concept

initial mass function

The distribution of stellar masses at birth, showing how many stars form at each mass.
34 related articles · 2 formulas

Description

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.

History

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.

How it works

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.

In practice

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.

Fun fact

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.

Concept graph →

Formulas

$$\log_{10}(M/M_\odot) = a \log_{10}(L/L_\odot) + b$$
Relates stellar mass to luminosity.
What is in the formula
Mvariablestellar mass — mass kilogram
Lvariablestellar luminosity — luminosity watt
M_sunvariablesolar mass — mass kilogram
L_sunvariablesolar luminosity — luminosity watt
aconstantempirical slope of the relation — empirical slope = 3.5
bconstantempirical intercept of the relation — empirical intercept = 0
log10operatorbase-10 logarithm — logarithm base 10
\log_{10}(m_{{he}}/m_\odot)=0.659\log_{10}(l/l_\odot)-2.630 · 2601.06577
$$q = \frac{m_2}{m_1}$$
Ratio of secondary to primary mass in a binary system.
What is in the formula
qvariableMass ratio of the binary system — mass ratio
m_2variableMass of the secondary component — mass kilogram
m_1variableMass of the primary component — mass kilogram
q=m_{\rmp}/m_* · 2607.04594v1
s_{δ_1,δ_2}=\frac{m_{δ_1}}{m_{δ_2}} · 2607.20721v1

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