Check out Snow's Universe with all its Sun links (temporarely offline) and Strobel's great lectures on our Sun.

 Let's take a multimedia tour first.

 Well, although I can read some Dutch, let's try it in English.
Our Sun is an ordinary star! It's much _________ than all other stars, therefore we call it Sun.

 Note that qualitatively all stars behave the same as our Sun does - with differences in detail.

Data we can easily measure or compute (from easily measured data): distance Earth-Sun, size, mass, average density, luminosity of Sun.

The DISTANCE to our Sun can be measured via two different ways (which is great because one can confirm the other):

1. Parallax: of course we can't take the Earth's orbit as our baseline (why not?), but the Earth's diameter (12,800 km) will do.  Two people at opposite sides of the Earths (12,800 km distant from each other) eye our Sun and make very accurate position measurements.  Their combined data give a parallax/triangulation of a very small (but measurable!) 0.005 degrees.  Given the 12,800 km baseline, this gives a distance of a = 12,800 [km] / 0.005 * 360 / 2 p = 150 million km, defined as 1 A.U.

 2. Radar: a radar beam (at speed c = 300,000 km/s) sent out on Earth towards our Sun is reflected off our Sun and returns after 17 min.  Since this is forth and back, one way is 8.5 min.  And since distance is speed times time, a = 300,000 [km/s] * 8.5 * 60 [sec] = 150 million km == 1 A.U. = 93 million miles.  Voila!

Its size (DIAMETER) is determined from its apparent size of 0.5 degrees (a pinkie (but use your thumb to be on the safe side) at arm's length covers our Sun - as well as our Moon) and the distance. d = 0.5 / 360 * 2 p *150,000,000 [km] = 1.3 million km = 800,000 miles.

Our Sun's MASS is determined by Kepler's 3rd law: we saw the period-distance relationship of planets and noted that this depends on the mass of the central object (see lab F9 and lecture on Gravitation).  Our Sun's mass is 1 solar Mass M = 4 p² / G * a³ / P² = 2.0 10³⁰ kg .  (G is the gravitational constant, for a (in meters!) and P (in seconds!) you can use any planet's data.)

Solar constant (energy received from sun on Earth - measured on Earth and with satellites): 1,370 Watts/m² . Since the Earth intercepts only a small part of our Sun's radiation and since our Sun's radiation is isotropic (the same in all directions), we multiply this number by the area of a hypothetical sphere of radius 1 A.U. = 150 million km = 1.5  10¹¹ m   (Area = 4 p r²), which then gives us the total energy that our Sun gives off per second: 3.9 10²⁶ Watts (1 Watt = 1 Joule per second), which we also call its Luminosity: 1 solar L = 3.9  10²⁶ W.

 Compare: All nations in the world together use about 10²² Joules per year. For how many years would our Sun's energy emitted in a single second last, if we could harvest it completely?

 _____________________ - of course, we can't harvest all the Sun's energy, just a small part of what reaches Earth.

 What generates this huge amount of energy?

 Guesses: ...

 elves and dwarfs treading the mill

 ...
...
...
...

 Sun's composition by # atoms (and by mass): 92% Hydrogen (73% by mass), 7% Helium (25% by mass), all others less than 1% "metals" (2% by mass).  Note that Helium is 4 times as massive as Hydrogen, hence the numbers for abundance and mass are different.
Interesting is also that almost ALL stars (99% of them) have about the same amount of H and He as our Sun does, and so does the Interstellar Medium!  (see lectures on Measuring Stars and Stellar Evolution)

Sun is in balance
Gravitation: Sun's own mass pulls itself inwards
-> matter is compressed
-> creating high temperature and pressure
-> which pushes outwards and balances gravitation
-> hydrostatic equilibrium
- otherwise our Sun would contract or expand, which it doesn't
 

Energy given off is constant
-> energy supplied at a constant rate (due to nuclear fusion)
-> i.e. as much energy is produced as is given off
-> thermal equilibrium
- otherwise our Sun would get brighter and hotter or dimmer and colder, which it doesn't
 
 
 
 
 

Nuclear fusion
 

Two protons at a time fuse ...	... into a deuteron, emitting a positron and a neutrino.
The deuteron and another proton fuse ...	... into Helium-3, emitting photons.
Two Helium-3 fuse ...	... into Helium-4, emitting two protons.

