# Inner Planetary System Gap Complexity is a Predictor of Outer Giant Planets

**Authors:** Matthias Y. He, Lauren M. Weiss  
**arXiv:** [2306.08846](https://arxiv.org/abs/2306.08846)  
**Date:** 2023-06-15  
**Summary page:** https://www.summarizepaper.com/en/paper/2306.08846v1/

## Key points

- The study of the connection between inner small planets and outer giant planets is crucial for understanding planet formation across a wide range of orbital separations.
- Kepler provided many compact multi-planet systems at short separations, but little is known about the occurrence of giant companions at larger separations and how they impact inner system architectures.
- Matthias Y. He and Lauren M. Weiss used the catalog of systems from the Kepler Giant Planet Search (KGPS) to investigate how the architectures of inner transiting planets correlate with the presence of outer giant planets.
- For systems with at least three small transiting planets, there appears to be a difference in the distribution of inner-system gap complexity between those with an outer giant planet and those without any outer giants.
- All four inner systems (with 3+ transiting planets) with outer giants have a higher gap complexity than 79% of the inner systems without any outer giants.
- This suggests that one can predict the occurrence of outer giant companions by selecting multi-transiting systems with highly irregular spacings.
- No correlation was found between outer giant occurrence and size similarity or ordering patterns of the inner planets.
- Larger gap complexities in inner systems with an outer giant may indicate that massive external planets play an important role in forming or disrupting these configurations.
- Considering irregularities in spacing is important when predicting occurrences of outer giant companions.

## Summary

The study of the connection between inner small planets and outer giant planets is crucial for our understanding of planet formation across a wide range of orbital separations. While Kepler provided a plethora of compact multi-planet systems at short separations ($\lesssim 1$ AU), relatively little is known about the occurrence of giant companions at larger separations and how they impact the architectures of the inner systems. In this paper, Matthias Y. He and Lauren M. Weiss use the catalog of systems from the Kepler Giant Planet Search (KGPS) to investigate how the architectures of inner transiting planets correlate with the presence of outer giant planets. The authors find that for systems with at least three small transiting planets, there appears to be a difference in the distribution of inner-system gap complexity ($\mathcal{C}$), a measure of deviation from uniform spacings, between those with an outer giant planet ($50 M_\oplus \leq M_p\sin{i} \leq 13 M_{\rm Jup}$) and those without any outer giants. All four inner systems (with 3+ transiting planets) with outer giant(s) have a higher gap complexity ($\mathcal{C} > 0.32$) than 79% (19/24) of the inner systems without any outer giants (median $\mathcal{C} \simeq 0.06$). This suggests that one can predict the occurrence of outer giant companions by selecting multi-transiting systems with highly irregular spacings. To address concerns about multiple comparisons due to several tests and metrics used in this study to test for differences in architectures between inner systems with versus without outer giant planets, additional analyses such as bootstrapping and permutation tests were conducted. Interestingly, no correlation was found between outer giant occurrence and size similarity or ordering patterns of the inner planets. This implies that larger gap complexities in inner systems with an outer giant may indicate that massive external planets play an important role in forming or disrupting these configurations. Overall, this study provides valuable insights into the connection between inner and outer planetary systems and highlights the importance of considering irregularities in spacing when predicting occurrences of outer giant companions.