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The temperatures of observed protoplanetary disks are not sufficiently high to produce the accretion rate needed to form stars, nor are they sufficient to explain the volatile depletion patterns in CM, CO, and CV chondrites and terrestrial planets. We revisit the role that stellar outbursts, caused by high-accretion episodes, play in resolving these two issues. These outbursts provide the necessary mass to form the star during the disk lifetime and provide enough heat to vaporize planet-forming materials. We show that these outbursts can reproduce the observed chondrite abundances at distances near 1 au. These outbursts would also affect the growth of calcium-aluminum-rich inclusions and the isotopic compositions of carbonaceous and noncarbonaceous chondrites.

 

Tidally locked worlds provide a unique opportunity for constraining the probable climates of certain exoplanets. They are unique in that few exoplanet spin and obliquity states are known or will be determined in the near future: both of which are critical in modelling climate. A recent study shows the dynamical conditions present in the TRAPPIST-1 system make rotation and large librations of the substellar point possible for these planets, which are usually assumed to be tidally locked. We independently confirm the tendency for planets in TRAPPIST-1-like systems to sporadically transition from tidally locked libration to slow rotation using N-body simulations. We examine the nature and frequency of these spin states to best inform energy balance models which predict the temperature profile of the planet’s surface. Our findings show that tidally locked planets with sporadic rotation are able to be in both long-term persistent states and states with prolonged transient behaviour: where frequent transitions between behaviours occur. Quasi-stable spin regimes, where the planet exhibits one spin behaviour for up to hundreds of millennia, are likely able to form stable climate systems while the spin behaviour is constant. 1D energy balance models show that tidally locked planets with sporadic rotation around M-dwarfs will experience a relatively small change in substellar temperature due to the lower albedo of ice in an infrared dominant stellar spectrum. The exact effects of large changes in temperature profiles on these planets as they rotate require more robust climate models, like 3D global circulation models, to better examine.

 

We study the formation of the TRAPPIST-1 (T1) planets starting shortly after Moon-sized bodies form just exterior to the ice line. Our model includes mass growth from pebble accretion and mergers, fragmentation, type-I migration, and eccentricity and inclination dampening from gas drag. We follow the composition evolution of the planets fed by a dust condensation code that tracks how various dust species condense out of the disc as it cools. We use the final planet compositions to calculate the resulting radii of the planets using a new planet interior structure code and explore various interior structure models. Our model reproduces the broader architecture of the T1 system and constrains the initial water mass fraction of the early embryos and the final relative abundances of the major refractory elements. We find that the inner two planets likely experienced giant impacts and fragments from collisions between planetary embryos often seed the small planets that subsequently grow through pebble accretion. Using our composition constraints, we find solutions for a two-layer model, a planet comprised of only a core and mantle, that match observed bulk densities for the two inner planets b and c. This, along with the high number of giant impacts the inner planets experienced, is consistent with recent observations that these planets are likely desiccated. However, two-layer models seem unlikely for most of the remaining outer planets, which suggests that these planets have a primordial hydrosphere. Our composition constraints also indicate that no planets are consistent with a core-free interior structure.

 

We present a fragmentation module and a composition tracking code for the N-body code rebound. Our fragmentation code utilizes previous semi-analytical models and follows an implementation method similar to fragmentation for the N-body code mercury. In our N-body simulations with fragmentation, we decrease the collision and planet formation time-scales by inflating the particle radii by an expansion factor f and experiment with various values of f to understand how expansion factors affect the collision history and final planetary system. As the expansion factor increases, so do the rate of mergers which produces planetary systems with more planets and planets at larger orbits. Additionally, we present a composition tracking code which follows the compositional change of homogeneous bodies as a function of mass exchange and use it to study how fragmentation and the use of an expansion factor affects volatile delivery to the inner terrestrial disc. We find that fragmentation enhances radial mixing relative to perfect merging and that on average, as f increases so does the average water mass fraction of the planets. Radial mixing decreases with increasing f as collisions happen early on, before the bodies have time to grow to excited orbits and move away from their original location.