The proton-proton cycle.  Image "List-O-Particles" (c) ZEBU, Oregon. (Remember that a proton is simply the nucleus of a Hydrogen atom (with the electron removed).)
The fifth step, where two He-3 fuse, requires that the first four steps happen twice (in order to produce two He-3).  So by counting all protons involved (a total of six, but two are re-emitted at the end), this leads to a net equation of   4 p  ->  He-4  &  2 e⁺  &  Energy .  The emitted photons (nuclear fusion produces g rays) and the additional radiation due to the core's 15 million K temperature is what eventually reaches us as EM radiation (see discussion below).  Oregon's Zebu shows the processes really well in its animations.
More massive Main Sequence, Population I (with enough metals), stars (spectral types O, B, A, F) have higher core temperatures (see SEA-5) and use the CNO cycle, but yield the same net equation.

The above processes occur 10³⁷ times every single second (see below)!!!!
 
 

Sun's core
-> temperature (15 million K) and pressure (200 billion atm) high enough
-> to overcome the electric repulsion of the positive protons
-> to ignite nuclear fusion

and density of Hydrogen high enough (about 20 times that of iron)
-> to keep nuclear fusion going

ZEBU-Oregon's mpeg-movies on nuclear fusion

Hydrogen nuclei (protons) fuse into Helium and give off energy in form of g rays (see Chaisson p.270 and p.275, qu.18). Does it generate enough energy for the sun to give off the above mentioned 390,000,000,000,000,000,000,000,000 Watts?

 You bet.

 Shall we calculate and confirm it?

• Yes (let's have it as a problem on the final).
• No (let's omit it and believe that astronomers can do easy calculations).

        In a nutshell: mass of proton is 1.67 10^-27 kg = 1.0078 amu.  (The "atomic mass unit" is more convenient.)  Four protons make a mass of  4.0312 amu ("input mass").  This compares to the He-4 with 4.0026 amu and the 2 positrons of 0.00055 amu each, making a total of 4.0037 amu ("output mass").  So after the reaction, there is less mass than there was before!!!  Where did this mass deficit Dm=0.0285 amu go?  The most famous formula in the world supplies the answer: E = Dm c² !  Since the speed of light  c=3.0 10⁸ m/s  is so large, this gives an energy of 4.3 10^-12 Joules per reaction (back from amu to kg).
        With a luminosity of L=3.9 10²⁶ J/s, this means that the tremendous amount of 9.0 10³⁷ He-4 nuclei are produced every second (and 3.6 10³⁸ protons fuse each second).  That's a 9 with 37 zeroes!  That's a huge number of reactions required - but compare this to the number of Hydrogen nuclei (protons) available:  # p ~ (total mass of Sun) / (mass of proton) ~ 2.0 10³⁰ kg / 1.67 10^-27 kg ~ 1.0 10⁵⁷ , a "One" with 57 zeroes!
        Computer simulations show that our Sun used/uses/will use about 10% of its total Hydrogen supply (the Hydrogen in and around the core where it's hot enough for nuclear fusion).  Given that the luminosity is fairly constant (again, computer simulations) throughout our Sun's Main Sequence life, this means that the lifetime of our Sun is t = (total Energy available) / Luminosity = (0.1 [%] * 2.0 10³⁰ [kg] * 0.0285 [amu] / 4 [p] * (3.0 10⁸ [m/s])² ) / 3.9 10²⁶ [J/s] = 3.3 10¹⁷ [sec] = 10 billion years

Now, this wasn't too hard after all - Intermediate Algebra, a scientific calculator and straightforward computations was all we needed.
 

 Do we get them?

 If not, what happens?
 

Energy transfer

A pot of boiling water on a stove is a good example of all three possible ways by which energy can be transported.  Touch the outside of the pot - that's conduction.  Watch the water bubbles rising from the bottom of the pot to the surface - that's convection.  Lift the pot off the burner, the flame or the glowing heating coil - that's radiation.

