Initial mass function

In astronomy, the initial mass function (IMF) is an empirical function that describes the distribution of initial masses for a population of stars. The IMF is often given as a probability distribution function (PDF) for the mass at which a star enters the main sequence (begins hydrogen fusion). The distribution function can then be used to construct the mass distribution (the histogram of stellar masses) of a population of stars. The properties and evolution of a star are closely related to its mass, so the IMF is an important diagnostic tool for astronomers studying large quantities of stars. For example, the initial mass of a star is the primary factor determining its colour, luminosity, and lifetime. The IMF is relatively invariant from one group of stars to another, though some observations suggest that the IMF is different in different environments.

The IMF is often stated in terms of a series of power laws, where ${\displaystyle N(m)\mathrm {d} m}$ (sometimes also represented as ${\displaystyle \xi (m)\Delta m}$), the number of stars with masses in the range ${\displaystyle m}$ to ${\displaystyle m+\mathrm {d} m}$ within a specified volume of space, is proportional to ${\displaystyle m^{-\alpha }}$, where ${\displaystyle \alpha }$ is a dimensionless exponent. The IMF can be inferred from the present day stellar luminosity function by using the stellar mass-luminosity relation together with a model of how the star formation rate varies with time. Commonly used forms of the IMF are the Kroupa (2001) broken power law and the Chabrier (2003) log-normal.

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