Based on statistical study of approximately 15,500 ultraviolet images of auroral emission regions provided by the UVI experiment on the POLAR spacecraft, we show that energy and duration probability distributions of particle precipitation events obey finite-size scaling relations indicative of a self-organized critical (SOC) dynamical state. The revealed relations are invariant with respect to significant changes in the spatial scale of the emission areas, and involve a set of mutually consistent critical exponents providing a quantitative basis for future theoretical studies of multiscale magnetospheric fluctuations. The reported statistical results highlight the importance of cross-scale coupling in the development of nighttime geomagnetic disturbances and suggest that various manifestations of substorm activity associated with localized magnetic reconnections in the magnetotail (small to large scale substorms, pseudo-breakups, BBFs and other types of short-term localized excitations) can be coordinated on the global scale by universal dynamical principle represented by scale-free avalanching in numerical SOC models.