  Much of our knowledge of galaxies comes from analysing the radiation emitted
by their stars. It depends on the stellar initial mass function (IMF)
describing the distribution of stellar masses when the population formed.
Consequently knowledge of the IMF is critical to virtually every aspect of
galaxy evolution. More than half a century after the first IMF determination,
no consensus has emerged on whether it is universal in different galaxies.
Previous studies indicated that the IMF and the dark matter fraction in galaxy
centres cannot be both universal, but they could not break the degeneracy
between the two effects. Only recently indications were found that massive
elliptical galaxies may not have the same IMF as our Milky Way. Here we report
unambiguous evidence for a strong systematic variation of the IMF in early-type
galaxies as a function of their stellar mass-to-light ratio, producing
differences up to a factor of three in mass. This was inferred from detailed
dynamical models of the two-dimensional stellar kinematics for the large
Atlas3D representative sample of nearby early-type galaxies spanning two orders
of magnitude in stellar mass. Our finding indicates that the IMF depends
intimately on a galaxy's formation history.
