Dark halo properties from rotation curves

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 (d) and the spin parameter of the halo lambda', between f(d) and the dark halo mass M-200 , and between M-200 and 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 lambda' 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 lambda' for a given f(d) and 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.