Mass Function Gradients and the Need for Dark Matter
  There is substantial evidence that the initial mass function (IMF) may be a function of the local star formation conditions. In particular, the IMF is predicted to flatten with increasing local luminosity density, with the formation of massive stars being preferentially enhanced in brighter regions. If IMF gradients are general features of galaxies, several previous astrophysical measurements, such as the surface mass densities of spirals (obtained assuming constant mass to light ratios), were plagued by substantial systematic errors. In this Letter, calculations which account for possible IMF gradients are presented of surface densities of spiral galaxies. Compared to previous estimates, the mass densities corrected for IMF gradients are higher in the outer regions of the disks. For a model based on the Milky Way but with an IMF scaled according to R136, the rotation curve without the traditional dark halo component falls with Galactocentric radius, though slower than it would without IMF gradients. For a second model of the Milky Way in which the IMF gradient is increased by 50%, the rotation curve is approximately flat in the outer disk, with a rotational velocity below ~220 km/s only before the traditional dark halo component is added. These results, if generalizable to other galaxies, not only call into question the assertion that dark matter halos are compatible with the flat rotation curves of spiral galaxies, but also may clarify our understanding of a wide variety of other astrophysical phenomena such as the G-dwarf problem, metallicity gradients, and the Tully-Fisher relation. 
Jason A. Taylor