Abstract

Astrophysical jets are associated with the formation of young stars of all masses, stellar and massive black holes, and perhaps even with the formation of massive planets. Their role in the formation of planets, stars and galaxies is increasingly appreciated and probably reflects a deep connection between the accretion flows – by which stars and black holes may be formed – and the efficiency by which magnetic torques can remove angular momentum from such flows. We compare the properties and physics of jets in both non-relativistic and relativistic systems and trace, by means of theoretical argument and numerical simulations, the physical connections between these different phenomena. We discuss the properties of jets from young stars and black holes, give some basic theoretical results that underpin the origin of jets in these systems, and then show results of recent simulations on jet production in collapsing star-forming cores as well as from jets around rotating Kerr black holes.

Introduction

The goal of this book, to explore structure formation in the cosmos and the physical linkage of astrophysical phenomena on different physical scales, is both timely and important. The emergence of multi-wavelength astronomy in the late twentieth century with its unprecedented ground- and space-based observatories, as well as the arrival of powerful new computational capabilities and numerical codes, has opened up unanticipated new vistas in understanding how planets, stars and galaxies form.

Introduction

Observations of distant objects, notably high-redshift star-forming (‘Lymanbreak’) galaxies and absorption line systems on the line of sight to quasars, give some information on chemical evolution at epochs not too far from when the first stars and most galaxies were presumably formed.

This book is based on a lecture course given at Copenhagen University in the past few years to a mixed audience of advanced undergraduates, graduate students and some senior colleagues with backgrounds in either physics or astronomy. It is intended to cover a wide range of interconnected topics including thermonuclear reactions, cosmic abundances, primordial synthesis of elements in the Big Bang, stellar evolution and nucleosynthesis. There is also a (mainly analytical) treatment of factors governing the distribution of element abundances in stars, gas clouds and galaxies and related observational data are presented.

Some of the content of the course is a concise summary of fairly standard material concerning abundance determinations in stars, cold gas and ionized nebulae, cosmology, stellar evolution and nucleosynthesis that is available in much more detail elsewhere, notably in the books cited in the reading list or in review articles; here I have attempted to concentrate on giving up-to-date information, often in graphical form, and to give the simplest possible derivations of well-known results (e.g. exponential distribution of exposures in the main s-process). The section on Chemical Evolution of Galaxies deals with a rapidly growing subject in a more distinctive way, based on work in which I and some colleagues have been engaged over the years. The problem in this field is that uncertainties arising from problems in stellar and galactic evolution are compounded.

Introduction

This chapter is devoted to planet formation and to the early stages of evolution of low-mass objects, including low-mass stars, brown dwarfs and exoplanets. We first summarize the general properties of current exoplanet observations (Section 15.2) and describe the two main planet formation models based on disk instability and on the core-accretion scenario, respectively (Section 15.3). Recent progress of the latter formation model allows sophisticated population synthesis analyses which provide fully quantitative predictions that can be compared to the observed statistical properties of exoplanets (Section 15.3.5). The last part of this chapter is devoted to the distinction between brown dwarfs and planets, in terms of structure and evolutionary properties. The existence of a mass overlap between these two distinct populations of low-mass objects is highlighted by the increasing discoveries of very massive exoplanets (M ≳ 5MJ) and by the identification of planetary mass brown dwarfs in young clusters (M ≲ 10MJ) These discoveries stress the importance to define signatures which could allow to disentangle a brown dwarf from a planet. We first analyse the effect of accretion on the evolution of young brown dwarfs and the resulting uncertainties of evolutionary models at ages of a few million years. We also analyse different specific signatures of brown dwarfs and planets such as their luminosity at young ages, their radii and their atmospheric properties.

Abstract

The formation of massive stars is currently an unsolved problem in astrophysics. Understanding the formation of massive stars is essential because they dominate the luminous, kinematic and chemical output of stars. Furthermore, their feedback is likely to play a dominant role in the evolution of molecular clouds and any subsequent star formation therein. Although significant progress has been made observationally and theoretically, we still do not have a consensus as to how massive stars form. There are two contending models to explain the formation of massive stars: core accretion and competitive accretion. They differ primarily in how and when the mass that ultimately makes up the massive star is gathered. In the core accretion model, the mass is gathered in a pre-stellar stage due to the overlying pressure of a stellar cluster or a massive pre-cluster cloud clump. In contrast, competitive accretion envisions that the mass is gathered during the star formation process itself, being funnelled to the centre of a stellar cluster by the gravitational potential of the stellar cluster. Although these differences may not appear overly significant, they involve significant differences in terms of the physical processes involved. Furthermore, the differences also have important implications in terms of the evolutionary phases of massive star formation and ultimately that of stellar clusters and star formation on larger scales. Here, we review the dominant models and discuss prospects for developing a better understanding of massive star formation in the future.

