----- The following copyright 1991 by Dirk Terrell
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 Lecture #11 "Expanding Stars"

   While all this has been going on in the core, what has happened to the 
outside, or envelope? It turns out that the radius, luminosity, and surface 
temperature of the star change as changes in the core take place. That's 
kind of convenient since we can't directly probe the interiors of stars 
(Although neutrinos can be used to do this, in principle, our ability to 
detect and study them has only recently been developed. We still have a long 
way to go in this very promising field.). As you might suspect, the HR 
diagram is an invaluable tool for studying the changes in the appearance of 
stars. Clusters of stars, that is, stars that are actually gravitationally 
bound to one another, provide a very powerful test of our theories of 
stellar evolution. The reasons for this are (1) stars in a cluster are all 
approximately the same distance from the earth (not exactly, of course, but 
it's like the difference between the distance from my front door to the 
Washington Monument and the distance from my back door to the WM.) (2) All 
the stars are approximately the same age.

   Recall that the HR diagram is a plot of the luminosity (brightness) of a 
star versus its surface temperature. If we imagine watching a star as it 
evolves, plotting its luminosity and temperature every 100,000 years or so, 
we would see the star trace out a path on the HR diagram that we call an 
evolutionary track (Oh how painful it is not to be able to draw one for 
you!). If we develop a hypothesis of stellar evolution, we could predict 
evolutionary tracks and compare them with actual ones to test the 
hypothesis. But we can't watch a star for millions of years to see what 
happens. We are much too impatient for that. Then how do we know what the 
evolutionary tracks of real stars look like? If you said star clusters, take 
an electronic bow! Since stars in a cluster are at the same distance from 
us, we don't have to worry about the brightness differences that result from 
stars being at different distances. If two stars in a cluster have different 
brightnesses, it is because one star is intrinsically brighter than the 
other (and that is the quantity we need for the HR diagram- the intrinsic 
brightness). Any one cluster is a snapshot of the evolution of stars at some 
particular time. If we look at many clusters, we can see the evolution of 
stars as time progresses.

   When the core of the star collapses, a tremendous amount energy is 
released and a shell of hydrogen around the core begins to fuse hydrogen. 
The energy released in the shell source heats the lower layers of the 
envelope and causes them to expand. The layers above these are pushed 
outward, and the star expands. But expanding a gas causes it to cool, and 
when a star cools, its color changes and it becomes redder. So we have a 
star that is bigger and redder than before, and guess what we call it? A red 
giant (we're real original). The evolution of a star from the main sequence 
into a red giant is rather rapid. Usually, the red giant stage of a star's 
lifetime accounts for only a few percent of the total lifetime (it is about 
1% for our 15 solar mass star). Since the star is redder, that means it will 
move to the right in the HR diagram (recall that lower temperatures are on 
the right). The luminosity of the star doesn't change by a lot as the star 
becomes a red giant. For low mass stars it drops a little more than it does 
in high mass stars.

   Succesive depletions of nuclear fuels (helium, carbon, etc.) cause the 
star the expand. Eventually the star will become a red supergiant. 
Supergiants really are quite large. Betelgeuse is a red supergiant, and if 
we could replace the sun with it, the surface of Betelgeuse would extend 
beyond the orbit of Mars! 

   Stars in the red giant and supergiant stages are on their last leg. Next 
time we will talk about the ways in which stars 'retire'. I hope everyone is 
still hanging in there. We didn't have too much discussion last time, but we 
have gone into some detail for those who wanted it. We will soon be moving 
along to a different area of astronomy, so if you're bored, hang in there!

 Dirk