The temperature of the Sun's atmosphere

The sun is not a solid body. It is entirely gaseous. It looks solid because at various depths a particular wavelength of light can no longer penetrate the gas.
The sun becomes progressively cooler with distance from the center until a depth a little above the visible "surface". Then it becomes increasingly hotter. The ultraviolet and soft X-rays arise from increasingly higher regions. Gamma rays and very short wavelength X-rays come from patches in which the magnetic field is particularly high rather from the entire solar atmosphere. Draw the atmosphere of the sun showing from where gamma rays, X-rays, and visible light reach us.
 

Determining the temperature of a star's "surface"

The "surface" of the sun or a star is called the photosphere. Narrow regions of the spectrum are absorbed by atoms (and a few molecules in very cool stars). Because these atoms that give rise to spectral lines are slightly above the photosphere, they are cooler and hence appear dark against the photosphere in the background. Because they are narrow, they are called lines. Because, the atoms are only a little cooler than the photosphere, the hotter the photosphere, the hotter the atoms forming the lines and it is possible to determine the relative temperature of the stellar photosphere from the temperature of these atoms.

If the atoms were in a medium at absolute zero temperature, all of the electrons would be in the lowest possible energy level. At any warmer temperature, a few electrons would be in higher levels. The hotter the medium, the more electrons would be in higher energy levels. The various levels are distinguished by the amount of energy required to lift an electron from the lowest level to that level. This is measured in electron volts, that is, the energy required to move an electron against an electric field of that many volts. For example, to move an electron from the negative to the positive terminal of an electric outlet requires 110 electron volts. The table of spectral lines gives the wavelength of the line, the atom from which it arises, and the energy required to lift the electron from the level in which it would be at absolute zero to the level from which the line is absorbed. (See the energy levels for hydrogen.) Since the hotter the atom, the more energy it has, the energy of the levels from which lines arise gives the relative temperatures of the stars.
 
Line List
Wavelength Element Energy Level
3933 ionized calcium   6.1
3968 ionized calcium   6.1
3970 neutral hydrogen 10.2 
4026 neutral helium 20.9
4030 neutral manganese   0.0
4045 neutral iron   1.5
4102 neutral hydrogen 10.2
4200 ionized helium 50.8
4227 neutral calcium   0.0
4325 neutral iron   1.6
4340 neutral hydrogen 10.2
4384 neutral iron   1.5
4471 neutral helium 20.9
Note: Both neutral hydrogen and ionized calcium have lines very near 3970. If this line and the calcium line at 3933 are about the same strength, you can assume that the line at 3969-70 is from calcium. If the line at 3933 is much weaker, then you can assume that the line at 3969-70 is from hydrogen. The same coincidence in wavelength also occurs for lines of neutral hydrogen and ionized helium but the hydrogen contribution is almost always stronger.
 

Stellar temperatures - exercises

NOTE: All of the following exercises use the CLEA program: Spectra, although that was originally designed for a different exercise. You must have two files: clea_spe.exe and jspectra.zip and these must be uncompressed. For the first four exercises, click on "Classify Spectra", then "Load unknown spectrum", then "Program list".
You will then be asked to click on a particular star. Use the table of lines to identify lines and find their lower energy level.
The intensity of the line is measured by the area taken out of the spectrum. Thus both depth and width contribute. The normal view of the spectrum is that given by a modern electronic detector (intensity plot). However, you can also change to a view simulating a photographic spectrum. To see this, click on display, then on gray scale (Photo).

1) Click on "Feige 41". A portion of the spectrum of this star will appear.
    Identify each line you see.
    What elements do you observe?

2) Click on "HD 35619"
    Identify each line.
    Is HD 35619 hotter or cooler than Feige 41?

3) Click on HD 66171
    This star has lots of lines. Find the following:
        3933
        3968
        4030
        4045
        4102
        4226
        4325
        4340
This star is like the sun. Is it hotter or cooler than Feige 41?

4) Click on HD 5351
    Find the following lines:
        3933
        3968
        4045
        4226
        4384
     Arrange the four stars in order of temperature.

5) Next you are going to take a spectrum of another star as if you were really at an observatory. Then, working with the spectrum you take, you will study it in the same way you studied the four stars in the program list. You should put this star in the proper place in the temperature order.

Click on "Back". You will be asked if you want to leave the classification window. Click "Yes". Then click "Run", then "Take spectra".
At this point, you are in the dome, ready to start to observe. You cannot see the sky through the closed dome, so you must first open the slit. To do this, click on "Dome". "Closed" will change to "Opening" and you will see the slit open.
In order for the telescope to remain pointing to the star as the earth turns, you must turn on the "Tracking". This will counteract the rotation of the earth. The next item "Slew Rate" indicates how rapidly the telescope moves from one pointing to another. Leave it as it is for the moment. If you want to speed up the motion, set a higher number.
a star in the telescope field. The star will probably not yet be in the spectrograph slit.
Click on "Monitor". The reading will change from "Finder" to "Instrument" and you will see two parallel lines. These are the edges of the spectrograph slit. The star must be well within them.
When the star is well centered in the slit, click on "Take Reading", then on "Start Count". You will see a spectrum building up. When the Signal/Noise is above 200, stop count. (The actual stopping time is not serious, provided you do not stop too soon.)
You will be asked if you want to save the spectrum. Click "Yes". Then give it a number. You will be told the name that will be used.
You are now ready to study your spectrum. As in the first four exercises, click "Load", then "Classify Spectra", but this time, click on "Saved Spectra" instead of "Program List". You will see your star. Click on it and determine its characteristics.

If you wish, and have time, you can take more than one spectrum either while you are still in the dome or by returning to the dome after you have classified your spectrum.