Abstract
The decay index n of a horizontal magnetic field is considered to be an important parameter in judging the stability of a flux rope. However, the spatial distribution of this parameter has not been extensively explored so far. In this paper, we present a delineative study of the three-dimensional maps of n for two eruptive events, in which filaments underwent asymmetrical eruptions. The corresponding n-distributions are both found to show that the filaments tend to erupt at abnormal regions (dubbed ABN regions) of n. These ABN regions appear to be divided into two subregions, with larger and smaller n. Moreover, an analysis of the magnetic topological configuration of the ABN regions has been also performed. The results indicate that these ABN regions are associated with a kind of special quasi-separatrix layer across which the connectivity of magnetic field is discontinuous. The presented observations and analyses strongly suggest that the torus instability in ABN regions may play a crucial role for the triggering of an asymmetrical eruption. Additionally, our investigation can provide a way of forecasting how a filament might erupt, and predicting the location for an asymmetrically eruptive filament to be split through analyzing the spatial structure of n.