Introduction

During the last two decades, the focus of star formation research has shifted from understanding the collapse of a single dense core into a star to studying the formation of hundreds to thousands of stars in molecular clouds. In this chapter, we overview recent observational and theoretical progress towards understanding star formation on the scale of molecular clouds and complexes, i.e. the macrophysics of star formation (McKee & Ostriker 2007). We begin with an overview of recent surveys of young stellar objects (YSOs) in molecular clouds and embedded clusters, and we outline an emerging picture of cluster formation. We then discuss the role of turbulence to both support clouds and create dense, gravitationally unstable structures, with an emphasis on the role of magnetic fields (in the case of distributed stars), and feedback (in the case of clusters) to slow turbulent decay and mediate the rate and density of star formation. The discussion is followed by an overview of how gravity and turbulence may produce observed scaling laws for the properties of molecular clouds, stars and star clusters and how the observed, star formation rate (SFR) may result from self-regulated star formation. We end with some concluding remarks, including a number of questions to be addressed by future observations and simulations.

Observations of clustered and distributed populations in molecular clouds

Our knowledge of the distribution and kinematics of young stars, protostars and dense cores in molecular clouds is being rapidly improved by wide-field observations at X-ray, optical, infrared and (sub)millimeter wavelengths (Allen et al. 2007; Feigelson et al. 2007).

Abstract

Computational gas dynamics has become a prominent research field in both astrophysics and cosmology. In the first part of this chapter, we intend to briefly describe several of the numerical methods used in this field, discuss their range of application and present strategies for converting conditionally stable numerical methods into unconditionally stable solution procedures. The underlying aim of the conversion is to enhance the robustness and unification of numerical methods and subsequently enlarge their range of applications considerably. In the second part, Heitsch presents and discusses the implementation of a time-explicit magneto hydrodynamic (MHD) Boltzmann solver.

PART I

Numerical methods in AFD

Astrophysical fluid dynamics (AFD) deals with the properties of gaseous matter under a wide variety of circumstances. Most astrophysical fluid flows evolve over a large variety of different time and length scales, henceforth making their analytical treatment unfeasible.

On the contrary, numerical treatments by means of computer codes have witnessed an exponential growth during the last two decades due to the rapid development of hardware technology. Nowadays, the vast majority of numerical codes are capable of treating large and sophisticated multi-scale fluid problems with high resolutions and even in 3D.

The numerical methods employed in AFD can be classified into two categories (see Figure 5.1):

1. Microscopic-oriented methods: These are mostly based on N-body (NB), Monte Carlo (MC) and on the Smoothed Particle Hydrodynamics (SPH).

2. Grid-oriented methods: To this category belong the finite difference (FDM), finite volume (FVM) and finite element methods (FEM).

Every school child is aware that the Moon is not a planet. So why begin this discussion on planetary crusts with examples from a planetary satellite? The reason is that the two types of crusts on the Moon, that form the lighter highlands and the darker maria, are among our best examples of primary and secondary crusts. Their origin and evolution are better understood than those of any other examples in the Solar System, including the Earth. In addition, the Moon, in contrast to the Earth, forms a classic example of a one-plate planet, that is the norm for our Solar System.

The composition of the Moon

The mean lunar radius is 1737.1 km, which is intermediate between that of the two jovian satellites of Jupiter, Europa (r = 1561 km) and Io (r = 1818 km). The Moon is much smaller than the jovian satellite Ganymede (r = 2634 km), which in turn is the largest satellite in the Solar System and like the saturnian satellite Titan, is larger than Mercury. Although the jovian satellites and also Titan are comparable in mass, the Moon/Earth ratio is the largest satellite-to-parent ratio in the planetary system, a consequence of a distinctive origin.

In the following four chapters, we deal with the development of the continental crust on the Earth. The history of this planet, except for the past 200 Myr, is contained almost entirely in the continental crust that is subject to so many factors (erosion, tectonic activity, differentiation, metamorphism, volcanism, break-up and re-accretion among others) that it is surprising how good the record is. We begin with that dark period from which no rocks have survived. This however has not prevented, but rather encouraged speculation about the nature of the crust in that remote epoch. This, the so-named Hadean Eon, extends for several hundred million years, from the formation of the Earth to the first known occurrence of a preserved rock record, a period of time comparable to the extent of the Phanerozoic.

The Hadean crust and mantle

What indeed was the nature of the crust of the Hadean Earth? Extensive searches have failed to reveal rocks older than somewhere between 3850 and 4030 Myr. The only earlier remnants that have survived to record the existence of Hadean surface rocks are some relict detrital zircon crystals up to 4100 Myr in age, with a handful as old as 4363 Myr, that are found in younger sedimentary rocks in the Jack Hills in Western Australia.

The enigma of Venus

Venus has historically been regarded as a “twin planet” to the Earth as amongst the planets, it is closest to the Earth in mass, density, size and in distance from the Sun. However it has, by terrestrial standards, extraordinary crustal features and a geological history that bears little resemblance to that of the Earth. In addition, it does not possess a satellite and has a retrograde rotation with a period of 243 days.

