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The coevolution of migrating planets and their pulsating stars through episodic resonance locking

Nature Astronomy (2024)Cite this article

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Abstract

Hot Jupiters are expected to form far from their host star and move to a close-in, circular orbit through a smooth, monotonic decay due to mild and constant tidal dissipation. Yet, systems exhibiting planet-induced stellar pulsations have recently been found, suggesting unexpectedly strong tidal interactions. Here we combine stellar evolution and tide models to show that dynamical tides raised by eccentric gas giants can excite chains of resonance locks with several modes, which enriches the dynamics seen in single-mode resonance locking of circularized systems. These series of resonance locks yield orders of magnitude larger changes in eccentricity and harmonic pulsations relative to those expected from a single episode of resonance locking or non-resonant tidal interactions. Resonances become more frequent as a star evolves off the main sequence, which provides an alternative explanation for the origin of some stellar pulsators and leads to the concept of ‘dormant migrating giants’. Evolution trajectories are characterized by competing episodes of inward and outward migration and the spin-up or spin-down of the star, which are sensitive to the system parameters. This is a new challenge in modelling migration paths and in contextualizing the observed populations of giant exoplanets and stellar binaries. This sensitivity, however, offers a new window for constraining the stellar properties of planetary hosts through tidal asteroseismology.

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Fig. 1: The rich tidal forcing spectrum of eccentric orbits.
Fig. 2: Episodic and wandering tidal migration by alternating resonance locks.
Fig. 3: Diversity of senses of orbital evolution.
Fig. 4: Sensitivity of orbital evolution to stellar and orbital initial conditions.
Fig. 5: Observability of tidally excited oscillations.

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Data availability

We made use of the orbital configuration of HAT-P-2b and the stellar properties of HAT-P-2 (refs. 15,63). The stellar tidal response was converted to synthetic photometry using the CAP18 photospheric grids71. Simulation results are available via Zenodo at https://doi.org/10.5281/zenodo.11509036 (ref. 68).

Code availability

This work made use of the following publicly available codes: MESA53,54,55,56,57,58 for stellar evolution, GYRE35,60,61,62 for calculating stellar pulsation properties and orbital evolution rates and MSG72 for converting the stellar tidal response into synthetic photometric observables. Tools for coupling these codes for live-planet simulations are publicly available at https://github.com/jaredbryan881/orbev.

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Acknowledgements

J.B. and Z.L.d.B. acknowledge the National Science Foundation for supporting this work through the Graduate Research Fellowship programme (grant no. 1745302) and the Massachusetts Institute of Technology Presidential Fellowship. The simulations presented in this paper were performed on the Engaging cluster at the Massachusetts Green High Performance Computing Center.

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Authors and Affiliations

  1. Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA

    Jared Bryan, Julien de Wit & Zoë L. de Beurs

  2. Department of Astronomy, University of Wisconsin – Madison, Madison, WI, USA

    Meng Sun & Richard H. D. Townsend

  3. Center for Interdisciplinary Exploration and Research in Astrophysics, Department of Physics & Astronomy, Northwestern University, Evanston, IL, USA

    Meng Sun

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Contributions

J.d.W. designed the study. J.B. developed the computational framework for the study with notable support from M.S. and R.H.D.T regarding the stellar and orbital modelling and from J.d.W. and Z.L.d.B. regarding the exoplanetary context and observables. All authors contributed to the manuscript writing, which was led by J.B.

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Correspondence to Jared Bryan or Julien de Wit.

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Extended data

Extended Data Fig. 1 Coherence of single mode damping rates across stellar models.

HR diagram showing the contribution to de/dt of the m = 2, k = 10 orbital harmonic excited by tidal forcing with a fixed orbital configuration and a fixed Z = 0.02 for a range of masses.

Extended Data Fig. 2 Coherence of individual modes across stellar models.

HR diagrams of the amplitude of the (a) k = 10 and (b) k = 30 orbital harmonics excited by tidal forcing of a host star with M = 1.36M⊙ and Z = 0.02262 with a fixed orbital configuration. Amplitudes are for an edge-on view angle.

Extended Data Fig. 3 Decomposition of tidal response of a slowly rotating star into different modes.

