The Impact of Binaries on the Stellar Initial Mass Function
  (abridged) The stellar initial mass function (IMF) can be conveniently
represented as a canonical two-part power law function and is largely invariant
for star formation regions evident in the Local Group of galaxies. The IMF is a
hilfskonstrukt. It is a mathematical formulation of an idealised population of
stars formed together in one star formation event. The nature of the IMF (is it
a probability density or an optimal sampling distribution function?) is raised.
Binary stars, if unresolved, have a very significant influence at low stellar
masses. Especially important is to take care of the changing binary fraction as
a result of stellar-dynamical evolution of the embedded clusters which spawn
the field populations of galaxies, given that the binary fraction at birth is
very high and independent of primary-star mass. The high multiplicity fraction
amongst massive stars leads to a substantial fraction of these being ejected
out of their birth clusters and to massive stars merging. This explains the
top-lightness of the IMF in star clusters in M31. In close binaries also the
masses of the components can be changed due to mass transfer. A large amount of
evidence points to the IMF becoming top-heavy with decreasing metallicity and
above a star-formation-rate density of about 0.1 Msun/(pc^3 yr) of the
cluster-forming cloud core. This is also indicated through the observed
supernova rates in star-bursting galaxies. At the same time, the IMF may be
bottom light at low metallicity and bottom-heavy at high metallicity, possibly
accounting for the results on elliptical galaxies and ultra-faint dwarf
galaxies, respectively.
