M ar 1 99 8 Mass Function Gradients and the Need for Dark Matter

There is both theoretical and empirical 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 ρl, with the formation of massive stars being preferentially enhanced in brighter regions. In R136, the bright stellar cluster in 30 Doradus, the IMF gradient is ∂Γ/∂ log ρl = 0.28 ± 0.06, where Γ is the slope of the IMF. If such IMF gradients are indeed general features of galaxies, this implies that 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 surface 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 to 0.42, the rotation curve is approximately flat in the outer disk, with a rotational velocity below ≃ 220 km s−1 only before the traditional dark halo component is added. For a third model in which substantial arm/interarm density contrasts are additionally assumed, the solar vicinity mass density drops to 0.10M⊙pc −3, which is consistent with observations. 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. Subject headings: galaxies: luminosity function, mass function — galaxies: kinematics and dynamics — dark matter — galaxies: halos — Magellanic Clouds — galaxies: evolution Postal address: NASA/GSFC, Laboratory for High Energy Astrophysics, Code 661, Greenbelt MD 20771, USA Department of Physics, University of Maryland, College Park, MD 20742, USA