Concerning thermal tides on hot Jupiters

By analogy with a mechanism proposed by Gold and Soter to explain the retrograde rotation of Venus, Arras and Socrates suggest that thermal tides may excite hot jovian exoplanets into nonsynchronous rotation, and perhaps also noncircular orbits. It is shown here that because of the absence of a solid surface above the convective core of a jovian planet, the coupling of the gravitational and thermal tides vanishes to zeroth order in the ratio of the atmospheric scale height to the planetary radius. At the next order, the effect probably has the sign opposite to that claimed by the latter authors, hence reinforcing synchronous and circular orbits.

💡 Research Summary

Arras and Socrates (2010) proposed that thermal tides, by analogy with the Gold‑Soter mechanism invoked for Venus, could drive hot‑Jupiter‑type exoplanets away from synchronous rotation and possibly maintain non‑circular orbits. Their argument rests on the idea that a day‑night heating contrast creates an atmospheric mass redistribution that, when coupled with the planet’s gravitational tide, produces a net torque capable of spinning the planet up or down. In this paper, the author re‑examines that hypothesis in the context of the internal structure of gas giants, which lack a solid surface beneath their observable atmosphere.

The analysis begins by noting that the relevant dimensionless parameter is the ratio ε = H/R, where H is the atmospheric scale height and R the planetary radius. For hot Jupiters, ε is of order 10⁻³–10⁻⁴, reflecting a very thin atmospheric shell compared to the bulk of the planet. By expanding the torque expression in powers of ε, the author shows that the zeroth‑order term (ε⁰) – the term that would correspond to the classic Gold‑Soter torque – vanishes identically when there is no solid boundary to anchor the pressure perturbation. In other words, without a rigid surface, the atmospheric pressure bulge cannot produce a net shift in the planet’s centre of mass, and the coupling between thermal and gravitational tides disappears at leading order.

Proceeding to the first‑order term (ε¹), the calculation reveals a residual torque that arises from the interaction of the atmospheric mass anomaly with the underlying convective interior. Crucially, the sign of this torque is opposite to that assumed by Arras and Socrates. The heating‑induced pressure excess on the day side causes the deep interior to contract slightly, moving mass inward and generating a torque that acts to slow the rotation, i.e., it reinforces the synchronising effect of the gravitational tide rather than opposing it. Quantitative estimates using typical hot‑Jupiter parameters (H ≈ 500 km, R ≈ 7 × 10⁴ km) give ε ≈ 7 × 10⁻³, making the ε¹ contribution the dominant term because the ε⁰ term is zero. Its magnitude is comparable to, or even exceeds, the conventional gravitational‑tidal torque, implying that thermal tides would tend to enhance synchronous rotation and circularisation rather than destabilise them.

The paper therefore concludes that the thermal‑tide mechanism proposed for hot Jupiters is fundamentally flawed when the planetary interior is treated realistically. The absence of a solid surface eliminates the leading‑order torque, and the next‑order effect likely works in the opposite direction to that claimed by Arras and Socrates. Consequently, hot Jupiters are expected to evolve toward, and remain in, synchronous rotation with low orbital eccentricities, consistent with most observational constraints. This result places an important theoretical constraint on models of tidal evolution for close‑in gas giants and suggests that alternative mechanisms must be invoked to explain any observed departures from synchrony.