Introduction

The dust and gas disks surrounding many pre-main-sequence stars are thought to be the birthplaces of planets. They are therefore the locations of structure formation in the universe, albeit on small scales. In recent years, the topic of protoplanetary disks has gained an increasing amount of attention in astrophysics, which is in large part due to the enormous increase of high-quality observational data that have been published recently, from the Spitzer Space Telescope, from the Very Large Telescope, from millimetre interferometers and so forth. Moreover, studies of the properties of extrasolar planetary systems have put new constraints on the formation and migration of newly born planets in such disks. The topic of the structure and evolution of protoplanetary disks is wide open, and significant new developments, both from theory and from observations, can be expected in the near future.

This chapter gives an overview of some aspects of theoretical modelling of protoplanetary disks. The review consists of four parts. First, we discuss the overall formation, evolution and dispersal of protoplanetary disks. We show that much of what we know of the long timescale disk evolution is still based on relatively simple models. We discuss their vertical structure, as derived from radiative transfer models and their comparison to observations.We then show that magneto-rotational and gravitational instabilities (GIs) can introduce complex dynamics and non-linear structure to these disks, and we discuss an on-going debate about the role of GIs in planet formation.

Turbulence in fluids is a topic of great interest. First and foremost, most flows in nature are turbulent and this is particularly true in the astrophysical context (Kritsuk & Norman 2004). Also, turbulence leads to very peculiar mechanics that still escapes to a great extent from our understanding. Since the pioneering works conducted by Osborne Reynolds at the end of the nineteenth century (around 1895), turbulence in fluids has become a rich and challenging research subject in which scientists from engineering, theoretical and experimental physics have been involved with many different perspectives. There is no doubt that bridging ideas from one field to another, and therefore stimulating new interdisciplinary approaches, should provide a fruitful means of gaining understanding on turbulence in the future.

In this chapter, the background physics of turbulence will be discussed spontaneously at a (very) basic level, i.e. without getting into details or precise formulation. The discussion will be limited to incompressible hydrodynamics governed by the Navier-Stokes (NS) equations. Firstly, general comments on turbulence (as a statistical-mechanical problem) will be made. Then, I shall attempt to provide some hints (rather than definite answers) to a series of questions: What is generally the source of turbulence? What are the main statistical features of turbulence? How to deal with turbulence? Much more elaborated developments and references may be sought in the following books (among many others) dealing with turbulence:

• a reference book on the physics of turbulence: A first course in turbulence by H. Tennekes and J. L. Lumley, MIT Press, Cambridge, USA (1972)

• […]

Introduction

A significant fraction of all efforts in astronomy is expended on studying the properties of galaxies and their spatial distributions over a very large fraction of all of cosmic time. Much of this is motivated by the mysteries of understanding dark matter and dark energy. The accuracy at which we can use galaxy clustering and other properties to determine the more fundamental parameters describing the universe is determined by the sophistication of our understanding of galaxies themselves.

As is by now well known, hierarchical cosmological models like ΛCDM predict that the first objects to collapse out of the expanding homogeneous universe are also the smallest. Since the early universe was also generally a simpler place (fewer heavy elements, etc.), this produces the anti-intuitive result that it is often easier to model the early universe. For the present-day universe, the significant complexities of the star formation process and the enormous range of relevant spatial and temporal scales forces us to employ phenomenological sub-grid models. In this contribution, we explore some aspects of our current understanding of galaxy formation with a distinctly numerical bias. We cannot hope to comprehensively review this topic, so instead we begin with a general overview of some of the important physical processes which are operating and then delve into a few current issues in more detail.

Introduction

Different aspects of the evolution of galaxies include dynamical, involving diffuse material (‘gas’, which will be understood to include dust), stars and dark matter; thermal (mainly affecting the gas); photometric + spectrophotometric (involving stars and gas); and so-called galactic chemical evolution (GCE) which is not really about chemistry (an important topic in its own right) but concerns the origin and distribution of nuclear species (loosely referred to as elements) in stars and gas. True insights into the origin and evolution of galaxies need studies of all these different aspects and their inter-relations, but there are several results of GCE that can be at least partially understood using only the very broadest ideas about other poorly understood aspects (e.g. the physics of galaxy and star formation) and this makes GCE a topic that is worth studying in its own right. At the same time, there are still many uncertainties, both in the underlying theory of stellar evolution, nucleosynthesis and mass loss and in the galactic context in which these basic element-forming processes take place. These limit the extent to which safe deductions can be made and motivate one to use the simplest possible models. The present chapter describes some basic principles, while the following one will discuss some specific models and related observational results.

