The number of missing ordinal patterns (NMP) is the number of ordinal patterns that do not appear in a series after it has been symbolized using the Bandt and Pompe methodology. In this paper, the NMP is demonstrated as a test for nonlinearity using a surrogate framework in order to see if the NMP for a series is statistically different from the NMP of iterative amplitude adjusted Fourier transform (IAAFT) surrogates. It is found that the NMP works well as a test statistic for nonlinearity, even in the cases of very short time series. Both model and experimental time series are used to demonstrate the efficacy of the NMP as a test for nonlinearity.

NASA’s TESS mission is expected to discover hundreds of M dwarf planets. However, few studies focus on how planets form around low-mass stars. We aim to better characterize the formation process of M dwarf planets to fill this gap and aid in the interpretation of TESS results. We use ten sets of N-body planet formation simulations which vary in whether a gas disc is present, initial range of embryo semi-major axes, and initial solid surface density profile. Each simulation begins with 147 equal-mass embryos around a 0.2 solar mass star and runs for 100 Myr. We find that planets form rapidly, with most collisions occurring within the first 1 Myr. The presence of a gas disc reduces the final number of planets relative to a gas-free environment and causes planets to migrate inward. We find that roughly a quarter of planetary systems experience their final giant impact inside the gas disc, suggesting that some super-Earths may be able to reaccrete an extended gaseous envelope after their final giant impact, though these may be affected by additional process such as photoevaporation. In addition, we find that the final distribution of planets does not retain a memory of the slope of the initial surface density profile, regardless of whether or not a gas disc is present. Thus, our results suggest that present-day observations are unlikely to provide sufficient information to accurately reverse-engineer the initial distribution of solids.

It is often assumed that the "Kepler dichotomy" -the apparent excess of planetary systems with a single detected transiting planet in the Kepler catalog -reflects an intrinsic bimodality in the mutual inclinations of planetary orbits. After conducting 600 simulations of planet formation followed by simulated Kepler observations, we instead propose that the apparent dichotomy reflects a divergence in the amount of migration and the separation of planetary semimajor axes into distinct "clusters". We find that our simulated high-mass systems migrate rapidly, bringing more planets into orbital periods of less than 200 days. The outer planets are often caught in a migration trap -a range of planet masses and locations in which a dominant co-rotation torque prevents inward migration -which splits the system into two clusters. If clusters are sufficiently separated, the inner cluster remains dynamically cold, leading to low mutual inclinations and a higher probability of detecting multiple transiting planets. Conversely, our simulated low-mass systems typically bring fewer planets inside 200 days, forming a single cluster that quickly becomes dynamically unstable, leading to collisions and high mutual inclinations. We propose an alternative explanation for the apparent Kepler dichotomy in which migration traps during formation lead to fewer planets inside the Kepler detection window, and where mutual inclinations play only a secondary role. If our scenario is correct, then Kepler's STIPs (Systems with Tightly-packed Inner Planets) are a sample of planets that escaped capture by co-rotation traps, and their sizes may be a valuable probe into the structure of protoplanetary discs.

It is often assumed that the “Kepler dichotomy”—the apparent excess of planetary systems with a single detected transiting planet in the Kepler catalog—reflects an intrinsic bimodality in the mutual inclinations of planetary orbits. After conducting 600 simulations of planet formation followed by simulated Kepler observations, we instead propose that the apparent dichotomy reflects a divergence in the amount of migration and the separation of planetary semimajor axes into distinct “clusters.” We find that our simulated high-mass systems migrate rapidly, bringing more planets into orbital periods of less than 200 days. The outer planets are often caught in a migration trap—a range of planet masses and locations in which a dominant corotation torque prevents inward migration—which splits the system into two clusters. If clusters are sufficiently separated, the inner cluster remains dynamically cold, leading to low mutual inclinations and a higher probability of detecting multiple transiting planets. Conversely, our simulated low-mass systems typically bring fewer planets within 200 days, forming a single cluster that quickly becomes dynamically unstable, leading to collisions and high mutual inclinations. We propose an alternative explanation for the apparent Kepler dichotomy in which migration traps during formation lead to fewer planets within the Kepler detection window, and where mutual inclinations play only a secondary role. If our scenario is correct, then Kepler’s Systems with Tightly packed Inner Planets are a sample of planets that escaped capture by corotation traps, and their sizes may be a valuable probe into the structure of protoplanetary disks.