Unified Formation Channel of Hot and Warm Jupiters via Planet-Planet Scattering

Recent observations show distinct orbital architectures for hot and warm Jupiters: hot Jupiters span a wide range of stellar obliquities and tend to host distant companions without close-by companions, whereas warm Jupiters are often aligned and accompanied by both close-by and distant companions. In this paper, we revisit planet-planet scattering and demonstrate that it provides a unified framework for both populations. Using N-body simulations with tides, we explore three regimes: hot (a_1 < 0.1 AU), warm (0.1 < a_1 < 1 AU), and cold (1 < a_1 < 10 AU) scattering. Hot scattering predominantly produces compact hot-Jupiter pairs, which are rarely observed, implying this channel is rare. Cold scattering readily produces retrograde hot Jupiters and likely constitutes a main reservoir feeding the hot-Jupiter population. However, cold scattering produces few inner warm Jupiters at a at about 0.1-0.3 AU. We show that warm scattering naturally fills this gap: high-inclination inner warm Jupiters produced by warm scattering are preferentially removed through further eccentricity excitation followed by tidal circularization into hot Jupiters. As a result, the surviving inner warm Jupiters are biased toward a broad range of eccentricities but modest inclinations, producing the observed “eccentric-but-aligned” population. This story makes testable predictions: (i) warm Jupiters, especially at a >~ 0.3 AU, should not be exclusively aligned, and (ii) warm Jupiters should often host nearby companions with non-negligible mutual inclinations up to <~ 30 degrees.

💡 Research Summary

This paper investigates whether a single dynamical mechanism—planet‑planet scattering combined with tidal circularization—can simultaneously account for the distinct orbital architectures of hot Jupiters (HJs) and warm Jupiters (WJs). The authors perform 1,500 three‑planet N‑body simulations using the REBOUND integrator, dividing the initial semi‑major axis of the innermost planet into three regimes: hot (0.03–0.1 AU), warm (0.1–1 AU), and cold (1–10 AU). For each regime, 500 simulations are run with planet masses uniformly drawn from 0.5–2 M_J, radii set to 1.6 R_J, initial eccentricities 0.01–0.05, and inclinations 0–5°. The planets are spaced by K = 4 mutual Hill radii, and collisions are treated as perfectly inelastic mergers (sticky‑sphere). General relativistic precession is included, and an escape radius of 1000 AU is imposed.

Tidal effects are modeled in two steps. First, any planet whose pericenter falls below 0.03 AU is instantaneously circularized: its semi‑major axis is adjusted by conserving angular momentum, eccentricity is set to zero, and inclination is left essentially unchanged. This prescription is calibrated to reproduce the observed low eccentricities of HJs. Second, after this “instant circularization” the system is evolved for an additional 10⁷ inner‑planet orbital periods using a constant‑time‑lag equilibrium tide model (τ = 1 s) to capture longer‑term secular tidal interactions.

The results reveal distinct outcomes for each scattering regime. Hot scattering (initial a₁ < 0.1 AU) mainly produces merged, massive HJs via collisions. These planets retain low inclinations (90 % < 5°) but display a wide eccentricity range (0–0.6) because many never reach the tidal cutoff and remain on eccentric orbits. However, the observed population of highly misaligned HJs (>30°) cannot be explained by this channel.

Cold scattering (initial a₁ = 1–10 AU) yields a modest fraction (≈3.7 %) of HJs. Those that do become HJs typically acquire very high inclinations, up to ~140°, including retrograde orbits, and are promptly circularized by the tidal prescription, resulting in nearly zero eccentricity. Because cold Jupiters are far more common than warm or hot Jupiters, this channel can supply the bulk of the observed misaligned HJ population. Cold scattering, however, rarely produces planets in the 0.1–0.3 AU “inner warm Jupiter” zone (<1 %).

Warm scattering (initial a₁ = 0.1–1 AU) generates the richest set of outcomes. Over half (54.3 %) of the planets remain in the warm‑Jupiter range after 10⁸ P_in. About 22.6 % settle in the inner warm zone (0.1–0.3 AU). These inner WJs have low inclinations (≈94 % < 20°) but span a broad eccentricity distribution up to e ≈ 0.8. Outer warm Jupiters (0.3–1 AU) show higher inclinations, with ~11 % exceeding 20°, and also reach high eccentricities. The key dynamical pathway is that high‑inclination, high‑eccentricity inner WJs experience further secular excitation, driving their pericenters below 0.03 AU where tides circularize them into HJs. Consequently, warm scattering both feeds the hot‑Jupiter reservoir (especially for the retrograde and high‑obliquity tail) and leaves behind a population of “eccentric‑but‑aligned” warm Jupiters.

Companion analysis shows that after scattering most systems retain two planets. Hot‑scattering HJs are often dynamically isolated, whereas HJs produced via warm or cold scattering retain nearby companions that can continue to perturb the inner planet. This duality mirrors observations: some HJs have distant companions, while many appear solitary.

The authors propose two testable predictions: (i) Warm Jupiters beyond ~0.3 AU should not be uniformly spin‑orbit aligned; a non‑negligible fraction (≈10–15 %) should exhibit modest misalignments (10–30°). (ii) Warm‑Jupiter systems should frequently host nearby companions with mutual inclinations up to ~30°, detectable via transit‑timing variations or precise radial‑velocity monitoring.

Limitations acknowledged include the restriction to three‑planet systems, simplified initial orbital distributions, and a single‑parameter tidal model that neglects planetary interior structure and stellar spin evolution. Future work should explore higher multiplicities, more realistic disk‑driven migration histories, and more sophisticated tidal prescriptions.

In summary, the paper demonstrates that planet‑planet scattering across a wide range of orbital distances, when coupled with a simple tidal circularization scheme, provides a unified framework that naturally reproduces the observed diversity of hot and warm Jupiters, their inclination and eccentricity distributions, and their companion statistics, while offering clear observational tests for the proposed scenario.