The initial mass function is the distribution of stellar birth masses. It records the mass scales selected by cloud fragmentation, accretion, feedback, and stellar multiplicity.
For an initial mass function proportional to on with , integration and normalization give the displayed upper-tail fraction. The probability integral transform makes uniform on for a randomly sampled birth mass. Evolutionary lifetime regions can then be measured as ordinary areas when the independent age coordinate is also uniform.
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The Initial Mass Function (IMF) is a crucial concept in astrophysics that describes the distribution of masses for a population of stars when they form. It provides a statistical representation of how many stars are born within a certain mass range in a stellar population, essentially outlining the relationship between the number of stars and their masses at the time of formation.