Initial mass function IMF of stars The Salpeter 1955 IMF of

Initial mass function (IMF) of stars. The Salpeter (1955) IMF of stars between 0.2 and 100 M_ is given by n(M)dM M^2.3 dM, where n(M)dM is the number of stars within interval dM around M. (4.4.2 in the book.) One can define a characteristic stellar mass such that half of the total (initial) mass of all stars goes into stars below this mass, and half into stars above it. Call this the \"center of mass\" of the IMF. Calculate this characteristic mass, in units of M_ for the Salpeter IMF. In the same spirit one can define the \"center of number\" of the IMF, as the mass such that half the all stars are below that mass and half are above. Calculate this mass for the Salpeter IMF. One can further define the \"center of light\" of the IMF, as the stellar mass such that stars below that mass emit half of the total luminosity of a star cluster born with that IMF, and half of the total luminosity is emitted by stars above that mass. Calculate the \"center of light\" of the above IMF assuming that stellar luminosity scales as L infinity M^3, for stars on the Main Sequence.

Solution

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