"Popcorn Planets" are Not Actively Inflated by Eccentricity Tides

TL;DR

This work tests whether eccentricity tides actively inflate popcorn planets by obtaining high-precision MAROON-X radial velocities for three archetypes (TOI-1173 b, WASP-107 b, HAT-P-18 b) and combining them with TESS transit data. The analysis yields tight constraints on the eccentricity vector components, with 95% upper limits of $e<0.037$, $e<0.052$, and $e<0.030$, respectively, effectively ruling out significant ongoing eccentricity-tide heating under typical tidal quality factors $Q_p'$. The findings imply that eccentricity tides cannot explain the observed radii and warm interiors (unless $Q_p'\lesssim 10^{2}$), pointing to alternative heating mechanisms such as obliquity tides or Ohmic dissipation. The results also enhance eclipse-timing precision, enabling efficient planning of thermal-emission studies to further probe the inflationary physics of these low-density planets.

Abstract

Recent discoveries have revealed a population of "popcorn planets" that have masses similar to that of Neptune but radii comparable to Jupiter, leading to exceptionally low bulk densities $ρ_p \lesssim 0.3\,\mathrm{g}\,\mathrm{cm}^{-3}$. Their anomalously-inflated radii, along with recent JWST atmospheric observations, suggest a source of internal heating. Because these planets are nominally too cool to be affected by the hot Jupiter inflation mechanism, dissipation of eccentricity tides within the planet has been proposed as a leading explanation for the source of this heat flux. Using the MAROON-X spectrograph on Gemini-North, we conducted a high-precision radial-velocity campaign to precisely measure the eccentricities of three of these popcorn planets: WASP-107 b, TOI-1173 b, and HAT-P-18 b. We constrained their eccentricities below $e < 0.03$--$0.05$ to 95% confidence, decisively ruling out active heating from eccentricity tides as the cause of these planets' inflated radii (except for the unlikely scenario in which their tidal quality factors are less than the Earth's). An alternative heating mechanism is likely responsible for inflating these planets. Our measurements also provide new constraints on $e\cosω$, significantly shrinking the eclipse timing uncertainties to better than $\pm2.5$ hr and allowing for confident scheduling of thermal emission measurements for these enigmatic planets.

Figures (6)

• Figure 1: Top: RV measurements of TOI-1173, phase-folded to the ephemeris for TOI-1173 b. Per-instrument offsets as well as a global RV trend have been subtracted from the data. The error bars represent the quadrature sum of the reported instrumental uncertainties and an additional RV jitter term unique for each instrument. The black line shows the maximum a-posteriori model for the RV variation caused by TOI-1173 b, while the 1-$\sigma$ limits are shown in light gray. Bottom: Corner plot showing the posterior distribution for the key RV fitted parameters $K$, $\sqrt{e}\cos{\omega}$, and $\sqrt{e}\sin{\omega}$. The inset panel shows the posterior distribution for the planet's orbital eccentricity $e$, with vertical dashed lines denoting the 68%, 95%, and 99.7% upper limits.
• Figure 2: Same as Figure \ref{['fig:toi1173']}, but for WASP-107. In the top panel, the RV variation due to the outer planet WASP-107 c has been subtracted from the data.
• Figure 3: Same as Figure \ref{['fig:toi1173']}, but for HAT-P-18.
• Figure 4: Luminosity due to eccentricity tides for WASP-107 b, as a function of $Q_p^\prime$. The solid and dashed lines correspond to the 68% and 95% upper limits on the tidal luminsoity. Based on JWST atmospheric observations, Sing2024 measured an internal temperature of $460\pm40$ K (blue shaded region). For eccentricity tides to be the source of this internal heat flux, the tidal quality factor would have to be $\log_{10}{Q_p^\prime\xspace} \lesssim 2.5$ given our 1-$\sigma$ upper limit on $e$.
• Figure 5: RV data for WASP-107, with the signal of the inner transiting planet removed and phase-folded to the period of WASP-107c. The best-fit model for WASP-107c is shown in black.