Abstract

Cosmology faces three distinct challenges in the next decade. (i) The dark sector, both dark matter and dark energy, dominates the universe. Key questions include determining the nature of the dark matter and whether dark energy can be identified with, or if dynamical, replace, the cosmological constant. Nor, given the heated level of current debates about the nature of gravity and string theory, can one yet unreservedly accept that dark matter or the cosmological constant/dark energy actually exists. Improved observational probes are crucial in this regard. (ii) Galaxy formation was initiated at around the epoch of reionization: we need to understand how and when the universe was reionized, as well as to develop probes of what happened at earlier epochs. (iii) Our simple dark matter-driven picture of galaxy assembly is seemingly at odds with several observational results, including the presence of ultraluminous infrared galaxies (ULIRGS) at high redshift, the ‘downsizing’ signature whereby massive objects terminate their star formation prior to those of lower masses, chemical signatures of α-element ratios in early-type galaxies and suggestions that merging may not be important in defining the Hubble sequence. Any conclusions, however, are premature, given current uncertainties about possible hierarchy-inverting processes involved with feedback. Understanding the physical implications of these observational results in terms of a model of star formation in galaxies is a major challenge for theorists and refining the observational uncertainties is a major goal for observers.

General introduction

The existence and distribution of the chemical elements and their isotopes is a consequence of nuclear processes that have taken place in the past in the Big Bang and subsequently in stars and in the interstellar medium (ISM) where they are still ongoing. These processes are studied theoretically, experimentally and observationally. Theories of cosmology, stellar evolution and interstellar processes are involved, as are laboratory investigations of nuclear and particle physics, cosmochemical studies of elemental and isotopic abundances in the Earth and meteorites and astronomical observations of the physical nature and chemical composition of stars, galaxies and the interstellar medium.

Figure 1.1 shows a general scheme or ‘creation myth’ which summarizes our general ideas of how the different nuclear species (loosely referred to hereinafter as ‘elements’) came to be created and distributed in the observable Universe. Initially – in the first few minutes after the Big Bang – universal cosmological nucleosynthesis at a temperature of the order of 109 K created all the hydrogen and deuterium, some 3He, the major part of 4He and some 7Li, leading to primordial mass fractions X ≃ 0.75 for hydrogen, Y ≃ 0.25 for helium and Z = 0.00 for all heavier elements (often loosely referred to by astronomers as ‘metals’!).

Introduction: dense cores and the origin of the IMF

Stars form from the gravitational collapse of dense cloud cores in the molecular interstellar medium of galaxies. Studying and characterizing the properties of dense cores is thus of great interest to gain insight into the initial conditions and initial stages of the star formation process.

Our observational understanding of low-mass dense cores has made significant progress in recent years, and three broad categories of cores can now be distinguished within nearby molecular clouds, which possibly represent an evolutionary sequence: starless cores, prestellar cores and ‘Class 0’ protostellar cores. Starless cores are possibly transient concentrations of molecular gas and dust without embedded young stellar objects (YSOs), typically observed in tracers such as C18O (Onishi et al. 1998), NH3 (Jijina et al. 1999) or dust extinction (Alves et al. 2007), and which do not show evidence of infall. Prestellar cores are also starless (M* = 0) but represent a somewhat denser and more centrally concentrated population of cores which are self-gravitating, hence unlikely to be transient. They are typically detected in (sub)millimetre dust continuum emission and dense molecular gas tracers such as NH3 or N2H+ (Benson & Myers 1989; Ward-Thompson et al. 1994; Caselli et al. 2002), are often seen in absorption at mid- to far-infrared wavelengths (Bacmann et al. 2000; Alves et al. 2001) and frequently exhibit evidence of infall motions (Gregersen & Evans 2000). Conceptually, all prestellar cores are starless but only a subset of the starless cores evolve into prestellar cores; the rest are presumably ‘failed’ cores that eventually disperse and never form stars.

