RJ-plots: An improved method to classify structures objectively

The interstellar medium is highly structured, presenting a range of morphologies across spatial scales. The large data sets resulting from observational surveys and state-of-the-art simulations studying these hierarchical structures means that identification and classification must be done in an automated fashion to be efficient. Here we present RJ-plots, an improved version of the automated morphological classification technique J-plots developed by Jaffa et al. (2018). This method allows clear distinctions between quasi-circular/elongated structures and centrally over/under-dense structures. We use the recent morphological SEDIGISM catalogue of Neralwar et al. (2022) to show the improvement in classification resulting from RJ-plots, especially for ring-like and concentrated cloud types. We also find a strong correlation between the central concentration of a structure and its star formation efficiency and dense gas fraction, as well as a lack of correlation with elongation. Furthermore, we use the accreting filament simulations of Clarke et al. (2020) to highlight a multi-scale application of RJ-plots, finding that while spherical structures become more common at smaller scales they are never the dominant structure down to $r\sim0.03$ pc.