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

Abstract

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.

Figures (6)

• Figure 1: A visualization of pathways from hot, warm, and cold scattering. Each percentage is out of the total number of planets at the end of the simulation. Planets involved in collisions are only counted as one planet. The range of 0.1 to 0.3 AU shows the region that best characterizes and defines a warm Jupiter. We refer to these planets as "inner warm Jupiters." This range for warm Jupiters is used in Figure \ref{['fig:a_i_e']}.
• Figure 2: Semi-major axis versus eccentricity and inclination for planets resulting from hot scattering (dark red), warm scattering (orange) and cold scattering (blue). Only 100 of the hot scattering simulations are included for clarity in the hot Jupiter region and to lead to equitable representation of hot Jupiters (since hot scattering produces far more hot Jupiters than warm or cold). In the top left panel, the gray dotted line shows the boundary for a radius of pericenter of 0.03 AU which is used in our tidal prescription. The bottom panel shows eccentricity versus inclination for all planets with a semi-major axis below 0.3 AU (inner warm and hot Jupiters). 5.9% of the inner warm Jupiters have eccentricities above 0.2 and inclinations above 20$^\circ$.
• Figure 3: An analysis of the minimum pericenter distance reached during a simulation compared to the inclination at this moment of minimum radius of pericenter, specifically in simulations excluding our tidal prescription. Our tidal distance of 0.03 AU is added for reference. Each point represents a planet from the 500 warm scattering simulations.
• Figure 4: Distributions of the separation in semi-major axis between the inner and outer planet for two-planet systems in terms of their mutual Hill radius from hot, warm, and cold scattering. Only two-planet systems where the inner planet is an inner warm Jupiter ($0.1 < a < 0.3$ AU) or hot Jupiter ($a < 0.1$) are shown. The red bars indicate hot Jupiters, while the orange bars indicate inner warm Jupiters.
• Figure 5: Period ratio versus semi-major axis of the innermost planet with a color bar representing mutual inclination (left-most column), eccentricity of the outer planet (middle column), and eccentricity of the inner planet (right-most column) shown. Only systems with 2 or more planets are accounted for and 1 planet systems are ignored.