How martian araneiforms get their shapes: morphological analysis and diffusion-limited aggregation model for polar surface erosion

Abstract

Araneiforms are radially converging systems of branching troughs exhibiting fractal properties. They are found exclusively in the Southern polar regions of Mars and believed to be result of multiple repetitions of cold CO2 gas jets eruptions. Araneiform troughs get carved by the overpressurized gas rushing underneath a seasonal ice layer towards a newly created opening. Current work is an attempt to quantitatively analyze araneiforms patterns and model their formation mechanism. Araneiform shapes range from small and simple structures of one or two connected branches to intricate dendritic patterns several kilometers across. The dendritic quality of most araneiforms are suggestive that they can be described in terms commonly applied to terrestrial rivers. The main difference between rivers and araneiforms from the morphological point of view is that araneiform patterns are not directed or in any way influenced by the local gravitational gradient. We have adapted and for the first time applied to Martian araneiforms qualitative morphological analysis typically used for terrestrial rivers. For several locations in the Martian Southern polar regions we have calculated the largest order of tributaries, tributary densities, and bifurcation ratios. We have shown that the large and well-developed araneiforms (with tributary orders larger than 4) closely follow Horton's law of tributary orders and have bifurcation ratio that falls well inside the range of terrestrial rivers. We have implemented a two-dimensional Diffusion-Limited Aggregation (DLA) model that describes formation of dendrite shapes by mathematical probabilistic means. We compared modeled dendrite shapes to the araneiform shapes observed in the Martian polar regions and evaluated their similarity using the morphological analysis of araneiforms. We showed that DLA model can successfully recreate 2D shapes of different observed araneiforms. To simulate the patterns that deviate from central symmetry it is required to modify the main governing parameter of DLA model: its two-dimensional probability field. An analog to the governing probability field in the case of araneiforms is the gas pressure in the cavity underneath the ice layer right before the gas starts moving towards the newly created escape vent. Thus modeling the creation of araneiform patterns with DLA leads to better understanding of seasonal processes that create them.