 Energy can be transported by 3 different means:

• Conduction - primarily in solids
• Convection - in liquids, gases, plasma (which is gases where atoms are stripped off their electrons)
• Radiation - photons; liquids, gases, plasma, solids, vacuum - anywhere

From core, radiation (g rays) gets into thick sun's interior
-> g rays absorbed
-> radiation re-emitted in all parts of the EM-spectrum
-> after 100,000 years energy reaches convection zone

 In the convection zone, hot gases rise to the photosphere, cooled off gases sink back (observed granules), check Snow (temporarely offline).

From the photosphere, energy is emitted as black body radiation into space.

 In the upper photosphere, certain wavelengths (for each element; recall the chapter on radiation and lab F5) are absorbed, which gives rise to the sun's absorption spectrum (Chaisson p.260).

 Check your textbook's index under "Sun" (or other books written on our Sun): It covers almost an entire column with catchwords like color, composition, density, energy transport, lifetime, magnetic field, temperature, rotation, etc., etc. How do we know all of this?    _________________________________
 

Granules are rising (hot, bright) and sinking (cooler, dark) convection cells.
-> entire surface is covered with them (Chaisson p.258).
(c) Kiepenheuer Institut für Sonnenphysik, Freiburg, Germany.
The picture is about 25,000 miles vertical and horizontal, about 0.02 % of the Sun's surface.  Of course the most prominent feature in this image is a sunspot about as big as Earth.  But granules are the texture covering the entire area, they have an average diameter of 500 miles.
 
 

 Sunspots: Our Sun is a liquid/gaseous body
-> it rotates at different rates at different latitudes (29 days at equator, 24 days near poles)
-> this "differential" (i.e. non uniform) rotation disturbs (wraps) the magnetic field lines
-> producing sunspot pairs (one North, one South polarity)
-> lifetime: hours (small ones) to weeks (large ones)
-> since they stay in the same position
-> observing them over several days reveals how fast the sun rotates

 -> my Lab G0 Sunspots and Sun's rotation
-> SoHO: Observe the motions of sunspots and use them to measure the solar rotation rate, also at the University of Montana, at Stanford, and a movie of the giant sunspot from March/April 2001.

and Sun's magnetic field reverses every 11 years (North pole becomes South pole),
actually a 22 year cycle (when the North pole becomes again a North pole).
-> during reversing, magnetic field becomes weak
-> few sunspots, minimum (last one in 1995)
-> next maximum around 2000 (see Chaisson p.265)

Short-wave and HAM radio enthusiasts like sunspot maxima because the increased solar activity makes reception of far away stations much clearer.  People in Quebec sure didn't like the power outage during the last sunspot maximum in 1989 (Quebec is closest to the Earth's Northern magnetic pole).
You may want to look for yourself for the causal connection between increased solar activity and its influence upon the Earth's atmosphere.
 
 

Solar Atmosphere

Photosphere

- emits the energy that reaches us (Planck's law)

- absorption spectrum (Fraunhofer; spectral type G2)
- maximum in yellow part of spectrum
-> surface temperature at 5,800 K ( __________ law)

To confirm this surface temperature, use the Stefan-Boltzmann law   L = 4 p s r² T⁴   and solve for temperature:  T = ( 3.9 10²⁶ / 4 p / 5.67 10^-8 / (6.5 10⁸ m)² ) ^.25 = 6,000 K .
 
 

Chromosphere

- chromo means color

- pinkish color (due to Hydrogen emission lines)
- thin layer of hydrogen above photosphere
-> cooler and much fainter than photosphere
- visible during solar eclipses and through filters (Hydrogen H_a and Calcium H and K lines)
 
 

Solar Eclipse in the Caribbean.  (c) Jamalee and Dan Clark, Scottsbluff, NE.  February 26, 1997.

