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Chapter 2 discusses the structure of gaseous protoplanetary disks. It begins by explaining how observations can be used to infer disk mass, disk structure, and stellar accretion rate. The vertical structure of a gas disk in hydrostatic equilibrium is derived, and the considerations that determine the surface density and temperature profile of a passive disk are described. The concept of the condensation sequence is outlined, along with the ionization and recombination processes that determine the ionization state. Physical processes that can produce large-scale structure in disks - zonal flows, vortices, and ice lines - are discussed.
Chapter 4 covers the evolution of the solid component of protoplanetary disks, from dust through to the formation of km-scale planetesimals. The physics of how dust particles interact with the gas through aerodynamic drag is described, together with the consequences - vertical settling, radial drift, particle trapping, and particle pile-up. The outcome of particle collisions, and their theoretical description using the coagulation equation, are reviewed. Collective mechanisms for planetesimal formation via gravitational collapse are discussed, starting with the classical Goldreich-Ward theory, and concluding with the streaming instability of aerodynamically coupled mixtures of gas and dust.
Chapter 6 describes theoretical models for the formation of giant planets, and relevant observational constraints from the Solar System. The core accretion theory for giant planet formation is introduced, including the equations describing planetary envelope structure, the concept of a critical core mass, and illustrative evolutionary tracks for giant planet growth. Current knowledge of the internal structure of Jupiter, based on measurements of the gravitational field, is summarized. The conditions under which a massive gas disk becomes unstable and fragments are described, together with the likely outcome of disk instability.
Chapter 5 focuses on the formation of rocky planetary-scale bodies, including terrestrial planets, super-Earths, and giant planet cores. The concepts of gravitational focusing, shear and dispersion dominated encounters, and catastrophic disruption are introduced. A simple "particle in a box" statistical model for planetary growth is described, along with the ideas of orderly, runaway, and oligarchic growth. Factors that determine the planetesimal velocity dispersion, including viscous stirring, dynamical friction, and gas drag, are discussed. The regimes of pebble accretion, the conditions under which it operates, and the pebble accretion rate, are discussed. The standard model for the final assembly of the Solar System's terrestrial planets is outlined.
Chapter 7 covers processes that lead to the evolution of planetary systems. Planetary migration in gaseous disks is described, starting with an elementary derivation of the torque in the impulse approximation and continuing with a discussion of the physics of Lindblad and co-rotation torques. Type I and Type 2 planetary migration, gap opening, and eccentricity evolution are described. The regimes of secular and resonant dynamics are defined, together with an intuitive physical description of mean-motion resonance. Resonant capture, Kozai-Lidov dynamics, and planetesimal disk migration are discussed. The concept of Hill stability is introduced and derived, and the outcome of planetary system instability leading to planet-planet scattering is reviewed. The Nice model and the Grand Tack model for the early evolution of the Solar System are discussed. The size distribution resulting from a steady-state collisional cascade is derived, and stellar and white dwarf debris disk evolution described.
Chapter 3 introduces physical processes that lead to the evolution of gaseous protoplanetary disks. It begins with a derivation of the equation describing the evolution of a thin viscous accretion disk, a discussion of solutions, and introduction of the Shakura-Sunyaev alpha prescription. Hydrodynamic sources of angular momentum transport, including self-gravity, the vertical shear instability, and vortices, are discussed. Magnetohydrodynamic (MHD) sources of angular momentum transport are reviewed, starting with the magnetorotational instability in ideal MHD. The non-ideal induction equation of MHD is derived, and the importance of Ohmic diffusion, ambipolar diffusion, and the Hall effect for protoplanetary disks is reviewed. A simple model for angular momentum loss due to a magnetized disk wind is discussed. The chapter concludes with a description of disk dispersal via photoevaporation, and magnetospheric star-disk interaction.
Chapter 1 introduces key observational constraints for the theory of planet formation. It reviews the properties of the Solar System's planets and minor bodies, explains the principle of radioactive dating of primitive meteorites, and defines the minimum mass Solar Nebula. The main methods used to detect extrasolar planets - radial velocity monitoring, transits, direct imaging, microlensing, and astrometry - are introduced and compared. Observed properties of extrasolar planetary systems are reviewed, including the orbital distribution of planets, their mass-radius relation, and the dependence of planet frequency on stellar host properties. The concept of the habitable zone and the factors that influence planetary habitability are described.
