The distribution of dark matter in galaxies. I - Models of spiral galaxies

We examine the limits on the distribution of dark matter in galaxies from published rotation curves and photometry. We assume constant mass-to-light ratios for the luminous components and an isothermal model for the halo, and examine a collection of 37 optical rotation curves of Sb and Sc galaxies and 16 H I rotation curves to constrain the halo's core radius rc_, and the asymptotic velocity vₘax_. We find that the central density of the halo (proportional to v²^ₘax_ r^-2ᶜ_) is often well determined. In only three cases, NGC 2403, NGC 2903, and NGC 3198, do we find that the data constrain both rc_, and υₘax_ rather than just the ratio vₘax_/rc_. These three galaxies are all Sc's and span less than a factor of 2 in luminosity. The constraints are similar in each of the three cases. The limits are typically rc_ <~ 8 kpc and vₘax_ <~ 170 km s^-1^. Experimenting with rotation curves constructed by manipulating that observed for NGC 3198, we find that high-quality data to 6. 5-8 disk scalelengths is needed to constrain the parameters. We test whether the observations determine the form of the density distribution by fitting models with r^-3^ and r^-4^ density profiles outside a core radius. We find acceptable fits for such models.