Observational imprints of tidal internal gravity wave dissipation in star-planet systems

TL;DR

This work shows that tidal dissipation via internal gravity waves (IGWs) in stars—through wave breaking in radiative cores and magnetic wave conversion in convective cores—significantly affects star–planet tidal evolution and hot Jupiter demographics. By combining a $Q'$-based tidal framework with IGW-specific onset criteria and wind braking, the authors reproduce both individual spin-up events (e.g., TOI-2458 and GJ 504) and the observed bifurcation in the hot Jupiter population into young and old subsamples, predicting an engendered engulfment fraction of up to about 20% for main-sequence stars in the $0.7$–$1.5\,M_\odot$ range. A population synthesis, anchored to young observed systems, successfully regenerates the orbital-period distribution of older HJs under IGW-driven migration, and yields testable predictions including 2.1–2.4 systems per 100 migrating HJs with cumulative transit-timing shifts $>10$ s over 10 years. The study highlights IGW dissipation as a key mechanism shaping planetary system architectures and provides concrete targets (e.g., transit-timing campaigns) to constrain these processes further.

Abstract

Tidal interactions play a crucial role in the orbital evolution of close-in star-planet systems. There are numerous manifestations of tides, including planetary orbital migration, breaking resonant chains, tidal heating, orbital circularization, spin-orbit alignment, and stellar and planetary spin synchronization. In the present study, we focus on the dissipation of internal gravity waves within stars. We examine two mechanisms: wave breaking in stars with radiative cores and magnetic wave conversion in stars with convective cores. Applying tidal prescriptions modelling these processes, we demonstrate that the enhanced stellar rotation of both TOI-2458 and GJ 504 can be explained by the previous engulfment of a hot Jupiter caused by gravity wave damping. Furthermore, we show that the observed population of hot Jupiters can be divided into two distinct subsamples: those that are too young for gravity wave dissipation and those where it is ongoing. These subsamples exhibit qualitatively different orbital period distributions: young systems have a uniform distribution, while older systems show a steep decline at short orbital periods. Using a population synthesis approach, we successfully reproduce the main features of the older hot Jupiter sample based on the distribution of the younger systems. According to our estimates, up to 20% of the main-sequence stars within the mass range [0.7,1.5] $M_{\odot}$ that once hosted a hot Jupiter may have since engulfed it. Our results highlight the key role of internal gravity wave dissipation in shaping the orbital architectures of hot Jupiter systems.

Figures (22)

• Figure 1: Evolution of the critical magnetic field strength, $B_\mathrm{crit}$, for a 1.2 $M_{\odot}$ solar-metallicity model and tidal period of 0.5 days. Each color represents a different grid resolution, defined by the parameter mesh_delta_coeff, given in the legend. Solid (dotted) lines correspond to models without (with) element diffusion. Gray dashed line shows the radial magnetic field strength of the convective core, $B_r$.
• Figure 2: Critical planetary mass for wave breaking as a function of age for TOI-2458 and tidal period of 0.5 days. Stellar mass and metallicity are $M_{*}$ = 1.05 $M_{\odot}$, [Fe/H] = -0.11. Blue vertical dashed line illustrates the TAMS age. Gray region indicates the age constraint from Subjak. Orange region indicates HJ mass range.
• Figure 3: Evolution of stellar rotation (top panel) and planetary orbital (bottom panel) periods for two star-planet systems, shown in blue and red. Left panel: $M_\mathrm{pl} =$ 0.7 and 4 $M_\mathrm{J}$, and $P_\mathrm{orb} =$ 1.5 and 2.5 days, respectively. Right panel: $M_\mathrm{pl} =$ 10 and 2 $M_\mathrm{J}$, and $P_\mathrm{orb} =$ 1 and 2.5 days, respectively. The black dotted line depicts the rotation period evolution of a solitary star. Circles and crosses denote the onset of IGW breaking and Roche-lobe overflow (and planetary engulfment), respectively. The green square with error bars shows TOI-2458's observed rotation period and age, along with their uncertainties from Subjak.
• Figure 4: Mass of the engulfed planet as a function of "lookback" time. Black lines represent the mass of the planet required to spin-up the host star to the observed present-day rotation ($M_\mathrm{spin-up}$). Red lines indicate the mass of the planet that completes its orbital decay as a result of IGW breaking ($M_\mathrm{decay}$). Solid (dashed) lines correspond to the initial orbital period of 1.5 (2.5) days. Grey and red shaded regions correspond to the uncertainties in $M_\mathrm{spin-up}$ and $M_\mathrm{decay}$ for a 1.5-day planet due to the uncertainties in TOI-2458's measured rotation rate and age, respectively.
• Figure 5: Evolution of stellar rotation period as a function of age for a 1.22 $M_\mathrm{\odot}$ solitary star. Solid black line corresponds to the metallicity from D'Orazi2017; dashed red line represents metallicity from Baburaj2025. Green square depicts GJ 504's observed rotation rate (from DiMauro2022) and age (from D'Orazi2017).