Interiors of ice-rich planets: mixed ice and rock
Although water is necessary for life as we know it, a large fraction of water in exoplanet interiors may lead to unique conditions, under which the interior structure differs from the simple layered structure of a water ocean on top of a rocky surface, that supports life. In this work we use experimental data of ice-rock interaction at high pressure, and calculate detailed thermal evolution for possible interior configurations of ice-rich planets, in the mass range of super-Earth to Neptunes (5-15 Earth masses). We model the effect of migration inward on the ice-rich interior by including the influences of stellar flux and envelope mass loss.
Our main findings are:
- Ice (water) and rock are expected to remain mixed, due to miscibility at high pressure, in substantial parts of the interiors of ice-rich planet in the mass range of 5-15 Earth masses, even after Gyrs of thermal evolution.
- Effect of migration on the thermal evolution of the deep interior is small. The deep interior of planetary twins that have migrated to different distances from the star (beyond 0.03AU) are similar, if mass loss is insignificant.
- Significant mass loss results in separation of the water from the rock on the surface and emergence of a volatile atmosphere of less than 1% of the planet's mass. In the absence of hydrogen-helium envelope the ice and rock demix at the surface (at distances larger than 0.02AU). The rock is then dissolved in the deeper layers where ice and rock remain mixed, and the outer envelope is composed of water in steam / condensed form.
- The mass of the atmosphere of water / steam is limited by the ice-rock interaction. The total ice / water content of a planet cannot be inferred from the atmospheric mass and abundance, as large fraction of the ice may be stored in the interior, mixed with the rock.
- Mixing of elements by convection (convective-mixing) is limited in ice-rich planets. The gradual structure is mostly stable along the thermal evolution. Planets with gradual metal distribution have hotter deep interiors, in comparison to core-envelope structure.
- Ice-rich planets with substantial gas envelopes develop ice-rock demixing only in the outer gas envelope, where water is miscible in the hydrogen.
- Mass loss increases the metal enrichment of the envelope. For planets with gradual composition distribution the mass loss flattens the composition gradient, resulting in large scale convection and fast cooling.
A new perspective on interiors of ice-rich planets: Ice-rock mixture instead of ice on top of rock / Vazan, Allona; Sari Re’em; Kessel RonitArxiv version Journal version Pubic summary Pressure-temperature profiles of 15 Earth mass planets with 10% gas at the age of 10 Gyr. The same metal (ice and rock) content is gradually distributed (red) or located in a pure metal core surrounded by a gas envelope (blue). Core-envelope boundary is marked with blue CEB arrow, and the gradual composition distribution region expands between the red A-B arrows. The planets are located at 10AU (dashed) or migrated to 0.1AU (solid). In the shaded areas, taken from Fig. 2, ice and rock are expected to stay mixed. Above the hydrogen-water mix curve (green), water is miscible in hydrogen. The mass in the shaded area is > 99% of the planet’s mass for all cases. Schematic interior structure of ice-rich planets for different mass loss scenarios: no mass loss (left), hydrogen mass loss (middle), all gas mass loss (right). Each sketch is split to show the two interior structures we examined. The ice & rock mixture region covers more than 99% of the planet's mass for planets in the mass range of 5M⊕ to 15M⊕ (and above).
Explaining the low luminosity of Uranus – interior evolution model
The low luminosity of Uranus is a long-standing challenge in planetary science. Simple adiabatic models are inconsistent with the measured luminosity, which indicates that Uranus is non-adiabatic because it has thermal boundary layers and/or conductive regions. A gradual composition distribution acts as a thermal boundary to suppress convection and slow down the internal cooling. Here we investigate whether composition gradients in the deep interior of Uranus can explain its low luminosity, the required composition gradient, and whether it is stable for convective mixing on a timescale of some billion years. We varied the primordial composition distribution and the initial energy budget of the planet, and chose the models that fit the currently measured properties (radius, luminosity, and moment of inertia) of Uranus. We present several alternative non-adiabatic internal structures that fit the Uranus measurements.
Our main findings:
- A composition gradient in the interior of Uranus is stable and naturally explains Uranus low luminosity, without the need of artificial thermal boundaries. There are different types of composition gradients that are stable during the evolution and are sufficient to slow down the cooling and fit the observed radius, moment of inertia, and luminosity.
- The stable composition gradient suppresses convection and slows the interior cooling. As a result, the interior of Uranus might still be very hot, in spite of its low luminosity.
- The initial energy content of Uranus cannot be greater than 20% of its formation (solid accretion) energy. Primordial models with higher energy fail to fit the observations.
- Two- and three-layer models of Uranus are able to fit Uranus properties only if the interior is very cold and (partially) conductive. Therefore Uranus is probably non-adiabatic, and cannot be modelled by a simple large-scale convection model. The effect of the non-adiabatic cooling of Uranus (by composition gradient) on its current radius is 5–10%.
- The total heavy-element mass fraction in Uranus is affected by the non-adiabatic evolution. The hot gradual models are more metal rich (up to 95%) than the cold models (∼85%).
- Our models are consistent with its metal-rich atmosphere and with the predictions for the location where its magnetic field is generated.
