Alignment Parameters: Quantifying Dense Core Alignment in Star-forming Regions

Recent high-resolution observations at millimeter (mm) and sub-mm reveal a diverse spatial distribution for sub-pc scale dense cores within star-forming regions, ranging from clustered to aligned arrangements. To address the increasing volume of observational and simulation data, we introduce "alignment parameters" as a quantitative and reproducible method to automatically assess core alignment. We first demonstrate the effectiveness of these parameters by applying them to artificial test clumps and comparing the results with labels from visual inspection. A threshold value is then proposed to differentiate between "clustered" and "aligned" categories. Subsequently, we apply these parameters to dense cores identified from a sample of ALMA 1.3 mm dust continuum images in high-mass star-forming regions. Analysis exploring correlations between alignment parameters and clump properties rules out the presence of moderate or strong correlation, indicating that clump properties do not appear to strongly influence the outcome of fragmentation. One possible explanation for this is that the fragmentation process is chaotic, meaning that small variations in initial conditions can lead to significant differences in fragmentation outcomes, thus obscuring any direct link between clump properties and core alignment/distribution.