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Register a new userCan Rocky Exoplanets with Rings Pose as Sub-Neptunes?
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Anthony L. Piro
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In our solar system, the presence of rings is exclusive to the gas giants, but is this the case for all planetary systems? In principle, it seems that rocky exoplanets could also have rings, which could be searched for by studying their subtle imprint on the ingress and egress of transits. Unfortunately, such effects are difficult to measure and require high precision photometric and/or spectroscopic observations. At the most basic level though, the presence of rings would result in an increased transit depth that could be mistaken as an anonymously large radius. Motivated by this, I consider how a population of exoplanets with rings would impact radius measurements, focusing on Earth-like exoplanets. It is found that this population introduces an enhancement of inferred radii in the range of $sim2-3R_oplus$, not unlike the sub-Neptunes that have been identified in recent transit surveys. Whether rings can explain all or most sub-Neptunes seems difficult, since it would require a large fraction of rocky planets to have rings ($gtrsim40%$) and/or a factor of $sim2-3$ increase in the number of planets with radii $lesssim1.2R_oplus$. Even if rings cannot explain all sub-Neptunes, this work suggests that focusing on those planets currently classified as sub-Neptunes may be a good starting place for finding rocky planets with rings.
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Data suggest that most rocky exoplanets with orbital period $p$ $<$ 100 d (hot rocky exoplanets) formed as gas-rich sub-Neptunes that subsequently lost most of their envelopes, but whether these rocky exoplanets still have atmospheres is unknown. We identify a pathway by which 1-1.7 $R_{Earth}$ (1-10 $M_{Earth}$) rocky exoplanets with orbital periods of 10-100 days can acquire long-lived 10-2000 bar atmospheres that are H$_2$O-dominated, with mean molecular weight $>$10. These atmospheres form during the planets evolution from sub-Neptunes into rocky exoplanets. H$_2$O that is made by reduction of iron oxides in the silicate magma is highly soluble in the magma, forming a dissolved reservoir that is protected from loss so long as the H$_2$-dominated atmosphere persists. The large size of the dissolved reservoir buffers the H$_2$O atmosphere against loss after the H$_2$ has dispersed. Within our model, a long-lived, water-dominated atmosphere is a common outcome for efficient interaction between a nebula-derived atmosphere (peak atmosphere mass fraction 0.1-0.6 wt%) and oxidized magma ($>$5 wt% FeO), followed by atmospheric loss. This idea predicts that most rocky planets that have orbital periods of 10-100 days and that have radii within 0.1-0.2 $R_{Earth}$ of the lower edge of the radius valley still retain H$_2$O atmospheres. This prediction is imminently testable with JWST and has implications for the interpretation of data for transiting super-Earths.
Mass and radius of planets transiting their host stars are provided by radial velocity and photometric observations. Structural models of solid exoplanet interiors are then constructed by using equations of state for the radial density distribution, which are compliant with the thermodynamics of the high-pressure limit. However, to some extent those structural models suffer from inherent degeneracy or non-uniqueness problems owing to a principal lack of knowledge of the internal differentiation state and/or the possible presence of an optically thick atmosphere. We here discuss the role of corresponding measurement errors, which adversely affect determinations of a planets mean density and bulk chemical composition. Precise measurements of planet radii will become increasingly important as key observational constraints for radial density models of individual solid low-mass exoplanets or super-Earths.
To ascertain whether magnetic dynamos operate in rocky exoplanets more massive or hotter than the Earth, we developed a parametric model of a differentiated rocky planet and its thermal evolution. Our model reproduces the established properties of Earths interior and magnetic field at the present time. When applied to Venus, assuming that planet lacks plate tectonics and has a dehydrated mantle with an elevated viscosity, the model shows that the dynamo shuts down or never operated. Our model predicts that at a fixed planet mass, dynamo history is sensitive to core size, but not to the initial inventory of long-lived, heat-producing radionuclides. It predicts that rocky planets larger than 2.5 Earth masses will not develop inner cores because the temperature-pressure slope of the iron solidus becomes flatter than that of the core adiabat. Instead, iron snow will condense near or at the top of these cores, and the net transfer of latent heat upwards will suppress convection and a dynamo. More massive planets can have anemic dynamos due to core cooling, but only if they have mobile lids (plate tectonics). The lifetime of these dynamos is shorter with increasing planet mass but longer with higher surface temperature. Massive Venus-like planets with stagnant lids and more viscous mantles will lack dynamos altogether. We identify two alternative sources of magnetic fields on rocky planets: eddy currents induced in the hot or molten upper layers of planets on very short period orbits, and dynamos in the ionic conducting layers of ocean planets with ~10% mass in an upper mantle of water (ice).
Planets with 2 $R_{oplus}$ < $R$ < 3 $R_{oplus}$ and orbital period $<$100 d are abundant; these sub-Neptune exoplanets are not well understood. For example, $Kepler$ sub-Neptunes are likely to have deep magma oceans in contact with their atmospheres, but little is known about the effect of the magma on the atmosphere. Here we study this effect using a basic model, assuming that volatiles equilibrate with magma at $T$ $sim$ 3000 K. For our Fe-Mg-Si-O-H model system, we find that chemical reactions between the magma and the atmosphere and dissolution of volatiles into the magma are both important. Thus, magma matters. For H, most moles go into the magma, so the mass target for both H$_2$ accretion and H$_2$ loss models is weightier than is usually assumed. The known span of magma oxidation states can produce sub-Neptunes that have identical radius but with total volatile masses varying by 20-fold. Thus, planet radius is a proxy for atmospheric composition but not for total volatile content. This redox diversity degeneracy can be broken by measurements of atmosphere mean molecular weight. We emphasise H$_2$ supply by nebula gas, but also consider solid-derived H$_2$O. We find that adding H$_2$O to Fe probably cannot make enough H$_2$ to explain sub-Neptune radii because $>$10$^3$-km thick outgassed atmospheres have high mean molecular weight. The hypothesis of magma-atmosphere equilibration links observables such as atmosphere H$_2$O/H$_2$ ratio to magma FeO content and planet formation processes. Our models accuracy is limited by the lack of experiments (lab and/or numerical) that are specific to sub-Neptunes; we advocate for such experiments.
An intriguing, growing class of planets are the super-puffs, objects with exceptionally large radii for their masses and thus correspondingly low densities ($lesssim0.3rm,g,cm^{-3}$). Here we consider whether they could have large inferred radii because they are in fact ringed. This would naturally explain why super-puffs have thus far only shown featureless transit spectra. We find that this hypothesis can work in some cases but not all. The close proximity of the super-puffs to their parent stars necessitates rings with a rocky rather than icy composition. This limits the radius of the rings, and makes it challenging to explain the large size of Kepler 51b, 51c, 51d, and 79d unless the rings are composed of porous material. Furthermore, the short tidal locking timescales for Kepler 18d, 223d, and 223e mean that these planets may be spinning too slowly, resulting in a small oblateness and rings that are warped by their parent star. Kepler 87c and 177c have the best chance of being explained by rings. Using transit simulations, we show that testing this hypothesis requires photometry with a precision of somewhere between ~10 ppm and ~50 ppm, which roughly scales with the ratio of the planet and stars radii. We conclude with a note about the recently discovered super-puff HIP 41378f.
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