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 \rho _ { l } , 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 \partial \Gamma / \partial \log \rho _ { { \scriptsize l } } = 0.28 \pm 0.06 , where \Gamma 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 \simeq 220 km s ^ { { \scriptsize -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 0.10 M _ { \odot } 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 .