Corona

- high temperature (up to 2 million K)

-> many electrons stripped off from their atoms
-> unusual spectra (e.g. 13 times ionized Iron)

- visible during solar eclipses as huge extensions of the sun's atmosphere into space

Solar wind
- Sun expels protons, electrons at high speeds
-> when reaching earth caught by our magnetic field
-> spiraling around magnetic field lines (see this animation)
-> hitting the Earth's atmosphere at the poles
-> _________________ (Ch/Mc p.133)
 
 
 

Aurora in Scottsbluff, NE, (houses on the lower right, a couple of stars on the right - also, it was cloudy that evening).  (c) Andreas Veh, September 1998.  This was my first Aurora.  I saw vertical, hazy, whitish streaks rising high from the Northern horizon and lots of flickering in the Northeast, but no colors.  Instead the film picked up the green and red which are attributed to atmospheric Oxygen when it recombines after being hit by solar wind particles which were funneled by the magnetic field towards the Earth's magnetic poles.  Exposures are about 1 min with a 28 mm wide angle lens.  My wife's folks in Alaska saw it the same evening.
 
 

Visit Brian Rachford's Aurora alert page for 40 degrees latitude.

Read about the 1989 power outage  in Quebec in this 2000 USA Today article.

Read in your textbook what the solar wind has to do with comet tails.

Listen to the sounds of the Aurora.

Very strong activity in Europe on April 7, 2000.  Image made by NOAA's Polar-orbiting Operational Environmental Satellite (POES).  I used a negative representation so it would print better.

    Friday, 7 April, 2000, 11:06 GMT 12:06 UK
    Skywatchers marvel at light show
    Diffuse red glow
    Observers all over the Northern Hemisphere were stunned by the display.
    A report from Chester, UK, by Tom Teague said that a bright diffuse red glow was visible, with many broad rays orientated roughly north-south. Some narrower, more concentrated rays with a greenish tinge were also seen.
    Chartered engineer Ian Sheffield, of the Royal Observatory in Edinburgh, UK, who watched the display from his home in East Lothian, said: "It was the most amazing display I have seen in 10 years.
    "They started at 1900 GMT and they looked like Jacob's Ladders coming down to the horizon. They were pale green with streaks of red that was quite unusual. It was ghostly."
    Veils of pale green
    The Duty Controller at the Jodrell Bank radiotelescopein Cheshire, UK, described the lights as very spectacular, with curtains of red and green light seen between 1130 and 0200 GMT.
    A report from Dave Branchett in Florida, US, said: "These events are rare from this part of the world but even rarer was the sight of fingers or rays that shimmered and danced within the aurora."
    Another observer said: "I've just spent the last two hours gazing up at a sky literally on fire with swaying red curtains and billowing veils of pale green and white streamers. Beams are everywhere. At one point, everything merged overhead, and staring up at it was like staring into some kind of pink wormhole - unbelievable."
 
 
 
 
 

---

Our Sun's spectrum

(Link to my Fraunhofer spectrum page)

Also named the Fraunhofer spectrum (Snow's web site is temporarely offline).

For two

"In 1802, William Wollaston noted that the spectrum of sunlight did not appear to be a continuous band of colours, but rather had a series of dark lines superimposed on it. Wollaston attributed the lines to natural boundaries between colours. Joseph Fraunhofer made a more careful set of observations of the solar spectrum in 1814 and found some 600 dark lines, and he specifically measured the wavelength of 324 of them. Many of the Fraunhofer lines in the solar spectrum retain the notations he created to designate them. In 1864, Sir William Huggins matched some of these dark lines in spectra from other stars with terrestrial substances, demonstrating that stars are made of the same materials of everyday material rather than exotic substances. This paved the way for modern spectroscopy." from Jesse Allens' web site.

Here you can see how I assembled the entire solar spectrum from the Observatoire de Paris and from the McMath-Pierce Observatory on Kitt Peak, Arizona.

A star's spectrum gives us LOTS and LOTS and LOTS and LOTS of information.  Check my lectures on Measuring Stars and Light and Matter.

The above above spectrum gives as foremost the surface temperature of our Sun, not its composition.  Read through my lecture on Measuring Stars first about temperature and then composition.

.......

Now you know and you're able to determine the following correctly.

Access the Observatoire de Paris and follow my instructions.

Which of these elements' absorption lines show up fairly STRONG in our Sun's spectrum?
 
