Collisional fragmentation is shown to not be a barrier to rocky planet formation at small distances from the host star. Simple analytic arguments demonstrate that rocky planet formation via collisions of homogeneous gravity-dominated bodies is possible down to distances of order the Roche radius (r(Roche)). Extensive N-body simulations with initial bodies. greater than or similar to 1700 km that include plausible models for fragmentation and merging of gravity-dominated bodies confirm this conclusion and demonstrate that rocky planet formation is possible down to similar to 1.1r(Roche). At smaller distances, tidal effects cause collisions to be too fragmenting to allow mass buildup to a final, dynamically stable planetary system. We argue that even differentiated bodies can accumulate to form planets at distances that are not much larger than r(Roche).

In the core accretion model, gas-giant planets first form a solid core, which then accretes gas from a protoplanetary disk when the core exceeds a critical mass. Here, we model the atmosphere of a core that grows by accreting icerich pebbles. The ice fraction of pebbles evaporates in warm regions of the atmosphere, saturating it with water vapor. Excess water precipitates to lower altitudes. Beneath an outer radiative region, the atmosphere is convective, following a moist adiabat in saturated regions due to water condensation and precipitation. Atmospheric mass, density, and temperature increase with core mass. For nominal model parameters, planets with core masses (ice + rock) between 0.08 and 0.16 Earth masses have surface temperatures between 273 and 647 K and form an ocean. In more massive planets, water exists as a supercritical convecting fluid mixed with gas from the disk. Typically, the core mass reaches a maximum (the critical mass) as a function of the total mass when the core is 2-5 Earth masses. The critical mass depends in a complicated way on pebble size, mass flux, and dust opacity due to the occasional appearance of multiple core-mass maxima. The core mass for an atmosphere of 50% hydrogen and helium may be a more robust indicator of the onset of gas accretion. This mass is typically 1-3 Earth masses for pebbles that are 50% ice by mass, increasing with opacity and pebble flux and decreasing with pebble ice/rock ratio.

The physics of planet formation is investigated using a population synthesis approach. We develop a simple model for planetary growth including pebble and gas accretion, as well as orbital migration in an evolving protoplanetary disk. The model is run for a population of 2000 stars with a range of disk masses, disk radii, and initial protoplanet orbits. The resulting planetary distribution is compared with the observed population of extrasolar planets, and the model parameters are improved iteratively using a particle swarm optimization scheme. The characteristics of the final planetary systems are mainly controlled by the pebble isolation mass, which is the mass of a planet that perturbs nearby gas enough to halt the inward flux of drifting pebbles and stop growth. The pebble isolation mass increases with orbital distance such that giant planet cores can only form in the outer disk. Giants migrate inward, populating a wide range of final orbital distances. The best model fits have large initial protoplanet masses, short pebble drift timescales, low disk viscosities, and short atmospheric cooling times, all of which promote rapid growth. The model successfully reproduces the observed frequency and distribution of giant planets and brown dwarfs. The fit for super-Earths is poorer for single-planet systems, but improves steadily when more protoplanets are included. Although the study was designed to match the extrasolar planet distribution, analogs of the solar system form in 1-2% of systems that contain at least four protoplanets.

The solar system's dynamical state can be explained by an orbital instability among the giant planets. A recent model has proposed that the giant planet instability happened during terrestrial planet formation. This scenario has been shown to match the inner solar system by stunting Mars' growth and preventing planet formation in the asteroid belt. Here we present a large sample of new simulations of the "Early Instability" scenario. We use an N-body integration scheme that accounts for collisional fragmentation, and also perform a large set of control simulations that do not include an early giant planet instability. Since the total particle number decreases slower when collisional fragmentation is accounted for, the growing planets' orbits are damped more strongly via dynamical friction and encounters with small bodies that dissipate angular momentum (eg: hit-and-run impacts). Compared with simulations without collisional fragmentation, our fully evolved systems provide better matches to the solar system's terrestrial planets in terms of their compact mass distribution and dynamically cold orbits. Collisional processes also tend to lengthen the dynamical accretion timescales of Earth analogs, and shorten those of Mars analogs. This yields systems with relative growth timescales more consistent with those inferred from isotopic dating. Accounting for fragmentation is thus supremely important for any successful evolutionary model of the inner solar system.

Symplectic integrators separate a problem into parts that can be solved in isolation, alternately advancing these sub-problems to approximate the evolution of the complete system. Problems with a single, dominant mass can use mixed-variable symplectic (MVS) integrators that separate the problem into Keplerian motion of satellites about the primary, and satellite-satellite interactions. Here, we examine T + V algorithms, where the problem is separated into kinetic T and potential energy V terms. T + V integrators are typically less efficient than MVS algorithms. This difference is reduced by using different step sizes for primary-satellite and satellite-satellite interactions. The T + V method is improved further using fourth and sixth-order algorithms that include force gradients and symplectic correctors. We describe three sixth-order algorithms, containing two or three force evaluations per step, that are competitive with MVS in some cases. Round-off errors for T + V integrators can be reduced by several orders of magnitude, at almost no computational cost, using a simple modification that keeps track of accumulated changes in the coordinates and momenta. This makes T + V algorithms desirable for long term, high-accuracy calculations.

