In addition to the science fair projects I have already posted about evaporating black holes and the search for stellar identifications in the NASA/COBE data, here is another possibility.
When you look into the sky you see stars. If you were to take a piece of the sky about the size of the Full Moon, and count how many stars there were at different magnitudes of brightness, you would sample a variety of different kinds of stars of different distances and spectral types.
I would like to create a model of what kind of star field you expect to see near the North Galactic Pole of our Milky Way, where we are looking straight out of the galaxy into the depths of the distant universe. I want to be able to predict how many stars of each magnitude class I expect to see, not at visible wavelengths but in the infrared.
The procedure is rather straight forward. What you do is to first decide on how many stars of each Luminosity class there ought to be in the direction you are looking. Knowing their luminosities, you then assign distances to each of the stars and compute their apparent visual magnitude using the formula:
m = M - 5 + 5log(d)
where m = apparent visual magnitude
M = absolute magnitude corresponding to their luminosity
d = distance to the star in parsecs.
example, if you have a star with a luminosity of 10 times the mass of the
Sun whose absolute magnitude is +2.2 at a distance of 35 parsecs you get
m = +2.2 - 5 + 5 ( log(35) ) = +2.2 - 5 + 7.7 = +4.9.
From the visual magnitude and the luminosity and spectral classes, you can then use a standard table to look up its magnitude in the 'J', 'H' and 'K' infrared bands. There are also tables that tell how many stars of each spectral class and luminosity there are per cubic parsec.
What you have to do is to take, say, 200 or 300 stars and assign spectral types and luminosities and distances to them, then count up how many there will appear to be in each magnitude interval if you were to photograph this field at the three infrared wavelengths. Example suppose for 5 stars you assigned them to the following spectral classes and luminosity classes:
Star M Type distance apparent magnitude 1 +5.5 G0 20.0 +7.0 2 +2.2 A5 200.0 +8.7 3 -2.5 B0 1520.0 +8.4 4 +10.0 M5 3.0 +7.4 5 +8.0 K0 8.0 +7.5Then from your second 'model' of how these stars are distributed in distance, you assigned them to the above distances in parsecs. The apparent visual magnitudes would then be as indicated. So, your model would predict in the visual band, that there would be 3 stars with magnitudes of +7.0 to +7.9 and 2 stars with magnitudes from +8.0 to +8.9. The 'star counts' in the infrared bands would be obtained by adding to the visual magnitudes above a correction factor, and then 'binning' the data in similar magnitude bins as for the visual magnitudes.
The reason this is an interesting project is that counting stars in the infrared lets astronomers decide on how stars are distributed in the halo of the Milky Way. I will provide real data from the new infrared sky survey called 2MASS which is now starting to return images of the north galactic pole region in a search for distant galaxies in the infrared.