Introduction

One of the most important results of the last few years has been the realization that most, if not all, galaxies harbor supermassive black holes (BH) in their centers. The presence of a supermassive BH can manifest itself as luminous quasar “activity,” powered by accretion of matter onto the BH itself. Such a quasar phase, which peaks somewhere around redshift 2, is likely to play an important role in the build-up of these BHs.

Since the advent of the Hubble Space Telescope (HST), the progress in studying and understanding black holes has been impressive. Early questions regarding the very existence of black holes have been replaced by questions regarding the role that they play in the formation and evolution of galaxies, particularly at early epochs in the universe. However, the apparently well-established relationship between the mass of the black hole and the mass or luminosity of the galactic bulge rests on a relatively small number of direct observations, and while very few doubt that this relationship exists, it is essential to actually measure the properties of a number of black holes over a range of masses and host galaxies. The direct methods adopted to measure black holes in the nearby universe use gas or stellar kinematics to gather information on the gravitational potential in the nuclear region of the galaxy. The stellar-kinematical method has the advantage that stars are present in all galactic nuclei and their motion is always gravitational. The drawbacks are that it requires relatively long observation times in order to obtain high-quality observations, and that stellar-dynamical models are very complex and potentially plagued by indeterminacy. Conversely, the gas-kinematical method is relatively simple; it requires relatively short observation times for the brightest emission-line nuclei, even if not all galactic nuclei present detectable emission lines. However, an important drawback is that noncircular or non-gravitational motions can completely invalidate this method.

Introduction

General properties of black holes were studied extensively in the early 1970's, and the basic theory was developed. One of the key results was Hawking's proof that the area of a black hole cannot decrease (Hawking 1971). This led Bekenstein (1973) to suggest that a black hole should have an entropy proportional to its horizon area. This suggestion of a connection between black holes and thermodynamics was strengthened by the formulation of the laws of black-hole mechanics (Bardeen et al. 1973). In addition to the total mass M, angular momentum J, and horizon area A of the black holes, these laws are formulated in terms of the angular velocity of the horizon Ω, and its surface gravity k. Recall that the surface gravity is the force at infinity required to hold a unit mass stationary near the horizon of a black hole.

The Space Telescope Science Institute Symposium on Black Holes took place during April 23–26, 2007.

These proceedings represent a part of the invited talks that were presented at the symposium. They cover many aspects of black hole physics and astrophysics, regarding stellar-mass, intermediate-mass, and supermassive black holes. Topics range from black hole entropy and the fate of information to supermassive black holes at the centers of galaxies, and from the possibility to produce black holes in collider experiments to the measurements of black hole spins. Since these articles were written by world experts in their respective disciplines, this volume represents an extremely valuable collection for researchers and students alike.

The ST ScI Symposium on Black Holes attempted to capture all the aspects involved in the astrophysics of black holes.

We thank Sharon Toolan of ST ScI for her help in preparing this volume for publication.

Introduction

Black holes are natural products of stellar evolution in massive stars, and may also result from dynamical interactions in dense stellar systems, such as star clusters and galactic nuclei. They can significantly influence the dynamics of their parent cluster, and may also have important observational consequences, via their x-ray emission, the production of gravitational radiation, and their effect on the structural properties of the system in which they reside.

Globular clusters offer particularly rich environments for the production of black holes in statistically significant numbers. Direct evidence for black holes in globulars is scarce, although several independent lines of investigation now hint at their presence.

Introduction

Black holes (BHs), as physical entities, span the full range of masses, from tiny BHs predicted by string theory, to monsters weighing by themselves almost as much as a dwarf galaxy (massive black holes, MBHs). Notwithstanding the several orders of magnitude difference between the smallest and the largest BH known, we believe that all of them can be described by only three parameters: mass, spin, and charge.

Prolog: The classical view of accretion disks

It has been understood for decades that accretion through disks can be an extremely powerful source of energy for the generation of both photons and material outflows. When the central object is a black hole, the gravitational potential at the center of the disk is relativistically deep, so that the amount of energy that might be released per unit rest-mass accreted can be a substantial fraction of unity. If the central black hole spins, an additional store of tappable energy resides in its rotation.

Pre-main-sequence evolution

In this chapter we follow the evolution from a collapsing core in a molecular cloud to a newly formed star as it approaches the main sequence on the Hertzsprung–Russell (HR) diagram. Figure 6.1 sketches the paths followed during the various evolutionary stages on an HR diagram. In this section we briefly outline the various evolutionary stages, and in successive sections we deal with each stage in more detail.

Isothermal collapse

Once a pre-stellar core becomes gravitationally unstable and starts to collapse, then initially the released gravitational energy is freely radiated away and the collapsing fragment stays at roughly the same temperature (isothermal). Its temperature would place it on the right-hand side of the HR diagram (cool), and it has a relatively large radius and hence luminosity. Consequently, it should begin its evolution at the upper right of the HR diagram. Its luminosity is supplied by contraction and the consequent release of gravitational potential energy.

The isothermal collapse phase produces a central concentration of matter and ends with the formation of an opaque, hydrostatic object at the centre, surrounded by a gaseous envelope. We define a hydrostatic object as one which supports itself against gravity by its own internal pressure.

