Eccentricity Evolution of Warm Jupiters: The Role of Distant Perturbers and Nearby Companions

TL;DR

This paper investigates how warm Jupiters acquire their eccentric orbits in multiplanet systems by combining distant giant perturbers with nearby super‑Earth companions. Using large N‑body simulations (MERCURIUS/REBOUND with GR) across varied outer‑perturber masses, inclinations, and eccentricities, the authors show that strong inner coupling to a nearby super‑Earth suppresses vZLK‑driven eccentricity growth, producing a bimodal distribution. Reproducing the observed eccentricity spread for systems without companions requires a population of perturbers in dynamically extreme configurations; in contrast, systems with nearby companions stay near-circular. The results support a scenario in which warm Jupiters undergo substantial post‑disk dynamical evolution shaped jointly by distant perturbers and inner companions, with implications for the formation pathways of hot Jupiters and the architecture of exoplanet systems.

Abstract

Warm Jupiters-giant exoplanets with orbital periods between 10 and 200 days-exhibit a broad range of eccentricities and are often accompanied by nearby low-mass planets. Understanding the origins of their orbital architectures requires examining both their migration histories and subsequent dynamical interactions. In this study, we perform extensive N-body simulations to explore how distant giant planet perturbers affect the eccentricity evolution of warm Jupiters and the role of nearby super-Earth companions in mediating these interactions. We find that while distant perturbers can induce large-amplitude eccentricity oscillations in warm Jupiters via the von Zeipel-Lidov-Kozai mechanism, the presence of nearby super-Earth companions often suppresses these variations via strong dynamical coupling. This mechanism naturally leads to a bimodal eccentricity distribution: warm Jupiters with nearby companions tend to maintain low eccentricities, whereas those without exhibit significantly broader eccentricity distributions. We show that reproducing the observed eccentricity distribution of warm Jupiters lacking nearby companions is most naturally explained if a substantial fraction of distant perturbers occupy dynamically extreme orbits, either with large mutual inclinations or high orbital eccentricities. These results support a scenario in which warm Jupiters experience substantial post-disk dynamical evolution, shaped jointly by distant perturbers and nearby companions.

Figures (9)

• Figure 1: The instability rates as functions of the initial warm Jupiter (WJ)-super-Earth (SE) period ratio and perturber properties. The left panel shows how system stability depends on the inner pair's period ratio and the perturber's inclination, while the right panel shows the impact of the perturber's mass and orbital distance on dynamical instability.
• Figure 2: Left: distribution of the coupling parameter $\varepsilon$ and the inner pair's period ratio for stable (blue dots) and unstable (dark red dots) systems. The gray dashed lines mark $\varepsilon=1$ and a period ratio of 1.7. Numbers in each region indicate the corresponding stability rates. Right: distribution of $\varepsilon$ for stable (blue) and unstable (dark red) systems with inner period ratios $>1.7$.
• Figure 3: Maximum eccentricity versus semi-major axis of warm Jupiters in our simulations. Blue dots represent warm Jupiters that retained nearby super-Earths, while red dots indicate warm Jupiters that lose their nearby super-Earths. The dashed curve marks the tidal migration threshold, defined by $R_{\rm p} =a(1-e^2)=$ 0.1 au.
• Figure 4: Cumulative distribution function of the maximum eccentricity reached by warm Jupiters. Results are shown for: warm Jupiters that retain nearby super-Earths from our fiducial simulations (blue), warm Jupiters that lose nearby super-Earths (red), and warm Jupiters that initially lack nearby super-Earths (orange).
• Figure 5: $\Delta e_{\rm max}$ across the $\varepsilon$---mutual inclination space. Colors denote the absolute difference in mean $e_{\rm max}$ between warm Jupiters without primordial super-Earths and those retaining them. The first value in each cell represents the mean $e_{\rm max}$ of warm Jupiters without primordial super-Earths, while the second value corresponds to systems that consistently host nearby super-Earths. Blank cells indicate no stable warm Jupiters retaining nearby super-Earths in the bin.