one had seen the disc of another star recently this has been achieved for a few nearby very large stars, but there is still little detail to be seen.
The Sun is a typical star, so a lot of what we learn about the Sun tells us about stars in general.
Composition similar to Jupiter
Solar Dynamics Observatory Video

2. How do we know the Sun’s Diameter?
Trickier than you might think
We know only how big it appears
It appears as big as the Moon
Need to measure how far it is away
Kepler’s laws don’t help (only relative distances)
Use two observations of Venus transit in front of Sun
Modern way: bounce radio signal off of Venus

3. How do we know the Sun’s Mass?
Fairly easy calculation using Newton law of universal gravity
Again: need to know distance Earth-Sun
General idea: the faster the Earth goes around the Sun, the more gravitational pull  the more massive the Sun
Earth takes 1 year to travel 2π (93 million miles)  Sun’s Mass = 300,000  that of Earth

4. How do we know the Sun’s Density?
Divide the Sun’s mass by its Volume
Volume = 4π × (radius)3
Conclusion: Since the Sun’s density is so low, it must consist of very light materials

5. How do we know the Sun’s Temperature?
Use the fact that the Sun is a “blackbody” radiator
It puts out its peak energy in visible light, hence it must be about 6000 K at its surface

6. Black Body Spectrum Ipeak Ipeak Ipeak fpeak<fpeak <fpeak
Objects emit radiation of all frequencies, but with different intensities
Ipeak
Higher Temp.
Ipeak
EM waves are emitted at all frequencies.
Distribution of energy with respect to wavelength (or frequency) is called the Planck distribution
A continuous spectrum
Shape unchanged as T varies; location of peak and overall scale are shifted
Ipeak
Lower Temp.
fpeak<fpeak <fpeak

7. How do we know the Sun’s rotation period?
Crude method: observe sunspots as they travel around the Sun’s globe
More accurate: measure Doppler shift of spectral lines (blueshifted when coming towards us, redshifted when receding).
THE BIGGER THE SHIFT, THE HIGHER THE VELOCITY

8. How do we know the Sun’s composition?
Take a spectrum of the Sun, i.e. let sunlight fall unto a prism
Map out the dark (Fraunhofer) lines in the spectrum
Compare with known lines (“fingerprints”) of the chemical elements
The more pronounced the lines, the more abundant the element

9. Spectral Lines – Fingerprints of the Elements
Can use spectra to identify elements on distant objects!
Different elements yield different emission spectra
Called spectral lines because the instruments that are used to separate the light into its colors (spectroscope) usually makes images in the shape of lines.
Like a fingerprint

10. The energy of the electron depends on orbit
When an electron jumps from one orbital to another, it emits (emission line) or absorbs (absorption line) a photon of a certain energy
The frequency of emitted or absorbed photon is related to its energy
E = h f
(h is called Planck’s constant, f is frequency, another word for color )
 therefore tells us about energy levels and can be used to identify elements, or chemical compounds (molecules have more complex spectra because they can store energy in vibration and rotation as well as in electronic states)
Can also get information about magnetic fields and pressure
Applications: discovery of Helium in sun (1868; found on earth in 1895); identification of composition of bodies at a distance (spectroscopy)

11. Sun 
Compare Sun’s spectrum (above) to the fingerprints of the “usual suspects” (right)
Hydrogen: B,F Helium: C Sodium: D

12. “Sun spectrum” is the sum of many elements – some Earth-based!

13. The Sun’s Spectrum
The Balmer line is very thick  lots of Hydrogen on the Sun
How did Helium get its name?

14. How do we know how much energy the Sun produces each second?
The Sun’s energy spreads out in all directions
We can measure how much energy we receive on Earth
At a distance of 1 A.U., each square meter receives 1400 Watts of power (the solar constant)
Multiply by surface of sphere of radius bill. meter (=1 A.U.) to obtain total power output of the Sun
Why not use this directly on Earth? Not yet practical for large-scale power (small scale okay, though, e.g. solar calculators, solar heating)

15. Energy Output of the Sun
Total power output: 4  1026 Watts
The same as
100 billion 1 megaton nuclear bombs per second
4 trillion trillion 100 W light bulbs
$10 quintillion (10 billion billion) worth of energy per 9¢/kWh
The source of virtually all our energy (fossil fuels, wind, waterfalls, …)
Exceptions: nuclear power, geothermal

16. Where does the Energy come from?
Anaxagoras ( BC): Sun a large hot rock – No, it would cool down too fast
Combustion?
No, it could last a few thousand years
19th Century – gravitational contraction?
No! Even though the lifetime of sun would be about 100 million years, geological evidence showed that Earth was much older than this
Grav contraction -- Kelvin and Helmholtz. There probably do exist bodies that give off heat from this process, called brown dwarfs, but none has been decisively observed
By the end of the 19th century, geological evidence showed that the Earth was much older; and with the discovery of radioactivity, the age of the Earth was determined to be 4.5 billion years.
So, what is the process that powers the Sun?

