The present study focuses on investigating the magnetic properties and the critical particle size for developing sizable spontaneous magnetic moment of bare Au nanoparticles. Seven sets of bare Au nanoparticle assemblies, with diameters from 3.5 to 17.5 nm, were fabricated with the gas condensation method. Line profiles of the X-ray diffraction peaks were used to determine the mean particle diameters and size distributions of the nanoparticle assemblies. The magnetization curves M(H-a) reveal Langevin field profiles. Magnetic hysteresis was clearly revealed in the low field regime even at 300 K. Contributions to the magnetization from different size particles in the nanoparticle assemblies were considered when analyzing the M(H-a) curves. The results show that the maximum particle moment will appear in 2.4 nm Au particles. A similar result of the maximum saturation magnetization appearing in 2.3 nm Au particles is also concluded through analysis of the dependency of the saturation magnetization M-P on particle size. The M-P(d) curve departs significantly from the 1/d dependence, but can be described by a log-normal function. Magnetization can be barely detected for Au particles larger than 27 nm. Magnetic field induced Zeeman magnetization from the quantum confined Kubo gap opening appears in Au nanoparticles smaller than 9.5 nm in diameter.