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initial mass function (IMF) karyâ-ye âqâzin-e jerm Fr.: fonction initiale de masse A mathematical expression describing the relative number of stars found in different
ranges of mass for a cluster of stars at the time of its formation.
It is defined as
M is the mass of a star and N is the number of stars in a
logarithmic mass interval. The value of the slope found by Salpeter (1955) for
→ low-mass
and → intermediate-mass stars in the
→ solar neighborhood is Γ = 1.35.
The IMF can be expressed also in linear mass units:
χ(M) = dN / DM ∝ M.
Note that
^{ -α}χ(M) = (1 / M lm 10) φ(log M), and α = Γ + 1. In this
formalism the Salpeter slope is α = 2.35. There is a third way for
representing the IMF, in which the exponent is x = -α.
The IMF is not a single power law over all masses, from
→ brown dwarfs to → very massive stars
(Kroupa, 2002, Science 295, 82).
Different slopes have been found for different mass segments, as follows:
α = 1.3 for 0.08 ≤ M < 0.5;
α = 2.3 for 0.5 ≤ _{solar}M < 1;
α = 2.3 for 1 ≤ _{solar}M.
The IMF at low masses can be fitted by a
→ _{solar}lognormal distribution
(See Bastian et al., 2010, ARAA 48, 339 and references therein).
See also → canonical IMF. |