Determining the presence of characteristic fragmentation length-scales in filaments

Theories suggest that filament fragmentation should occur on a characteristic fragmentation length-scale. This fragmentation length-scale can be related to filament properties, such as the width and the dynamical state of the filament. Here, we present a study of a number of fragmentation analysis techniques applied to filaments, and their sensitivity to characteristic fragmentation length-scales. We test the sensitivity to both single-tier and two-tier fragmentation, i.e. when the fragmentation can be characterized with one or two fragmentation length-scales, respectively. The nearest neighbour separation, minimum spanning tree (MST) separation, and two-point correlation function are all able to robustly detect characteristic fragmentation length-scales. The Fourier power spectrum and the Nth nearest neighbour technique are both poor techniques, and require very little scatter in the core spacings for the characteristic length-scale to be successfully determined. We develop a null hypothesis test to compare the results of the nearest neighbour and MST separation distribution with randomly placed cores. We show that a larger number of cores is necessary to successfully reject the null hypothesis if the underlying fragmentation is two-tier, N ≳ 20. Once the null is rejected we show how one may decide if the observed fragmentation is best described by single-tier or two-tier fragmentation, using either Akaike's information criterion or the Bayes factor. The analysis techniques, null hypothesis tests, and model selection approaches are all included in a new open-source PYTHON/C library called FRAGMENT.