 

instructions:  make check marks for the settings "Plot dat", "Image data" 

Element		Wavelength(s)	color	weak or strong?	start wavelength	range
Calcium II	Ca II	3934 & 3968	UV	_________	3900	100
Sodium	Na	5890 & 5896	yellow	_________	5860	40
Helium	He	5870	yellow	_________	ditto	ditto
Titaniumoxide	TiO	6159	red	_________	6150	20
Hydrogen	H	6563	red	_________	6560	10
Gold	Au	7510.7	IR	_________	7510	2
Iron	Fe	7511.0	IR	_________	ditto	ditto

There are plenty more absorption lines for each element, but I only wanted to give you a sample.

In the above table, you should have four "yes's" and three "no's".  After you've read through the lectures that I had recommended, you should be able to figure out why some lines show up and others don't.

Answer:  _____________________________________________________________

(This is also part 1 of lab F6 Stellar Spectra.)

The absorption lines of Gold don't show up as strong lines at all in our Sun's spectrum (there is very few Gold to begin with).  How much is "very few"?  Let's estimate.  First check SEA-7: there are 7 Gold atoms for every one trillion Hydrogen atoms.  This means that roughly 7/1,000,000,000,000 = 10^-11 of our Sun is Gold.  Multiply that with our Sun's mass of roughly 10³⁰ kg (or pounds). Multiplying like bases (base 10) means to add exponents, so it's 10^30+(-11) = 10¹⁹ kg (or pounds) of Gold on our Sun.  Compare that to the 31 million kg (70 million pounds) of Gold that has been mined throughout the ages on Earth: Gold is 1 trillion times more abundant on our Sun than on Earth!!!

The above calculation serves several purposes: (i) see how exponents are added or subtracted (useful for a certain HW question), (ii) although the amount of Gold on our Sun is so very small when compared to other elements, because of our Sun's very huge mass, the net amount of Gold on our Sun is mind boggling.

(A more exact mass of Gold on our Sun would be determined by m_Au = M_ox .71 x 7 x 10^-12x 197 , where M_o = 2 x 10³⁰ kg our Sun's mass, .71 Hydrogen's part of that mass, 7 x 10^-12 is Gold's fraction when compared to Hydrogen, and 197 is how much more massive one Gold atom is than one Hydrogen atom.  This makes for 2 x 10²¹ kg = 4 x 10²¹ pounds, which is even a factor 400 larger than our above rough estimate.)

Our Sun's radius is about 450,000 miles. How do we know this?
... Sun's mass is about 2.0 10³⁰ kg. How do we know ..?
... Sun's density is 1.4 as much as that of water. How do we ...?
         ... surface temperature is 10,000 F. How do ...?
         ... luminosity is 3.9 10²⁶ Watts. How ...?
         ... core temperature is 24 million F. How ...?
         ... lifetime is estimated at 10 billion years (of which 5 billion are still ahead of us).  How ...?

What do the Northern and Southern lights have to do with our Sun? Why do they only occur at latitudes close to the poles?

Using the Doppler shift to determine the solar rotation

(Another procedure is to use the "movement" of Sunspots, Lab G2 Sunspots)

The diagram shows a very narrow part (close to the red H_a line) of the solar spectrum.  The equivalent total solar spectrum (purple 4000 to red 7000 Å) would be 600 feet long!

The broad absorption lines are in the red part of the spectrum, from iron on our Sun.  They have some width because our Sun is rotating: its Western limb is rotating towards us (blueshift) and its Eastern limb is rotating away from us (redshift).  Since the entire surface is rotating, it widens an absorption line, the more it's rotating, the more it's widened.

The thin absorption lines are from oxygen in the Earth's atmosphere.  They are the same red wavelengths that show up in photos of Aurora Borealis.  Sun and Earth's atmospheric lines can be distinguished by the former being broadened due to our Sun's rotation (we are rotating as well but the oxygen in the air is stationary relative to us).  These oxygen lines are of no interest in the following analysis.

Print the above image.  Carefully draw a sharp vertical line in the middle of a solar iron line from the top to the bottom of the "trough".

Half way draw a short horizontal line that touches the "trough's" edges.  Determine the width of this absorption line, this is  Dl .
 

