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.

In this chapter, we present the basics of the physics and phenomenology of FGKM-type stars. This review is based on recent developments in the observational and theoretical domains of stellar physics, including a variety of techniques – spectroscopy, interferometry, photometry and large-scale stellar surveys. We focus on the advances in radiative transfer modelling and spectroscopy of stars across the full metallicity range. To provide the reader with the essential supplementary information, we also give a brief qualitative account of the structure and evolution of low- and intermediate-mass stars and of stellar nucleosynthesis. We also provide a brief overview of new models of stellar atmospheres and stellar spectra, with emphasis on non-LTE and hydrodynamics. Lastly, we discuss some of the relevant observational studies of stellar abundances in the context of stellar populations, evolution of metal-poor stars and Galactic archeology.

Radiative transfer,i.e., the transport of radiant energy through a medium, can be described in several alternative ways, either atmacroscopic or microscopic level. In order to set a common physical background for the applications of radiative transfer to stellar and planetary atmospheres, presented in the second part of this book, a macroscopic representation of the radiation field derived from radiometry, a microscopic picture based on the kinetics of photons and the transport of radiant energy in terms of Maxwell's electromagnetic theory are discussed.

We consider the fundamental physical processes in stellar atmospheres, together with the basic equations, approximations and techniques used to model them.The coupling of the RT equations with the statistical equilibrium equations is discussed, as well as the role of the atomic properties. The structure equations (equation of state, momentum and energy conservation) that complete the set of equations required to compute a model atmosphere are examined, as well as the broadening mechanisms that change the appearance of the spectral line.

In many cases, the quantitative spectroscopy of early-type stars requires to account for their line-driven winds, and theoretical models of such winds are based on a consistent calculation of the radiative line acceleration. Both topics ask for a thorough understanding of radiative transfer in expanding atmospheres. In this chapter, we concentrate on three issues, and compare, when possible, with corresponding results forplane-parallel, hydrostatic conditions: First, we investigate how sphericity alone affects the radiation field in those cases where Doppler shifts can be neglected (continua). Subsequently, we consider the impact of velocity fields on the line transfer, both by applying the so-called Sobolev approximation,and by presenting the more exact comoving-frame approach. Restrictions and extensions of both methods are discussed. Finally, we concentrate on the coupling between radiation field and occupation numbers via the NLTE rate equations. We illustrate the basic problem within the conventional Lambda Iteration, which is then solved by means of the so-called Accelerated Lambda Iteration (ALI), and by a "preconditioning" of the rate equations.

This chapter considers a selection of numerical methods developed since 1960s for solving radiative transfer (RT) problems in stellar atmospheres and in all other diluted media where non-LTE effects are important. Special emphasis is put on the solution of the radiative transfer equation (RTE) when the source function is given, because its so-called formal solution constitutes a necessary step in any iterative procedure for the solution of more general RT problems. The application of different methods to the spectral line formation the line(s) radiation field and thestatistical equilibrium (SE) equation(s) for the atomic-level populations involved is discussed for both linear and nonlinear problems.

By absorbing and scattering both incident and emergent radiation, an atmosphere regulates a planet's thermal, chemical and cloud structure, and cooling through time. The photons transmitted through or scattered by an atmosphere provide one of our primary sources of information about planetary composition. Therefore, any effort to fully characterize an extrasolar planet must incorporate atmospheric models that attempt to fully describe the relevant processes and thereby predict a planet's reflected and emitted spectra. Brown dwarfs, ultracool substellar objects with atmospheric composition similar to those of many gas giant planets, provide a tractable training ground to test our ideas and models about atmospheric processes under conditions more exotic than found in the Solar System. This chapter aims to concisely summarize the various ingredients that must be included in any model and the overall process of atmospheric model creation for ultracool dwarfs and extrasolar planets. These considerations include the basic atmospheric structure equations, radiative transfer, atmospheric chemistry, clouds and various disequilibrium processes. Each of these topics is worthy of in-depth treatments, and pointers to appropriate review articles are provided for those wishing to understand each component in more detail.