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

Abstract

The observed mass-radius relationship of low-mass planets informs our understanding of their composition and evolution. Recent discoveries of low mass, large radii 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 (∼0.1-1 Gyr), warm (T eq ≥ 500 K), low mass objects (M c < 4M ⊕ ) 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 towards 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.

A Featureless Infrared Transmission Spectrum for the Super-puff Planet Kepler-79d

“…Rather than fitting a parameterized cloud model, we instead investigate whether microphysical models of photochemical hazes can match our observations. Although these same microphysical models can also be used to study condensate cloud formation, Gao & Zhang (2020) found that photochemical hazes dominate the scattering opacity for planets with temperatures similar to that of Kepler-79d.…”

“…The relatively low densities of super-puffs also make them highly vulnerable to atmospheric mass loss, either due to photoevaporation or Parker wind-like outflow (Lopez & Fortney 2014;Owen & Wu 2016;Cubillos et al 2017;Wang & Dai 2019;Gao & Zhang 2020). The latter mechanism is important for super-puffs because their low gravities result in non-negligible densities at the Bondi radius.…”

“…In principle, these aerosols could be either condensate clouds or photochemical hazes, but the temperature-pressure profiles for most super-puffs are not expected to cross condensation curves in the upper region (P<1 bar) of the atmosphere (e.g., Morley et al 2015;Crossfield & Kreidberg 2017;Gao & Zhang 2020). On the other hand, the relatively low (∼500 K) temperatures of these hydrogen-rich atmospheres make them favorable sites for photochemical haze production, which occurs at relatively low pressures (1-10 μbar) (e.g., He et al 2018aHe et al , 2018bHörst et al 2018;Kawashima & Ikoma 2018Adams et al 2019).…”

“…On the other hand, the relatively low (∼500 K) temperatures of these hydrogen-rich atmospheres make them favorable sites for photochemical haze production, which occurs at relatively low pressures (1-10 μbar) (e.g., He et al 2018aHe et al , 2018bHörst et al 2018;Kawashima & Ikoma 2018Adams et al 2019). Aerosols entrained in an outflowing atmospheric wind could be carried to even lower pressures (1 μbar), significantly reducing the gas density at the τ∼1 surface-and thus at the Bondi radius as well, leading to a reduction in the mass-loss rate (Wang & Dai 2019;Gao & Zhang 2020). This offers an explanation for how these planets have managed to retain their hydrogen-rich envelopes to the present day.…”

The TESS–Keck Survey. I. A Warm Sub-Saturn-mass Planet and a Caution about Stray Light in TESS Cameras*

“…boundary. Second, it is possible that high-altitude aerosols or hazes could be affecting the radius of HD332231b(e.g., Lammer et al 2016;Gao & Zhang 2020). This caveat could be tested through atmospheric characterization.…”