Initial mass function
empirical function that describes the initial distribution of masses for a population of stars
In astronomy, the initial mass function (IMF) is an empirical function that describes the initial distribution of masses for a population of stars during star formation. IMF not only describes the formation and evolution of individual stars, it also serves as an important link that describes the formation and evolution of galaxies.
The IMF is often given as a probability density function (PDF) that describes the probability for a star to have a certain mass during its formation. It differs from the present-day mass function (PDMF), which describes the current distribution of masses of stars, such as red giants, white dwarfs, neutron stars, and black holes, after some time of evolution away from the main sequence stars and after a certain amount of mass loss. Since there are not enough young clusters of stars available for the calculation of IMF, PDMF is used instead and the results are extrapolated back to IMF. IMF and PDMF can be linked through the "stellar creation function". Stellar creation function is defined as the number of stars per unit volume of space in a mass range and a time interval. In the case that all the main sequence stars have greater lifetimes than the galaxy, IMF and PDMF are equivalent. Similarly, IMF and PDMF are equivalent in brown dwarfs due to their unlimited lifetimes.
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 of determining its colour, luminosity, radius, radiation spectrum, and quantity of materials and energy it emitted into interstellar space during its lifetime.
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