Using the Doppler equation, determine the rotational velocity of the approaching and receding limbs of our Sun:  v_rot = c (Dl) / (l)  in  km/s .  The speed of light is   c = 3.0 10⁵ km/s  .

The period (the time it takes our Sun to rotate once) is given by   P = (2 p R) / v_rot  in seconds.  The solar radius is   R = 6.96 10⁵ km .  Convert period   P   to days by dividing by 86,400 (24*60*60).  Compare to a textbook value and to your value from Lab G2 Sunspots.
 
 

Solar Astronomy Timeline

1613 : Galileo Galilei uses sunspot observations to demonstrate the rotation of the Sun
1619 : Johannes Kepler postulates a solar wind to explain the direction of comet tails
1802 : William Wollaston observes dark lines in the solar spectrum
1814 : Joseph Fraunhofer systematically studies the dark lines in the solar spectrum
1834 : Hermann Helmholtz proposes gravitational contraction as the energy source for the Sun (Annotation: turns out that this could have lasted for only 10 million years and there is no evidence for the sun shrinking)
1843 : Heinrich Schwabe announces his discovery of the sunspot cycle and estimates its period to be about ten years
1852 : Edward Sabine shows that sunspot number is correlated with geomagnetic field variations
1859 : Richard Carrington discovers solar flares
1860 : Gustav Kirchoff and Robert Bunsen discover that each element has its own distinct set of spectral lines and use this fact to explain the solar dark lines
1861 : F.G.W. Spörer discovers the variation of sunspot latitudes during a solar cycle
1863 : Richard Carrington discovers the differential nature of solar rotation
1868 : Pierre-Jules-César Janssen and Norman Lockyer discover an unidentified yellow line in solar prominence spectra and suggest it comes from a new element which they name ``helium''
1893 : Edward Maunder discovers the 1645--1715 Maunder sunspot minimum
1904 : Edward Maunder plots the first sunspot ``butterfly diagram''
1906 : Karl Schwarzschild explains solar limb darkening
1908 : George Hale discovers the Zeeman splitting of spectral lines from sunspots
1942 : J.S. Hey detects solar radio waves
1949 : Herbert Friedman detects solar X-rays
1960 : Robert Leighton, Robert Noyes, and George Simon discover solar five-minute oscillations by observing the Doppler shifts of solar dark lines
1961 : H. Babcock proposes the magnetic coiling sunspot theory
1970 : Roger Ulrich, John Leibacher, and Robert Stein deduce from theoretical solar models that the interior of the Sun could act as a resonant acoustic cavity
1975 : Franz-Ludwig Deubner makes the first accurate measurements of the period and horizontal wavelength of the five-minute solar oscillations

Need:
- laptop, projector, long internet cord
- telescopes with filters, safety features, projection screen, eclipse glasses (no need at all, sun is way too low)
- SOHO screen saver on laptop
- various color filters to explain images taken in different parts of the spectrum
- Redshift
 
 
 

Web Site	internet address	comments
SpaceWeather.com	http://www.spaceweather.com/	my home page during the solar maximum to be alerted of upcoming auroras (Northern Lights)
NASA's "Solar Data Analysis Center"	http://umbra.nascom.nasa.gov/	found a nice prominence movie
Public Outreach for the Japanese solar x-ray satellite Yokhoh	http://www.lmsal.com/YPOP/homepage.html	found a nice movie of our rotating Sun in x-rays (they have a movie making web page too)
One of NASA's Solar Physics sites	http://wwwssl.msfc.nasa.gov/ssl/pad/solar/sunturn.htm	found one of many movies of our rotating Sun in visibile light
ESA's Solar and Heliospheric Observatory	http://sohowww.nascom.nasa.gov/	I've got their screen saver which permanently shows the latest images (giant sun spot 3-29-01)
Another NASA Solar Physics site	http://science.nasa.gov/headlines/y2001/ast27apr_1.htm	the giant sun spot from March/April 2001 develops on the rotating Sun
Laramie Aurora Visibility Alert	http://origins.colorado.edu/~rachford/aurora/lava.html	I'm on Brian Rachford's e-mail list to receive his aurora alerts for this part of the country