The Hot Jupiter Radius Anomaly and Stellar Connections

TL;DR

This paper addresses the enduring puzzle of hot Jupiter radius inflation by synthesizing population observations, interior-structure modeling, and the suite of proposed inflation mechanisms. It emphasizes that heating must deeply deposit energy, with the radiative-convective boundary near $\sim10$ bar in typical hot Jupiters, and that the observed radius enhancement correlates with incident flux rather than orbital period. A key contribution is the quantitative appraisal of heating efficiency, peaking near $T_{\mathrm{eq}}$ of about $1.6$--$1.9\times10^3$ K, and the recognition that multiple processes (e.g., Ohmic dissipation, thermal tides, and advection) may operate in tandem, with reinflation observed in some systems supporting deep heating. The work also highlights observational diagnostics such as intrinsic temperature indicators and Love numbers to break degeneracies in interior models, and calls for more sophisticated 3D atmospheric simulations and targeted observations of magnetic fields and atmospheric composition to further constrain the interior physics and heating pathways.

Abstract

The extremely close proximity of hot Jupiters to their parent stars has dramatically affected both their atmospheres and interiors, inflating them to up to twice the radius of Jupiter. The physical mechanism responsible for this inflation remains unknown, though many proposals have been put forward. I will review the known hot Jupiter population, the proposed inflation mechanisms, and the evidence for and against them collected thus far. In doing so, I will cover the ways that hot Jupiter interiors may be simulated computationally in detail, and present some useful formulas for estimating their radii, heating, intrinsic temperature, and tentative magnetic field strength. I will also cover the related issues of hot Jupiter intrinsic temperatures and radiative-convective boundaries, the potential connection with planetary magnetic fields, and the effects of stellar tides on the planet. Finally, I conclude with the suggestion that more than one mechanism may be operating in concert with each other and propose various avenues for future progress in understanding these objects.

Figures (5)

• Figure 1: The radius of hot (right of the vertical line at $2\times10^8$ erg s$^{-1}$ cm$^{-2}$) and warm Jupiters (left of the line) as a function of incident flux, or equivalently, equilibrium temperature for zero albedo and full heat redistribution. Planets are colored by their mass. The horizontal dashed line is the radius of a 4.5 Gyr old, 1 $M_J$, pure H/He planet (no metals), with no added heating, which is a rough upper-limit on evolved, unheated planets. Note that hot Jupiters are systematically larger than this limit, that their excess radius is correlated with flux, and that this effect is lessened for higher-mass planets.
• Figure 2: The radius of the giant planet population vs their mass, colored by the incident flux such that blue points indicate planets below the hot Jupiter inflation threshold and red points are for those above it. At around 0.3 $M_J$, electron degeneracy pressure dominates the mass-radius relation of the cooler giants, leveling off their radius with mass. For hot Jupiters the flux strongly influences the radius, most strongly for planets in the 0.5 to 2 $M_J$ range. The radii of planets below about 0.2 $M_J$ do not show correlation with either flux or mass.
• Figure 3: The temperature, pressure, and density of a 1 $M_J$ planet with a 15 $M_\oplus$ core and an envelope metallicity $Z_p=0.1$ at specific entropies of 9 and 7 $k_b$ per baryon. These roughly correspond to a hot Jupiter at $T_\mathrm{eq}\sim1500$ K and an evolved warm Jupiter. The cooler interior of the warm Jupiter has a higher density at a given pressure, which in turn also increases the pressures, compressing even the non-thermally-expansive core. The result is much smaller planet: $0.97~R_J$ vs $1.41~R_J$.
• Figure 4: The radius evolution of a Jupiter mass planet under various assumptions about the thermal evolution, with the evolution of the parent (sun-like) star shown in the top panel, as this sets the incident flux on the planet. Grey shading marks the pre- and post-main sequence. The solid blue line depicts a cool giant planet at 1 AU, which experiences no heating delayed cooling. The solid red line shows a hot Jupiter heated entirely by deep heating, which consequently exhibits reinflation; the dashed orange line shows a hot Jupiter experiencing delayed cooling (here a constant factor of 20) and so does not reinflate but is larger at young ages. Finally, the purple dashed line shows a combination of deep heating and reinflation, with the resulting slow initial cooling as well as reinflation.
• Figure 5: The magnetic field strength at the dynamo surface (solid) and polar surface (dashed) for a hot Jupiter as a function of incident flux for various masses (color) from the Christensen2009 scaling relations (Eq. \ref{['eq:bfield']}). Here the intrinsic temperatures from Eqs. \ref{['eq:epsilonThorngren']} and \ref{['eq:tint']} and radii from Eq. \ref{['eq:massRadiusFluxThorngren']} are used. The equivalent zero-albedo equilibrium temperature for efficient redistribution of heat is shown as the top x-axis.