Deflating Super-puffs: Impact of Photochemical Hazes on the Observed Mass-Radius Relationship of Low-mass Planets

The observed mass-radius relationship of low-mass planets informs our understanding of their composition and evolution. Recent discoveries of low-mass, large-radius objects ("super-puffs") have challenged theories of planet formation and atmospheric loss, as their high inferred gas masses make them vulnerable to runaway accretion and hydrodynamic escape. Here we propose that high-altitude photochemical hazes could enhance the observed radii of low-mass planets and explain the nature of super-puffs. We construct model atmospheres in radiative-convective equilibrium and compute rates of atmospheric escape and haze distributions, taking into account haze coagulation, sedimentation, diffusion, and advection by an outflow wind. We develop mass-radius diagrams that include atmospheric lifetimes and haze opacity, which is enhanced by the outflow, such that young (similar to 0.1-1 Gyr), warm (T-eq >= 500 K), low-mass objects (M-c < 4 M-circle plus) should experience the most apparent radius enhancement due to hazes, reaching factors of three. This reconciles the densities and ages of the most extreme super-puffs. For Kepler-51b, the inclusion of hazes reduces its inferred gas mass fraction to <10%, similar to that of planets on the large-radius side of the sub-Neptune radius gap. This suggests that Kepler-51b may be evolving toward that population and that some warm sub-Neptunes may have evolved from super-puffs. Hazes also render transmission spectra of super-puffs and sub-Neptunes featureless, consistent with recent measurements. Our hypothesis can be tested by future observations of super-puffs' transmission spectra at mid-infrared wavelengths, where we predict that the planet radius will be half of that observed in the near-infrared.