Introduction

In this chapter we deal with the physical processes that take place in he diffuse IGM and their signatures in the quasar spectra in the form of hydrogen absorption lines. It uses material developed in several previous chapters, especially Chap. 7.

Gunn–Peterson Effect

We have seen in Chap. 4 that the formation of neutral matter and the decoupling of radiation occurred at z ≃ 103. Because it is unlikely that the formation of structures at lower redshifts could have been 100% efficient, we would expect at least a fraction of the neutral material, especially hydrogen, to remain in the IGM with nearly uniform density. This neutral hydrogen could, in principle, be detected by an examination of the spectrum of a distant source, like a quasar. Neutral hydrogen absorbs Lyman-α photons, which are photons of wavelength 1216 Å that corresponds to the energy difference between the n = 1 and the n = 2 states of the H atom. Because of the cosmological redshift, the photons that are absorbed will have a shorter wavelength at the source and the signature of the absorption will be seen at longer wavelengths at the observer. We expect the spectrum of the quasar to show a dip (known as the Gunn–Peterson effect) at wavelengths on the blue side (shortwards) of the Lyman-α emission line if neutral hydrogen is present between the source and the observer.

Introduction

To understand the features of the universe today, it is necessary to grasp the past history of the universe. We now tackle this issue and describe the physical processes that occur in the earlier phase of the universe. Section 2 develops the basic thermodynamics needed to understand these processes. In Sections 4.3 and 4.4, we consider the possible existence of a relic background of massless or massive fermions (like the neutrinos) in our universe today. In Section 4.5 we discuss the primordial nucleosynthesis and its observational relevance; we study the decoupling of matter from radiation in Section 4.6. In the last section the very early universe and inflationary models are described.

Distribution Functions in the Early Universe

The analysis in Chap. 3 showed that the universe was dominated by radiation at redshifts higher than zeq ≃ 3.9 × 104(ΩNRh2). In the radiation-dominated phase, the temperature of the radiation will be higher than Teq ≃ 9.2 (ΩNRh2)eV ≃ 1.07 × 105(ΩNRh2)K and will be increasing as T ∝ (1 + z).

The contents of the universe, at these early epochs, will be in a form very different from that in the present-day universe. Atomic and nuclear structures have binding energies of the order of a few tens of electron-volts and mega-electron-volts, respectively. When the temperature of the universe was higher than these values, such systems could not have existed as bound objects.

Introduction

Attempts to understand extragalactic objects and the universe by using the laws of physics lead to difficulties that have no parallel in the application of the laws of physics to systems of a more moderate scale. The key difficulty arises from the fact that our universe exhibits temporal evolution and is not in steady state. Thus different epochs in the past evolutionary history of the universe are unique (and have occurred only once), and the current state of the universe is a direct consequence of the conditions that were prevalent in the past. For example, most of the galaxies in the universe have formed sometime in the past during a particular phase in the evolution of the universe. This is in contrast to star formation within a galaxy that we can observe directly and study by using standard statistical methods.

In principle, we should be able to see the events that took place in the universe in the past because of the finite light travel time. By observing sufficiently far-away regions of the universe, we will be able to observe the universe as it was in the past. Although technological innovation will eventually allow us to directly observe and understand all the past events in the history of the universe (especially when neutrino astronomy and gravitational wave astronomy start complementing photon-based observations), we are far from such a satisfactory state of affairs at present.

Introduction

This chapter deals with the Friedmann model for the universe, which is used throughout the study of extragalactic astronomy. The basic framework needed in all the later chapters is also introduced. Some of the discussion requires concepts from the general theory of relativity developed in Vol. I, Chap. 11. The Latin indices go over i, j = 0, 1, 2, 3, and the Greek indices go over α, β = 1, 2, 3. We shall use units with c = 1 in most sections.

The Friedmann Model

To construct the simplest model of the universe, we begin by assuming that the geometrical properties of three-dimensional space are the same at all spatial locations and that these geometrical properties do not single out any special direction in space. Such a three-dimensional space is called homogeneous and isotropic.