Explaining the low luminosity of Uranus: a self-consistent thermal and structural evolution / Vazan, Allona; Helled RavitPublisher ArXiv version Thermal and structural evolution of Uranus (color) as a function of the radius layer (y-axis) and age (x-axis). Upper panel: heavy-element mass fraction. Bottom panel: temperature profile. The four cases are of valid Uranus models of different types: distinct layers (left), steep gradient (second), shallow gradient (third), and metal-rich shallow gradient (right).
On the aspect ratio of ‘Omuamua – surface properties matter
As a first observed interstellar object, ’Oumuamua introduced new challenges to small bodies theories. Some of the challenges are related to the irregular elongated shape that is derived from its lightcurve ratio. The large brightness variation in the observed lightcurve of ’Oumuamua is probably related to its shape, i.e., to the ratio between its longest axis and its shortest axis (aspect ratio). Several approaches found the aspect ratio of ’Oumuamua to be unusually elongated. Moreover, the spin axis orientation has to be almost perpendicular to the observer in order to obtain such an extreme lightcurve, a configuration which is unlikely. However, interstellar ’Oumuamua may have different surface properties than we know in our solar system. Therefore, in this work we widen the parameter space for surface properties beyond the asteroid-like models and study its effect on ’Oumuamua’s lightcurve. We calculate reflection from a rotating ellipsoidal object for four models: Lambertian reflection, specular reflection, single scattering diffusive and backscatter . We then calculate the probability to obtain a lightcurve ratio larger than the observed, as a function of the object’s aspect ratio, assuming an isotopic spin orientation distribution. We find the elongation of ’Oumuamua to be less extreme for the Lambertian and specular reflection models. Consequently, the probability to observe the lightcurve ratio of ’Oumuamua given its unknown spin axis orientation is larger for those models. We conclude that different surface reflection properties may suggest alternatives to the extreme shape of ’Oumuamua, relieving the need for complicated formation scenario, extreme albedo variation, or unnatural origin. Although the models suggested in this work are for ideal ellipsoidal shape and ideal reflection method, the results emphasize the importance of surface properties for the derived aspect ratio.
On the aspect ratio of ’Oumuamua: less elongated shape for irregular surface properties / Vazan, Allona; Sari Re’emPublication in MNRAS ArXiv version An illustration of Lambertian (left) and specular (right) reflection. Up: reflection from a plane unit surface area. Bottom: overall reflection from an ellipsoid. The surface area on each ellipsoid that contributes the observed brightness appears in red. The probability to observe a lightcurve ratio of minimum 10 (left) and 6 (right) as a function of the object aspect ratio, for different surface reflection conditions: Lambertian (red), specular (green), backscatter (blue), and Lommel-Seeliger (black). For all cases phase angle is Θ = 24◦
Planet formation by pebble accretion – emergence of composition gradient in the interior
In this work we compute planet formation by pebble accretion, focusing on deposition of accreted solids in the planetary interior. In this scenario, planets grow by the accretion of cm- to-m-sized pebbles instead of km-sized planetesimals. One of the main differences with planetesimal-driven core accretion is the increased thermal ablation experienced by pebbles. Small silicate, pebble-sized particles will sublimate in the atmosphere when they hit the sublimation temperature (T ∼ 2000 K). We conduct numerical calculations of the atmosphere of an accreting planet, solving the stellar structure equations, augmented by a non-ideal equation of state that describes a hydrogen/helium-silicate vapor mixture. We follow the energy and material deposition of the accreted solids (rocks and ices) to find the effect of it on the formation process and on the interior structure of the planet at the end of the formation phases. When pebbles sublimate before reaching the core, insufficient (accretion) energy is available to mix dense, vapor-rich lower layers with the higher layers of lower metallicity. A gradual structure in which Z decreases with radius is therefore a natural outcome of planet formation by pebble accretion. Such composition gradient is consistent with indications in the solar system gas giants Jupiter and Saturn by the Juno and Cassini spacecraft.
Our main findings are:
- The typical core mass that we find is around 1.5–2 M⊕. Further accretion enriches the gas envelope with metal vapors.
- The complete vaporization of pebbles naturally enriches the atmosphere in heavy elements. Based on elementary energy considerations, the dense, heavy metal layer may only partially mix with the H/He gas. Consequentially, a compositional gradient naturally forms.
- Temperature and metallicity profiles differ significantly between the ideal and non-ideal EoS runs.
- In the outer disk regions, where the molecular opacity is low, small pebbles dominate the opacity. When also the pebble accretion rate is high, atmospheres become very polluted. The crossover mass becomes large and its value independent of distance.
- When planets stop accreting pebbles, accretion of nebular gas will quickly take over as the atmospheres loose their opacity. Thus more viable mechanism is required to prevent sub-Neptunes from reaching runaway gas accretion.
How planets grow by pebble accretion. III. Emergence of an interior composition gradient / Ormel, Chris; Vazan, Allona; Brouwers, MarcPublication in A&A ArXiv version Metallicity and temperature profiles for several runs at 0.2 au: with an accretion rate of 10^−5 M⊕ per year (top); a lower accretion rate of 10−6 M⊕ per year (center); and a pebble opacity corresponding to mm-sized pebbles. Profiles are shown when M = 5, 10 and 20 M⊕ are reached (unless crossover is reached sooner). The temperature in the classical core region, which is not modelled, indicates the temperature at the core-envelope boundary when the material was incorporated.