"Popcorn Planets" are Not Actively Inflated by Eccentricity Tides

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 $\rho_p \lesssim 0.3\,\mathrm{g}\,\mathrm{cm}^{-3}$. 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 $e\cos\omega$, 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.