Planet-star interactions with precise transit timing. V. Tidal decay of hot Jupiters through wave breaking

Abstract

Tidal interactions shape the evolution of close-in giant planets and internal gravity-wave breaking offers an efficient pathway for dynamical-tide dissipation, although its population-wide impact remains poorly constrained. We aim to quantify wave-breaking tidal dissipation for 550 hot Jupiters, accounting for stellar-parameter uncertainties. We also aim to identify the most promising systems for detecting orbital decay through transit timing.\\ Stellar masses, radii, and ages were homogeneously redetermined from spectroscopic and photometric data using an isochrone fitting. For each system, these parameters were propagated through a dedicated \texttt{MESA} model grid to calculate the tidal quality factor, wave-breaking probability, orbital decay rate, transit-timing diagnostics and destruction timescales.\\ Wave breaking is predicted to be largely inactive in pre-intermediate-age main sequence (pre-IAMS) stars. The tidal quality factor for systems undergoing wave breaking peaks between $10^6$ and $10^7$, consistent with population-level inferences. About 43\% of planets, primarily with periods $\lesssim3.5$~d, are expected to inspiral on the main sequence, providing a physical explanation for the observed tendency of hot Jupiters to orbit younger stars. A further 41\% inspiral during post-main-sequence evolution within the stages considered. Systems with periods $\lesssim 1$~d, which could in principle experience the strongest tidal forcing, are unlikely to trigger wave breaking, leaving planets on stable orbits. Conversely, the most rapidly inspiralling systems with high wave-breaking probability might display measurable orbital-period shortening only over multi-decade baselines, eluding immediate detection. In contrast, the demographic imprint of wave breaking on occurrence rates should emerge more readily, with the first signs already visible in current population statistics.

Figures (9)

• Figure 1: Predictions of tidal interactions in the WASP-4 system, shown as an illustrative example of our modelling outcome. The first column shows the histogram of $Q'_\mathrm{WB}$ values. The second column shows the evolution of $Q'_\mathrm{WB}$, with the top panel zoomed in around the $1 \sigma$ age estimate. Each line corresponds to one realisation of stellar parameters. Black lines indicate phases when the host's core is convective, grey lines mark phases when the host's core is radiative but wave breaking is not expected, and blue lines denote phases when the host's core is radiative and wave breaking occurs. The estimated $Q'_\mathrm{WB}$ with uncertainties is shown above the column. The third column shows the evolution of $M_\mathrm{crit}$, with red lines indicating phases when the host's core is radiative and wave breaking occurs. The estimated probability of wave breaking is shown above the column. The fourth column presents the evolution of $\dot{P}$, with green lines marking phases when the host's core is radiative and wave breaking occurs. The estimated value of $\dot{P}$ with uncertainties is displayed above the column.
• Figure 2: Orbital evolution of the planet MASCARA-3 A b, shown as an illustrative example of our modelling outcome. Each line in the panels corresponds to one of the 100 realisations used for this system. Colours indicate evolutionary regimes: red, brown, and blue show $M_\mathrm{crit}$, $P$, and $Q'_\mathrm{WB}$, respectively, during phases with active wave breaking. Grey denotes radiative cores where the wave-breaking criterion is not fulfilled. Black marks convective-core phases. The black dotted and dash-dotted vertical lines indicate the positions of the intermediate-age main sequence (IAMS; EEP 353) and terminal-age main sequence (TAMS; EEP 454), respectively. The planet's mass is shown as a purple dashed line in the top two panels. Orange solid and dashed lines trace the tracks ending in the median and $1 \sigma$ ranges of the age or EEP of destruction. Orange circles mark the starting points of these tracks, while orange crosses denote the moment of planetary destruction.
• Figure 3: Joint plot of EEP and orbital period, $P$, for the studied systems. The colour of the points, from blue to red, corresponds to the probability of wave breaking, $f_\mathrm{crit}$, as indicated by the colour bar in the top-right corner. Grey points denote systems with host stars with radiative cores and the wave breaking criterion being unfulfilled, while black points indicate systems with convective core stars. The purple point is the WASP-12 subgiant scenario, as described in Sect. \ref{['subsec: wasp12']}. The shape of the points indicates the evolutionary stage of the host: squares for systems before the IAMS, circles for those between the IAMS and TAMS, and triangles for those beyond the TAMS. The dotted and dash-dotted vertical lines mark IAMS and TAMS evolutionary phases, respectively. The colour scale in the histograms corresponds to the colour of the points. The grey lines show the engulfment period for stars with masses between 0.8 and 1.5 $M_\odot$.
• Figure 4: Relation between the tidal quality factor $Q'_\mathrm{WB}$ on the orbital period derivative, $\dot{P}$, due to wave breaking for the studied systems. Colours and shapes of the points follow the same scheme as in Fig. \ref{['fig: eep_P_orb']}.
• Figure 5: Joint plot of the host mass and EEP for the studied systems, with symbols and colours defined as in Fig. \ref{['fig: eep_P_orb']}.