Of the solar system's four terrestrial planets, the origin of Mercury is perhaps the most mysterious. Modern numerical simulations designed to model the dynamics of terrestrial planet formation systematically fail to replicate Mercury, which possesses just 5% of the mass of Earth and the highest orbital eccentricity and inclination among the planets. However, Mercury's large iron-rich core and low volatile inventory stand out among the inner planets, and seem to imply a violent collisional origin. Because most algorithms used for simulating terrestrial accretion do not consider the effects of collisional fragmentation, it has been difficult to test these collisional hypotheses within the larger context of planet formation. Here, we analyze a large suite of terrestrial accretion models that account for the fragmentation of colliding bodies. We find that planets with core mass fractions boosted as a result of repeated hit-and-run collisions are produced in 90% of our simulations. While many of these planets are similar to Mercury in mass, they rarely lie on Mercury-like orbits. Furthermore, we perform an additional batch of simulations designed to specifically test the single giant impact origin scenario. We find less than a 1% probability of simultaneously replicating the Mercury-Venus dynamical spacing and the terrestrial system's degree of orbital excitation after such an event. While dynamical models have made great strides in understanding Mars' low mass, their inability to form accurate Mercury analogs remains a glaring problem.

We describe an analytic model for an evolving protoplanetary disk driven by viscosity and a disk wind. The disk is heated by stellar irradiation and energy generated by viscosity. The evolution is controlled by three parameters: (i) the inflow velocity toward the central star at a reference distance and temperature, (ii) the fraction of this inflow caused by the disk wind, and (iii) the mass-loss rate via the wind relative to the inward flux in the disk. The model gives the disk midplane temperature and surface density as a function of time and distance from the star. It is intended to provide an efficient way to calculate conditions in a protoplanetary disk for use in simulations of planet formation. In the model, disks dominated by viscosity spread radially while losing mass onto the star. Radial spreading is the main factor reducing the surface density in the inner disk. The disk mass remains substantial at late times. Temperatures in the inner region are high at early times due to strong viscous heating. Disks dominated by a wind undergo much less radial spreading and weaker viscous heating. These disks have a much lower mass at late times than purely viscous disks. When mass loss via a wind is significant, the surface density gradient in the inner disk becomes shallower, and the slope can become positive in extreme cases.

How plants respond physiologically to leaf warming and low water availability may determine how they will perform under future climate change. In 2015-2016, an unprecedented drought occurred across Amazonia with record-breaking high temperatures and low soil moisture, offering a unique opportunity to evaluate the performances of Amazonian trees to a severe climatic event. We quantified the responses of leaf water potential, sap velocity, whole-tree hydraulic conductance (K-wt), turgor loss and xylem embolism, during and after the 2015-2016 El Nino for five canopy-tree species. Leaf/xylem safety margins (SMs), sap velocity and K-wt showed a sharp drop during warm periods. SMs were negatively correlated with vapour pressure deficit, but had no significant relationship with soil water storage. Based on our calculations of canopy stomatal and xylem resistances, the decrease in sap velocity and K-wt was due to a combination of xylem cavitation and stomatal closure. Our results suggest that warm droughts greatly amplify the degree of trees' physiological stress and can lead to mortality. Given the extreme nature of the 2015-2016 El Nino and that temperatures are predicted to increase, this work can serve as a case study of the possible impact climate warming can have on tropical trees.

Variations in the axial tilt, or obliquity, of terrestrial planets can affect their climates and therefore their habitability. Kepler-62f is a 1.4 R-circle plus planet orbiting within the habitable zone of its K2 dwarf host star. We perform N-body simulations that monitor the evolution of obliquity of Kepler-62f for 10-million-year timescales to explore the effects on model assumptions, such as the masses of the Kepler-62 planets and the possibility of outer bodies. Significant obliquity variation occurs when the rotational precession frequency overlaps with one or more of the secular orbital frequencies, but most variations are limited to less than or similar to 10 degrees. Moderate variations (similar to 10-20 degrees) can occur over a broader range of initial obliquities when the relative nodal longitude (Delta ohm) overlaps with the frequency and phase of a given secular mode. However, we find that adding outer gas giants on long-period orbits (similar to 1000 days) can produce large (similar to 60 degrees) variations in obliquity if Kepler-62f has a very rapid (4 h) rotation period. The possibility of giant planets on long-period orbits impacts the climate and habitability of Kepler-62f through variations in the latitudinal surface flux, where large variations can occur on million year timescales.

Conventionally, a habitable planet is one that can support liquid water on its surface. Habitability depends on temperature, which is set by insolation and the greenhouse effect, due mainly to CO(2)and water vapor. The CO(2)level is increased by volcanic outgassing and decreased by continental and seafloor weathering. Here, I examine the climate evolution of Earth-like planets using a globally averaged climate model that includes both weathering types. Climate is sensitive to the relative contributions of continental and seafloor weathering, even when the total weathering rate is fixed. Climate also depends strongly on the dependence of seafloor weathering on CO(2)partial pressure. Both these factors are uncertain. Earth-like planets have two equilibrium climate states: (i) an ice-free state where outgassing is balanced by both weathering types, and (ii) an ice-covered state where outgassing is balanced by seafloor weathering alone. The second of these has not been explored in detail before. For some planets, neither state exists, and the climate cycles between ice-covered and ice-free states. For some other planets, both equilibria exist, and the climate depends on the initial conditions. Insolation increases over time due to stellar evolution, so a planet usually encounters the ice-covered equilibrium first. Such a planet will remain ice covered, even if the ice-free state appears subsequently, unless the climate receives a large perturbation. The ice-covered equilibrium state covers a large fraction of phase space for Earth-like planets. Many planets conventionally assigned to a star's habitable zone may be rendered uninhabitable as a result.