# Moderately Eccentric Warm Jupiters from Secular Interactions with Exterior Companions

## TL;DR

This study investigates how external giant planet companions can induce moderate eccentricities in warm Jupiters through secular interactions, challenging simple in-situ or disk migration formation models.

## Contribution

It quantifies the conditions under which external companions can excite warm Jupiter eccentricities, highlighting the importance of mutual inclination and constraining unseen companions.

## Key findings

- High mutual inclinations (≥40°) are often required for eccentricity excitation.
- Most observed outer companions are not sufficiently eccentric to cause observed WJ eccentricities in low-inclination scenarios.
- External companions likely play a significant role in shaping warm Jupiter eccentricities.

## Abstract

Recent studies have proposed that most warm Jupiters (WJs, giant planets with semi-major axes in the range of 0.1-1 AU) probably form in-situ, or arrive in their observed orbits through disk migration. However, both in-situ formation and disk migration, in their simplest flavors, predict WJs to be in low-eccentricity orbits, in contradiction with many observed WJs that are moderately eccentric (e=0.2-0.7). This paper examines the possibility that the WJ eccentricities are raised by secular interactions with exterior giant planet companions, following in-situ formation or migration on a circular orbit. Eccentricity growth may arise from an inclined companion (through Lidov-Kozai cycles), or from an eccentric, nearly coplanar companion (through apsidal precession resonances). We quantify the necessary conditions (in terms of the eccentricity, semi-major axis and inclination) for external perturbers of various masses to raise the WJ eccentricity. We also consider the sample of eccentric WJs with detected outer companions, and for each system, identify the range of mutual inclinations needed to generate the observed eccentricity. For most systems, we find that relatively high inclinations (at least $\sim 40^\circ$) are needed so that Lidov-Kozai cycles are induced; the observed outer companions are typically not sufficiently eccentric to generate the observed WJ eccentricity in a low-inclination configuration. The results of this paper place constraints on possibly unseen external companions to eccentric WJs. Observations that probe mutual inclinations of giant planet systems will help clarify the origin of eccentric WJs and the role of external companions.