Introduction

In this chapter we take a more detailed look at the interstellar medium (ISM). We consider first the most abundant element in the Universe, hydrogen. We discuss the atomic hydrogen transition which occurs at 21 cm. We look at the 21-cm line in both absorption and emission. We then go on to consider the molecular gas and, in particular, the most abundant gas-phase molecule after hydrogen, carbon monoxide (CO). We also look at the use of absorption lines in the study of the ISM. In this context we consider some features of spectral lines, such as their equivalent widths, and we describe the curve of growth of a spectral line. In the next chapter we will go on to study the denser parts of the ISM, known as molecular clouds.

The 21-cm line of atomic hydrogen

The most abundant element in the Universe is hydrogen. We here discuss the main signature of cool atomic hydrogen, 21-cm line radiation. Figure 3.1 shows 21-cm images of some nearby galaxies, illustrating how the 21-cm radiation traces the atomic gas in the interstellar medium of these galaxies.

This book is directed at the student undertaking a course in star formation for the first time. This may be in the later years of an undergraduate degree in physics, astrophysics, or physics with astronomy. Alternatively, it may be that the student only meets this subject for the first time during the first years of a masters degree. In either case we have assumed that the student already has a grounding in physics and mathematics, including, for example, Maxwell's equations, quantum mechanics and the laws of thermodynamics. Nevertheless, we find from teaching experience that brief reminders to students of things they learnt in other courses are generally welcomed as helpful. Hence, we remind the reader of some of the important points from other branches of physics where they are relevant.

We assume only a minimal knowledge of astronomy, and we derive the necessary astrophysical equations as we go along. We assume no prior knowledge of the subject of star formation itself and begin from first principles. Throughout the book we attempt to stay on ground that is firmly established, and try to avoid that which is trendy or the latest discovery. Experience has taught us that these matters often become outdated much more quickly than the solid foundations on which the subject is based. In cases where we stray onto less sure footing, we inform the reader that we are doing so.

The road to star formation

Thus far we have studied the places where stars form – molecular clouds. We have discussed the ways in which molecular clouds can be observed. We have explored the various constituents of molecular clouds – gas, dust, magnetic fields, cosmic rays and electromagnetic radiation. We have, so to speak, assembled the ingredients. In this chapter we discuss how these ingredients might come together to begin to form a star.

In the first half of the chapter we discuss theoretical considerations. We consider the collapse of an isothermal sphere of gas, ignoring the effects of rotation and magnetic fields, and we examine qualitatively what happens. We describe the method of solving the problem using similarity solutions.

We go on to discuss hierarchical fragmentation, as a means of breaking a large molecular cloud into an ensemble of stars. We also discuss the thermodynamics of protostellar gas, and explain how the minimum mass for star formation might be determined by the protostellar gas becoming optically thick to its own cooling radiation. We discuss the manner of the collapse to form a star and the possible effects of a magnetic field on this process.

In the second half of the chapter we examine some of the observational evidence. At the end we consider the initial mass function for stars. Note that in this chapter we concentrate mainly on relatively low-mass stars, i.e. stars of less than a few times the mass of the Sun. In Chapter 6 we continue to discuss relatively low-mass star formation.

Introduction

In this chapter we discuss some of the phenomena observed as a consequence of star formation. We describe some of the phenomena surrounding star formation, such as discs, outflows, and binary and multiple stars, and we discuss the difference between hydrogen-burning stars and brown dwarf stars.

We then go on to detail some of the larger-scale consequences, such as how star formation affects the host galaxy in which it occurs. In this context we also discuss starburst galaxies and galaxy mergers. Finally, we outline current understanding on when the major epoch of star formation occurred in the Universe.

Circumstellar discs

In Chapter 6 we discussed accretion onto protostars. In particular, we discussed spherically symmetric accretion. However, if the material accreting onto a protostar has angular momentum (and in general it does), the infall is not spherically symmetric, nor is it direct. Instead, the material accumulates in a circumstellar disc, and then spirals inwards onto the equator of the star on a time-scale determined by the efficiency of the processes which redistribute or remove the angular momentum in the disc. Such a disc is often termed an accretion disc. We also mentioned this in Chapter 7 as a method for increasing the accretion onto a high-mass protostar in the context of significant radiation pressure potentially halting the accretion.

About this book

It can be argued that astronomy is the oldest science. Since pre-historic times humans have gazed at the night sky and wondered about the nature and origin of stars. We now believe we understand a great deal about the nature of stars, but many aspects of the origin of stars remain the subject of intense study to this day.

In this book we aim to introduce the reader to the fundamentals of the subject of star formation. We describe the background physics underlying theories of star formation, and take the reader to the frontiers of current knowledge of this subject. However, we will make clear as we go along the points where we reach material that is less well established.

One of the most fundamental observations in astronomy is the fact that the night sky appears to be full of stars. Yet the processes which lead to the formation of those stars have taken astronomers many years to work out. Unlocking the mysteries of star formation has required the use of new techniques and the opening of new wavelength regimes to astronomy. We describe the chief physical processes which are believed to be important for star formation, and point out the role which each branch of observational astronomy has played in solving the various problems associated with star formation.