High-Z material nanoparticles are being studied as localized dose enhancers in radiotherapeutic applications. Here, the nano-scale physical dose enhancement of proton, carbon and oxygen ion beam radiation by gold nanoparticles was studied by means of Monte Carlo track structure simulation with the TRAX code. We present 2D distributions and radial profiles of the additional dose and the dose enhancement factor for two geometries which consider an isolated and a water-embedded nanoparticle, respectively. Different nanoparticle sizes (radius of 1.2-22 nm) were found to yield qualitatively different absolute and relative dose enhancement distributions and different maximum dose enhancement factors (up to 20). Whereas the smallest nanoparticles produced the highest local dose enhancement factor close to the metal, larger ones led to lower, more diffuse dose enhancement factors that contributed more at larger distances. Differential absorption effects inside the metal were found to be responsible for those characteristics. For the energy range 15-204 MeVu-1, also a mild trend with ion E/A, regardless of the ion species, was found for embedded nanoparticles. In analogy to the width of the ion track itself, slower ions increased the enhancement at the nanoparticle surface. In contrast, no dependence on linear energy transfer was encountered. For slower ions (3-10 MeVu-1), the enhancement effect began to break down over all distances. Finally, the significance of any indirect physical effect was excluded, giving important hints especially in view of the low probabilities (at realistic concentrations and fluences) of direct ion-NP-hits. The very localized nature of the physical dose enhancement found suggests a strong action upon targets closeby, but no relevant effect at cellular distances. When pondering different possible damage enhancement mechanisms of gold nanoparticles in the context of published in vitro and in vivo experimental results, biological pathways are likely to play the key role.