
The distribution of stellar masses at birth, showing how many stars form at each mass.The initial mass function (IMF) describes the relative number of stars that form at different masses in a given star-forming event. It is a fundamental statistical distribution in astrophysics, typically showing that low-mass stars are far more numerous than high-mass stars. The IMF is essential for understanding star formation, galaxy evolution, and the chemical enrichment of the universe, as it determines how many stars of each type contribute to light, heavy elements, and supernovae.
The IMF was first quantified by Edwin Salpeter in 1955, who derived a power-law distribution for field stars in the solar neighborhood. Later work by Miller and Scalo in 1979 and Chabrier in 2003 refined the IMF, especially at low masses, where it flattens.
The IMF is usually expressed as a power law, where the number of stars per unit mass interval decreases with increasing mass. A common parameterization is the Salpeter IMF, which has a slope of -2.35 for stars above about one solar mass. The origin of the IMF is still debated, but it likely arises from the interplay of turbulence, gravity, and feedback in molecular clouds during star formation.
The IMF is used to convert observed galaxy luminosities into star formation rates and stellar masses, and it is a critical input for models of galaxy evolution and chemical enrichment.
The IMF appears to be remarkably universal across different environments in the Milky Way, but some recent observations suggest it may be top-heavy (more massive stars) in extreme starburst regions, though this remains controversial.
| M | variable | stellar mass — mass kilogram |
| L | variable | stellar luminosity — luminosity watt |
| M_sun | variable | solar mass — mass kilogram |
| L_sun | variable | solar luminosity — luminosity watt |
| a | constant | empirical slope of the relation — empirical slope = 3.5 |
| b | constant | empirical intercept of the relation — empirical intercept = 0 |
| log10 | operator | base-10 logarithm — logarithm base 10 |
| q | variable | Mass ratio of the binary system — mass ratio |
| m_2 | variable | Mass of the secondary component — mass kilogram |
| m_1 | variable | Mass of the primary component — mass kilogram |















