Towards a new understanding of star formation in galaxies

The stellar IMF is the distribution function of stellar masses born together in
one causally connected event within a spatial region of not more than a few pc
in extend. It cannot be measured in any system, but statistical methods
combined with corrections for dynamical bias allows one to infer the existence
of a universal canonical IMF as the parent distribution from which the various
simple stellar populations are drawn. There is no evidence for variation of the
IMF except at the highest star-burst cluster masses above 10^6 Msun and in the
immediate vicinity of the Galactic super massive black hole. The IMF in a whole
galaxy is, in contrast, that of a composite population such that the IMFs of
the individual simple populations must be added. This leads to an integral over
the currently forming star cluster population and implies the integrated
galactic IMF (IGIMF) to be top light. The steepness of the IGIMF for massive
stars can be shown to depend on the star formation rate of the galaxy. This
leads to an entirely new avenue of understanding galaxy evolution with
potentially deep insights into fundamental physics issues.