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Unformatted text preview: Astronomy 112: The Physics of Stars Class 19 Notes: The Stellar Life Cycle In this final class well begin to put stars in the larger astrophysical context. Stars are central players in what might be termed galactic ecology: the constant cycle of matter and energy that occurs in a galaxy, or in the universe. They are the main repositories of matter in galaxies (though not in the universe as a whole), and because they are the main sources of energy in the universe (at least today). For this reason, our understanding of stars is at the center of our understanding of all astrophysical processes. I. Stellar Populations Our first step toward putting stars in a larger context will be to examine populations of stars, and examine their collective behavior. A. Mass Functions We have seen that stars masses are the most important factor in determining their evolution, so the first thing we would like to know about a stellar population is the masses of the stars that comprise it. Such a description is generally written in the form of a number of stars per unit mass. A function of this sort is called a mass function. Formally, we define the mass function ( M ) such that ( M ) dM is the number of stars with masses between M and M + dM . With this definition, the total number of stars with masses between M 1 and M 2 is N ( M 1 ,M 2 ) = Z M 2 M 1 ( M ) dM. Equivalently, we can take the derivative of both sides: dN dM = Thus the function is the derivative of the number of stars with respect to mass, i.e. the number of stars dN within some mass interval dM . Often instead of the number of stars in some mass interval, we want to know the mass of the stars. In other words, we might be interested in knowing the total mass of stars between M 1 and M 2 , rather than the number of such stars. To determine this, we simply integrate times the mass per star. Thus the total mass of stars with masses between M 1 and M 2 is M * ( M 1 ,M 2 ) = Z M 2 M 1 M ( M ) dM or equivalently dM * dM = M ( M ) ( M ) . 1 Unfortunately the terminology is somewhat confusing, because ( M ) is also often called the mass function, even though it differs by a factor of M from ( M ). You will also often see ( M ) written using a change of variables: ( M ) = M ( M ) = M dN dM = M d ln M dM dN d ln M = dN d ln M . Thus gives the number of star per logarithm in mass, rather than per number in mass. This has an easy physical interpretation. Suppose that ( M ) were constant. This would mean that there are as many stars from 1- 2 M as there are from 2- 3 M as there are from 3- 4 M , etc. Instead suppose that ( M ) were constant. This would mean that there are equal numbers of stars in intervals that cover an equal range in logarithm, so there would be the same number from . 1- 1 M , from 1- 10 M , from 10- 100 M , etc....
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This note was uploaded on 09/25/2011 for the course ASTRO 112 taught by Professor Krumholz during the Spring '10 term at UCSC.
- Spring '10