Is the Diameter of Herschel Crater, Mimas, an Outlier? A Mathematical Framework for Analyzing Planetary Feature Size‐Frequency Distribution Anomalies. Issue 14 (26th July 2021) - Robbins, Stuart J.; Riggs, Jamie D.; Parker, Alex H.
Abstract: Many features on planetary bodies follow a distinct size‐frequency distribution (SFD), and there are practically always outliers. In impact crater studies, that SFD can be approximated with a power‐law, and the nature of power‐laws is there are often lone, singular largest features. An open question is whether these largest features are truly anomalous, or whether they emerge as a statistical feature of a large number of finite samples drawn from stochastic probability distributions, with significant implications for the population that formed them. Here, this question is explored by testing Mimas' largest crater, Herschel. The framework developed answers the question with two main tests, and both show Herschel is not an outlier. This is applied to other planetary bodies, where the null hypothesis is still not rejected. The framework developed is agnostic toward the probability distribution used and can be applied to many other features in planetary science. Plain Language Summary: In science, we try to understand what features fit with others. One way to study this is by looking at the sizes of objects. In many fields of science, histograms of object sizes follow different shapes that can be modeled. However, there will always be outliers—objects that seem like they might be too small or too large to fit with the rest. In many fields, these apparent outliers are ignored, or treated as anomalies, but rarely is there an attempt to understand if they really fit with the other data: Are they truly anomalous, or are they a reflection of the histogram distribution and actually expected? In this study, we provide a framework to answer that question, and we demonstrate it by looking at impact craters. Our test case is the "Death Star" moon around Saturn, named Mimas, and its prominent crater Herschel, which is nearly three times larger than the second‐largest crater on the moon. From our tests, we found that this large gap in size really is expected, so Herschel is not an anomaly. We looked at other bodies and tested their craters, and this framework is applicable to many other fields that ask the same question. Key Points: Some methods that are common in the field to determine if the largest crater is anomalous are statistically unsound We apply new methods to test the null hypothesis—that the largest craters are anomalous—with implications for impactor populations Analyzing Mimas, Moon, Phobos, Šteins, and Arrokoth, we find the null hypothesis cannot be rejected