2003MNRAS.339..243J

We study a large set of high spatial resolution optical rotation curves of galaxies with the goal of determining the model parameters for a disc embedded within a cold dark matter (CDM) halo, which we model with either a Navarro-Frenk-White (NFW) profile or pseudo-isothermal profile. We show that parameter degeneracies present in lower resolution data are lifted at these higher resolutions. 34 per cent of the galaxies do not have a meaningful fit when using the NFW profile and 32 per cent when using the pseudo-isothermal profile, however only 14 per cent do not have a meaningful fit in either model. In both models we find correlations between the disc baryon fraction f_dand the spin parameter of the halo λ', between f_dand the dark halo mass M₂₀₀, and between M₂₀₀and the concentration parameter c. We show that the distribution of the concentration parameter c, for a NFW halo, is in good agreement with CDM predictions; no significant galaxy population is found with very low values of c. The overall distribution of λ' is in good agreement with theoretical predictions from hierarchical tidal torque theory. The whole sample is also well fitted by a pseudo-isothermal dark halo with a core, but the size of the core is rather small (6 per cent of the virial radius or smaller; for 70 per cent of the sample the core size is less than 2 kpc). Thus we conclude that the profile of dark matter is steep (r^–1 or steeper) down to this radius; large dark matter cores (and therefore very low dark matter central densities) seem to be excluded. Low-surface-brightness galaxies tend to have higher values of λ' for a given f_dand lower values of c for a given mass than high-surface-brightness galaxies. In an appendix we give some useful formulae for pseudo-isothermal profile haloes and we discuss in detail the issue of parameter degeneracies.