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Theoretical concepts |
Initial mass function Jeans instability Kelvin–Helmholtz mechanism |
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The initial mass function (IMF) is an empirical function that describes the mass distribution (the histogram of stellar masses) of a population of stars in terms of their theoretical initial mass (the mass they were formed with). 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. The IMF is relatively invariant from one group of stars to another.
The IMF is often stated in terms of a series of power laws, where (sometimes also represented as ), the number of stars with masses in the range to within a specified volume of space, is proportional to , where 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.
The IMF of stars more massive than our sun was first quantified by Edwin Salpeter in 1955. His work favoured an exponent of . This form of the IMF is called the Salpeter function or a Salpeter IMF. It shows that the number of stars in each mass range decreases rapidly with increasing mass. The Salpeter Initial Mass Function is
Later authors extended the work below one solar mass. Glenn E. Miller and John M. Scalo suggested that the IMF "flattened" (approached ) below one solar mass. Pavel Kroupa kept above half a solar mass, but introduced between 0.08-0.5 solar masses and below 0.08 solar masses.
Commonly used forms of the IMF are the Kroupa 2001 broken power law and the Chabrier 2003 lognormal.
Chabrier 2003 for individual stars:
Chabrier 2003 for stellar systems:
Kroupa 2001:
for , for , for
There are large uncertainties concerning the substellar region.