Concise and self-contained, this textbook gives a graduate-level introduction to the physical processes that shape planetary systems, covering all stages of planet formation. Writing for readers with undergraduate backgrounds in physics, astronomy, and planetary science, Armitage begins with a description of the structure and evolution of protoplanetary disks, moves on to the formation of planetesimals, rocky, and giant planets, and concludes by describing the gravitational and gas dynamical evolution of planetary systems. He provides a self-contained account of the modern theory of planet formation and, for more advanced readers, carefully selected references to the research literature, noting areas where research is ongoing. The second edition has been thoroughly revised to include observational results from NASA's Kepler mission, ALMA observations and the JUNO mission to Jupiter, new theoretical ideas including pebble accretion, and an up-to-date understanding in areas such as disk evolution and planet migration.
Studies have demonstrated that decreases in slow-wave activity (SWA) predict decreases in depressive symptoms in those with major depressive disorder (MDD), suggesting that there may be a link between SWA and mood. The aim of the present study was to determine if the consequent change in SWA regulation following a mild homeostatic sleep challenge would predict mood disturbance.
Thirty-seven depressed and fifty-nine healthy adults spent three consecutive nights in the sleep laboratory. On the third night, bedtime was delayed by 3 h, as this procedure has been shown to provoke SWA. The Profile of Mood States questionnaire was administered on the morning following the baseline and sleep delay nights to measure mood disturbance.
Results revealed that following sleep delay, a lower delta sleep ratio, indicative of inadequate dissipation of SWA from the first to the second non-rapid eye movement period, predicted increased mood disturbance in only those with MDD.
These data demonstrate that in the first half of the night, individuals with MDD who have less SWA dissipation as a consequence of impaired SWA regulation have greater mood disturbance, and may suggest that appropriate homeostatic regulation of sleep is an important factor in the disorder.
The eccentric orbits of the known extrasolar giant planets provide evidence that most planet-forming environments undergo violent dynamical instabilities. Here, we numerically simulate the impact of giant planet instabilities on planetary systems as a whole. We find that populations of inner rocky and outer icy bodies are both shaped by the giant planet dynamics and are naturally correlated. Strong instabilities – those with very eccentric surviving giant planets – completely clear out their inner and outer regions. In contrast, systems with stable or low-mass giant planets form terrestrial planets in their inner regions and outer icy bodies produce dust that is observable as debris disks at mid-infrared wavelengths. Fifteen to twenty percent of old stars are observed to have bright debris disks (at λ ~ 70μm) and we predict that these signpost dynamically calm environments that should contain terrestrial planets.
Once planetesimals have formed, the dominant physical process that controls further growth is their mutual gravitational interaction. Conventionally the only further role the gas disk plays in terrestrial planet formation is to provide a modest degree of aerodynamic damping of protoplanetary eccentricity and inclination. In this limit the physics involved – Newtonian gravity – is simple and the problem of terrestrial planet formation is well posed. It is not, however, easy to solve. It would take 4 × 109 planetesimals with a radius of 5 km to build the Solar System's terrestrial planets, and it is infeasible to directly simulate the N-body evolution of such a system for long enough (and with sufficient accuracy) to watch planets form. Instead a hybrid approach is employed. For the earliest phases of terrestrial planet formation a statistical approach, similar to that used in the kinetic theory of gases, is both accurate and efficient. When the number of dynamically significant bodies has dropped to a manageable number (of the order of hundreds or thousands), direct N-body simulations become feasible, and these are used to study the final assembly of the terrestrial planets. Using this two-step approach has known drawbacks (for example, it is difficult to treat the situation where a small number of protoplanets co-exist with a large sea of very small bodies), but nevertheless it provides a reasonably successful picture for how the terrestrial planets formed.
Planets form from protoplanetary disks of gas and dust that are observed to surround young stars for the first few million years of their evolution. Disks form because stars are born from relatively diffuse gas (with particle number density n ~ 105 cm−3) that has too much angular momentum to collapse directly to stellar densities (n ~ 1024 cm−3). Disks survive as well-defined quasi-equilibrium structures because once gas settles into a disk around a young star its specific angular momentum increases with radius. To accrete, angular momentum must be lost from, or redistributed within, the disk gas, and this process turns out to require time scales that are much longer than the orbital or dynamical time scale.
In this chapter we discuss the structure of protoplanetary disks. Anticipating the fact that angular momentum transport is slow, we assume here that the disk is a static structure. This approximation suffices for a first study of the temperature, density, and composition profiles of protoplanetary disks, which are critical inputs for models of planet formation. It also permits investigation of the predicted emission from disks that can be compared to a large body of astronomical observations. We defer for Chapter 3 the tougher question of how the gas and solids within the disk evolve with time.