17. What process can produce so much power?
For the longest time we did not know
Only in the 1930’s had science advanced to the point where we could answer this question
Needed to develop very advanced physics: quantum mechanics and nuclear physics
Virtually the only process that can do it is nuclear fusion

18. Nuclear Fusion Atoms: electrons orbiting nuclei
Chemistry deals only with electron orbits (electron exchange glues atoms together to from molecules)
Nuclear power comes from the nucleus
Nuclei are very small
If electrons would orbit the statehouse on I-270, the nucleus would be a soccer ball in Gov. Strickland’s office
Nuclei: made out of protons (el. positive) and neutrons (neutral)
Nuclear Fusion
Nuclei ~ 10^-15 m, atom ~ 10^-10 m; nucleus discovered 1905 (Rutherford)
Nucleus = protons+neutrons in the 1930’s
The mass of the total products of the reaction is less than the original mass. Where does the mass go? Mass is not conserved: it can be converted into energy: E=mc2 (Einstein, 1905).
the speed of light c is very large, so a small amount of mass yields a lot of energy when it is converted!
to produce the amount of power emitted by the Sun, 600 million tons of hydrogen must be combined to form helium per second: a lot of mass, but small compared to the Sun
at this rate, the Sun has enough fuel to last another 5 billion years

19. The Structure of Matter
Atom: Nucleus and Electrons
The Structure of Matter
Nucleus: Protons and Neutrons (Nucleons)
Nucleon: 3 Quarks
| m |
| 10-14m |
|10-15m|

20. Nuclear fusion reaction
In essence, 4 hydrogen nuclei combine (fuse) to form a helium nucleus, plus some byproducts (actually, a total of 6 nuclei are involved)
Mass of products is less than the original mass
The missing mass is emitted in the form of energy, according to Einstein’s famous formulas:
E = mc2
(the speed of light is very large, so there is a lot of energy in even a tiny mass)

21. Hydrogen fuses to Helium
Heavier elements as well…
Start: protons  End: Helium nucleus + neutrinos
Hydrogen fuses to Helium

22. Harvesting Binding Energy
Small harvest by decay
Big harvest by fusion
Most stable element in the universe

23. The Standard Solar Model (SSM)
Sun is a gas ball of hydrogen & helium
Density and temperature increase towards center
Very hot & dense core produces all the energy by hydrogen nuclear fusion
Energy is released in the form of EM radiation and particles (neutrinos)
Energy transport well understood in physics

24. Standard Solar Model
Generally, temp and density drop as we move out from the center. Computer models must calculate the values of these parameters, as well as others, such as chemical composition, etc.
Density of core: 20 times that of iron
Density of photosphere: 10,000 times less dense than air
Core: region of nuclear fusion (source of power); temperature, 15 million K (27 million oF); high pressure (due to weight of gas above)
radiation zone: ("interior") temperature so high that atoms have lost their electrons. Energy in form of EM radiation travels through this region, occasionally scattered by nuclei.
convection zone: temperature is lower; atoms have their electrons. Light bumps into the atoms, excites the electrons and is absorbed. In this region energy (heat) is carried by convection. It can take 100 thousand years for heat from the core to escape this zone.
photosphere: where density of sun drops to the point that the gas becomes transparent to radiation, and heat is carried away from the Sun as black body radiation, traveling freely through space (8 minutes to Earth)
There are no sharp surfaces in the Sun, it's all gas

25. How much energy does the Sun produce in theory?
Short answer: As much as it has to …
Longer answer: … to maintain hydrostatic equilibrium

26. Hydrostatic Equilibrium
Two forces compete: gravity (inward) and energy pressure due to heat generated (outward)
Stars neither shrink nor expand, they are in hydrostatic equilibrium, i.e. the forces are equally strong
Heat
Gravity
Gravity

27. More Mass means more Energy
More mass means more gravitational pressure
More pressure means higher density, temperature
Higher density, temp. means faster reactions & more reactions per time
This means more energy is produced

28. Does too much Energy lead to Explosion?
No, there is regulative feedback:
More energy produced means more radiative pressure
This means the stars gets bigger
This means density, temperature falls off
This means less reactions per time
This means less energy produced

29. How do we know what happens in the Sun?
We can’t “look” into the Sun
But: come up with theory that explains all the features of the Sun and predicts new things
Do more experiments to test predictions
This lends plausibility to theory