Tropical forests harbor a significant portion of global biodiversity and are a critical component of the climate system. Reducing deforestation and forest degradation contributes to global climate-change mitigation efforts, yet emissions and removals from forest dynamics are still poorly quantified. We reviewed the main challenges to estimate changes in carbon stocks and biodiversity due to degradation and recovery of tropical forests, focusing on three main areas: (1) the combination of field surveys and remote sensing; (2) evaluation of biodiversity and carbon values under a unified strategy; and (3) research efforts needed to understand and quantify forest degradation and recovery. The improvement of models and estimates of changes of forest carbon can foster process-oriented monitoring of forest dynamics, including different variables and using spatially explicit algorithms that account for regional and local differences, such as variation in climate, soil, nutrient content, topography, biodiversity, disturbance history, recovery pathways, and socioeconomic factors. Generating the data for these models requires affordable large-scale remote-sensing tools associated with a robust network of field plots that can generate spatially explicit information on a range of variables through time. By combining ecosystem models, multiscale remote sensing, and networks of field plots, we will be able to evaluate forest degradation and recovery and their interactions with biodiversity and carbon cycling. Improving monitoring strategies will allow a better understanding of the role of forest dynamics in climate-change mitigation, adaptation, and carbon cycle feedbacks, thereby reducing uncertainties in models of the key processes in the carbon cycle, including their impacts on biodiversity, which are fundamental to support forest governance policies, such as Reducing Emissions from Deforestation and Forest Degradation.

Many features of the outer Solar system are replicated in numerical simulations if the giant planets undergo an orbital instability that ejects one or more ice giants. During this instability, Jupiter and Saturn's orbits diverge, crossing their 2:1 mean motion resonance (MMR), and this resonance-crossing can excite the terrestrial planet orbits. Using a large ensemble of simulations of this giant-planet instability, we directly model the evolution of the terrestrial planet orbits during this process, paying special attention to systems that reproduce the basic features of the outer planets. In systems that retain four giant planets and finish with Jupiter and Saturn beyond their 2:1 MMR, we find at least an 85 per cent probability that at least one terrestrial planet is lost. Moreover, systems that manage to retain all four terrestrial planets often finish with terrestrial planet eccentricities and inclinations larger than the observed ones. There is less than a similar to 5 per cent chance that the terrestrial planet orbits will have a level of excitation comparable to the observed orbits. If we factor in the probability that the outer planetary orbits are well replicated, we find a probability of 1 per cent or less that the orbital architectures of the inner and outer planets are simultaneously reproduced in the same system. These small probabilities raise the prospect that the giant-planet instability occurred before the terrestrial planets had formed. This scenario implies that the giant-planet instability is not the source of the Late Heavy Bombardment and that terrestrial planet formation finished with the giant planets in their modern configuration.

The late stages of terrestrial planet formation are dominated by giant impacts that collectively influence the growth, composition, and habitability of any planets that form. Hitherto, numerical models designed to explore these late stage collisions have been limited by assuming that all collisions lead to perfect accretion, and many of these studies lack the large number of realizations needed to account for the chaotic nature of N-body systems. We improve on these limitations by performing 280 simulations of planet formation around a Sun-like star, half of which used an N-body algorithm that has recently been modified to include fragmentation and hit-and-run (bouncing) collisions. We find that when fragmentation is included, the final planets formed are comparable in terms of mass and number; however, their collision histories differ significantly and the accretion time approximately doubles. We explored impacts onto Earth-like planets, which we parameterized in terms of their specific impact energies. Only 15 of our 164 Earth-analogs experienced an impact that was energetic enough to strip an entire atmosphere. To strip about half of an atmosphere requires energies comparable to recent models of the Moon-forming giant impact. Almost all Earth-analogs received at least one impact that met this criteria during the 2 Gyr simulations and the median was three giant impacts. The median time of the final giant impact was 43 Myr after the start of the simulations, leading us to conclude that the time-frame of the Moon-forming impact is typical among planetary systems around Sun-like stars.

Venus currently rotates slowly, with its spin controlled by solid-body and atmospheric thermal tides. However, conditions may have been far different 4 billion years ago, when the Sun was fainter and most of the carbon within Venus could have been in solid form, implying a low-mass atmosphere. We investigate how the obliquity would have varied for a hypothetical rapidly rotating Early Venus. The obliquity variation structure of an ensemble of hypothetical Early Venuses is simpler than that Earth would have if it lacked its large moon (Lissauer et al., 2012), having just one primary chaotic regime at high prograde obliquities. We note an unexpected long-term variability of up to +/- 7 degrees for retrograde Venuses. Low-obliquity Venuses show very low total obliquity variability over billion-year timescales-comparable to that of the real Moon-influenced Earth.

This paper examines the standard model of planet formation, including pebble accretion, using numerical simulations. Planetary embryos that are large enough to become giant planets do not form beyond the ice line within a typical disk lifetime unless icy pebbles stick at higher speeds than in experiments using rocky pebbles. Systems like the solar system (small inner planets and giant outer planets) can form if icy pebbles are stickier than rocky pebbles, and if the planetesimal formation efficiency increases with pebble size, which prevents the formation of massive terrestrial planets. Growth beyond the ice line is dominated by pebble accretion. Most growth occurs early, when the surface density of the pebbles is high due to inward drift of the pebbles from the outer disk. Growth is much slower after the outer disk is depleted. The outcome is sensitive to the disk radius and turbulence level, which control the lifetime and maximum size of pebbles. The outcome is sensitive to the size of the largest planetesimals because there is a threshold mass for the onset of pebble accretion. The planetesimal formation rate is unimportant, provided that some large planetesimals form while the pebbles remain abundant. Two outcomes are seen, depending on whether pebble accretion begins while the pebbles are still abundant. Either multiple gas-giant planets form beyond the ice line, small planets form close to the star, and a Kuiper-belt-like disk of bodies is scattered outward by the giant planets; or no giants form and the bodies remain an Earth-mass or smaller.

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.