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Register a new userDeflating Super-Puffs: Impact of Photochemical Hazes on the Observed Mass-Radius Relationship of Low Mass Planets
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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$_{eq}$ $geq$ 500 K), low mass objects ($M_c$ < 4M$_{rm Earth}$) 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.
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Stimulated by the discovery of a number of close-in low-density planets, we generalise the Jeans escape parameter taking hydrodynamic and Roche lobe effects into account. We furthermore define $Lambda$ as the value of the Jeans escape parameter calculated at the observed planetary radius and mass for the planets equilibrium temperature and considering atomic hydrogen, independently of the atmospheric temperature profile. We consider 5 and 10 $M_{oplus}$ planets with an equilibrium temperature of 500 and 1000 K, orbiting early G-, K-, and M-type stars. Assuming a clear atmosphere and by comparing escape rates obtained from the energy-limited formula, which only accounts for the heating induced by the absorption of the high-energy stellar radiation, and from a hydrodynamic atmosphere code, which also accounts for the bolometric heating, we find that planets whose $Lambda$ is smaller than 15-35 lie in the boil-off regime, where the escape is driven by the atmospheric thermal energy and low planetary gravity. We find that the atmosphere of hot (i.e. $T_{rm eq}gtrapprox$ 1000 K) low-mass ($M_{rm pl}lessapprox$ 5 $M_{oplus}$) planets with $Lambda$ < 15-35 shrinks to smaller radii so that their $Lambda$ evolves to values higher than 15-35, hence out of the boil-off regime, in less than $approx$500 Myr. Because of their small Roche lobe radius, we find the same result also for hot (i.e. $T_{rm eq}gtrapprox$ 1000 K) higher mass ($M_{rm pl}lessapprox$ 10 $M_{oplus}$) planets with $Lambda$ < 15-35, when they orbit M-dwarfs. For old, hydrogen-dominated planets in this range of parameters, $Lambda$ should therefore be $geq$15-35, which provides a strong constraint on the planetary minimum mass and maximum radius and can be used to predict the presence of aerosols and/or constrain planetary masses, for example.
Super-puffs -- low-mass exoplanets with extremely low bulk density -- are attractive targets for exploring their atmospheres and formation processes. Recent studies suggested that the large radii of super-puffs may be caused by atmospheric dust entrained in the escaping atmospheres. In this study, we investigate how the dust grows in escaping atmospheres and influence the transit radii using a microphysical model of grain growth. Collision growth is efficient in many cases, leading to hinder the upward transport of dust via enhanced gravitational settling. We find that dust abundance in the outflow hardly exceeds the Mach number at the dust production region. Thus, dust formed at upper atmospheres, say $Plesssim{10}^{-5}$ bar, are needed to launch a dusty outflow with high dust abundance. With sufficiently high dust production altitudes and rates, the dusty outflow can enhance the observable radius by a factor of $sim$2 or even more. We suggest that photochemical haze is a promising candidate of high-altitude dust that can be entrained in the outflow. We also compute the synthetic transmission spectra of super-puff atmospheres and demonstrate that the dusty outflow produces a broad spectral slope and obscures molecular features, in agreement with recently reported featureless spectra. Lastly, using an interior structure model, we suggest that the atmospheric dust could drastically enhance the observable radius only for planets in a narrow mass range of $sim2$--$5M_{rm oplus}$, in which the boil-off tends to cause total atmospheric loss. This may explain why super-puffs are uncommon despite the suggested universality of photochemical hazes.
We present the mass-density relationship (log M - log rho) for objects with masses ranging from planets (M ~ 0.01 M_Jup) through stars (M > 0.08 M_Sun). This relationship shows three distinct regions separated by a change in slope in log M -- log rho plane. In particular, objects with masses in the range 0.3 M_Jup to 60 M_Jup follow a tight linear relationship with no distinguishing feature to separate the low mass end (giant planets) from the high mass end (brown dwarfs). The distinction between giant planets and brown dwarfs thus seems arbitrary. We propose a new definition of giant planets based simply on changes in the slope of the log $M$ versus log rho relationship. By this criterion, objects with masses less than ~ 0.3 M_Jup are low mass planets, either icy or rocky. Giant planets cover the mass range 0.3 M_Jup to 60 M_Jup. Analogous to the stellar main sequence, objects on the upper end of the giant planet sequence (brown dwarfs) can simply be referred to as high mass giant planets, while planets with masses near that of Jupiter can be considered to be low mass giant planets.
We study torques on migrating low-mass planets in locally isothermal discs. Previous work on low-mass planets generally kept the planet on a fixed orbit, after which the torque on the planet was measured. In addition to these static torques, when the planet is allowed to migrate it experiences dynamical torques, which are proportional to the migration rate and whose sign depends on the background vortensity gradient. We show that in discs a few times more massive than the Minimum Mass Solar Nebula, these dynamical torques can have a profound impact on planet migration. Inward migration can be slowed down significantly, and if static torques lead to outward migration, dynamical torques can take over, taking the planet beyond zero-torque lines set by saturation of the corotation torque in a runaway fashion. This means the region in non-isothermal discs where outward migration is possible can be larger than what would be concluded from static torques alone.
As planets grow the exchange of angular momentum with the gaseous component of the protoplanetary disc produces a net torque resulting in a variation of the semi-major axis of the planet. For low-mass planets not able to open a gap in the gaseous disc this regime is known as type I migration. Pioneer works studied this mechanism in isothermal discs finding fast inward type I migration rates that were unable to reproduce the observed properties of extrasolar planets. In the last years, several improvements have been made in order to extend the study of type I migration rates to non-isothermal discs. Moreover, it was recently shown that if the planets luminosity due to solid accretion is taken into account, inward migration could be slowed down and even reversed. In this work, we study the planet formation process incorporating, and comparing, updated type I migration rates for non-isothermal discs and the role of planets luminosity over such rates. We find that the latter can have important effects on planetary evolution, producing a significant outward migration for the growing planets.
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