Initial mass function

Definition

Consider a population of stars that form together. Let $m$ denote the mass of a star at birth, ranging over an interval $(m_{\min}, m_{\max})$ with $0 < m_{\min} < m_{\max}$ . The initial mass function of the population is a function $\xi \colon (m_{\min}, m_{\max}) \to [0, \infty)$ such that $\xi(m) \, dm$ is the number of stars born with mass in $[m, m + dm]$ . Equivalently, after normalising to total number $1$ , it is the probability density function of the birth mass of a star drawn from the population.

Remarks

Example: the Salpeter initial mass function, proposed in 1955, is $\xi(m) = A \, m^{-2.35}$ with a constant $A > 0$ . For it, equal small mass intervals at $m = 1$ and at $m = 10$ solar masses contain numbers of stars in the ratio $10^{2.35} \approx 224$ . Non-example: the present-day mass function of the stars in the solar neighbourhood is not an initial mass function, because massive stars have already died and are missing from the count. Many authors use instead the density per logarithmic mass interval, $m \, \xi(m)$ , which changes the power law exponent by $1$ . Observed initial mass functions flatten below about half a solar mass, so a single power law overestimates the number of very low-mass stars.

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Probability density function concept
Initial mass function definition

Tag	`VXFPHHXKXV`
URI	`m2://VXFPHHXKXV`
Kind	definition
Writing	W0 stub
MSC	85A35, 85A15
Defines	Initial mass function
Uses	Probability density function
Changed	3 November 2026

Initial mass function

Definition

Remarks

Reading path

Further reading

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