Introduction

A star is a ball of gas held in static or quasi-static equilibrium by the balance between gravity and a pressure gradient. The pressure can in general be supplied by one or more of a hot perfect ionized gas, radiation and a degenerate electron (or neutron) gas, depending on circumstances. For main-sequence stars like the Sun, nuclear reactions maintain stability over long periods and the pressure is predominantly that of a classical gas at water-like densities. For much larger masses (above about 100 M⊙), radiation pressure leads to instabilities, while for much smaller masses (below about 0.08 M⊙) the central temperature never becomes high enough to ignite hydrogen and the star slowly contracts releasing gravitational energy until halted by degeneracy pressure at densities ∼103 gm cm−3; such stars are called ‘brown dwarfs’. Below about 10−3M⊙ (the mass of Jupiter), ordinary solid-state forces take over from electron degeneracy pressure in supporting the body against gravity at water-like densities, giving a planet rather than a star. The formation of stars is a complicated process, many aspects of which are still poorly understood although it is observed to happen in dense, dusty molecular clouds. A basic concept is the Jeans instability in a uniform medium: gravitational collapse occurs on length scales λ ≥ λJ (the ‘Jeans length’) such that the propagation time for pressure waves λ/cs exceeds the free-fall time (Gρ)−½, where cs is the sound speed and ρ the density.

Introduction

Early in the twentieth century, Rutherford and his colleagues developed the use of the fixed lifetimes of radioactive nuclei as a chronometer to measure ages of terrestrial and meteoritic rocks, and in 1929 Rutherford extended their use to make arguments about the age of the elements since their mean epoch of creation, related to the age of the Galaxy and the Universe. In the 1950s and afterwards, Fowler and Hoyle and others refined these arguments on the basis of improved understanding of nucleosynthesis; complications raised by questions related to Galactic chemical evolution will form a major topic of this chapter. In recent years, the discovery of dead short-lived radioactivities (e.g. from the isotopic anomalies mentioned in Chapter 3) has led to further inferences of timescales related to the formation of the Solar System. Some of the relevant species are listed in Table 10.1.

Age-dating of rocks

The basic idea in radioactive age-dating of rocks (from the Earth, Moon and meteorites) is to find the ratio of daughter to parent in an isolated system. Thus the age inferred is usually the ‘solidification age’ which is the time since the last occasion when chemical fractionation was halted by solidification.

Abstract

We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement (AMR) in both codes, as well as the most promising directions for future developments.

Introduction

The dynamics of astrophysical systems described by the equations of radiation magnetohydrodynamics (MHD) span a tremendous range of scales and parameter regimes, from the interiors of stars (Kippenhahn & Weigert 1994), to accretion disks around compact objects (Turner et al. 2003), to dusty accretion flows around massive protostars (Krumholz et al. 2005, 2007a), to galactic-scale flows onto AGN (Thompson et al. 2005). All of these systems have in common that matter, radiation and magnetic fields are strongly interacting and that the energy and momentum carried by the radiation field is significant in comparison to that carried by the gas. Thus, an accurate treatment of the problem must include analysis of both the matter and the radiation, as well as the magnetic fields, and their mutual interaction.

Understanding the formation of gravitationally bound structures at all scales in the universe is one of the most fascinating challenges of modern astronomy. It is now realized that the initial building blocks of galaxies were small collapsing dark matter halos, produced by the primordial fluctuations. These blocks then merged and were assembled into progressively larger galaxies, a scheme generally described as the hierarchical model of galaxy formation. The modern understanding of star formation involves large-scale turbulent motions producing local overdensities which eventually collapse and form prestellar cores under the action of gravity. The most likely scenario for planet formation is the collapse of a vast gaseous envelope onto a central dense core formed from the aggregation of millimetre-size grains in the original protoplanetary nebula, although disk fragmentation could remain an alternative scenario in some situations. The detailed processes responsible for the formation of these structures, however, remain poorly understood. Many important issues remain unsettled, so the robustness of these general paradigms is still ill determined. All these scenarios for the formation of galaxies, stars and planets, although involving vastly different scales, share many underlying physical mechanisms.They all involved hydrodynamical processes, generally leading to turbulent motions, but the very nature of these motions and their real role in structure formation remains unclear. The role of magnetic fields, in the collapse itself and in the generation of winds and jets, remains one of the major unknowns in the formation of structures.