Introduction

How did the first stars in the universe form, how did they evolve and die and what was their impact on cosmic history (Woosley et al. 2002; Bromm & Larson 2004; Ciardi & Ferrara 2005)? The first stars formed at the end of the cosmic dark ages beyond the current horizon of observability (Couchman & Rees 1986; Haiman et al. 1996; Tegmark et al. 1997). These so-called Population III (Pop III) stars ionized (Kitayama et al. 2004; Whalen et al. 2004; Alvarez et al. 2006; Johnson et al. 2007) and metal-enriched (Furlanetto & Loeb 2003; Tornatore et al. 2007) the intergalactic medium (IGM) and consequently had important effects on subsequent galaxy formation (Barkana & Loeb 2001; Mackey et al. 2003).

Turbulence is a remarkable subject in physics. The underlying equations, which are in their simplest formulation the Euler equations, were published 250 years ago (Euler 1757). Yet a theoretical grasp of the phenomenology emerging from these equations had not been achieved before the mid-twentieth century, when Heisenberg (1923) and Kolmogorov (1941) obtained their first analytical results. Eventually, it took the capabilities of modern supercomputers to obtain a full appreciation of the complexity that is inherent to the Euler equations. Astrophysics is now at the very frontier of numerical turbulence modelling. Among the additional ingredients for making turbulence in astrophysics even more complex are supersonic flow, self-gravity, magnetic fields and radiation transport. In contrast, terrestrial turbulence is mostly incompressible or only weakly compressible. External gravity is, of course, an issue in the computation of atmospheric processes on Earth. Self-gravity, however, is only encountered on large, astrophysical scales. The dynamics of turbulent plasma has met vivid attention in research related to nuclear fusion reactors but, otherwise, is not encountered under terrestrial conditions.

In this chapter, I give an overview of the various approaches towards the numerical modelling of turbulence, particularly, in the interstellar medium (ISM). The discussion is placed in a physical context, i.e. computational problems are motivated from basic physical considerations. Presenting selected examples for solutions to these problems, I introduce the basic ideas of the most commonly used numerical methods. For detailed methodological accounts, the reader is invited to follow the references.

Introduction

Although not precisely in its infancy, the question of building planets and planetary systems still faces many challenges: how are planetesimals assembled from micrometre-sized grains? What does radial transport do to growing dust aggregates? Do solids concentrate close to the star or do (metre size) objects vanish rapidly into the central star? How are planets formed from planetesimals? And how do giant planets form that have to acquire hydrogen and helium before the gas is accreted onto the star or is swept away by stellar winds and photoevaporation? Are many generations of planets formed and then lost? Can we explain the compositions of planets in the structure of our present solar system?

These are but a few of the basic questions which are currently the focus of a highly active research field. Presenting a complete overview of the problem is beyond the scope of this short chapter and would not be a long-lasting one as the field is rapidly evolving. We present here what we believe are some important pieces of the puzzle, in the domain of planetesimal formation and giant planet composition.

Planetesimals

There are several important steps of structure formation after the solar nebula formed and before full-size planets came into existence. One of them is the formation of planetesimals. There is some ambiguity in the term planetesimal as it is used throughout the literature.

We have heard a lot about probability functions p(M) at this meeting for mass M of planets or stars or clouds or clusters under various conditions. Since we have covered such an enormous range of masses, it is not surprising that power-law distributions close to the scale-invariant power have recurred so often. A power law differing from this distribution in the direction of favouring either low or high masses must of course have a turnover (or termination) towards this end to avoid a divergence. The physical reason for such a turnover is of interest, as is the question of continuity between the various types of objects. Bingelli and Hascher (PASP 119, 592, 2007) have followed this power-law continuity over 36 orders of magnitude in mass from asteroids to galaxy superclusters. It is instructive to look at similar probability distribution functions in quite different fields. I will give only the examples of two different kinds of human aggregates. One example, which has been discussed for more than a century or so, is the probability distribution for the size (i.e. the number of inhabitants) of a village, town or city. Near the end of the nineteenth century, the deviation from scale invariance was a slight increase towards the bottom end, i.e. overall slightly more people lived in a village of population 100-200 than in a city of 250 000 to 500 000.

