Warm Jupiter Tidal Migration Can Spare Inner Planets; Hot Jupiter Tidal Migration May Not

TL;DR

This paper addresses whether an inner, ultra-compact planet can endure the high-eccentricity tidal migration of an outer Jupiter-mass companion. It combines analytic scaling with N-body simulations that include equilibrium tides and general-relativistic precession to map a survival boundary in terms of periastron distance and mutual Hill spacing, identifying a critical region around Delta_H_peri ≈ 14 where survival is possible for warm Jupiters, and showing that hot Jupiters typically destabilize inner companions. Applying the framework to observed systems reveals that none of the known hot/warm Jupiter-plus-inner-planet configurations could have formed via tidal high-eccentricity migration, though a narrow parameter space exists for warm Jupiters to preserve inner planets and still circularize within ~1 Gyr. The results offer a practical diagnostic to distinguish disk-driven from tidal migration in multi-planet systems with close-in gas giants and highlight the rarity of tidal assembly scenarios in current exoplanet demographics.

Abstract

In this work, we investigate the dynamical survival of short-period inner planets during the high-eccentricity tidal migration of companion exterior giant planets. Using a combination of analytic arguments and N-body simulations including equilibrium tides and general relativistic precession, we find the boundary in parameter space where an inner companion can remain dynamically stable. We find that survival requires a periastron separation exceeding roughly 14 mutual Hill radii at closest approach. Below this threshold, secular eccentricity exchange, orbit crossing, and/or tidal evolution can lead to the destruction of the inner planet. We apply our methodology to the current exoplanet sample and find that none of the known systems containing a short-period giant and an inner companion could have assembled via high-eccentricity tidal migration. However, warm Jupiters with larger periastron distances ($q_{\mathrm{out}} \sim 0.05-0.08$ AU, corresponding to final observed semi-major axis values $a_{\mathrm{out}} \sim 0.10-0.16$ AU) can allow the survival of short-period inner planets while potentially also circularizing on $\lesssim 1$ Gyr timescales. Our results provide a framework for distinguishing disk migration from tidal migration in observed multi-planet systems containing close-in gas giants.

Figures (8)

• Figure 1: Schematic representation of planetary systems known to contain an inner small planet and an outer short-period giant planet (hot or warm Jupiters) and no other nearby planets. The horizontal axis shows the semi-major axis of each planet. Marker size scales with planet radius. Hot Jupiters (orange) and warm Jupiters (yellow) are distinguished from smaller inner companions (dark blue). Data obtained from the NASA Exoplanet Archive Christiansen2025, 05/13/2025.
• Figure 2: Mutual Hill‐radius separation $\Delta_H$ at periastron between a fixed inner planet ($a_{\rm{in}} = 0.02\,$AU, $m_{\rm{in}}=1\ M_\oplus$) and a migrating outer Jupiter-mass planet ($m_{\rm{out}}=1 \ M_{J}$, initial $a_{\rm{out}} = 2$ AU) around a $1\,M_\odot$ star. The bottom x-axis shows the outer Jupiter’s periastron distance $q_{\rm{out}}$ during tidal migration, while the top x‐axis gives the corresponding final semi-major axis $a_{\rm{out}}$ after tidal migration is complete. The horizontal dashed lines mark common literature stability thresholds at $\Delta_H = 2\sqrt3$Chambers1996 and $\Delta_H=10$. The vertical dashed line indicates the periastron corresponding to a 10 day orbital period, the commonly used demarcation between hot and warm Jupiters.
• Figure 3: Mutual Hill–radius separations $\Delta_H$ for each two‐planet system, sorted by their initial separation $\Delta_{H,i}$ along the horizontal axis. Teal circles mark the initial $\Delta_{H}$; those falling below zero (shaded red region) represent systems where the orbits would have crossed during tidal migration, thus excluding that assembly pathway. Black circles show the current-day observed separations $\Delta_{H}$, and vertical lines connect each system’s initial and final values. Dashed horizontal lines at $\Delta=2\sqrt{3}$ and $\Delta=10$ denote two typical literature stability thresholds in units of mutual Hill radii. Planet parameters obtained from Tingley2014Bruno2015Morton2016Hjorth2019Huang2020Canas2019Dawson2021Valizadegan2022Tran2022Trifonov2023Maciejewski2023Mantovan2024Korth_2024Borsato2024.
• Figure 4: Tidal circularization timescales, computed using Equation \ref{['eq:tcirc']}, as a function of periastron distance $q_{\mathrm{out}}$ for a highly eccentric ($e = 0.9$) hot Jupiter orbiting a Sun-like star. The planet is assumed to have Jupiter-like mass and radius ($M_p = 1\,M_{jup}$, $R_p = 1\,R_{jup}$), while the host star has mass $M_\star = 1\,M_\odot$ and radius $R_\star = 1\,R_\odot$. The tidal quality factors are set to $Q_p = 10^4$ and $Q_\star = 10^6$, with a planetary Love number $k_2 = 0.5$. The secondary x-axis shows the corresponding final semi-major axis for the hot Jupiter after full circularization according to Equation \ref{['eq:ang_conservation']}. All timescales are computed assuming non-time-varying planetary and stellar structure. For these fiducial values, proto-hot Jupiters outside of periastron distance $q_{\mathrm{out}}\sim0.06 - 0.08$ are unlikely to circularize by the time that we observe them.
• Figure 5: One illustrative simulation from our sample, showing a dynamically stable evolution in which an inner companion at $a_{\rm{in}} \approx 0.015$ remains stable, bound, and with relatively low orbital eccentricity as its outer Jupiter-mass companion tidally migrates from an initial periastron distance $q_{\rm{out}} \approx 0.063$ AU. Top panel: The evolution of the inner planet in $(\omega_{\mathrm{in}} - \omega_{\mathrm{out}}, e_{\mathrm{in}})$ phase space at three distinct times during the integration, illustrating the transition of the inner planet's dynamics from planet-planet induced libration at early times to circularization driven by stellar effects at late times. Bottom panel: The orbital evolution of both planets over time. Solid lines represent the semi-major axes, while the shaded regions indicate the range between periastron and apastron distances.