(a-b) Rate-change of the orbital eccentricity induced by excitation of quadrupolar (l=2) modes with m = 0, 2 in a host star with M = 1.36M⊙ and Z = 0.02262 by a tidal perturber with evolving orbital configuration. The tidal migration in this case begins at t0 + 1σ. Red and blue points correspond to positive and negative de/dt, respectively. (c-d) Rate-change of the orbital eccentricity decomposed into orbital harmonics k = σm,k/Ωorb. The baseline Ωrot is set to the value estimated for HAT-P-2 by Bonomo et al. (2017). Colors correspond to those in Fig. 2.

Extended Data Fig. 4 Accelerated tidal evolution by intermittent resonance locking.

Comparison between GYRE-tides and constant-Q tidal evolution models. Forward and time-reversed orbital evolution trajectories (left column: eccentricity \(e\) / right column; semi-major axis \(a\)) with perturbations in each of the system parameters: eccentricity \(e\) (a, b), semi-major axis \(a\) (c, d), stellar rotation frequency \(\Omega_{rot}\) (e, f), initial stellar age \(t_0\) (g, h), stellar mass \(M\) (i, j), and stellar metallicity \(Z\) (k, l). The baseline \(\Omega_\mathrm{rot}\) is set to the value estimated for HAT-P-2 by Ref.\cite{bonomo2017gaps}. The solid black line corresponds to the baseline GYRE-tides model. Colored lines correspond to perturbations in the initial orbital and stellar initial conditions as in Fig. 4b. The dotted black line corresponds to the best-fit constant-Q model from Jackson et al.12. Gray lines are evenly spaced between \(\pm 3 \sigma\) in the given parameter except for \(Q_\ast\) (m, n) and \(Q_p\) (o, p), which span the full range considered by Jackson et al.12.

Extended Data Fig. 5 Limits of tidal evolution predictability for small stellar perturbations.

(a-p) Rate-change of orbital eccentricity from 2.6 Gyr to the end of the main sequence for a Z = 0.02262 star with a range of mass perturbations, using a base mass of M = 1.36M⊙, decomposed into m = 0 and m = 2 modes. The orbital evolution rate is calculated with a fixed-orbit tidal perturber with e = 0.575, a = 0.153 and a pseudo synchronous stellar rotation rate. (q) Distribution of \(\dot{e}\) and (r) distribution of \(\dot{a}\) for each mass perturbation in (a-p). (s) Distribution of \(\Delta \dot{e}\) and (t) distribution of \(\Delta \dot{a}\). (u) Distribution of time needed to accumulate a 1σ deviation in e and (v) distribution of time needed to accumulate a 1σ deviation in a. The different colors of distributions are given by the colorbar and denote the perturbations in stellar mass.

Extended Data Fig. 6 Limits of tidal evolution predictability for small stellar perturbations.

(a-p) Rate-change of orbital eccentricity from 2.6 Gyr to the end of the main sequence for a M = 1.36M⊙ star with a range of metallicity perturbations, using a base metallicity of Z = 0.02262, decomposed into m = 0 and m = 2 modes. The orbital evolution rate is calculated with a fixed-orbit tidal perturber with e = 0.575, a = 0.153 and a pseudo synchronous stellar rotation rate. (q) Distribution of \(\dot{e}\) and (r) distribution of \(\dot{a}\) for each metallicity perturbation in (a-p). (s) Distribution of \(\Delta \dot{e}\) and (t) distribution of \(\Delta \dot{a}\). (u) Distribution of time needed to accumulate a 1σ deviation in e and (v) distribution of time needed to accumulate a 1σ deviation in a. The different colors of distributions are given by the colorbar and denote the perturbations in stellar metallicity.

Extended Data Fig. 7 Limits of tidal evolution predictability within observational bounds.

(a-f) Distribution of \(\dot{e}\) and (g-l) distribution of \(\dot{a}\) corresponding to the orbital evolution trajectories of Fig. 4b in the main text. The panels follow Fig. 4b with trajectories differing by perturbations to the initial eccentricity e0, semi-major axis a0, stellar rotation rate Ωrot0, stellar age t0, stellar mass M0, and stellar metallicity Z0. The distribution of time needed to accumulate a 1σ deviation in e is given by Te (m-r) and the distribution of time needed to accumulate a 1σ deviation in a is given by Ta (s-x). The panels follow Fig. 4b with trajectories differing by perturbations to the initial stellar and orbital parameters. The colors are given by the legend on the right and denote perturbations to the stellar and orbital parameters.

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Bryan, J., de Wit, J., Sun, M. et al. The coevolution of migrating planets and their pulsating stars through episodic resonance locking. Nat Astron (2024). https://doi.org/10.1038/s41550-024-02351-3

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