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Initial mass function for three young clusters. Note that masses are in solar masses, so log(mass) = 0 corresponds to one solar mass. [John Scalo, University of Texas, Austin]

A single value of a does not work for the full range of masses along the main sequence. The approximate values are:

(low mass)

a = 4.0 for 0.3 M0 < M < 3 M0 (intermediate mass)

(high mass)

In understanding how stars are formed (Chapter 14) we would like to know the distribution of stellar masses. That is, we would like to know the proportions of stars of various masses. Since we now know how to relate mass and spectral type, we can carry out such studies by looking at the relative numbers of different spectral types or luminosities. These studies are difficult, because we can see brighter stars to greater distances than faint stars. This is called a selection effect, because it makes it difficult to select an unbiased sample.

It is of interest to study the number of stars in different mass ranges. This is called the mass function. This is a good check on various theories of star formation, which we will discuss further in Chapter 15. When we discuss stellar evolution (Chapters 10 and 11), we will see that low mass stars live longer than high mass stars. So, if we study the mass function in a group of stars (usually clusters, as we will discuss in Chapter 13), it will change with time. As the higher mass stars die, they leave behind a cluster with a depleted number of high mass stars. So, if we want to really see what the mix of masses are when the cluster forms, we need to look at young clusters. This allows us to study what we call the initial mass function (IMF). Data for some sample clusters are shown in Fig. 5.13. Note: the number of low

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