Dwarf galaxies

Introduction

Nearby dwarf galaxies are classified in four main types: (i) dwarf irregular (dIrr) galaxies are the most common type by number, and are usually unstructured gasrich systems with varying levels of star formation occurring in a haphazard manner across the galaxy. (ii) Blue compact dwarf (BCD) or H II galaxies are gas-rich systems dominated by very active star formation and resembling giant H II regions found in large galaxies. They appear to be forming stars at a rate which they can only maintain for a short period. (iii) Dwarf spheroidal (dSph) galaxies usually have no gas in their centre down to very low limits. Their stellar distribution is similar to that of globular clusters, although less centrally concentrated, but a detailed study of their HR diagrams often reveals that several distinct bursts of star formation have occurred in the past.

Introduction

The light elements (D to B, apart from 4He) have such fragile nuclei (see Table 9.1) that they tend to be destroyed, rather than created, in thermonuclear burning, although certain special processes can lead to stellar production of 3He, 7Li and 11B.

B2FH accordingly postulated for their creation an ‘x’-process involving spallation by fast particles at high energy, but low temperature and density. They considered stellar flares and supernova shells as possible sites, while also envisaging the possibility of 7Li creation in H-free helium zones in stars. Since then, it has been accepted that all D, some 3He and some 7Li come from the Big Bang (see Chapter 4), where rapid expansion and cooling allow traces of these elements to be preserved; and that a significant clue to the origin of Li, Be and B comes from their relative overabundance (by factors of 104 to 105) in Galactic cosmic rays (Fig. 9.1).

Sketch of cosmic-ray physics

Cosmic rays reaching the ground are secondary particles resulting from the impact of primary cosmic rays coming mainly from the Galaxy. The latter are mostly protons and α-particles with a sprinkling of heavier nuclei, coming in with a broad distribution of energies. The most energetic, with energies up to 1020 eV or so, are quite rare but are detected occasionally in the form of extensive air showers.

Much has happened since the book first came out in 1997. Cosmology has been transformed by balloon and satellite studies of the microwave background and by studies of distant supernovae. Host galaxies of γ-ray burst sources have been identified and some of their properties revealed. Cosmological simulations have been very successful in accounting for the large-scale structure of the Universe, although they are still challenged by observed element:element ratios suggesting that the largest galaxies were formed rapidly a long time ago, limiting the time available for their formation by mergers. The coming of 10-metre class telescopes, supplementing the Hubble Space Telescope, has led to enormous advances in abundance determinations in stars of all kinds and in galaxies, notably at high redshifts. Some stellar atmospheres can now be modelled by ab initio hydrodynamical simulations which account for granulation and eliminate the need for ad hoc parameters describing ‘macro-turbulence’ and ‘micro-turbulence’, leading to increasingly sophisticated abundance determinations. Nevertheless, simple analytical treatments retain their usefulness because of the insight they provide into the essential ingredients of more elaborate numerical models, whether of stellar atmospheres or of galactic chemical evolution.

I thank Monica Grady, Chris Tout and Max Pettini for critically reading through the revised Chapters 3, 5 and 12 respectively, and Mike Edmunds for continued cooperation and enlightening discussions. I owe particular thanks to my wife Annabel Tuby Pagel for her loving care during difficult times.

Introduction

The formation of molecular clouds (MCs) from the diffuse interstellar gas is a necessary step for star formation, as young stars invariably occur within them. However, the mechanisms controlling the formation of MCs remain controversial. In this contribution, we focus on their formation in compressive flows driven by interstellar turbulence and large-scale gravitational instability.

Turbulent compression driven by supernovae appears insufficient to explain the bulk of cloud and star formation. Rather, gravity must be important at all scales, driving the compressive flows that form both clouds and cores. Cooling and thermal instability allow the formation of dense gas out of moderate, transonic compressions in the warm diffuse gas and drive turbulence into the dense clouds. MCs may be produced by an overshoot beyond the thermal-pressure equilibrium between the cold and the warm phases of atomic gas, caused by some combination of the ram pressure of compression and the self-gravity of the compressed gas.