The planet clearly warrants closer study particularly as the differences between these twin planets emphasize the problems of building crusts or discovering habitable planets in other planetary systems. So it is useful to contrast crustal development on Venus with that of its twin planet Earth, that occupy the following five chapters.

The density of Venus (5.24 g/cm3) is about 5% less than that of the Earth (5.514 g/cm3). This difference is mostly due to the slightly lower internal pressures as the planetary radius is 320 km less than that of the Earth. But the uncompressed density of both planets is very close (Earth 3.96 g/cm3; Venus 3.9 g/cm3). The similar density of Venus to the Earth and the presence of a basaltic crust on the planet are the basis for assuming a broadly similar composition and internal structure.

The Archean

More so than most of the past, the Archean is truly another country, with a geological record that is distinct from that of more recent epochs. The Archean covers a crucial 1500 Myr of Earth history, nearly three times the length of the entire Phanerozoic, from the earliest recorded rocks at its beginning to the growth of 60–70% of the continental crust by its close.

Much confusion has arisen through the imprecise use of the term Archean, or even Precambrian, in referring to the “Archean crust”. Thus the “Precambrian” includes two totally distinct periods of Earth history that are separated by the great transition between the Archean and Proterozoic. Although the Archean has been formally divided into the following eras: Eoarchean (3800?–3600 Myr), Paleoarchean (3600–3200 Myr), Mesoarchean (3200–2800 Myr) and Neoarchean (2800–2500 Myr) it will be interesting to see if this classification is widely adopted. However, we are less concerned here with the details of the tectonic evolution of the Archean terrains to which this scheme might be applicable, so that we use the somewhat broader and commonly employed subdivision of that epoch into Early (3.9–3.5 Gyr), Middle (3.5–3.0 Gyr) and Late Archean (3.0–2.5 Gyr).

Yet even within the Archean, there is a vast difference between the scattered remnants that remain of the earliest crust, preserved at locations such as Isua in Greenland and the massive cratons in Canada, Australia, Africa and elsewhere, that developed in the Late Archean over a billion years later.

The next five chapters deal with the formation of crusts on the Earth. These occupy a significant fraction of this book, partly on account of their intrinsic importance to us, but also because we know so much about them. We begin by considering the oceanic crust, both because it forms a good example of a secondary crust and because the continental crust, discussed in the succeeding four chapters is effectively derived from it.

The sea floor and plate tectonics

The oceanic crust differs significantly in composition from the continental crust, a fact that has been known only for the past half-century. Before that time, the ocean floors were commonly thought to be underlain by sunken continental crust. Land bridges were invoked to explain puzzling cross-ocean similarities in fossil faunas. But in the 1950s, it was established that the oceanic crust, in great contrast to the continental crust, was both more dense and only a few kilometers thick. Thus it was most likely to be composed of dense basalt, or “sima” in the jargon of the time, that contrasted with the less dense continental granitic crust or “sial”.

It seems inevitable that rocky planets, like bakers, cannot resist making crusts, heat being the prime cause in both cases. Although trivial in volume relative to their parent planets, crusts often contain a major fraction of the planetary budget of elements such as the heat-producing elements potassium, uranium and thorium as well as many other rare elements while the familiar continental crust of the Earth on which most of us live is of unique importance to Homo sapiens. It was on this platform that the later stages of evolution occurred and so has enabled this enquiry to proceed.

Planetary crusts in the Solar System indeed have undeniable advantages for scientists: they are accessible. Unlike the other regions of planets that we wish to study, such as cores and mantles, you can walk on crusts, land spacecraft on them, collect samples from them, measure their surface compositions remotely, study photographs, or use radar to penetrate obscuring atmospheres. Despite this accessibility, the problems both of sampling or observing crusts are non-trivial: most of our confusion in deciphering the history of crusts ultimately turns on our ability to sample them in an adequate fashion. We discuss these diverse problems in the appropriate chapters.

This advantage of relatively easy access to crusts is also offset by the distressing tendency for crusts to be complex, so that one may easily become lost in the detail, failing to see the forest for the trees.

The continental crust of the Earth is so familiar to us that perhaps we underestimate its significance as a platform for human existence while at the same time overestimate its significance for understanding planetary crusts. Without such a haven above sea level, the later stages of evolution would have taken a very different course. If oceanic islands had formed the only dry land, birds rather than mammals might have become dominant as they did in Mauritius and New Zealand. However, the buoyant extensive continental crust has provided a useful platform for the land-based stages of evolution. After the extinction of the dinosaurs and much else 65 Myr ago, the way was cleared on the continental massifs for mammalian evolution to flourish. This led ultimately to the emergence of primates and to the appearance of many species of the genus Homo, ultimately enabling this account.

The Archean–Proterozoic transition

Following the Archean, that had lasted for 1500 Myr, the Proterozoic Eon continued for an even longer period (2000 Myr).