 

MAGRATHEA is an open-source planet structure code that considers the case of fully differentiated spherically symmetric interiors. Given the mass of each layer and the surface temperature, the code iterates the boundary conditions of the hydrostatic equations using the method of shooting to a fitting point in order to find the planet radius. The first version of MAGRATHEA supports a maximum of four layers of iron, silicates, water, and ideal gas. With a few exceptions, the temperature profile can be chosen between isothermal, isentropic, and user-defined functions. The user has many options for the phase diagram and equation of state in each layer and we document how to add additional equations of state. We present MAGRATHEA’s capabilities and discuss its applications. We encourage the community to participate in the development of MAGRATHEA at https://github.com/Huang-CL/Magrathea.

 

ABSTRACT The maximum temperature and radial temperature profile in a protoplanetary disc are important for the condensation of different elements in the disc. We simulate the evolution of a set of protoplanetary discs from the collapse of their progenitor molecular cloud cores as well as the dust decoupling within the discs as they evolve. We show how the initial properties of the cloud cores affect the thermal history of the protoplanetary discs using a simple viscous disc model. Our results show that the maximum mid-plane temperature in the disc occurs within 0.5 au. It increases with the initial cloud temperature and decreases with its angular velocity and the viscosity of the disc. From the observed properties of the molecular cloud cores, we find the median value of the maximum temperature is around 1250 K, with roughly 90 per cent of them being less than 1500 K – a value that is lower than the 50 per cent condensation temperatures of most refractory elements. Therefore, only cloud cores with high initial temperatures or low-angular velocities and/or low viscosities within the planet-forming discs will result in refractory-rich planetesimals. To reproduce the volatile depletion pattern of CM, CO, and CV chondrites and the terrestrial planets in Solar system, one must either have rare properties of the initial molecular cloud cores like high core temperature, or other sources of energy to heat the disc to sufficiently high temperatures. Alternatively, the volatile depletion observed in these chondrites may be inherited from the progenitor molecular cloud. 

ABSTRACT Partial condensation of dust from the Solar nebula is likely responsible for the diverse chemical compositions of chondrites and rocky planets/planetesimals in the inner Solar system. We present a forward physical–chemical model of a protoplanetary disc to predict the chemical compositions of planetary building blocks that may form from such a disc. Our model includes the physical evolution of the disc and the condensation, partial advection, and decoupling of the dust within it. The chemical composition of the condensate changes with time and radius. We compare the results of two dust condensation models: one where an element condenses when the mid-plane temperature in the disc is lower than the 50 per cent condensation temperature ($\rm T_{50}$) of that element and the other where the condensation of the dust is calculated by a Gibbs free energy minimization technique assuming chemical equilibrium at local disc temperature and pressure. The results of two models are generally consistent with some systematic differences of ∼10 per cent depending upon the radial distance and an element’s condensation temperature. Both models predict compositions similar to CM, CO, and CV chondrites provided that the decoupling time-scale of the dust is of the order of the evolution time-scale of the disc or longer. If the decoupling time-scale is too short, the composition deviates significantly from the measured values. These models may contribute to our understanding of the chemical compositions of chondrites, and ultimately the terrestrial planets in the Solar system, and may constrain the potential chemical compositions of rocky exoplanets. 

Abstract We present the occurrence rates for rocky planets in the habitable zones (HZs) of main-sequence dwarf stars based on the Kepler DR25 planet candidate catalog and Gaia-based stellar properties. We provide the first analysis in terms of star-dependent instellation flux, which allows us to track HZ planets. We define η ⊕ as the HZ occurrence of planets with radii between 0.5 and 1.5 R ⊕ orbiting stars with effective temperatures between 4800 and 6300 K. We find that η ⊕ for the conservative HZ is between (errors reflect 68% credible intervals) and planets per star, while the optimistic HZ occurrence is between and planets per star. These bounds reflect two extreme assumptions about the extrapolation of completeness beyond orbital periods where DR25 completeness data are available. The large uncertainties are due to the small number of detected small HZ planets. We find similar occurrence rates between using Poisson likelihood Bayesian analysis and using Approximate Bayesian Computation. Our results are corrected for catalog completeness and reliability. Both completeness and the planet occurrence rate are dependent on stellar effective temperature. We also present occurrence rates for various stellar populations and planet size ranges. We estimate with 95% confidence that, on average, the nearest HZ planet around G and K dwarfs is ∼6 pc away and there are ∼4 HZ rocky planets around G and K dwarfs within 10 pc of the Sun.