In this case, properties of the clouds such as their mass, mass-to-magnetic flux ratio, and total kinetic and gravitational energies are in general time-variable quantities. MCs may never enter a quasi-equilibrium or virial equilibrium state but rather continuously collapse to stars. Gravitationally collapsing clouds exhibit a pseudo-virial energy balance |Egrav|~2Ekin, which, however, is representative of contraction rather than of virial equilibrium in this case. However, compression-driven cloud and core formation still involves significant delays as additional material accretes, leading to lifetimes longer than the free-fall time.

Introduction

The ‘Hot Big Bang’ theory of the Universe was pioneered by George Gamow, R. A. Alpher and R. C. Herman in the late 1940s and early 50s. They supposed that during the first few minutes of the (then radiation-dominated) Universe, matter was originally present in the form of neutrons and that, after some free decay, protons captured neutrons and successive captures, followed by β-decays, built up all the elements (Alpher & Herman 1950).

C. Hayashi (1950) first put the theory on a sound physical basis by pointing out that, at the high densities and temperatures involved, there would be thermal equilibrium between protons and neutrons at first, followed by a freeze-out, and this did nothing to overcome the difficulty already known to be inherent in that theory that the absence of stable nuclei at mass numbers 5 and 8 would prevent significant nucleosynthesis beyond helium. In the meantime, progress in the theory of stellar evolution and nucleosynthesis (see Chapter 5) led to comparative neglect of Big Bang nucleosynthesis theory (BBNS) until the discovery by A. A. Penzias and R. Wilson in 1964 of the microwave background radiation, existence of which Gamow and his colleagues had predicted.

Introduction

This conference has brought together researchers studying structure formation in astrophysics, at scales ranging from planet and star formation through galaxy formation to cosmic structure formation. Aside from gravity, these fields require knowledge about many further physical processes and phenomena, such as turbulent gas dynamics, magnetic fields, non-equilibrium chemistry and the interaction of radiation with matter. The different communities also all rely on numerical simulations and the same modern, general-purpose, ground-based and space-borne telescopes.

In this proceedings contribution, we attempt to identify some of the major challenges for the future. We furthermore debate whether the physical processes relevant for each field exhibit sufficient overlap to warrant concerted cross-disciplinary efforts or whether the features that define and distinguish these fields prevail and make successful cross-fertilization less likely.

Planet formation

With the first discovery of a planet around another star in 1995, we have begun to place our solar system in the context of other planetary systems. More than 250 extrasolar planets have been identified, most with characteristics vastly different from our own solar system. Planets around stars such as our Sun may be the rule, rather than the exception, but the observed properties exhibit an enormous spread (see Udry & Santos 2007).

In the core instability model, planet formation begins with the coagulation of dust in protoplanetary disks, forming larger aggregates of solid material through a sequence of collisions and agglomeration.

Introduction

The collapse of a molecular cloud core leads to the creation of a newborn star and attendant circumstellar accretion disk. The action of disk accretion during and after collapse likely controls the initial mass and angular momentum of these young stellar objects (YSOs). It also has a hand in shaping the conditions under which planetary systems are born. Determining the observational properties of YSOs, particularly their variations with environment, mass and time, can therefore place stringent constraints on the physical processes at play during both stellar and planetary formation. In this chapter, we give an overview of the current knowledge of YSO properties, with an emphasis on their implications for both processes.

Circumstellar disks are a ubiquitous outcome of the star formation process, making them a powerful probe of YSO evolution. In addition, disks are the birthsite of planetary systems and can therefore be used to constrain the overall planet formation process (via statistical analyses) and some of the key physical mechanisms, such as grain growth, vertical settling or radial migration (via detailed studies of individual objects). We focus our discussion on the analysis of young, optically thick, gas-rich protoplanetary disks. In particular, we focus on their dust component which, although it amounts to only a tiny fraction (on the order of 1%) of the total mass, represents the building blocks of planetesimals and planets. We also address some observations of more evolved debris disks.