Effect of the galactic halo modeling on the DAMA-NaI annual modulation result: An extended analysis of the data for weakly interacting massive particles with a purely spin-independent coupling

The DAMA-NaI Collaboration has observed a $4\sigma$ C.L. model-independent effect investigating the annual modulation signature in the counting rate of an NaI(Tl) setup (total exposure of 57986 kg day) and the implications of this effect have been studied under different model-dependent assumptions. In this paper we extend one of the previous analyses, the case of a WIMP with a purely spin-independent coupling, by discussing in detail the implications on the results of the uncertainties on the dark matter galactic velocity distribution. We study in a systematic way possible departures from the isothermal sphere model, which is the parametrization usually adopted to describe the halo. We specifically consider modifications arising from various matter density profiles, effects due to anisotropies of the velocity dispersion tensor and rotation of the galactic halo. The hypothesis of WIMP annual modulation, already favored in the previous analysis using an isothermal sphere, is confirmed in all the investigated scenarios, and the effects of the different halo models on the determination of the allowed maximum-likelihood region in the WIMP mass and WIMP-nucleon cross section are derived and discussed.