The geometrical properties of the space are determined by the distribution of matter through Einstein's equations. It follows therefore that the matter distribution should also be homogeneous and isotropic. This is certainly not true in the observed universe, in which there exists a significant degree of inhomogeneity in the form of galaxies, clusters, etc. We assume that these inhomogeneities can be ignored and the matter distribution may be described by a smoothed-out average density in studying the large-scale dynamics of the universe.

Introduction

The formalism developed in Chaps. 3 and 4 needs to be modified to take into account the inhomogeneities present in our universe, and we shall try to reconstruct the observed universe in the following manner: We assume that, at some time in the past, there were small deviations from homogeneity in our universe. These deviations can then grow because of gravitational instability over a period of time and, eventually, form galaxies, clusters etc. The first task is to develop the mathematical machinery capable of describing the growth of structures.

In a universe made of nonbaryonic dark matter, baryons, and radiation, we need to discuss each component separately. The simplest of the three components is the dark matter, which is affected only by gravity and is collisionless. In the fluid limit, we can ignore the velocity dispersion of the dark-matter particles, and there is no effective pressure term in the equations. If the velocity dispersion is important, there will arise an effect called free streaming, which we will discuss in Section 5.6. The physics of radiation is complicated by the fact that a photon can traverse a distance of the order of dH ≈ ct within a cosmic time t; hence any perturbation in δR at length scales λ ≲ ct will be wiped out by the free propagation of photons. At λ > ct, radiation can be treated as a fluid influenced only by the gravitational perturbations.

Introduction

In this chapter several aspects of galactic structure and evolution are discussed. Some of the ideas introduced in Chap. 1 are used and the contents of this chapter will be needed in Chaps. 7–10.

In the study of stellar structure and evolution in Vol. II, we could begin with a series of physically justifiable assumptions, derive the relevant equations describing the stars, and integrate these equations to understand the structure and evolution of stars. Such an approach is impossible in the case of galaxies for several reasons. To begin with, we do not understand how galaxies have formed. (It is true that there are several uncertainties in the case of star formation as well but they refer to details rather than to the fundamental process itself.) Second, observational data related to the galaxies are by no means statistically as well determined and abundant as data related to the stars. The reason essentially has to do with the fact that galaxies are located farther away from us and thus are more difficult to observe with the same level of accuracy. Third, galaxies, being collisionless systems of stars, are intrinsically more complicated compared with stars – which are made of collisional gas – from the point of view of mathematical description.

Given these difficulties, it is better to divide the study of galactic structure and dynamics into several separate aspects and investigate each of them as though they are disconnected from each other.

Introduction

The purpose of this chapter is to give an overview and summarise several observations that are of cosmological relevance. Many of the results (like the existence of dark matter) described here were taken for granted in the earlier chapters, and we shall make an attempt to provide the description of the evidence in support of these results. This chapter also provides a summary of the current knowledge of different parameters of cosmological significance.

Cosmic Distance Scale

The measurement of distances to different celestial bodies is of primary importance not only in understanding their properties but also – for objects at cosmological distances – in determining the geometry of the universe and the cosmological parameters. Obviously the technique used to measure the distance will depend on the properties of the object that is being studied; we shall concentrate on the measurement of extragalactic distances.

The procedures used for distance measurements can be divided into two natural classes. The first one uses what could be called the absolute distance estimator. These estimators are certain properties of (or features in) an object that can be used to directly measure the distance to the object. The second approach uses a relative distance estimator that allows us to determine the ratio between the distances to two different objects. By choosing a wide class of overlapping relative distance estimators, we can build what is known as a cosmic distance ladder.

Introduction

We now take up the study of galaxy formation, which requires understanding the growth of structure in the baryonic component of the universe. This chapter uses concepts from several earlier chapters, especially Chaps. 3–5, and will be needed for Chap. 9.

The study of galaxy formation from fundamental physical considerations is made difficult by a wide variety of physical processes that we need to take into account. To begin with, galaxies by themselves show a variety of morphological and physical properties, even at z = 0. The formation process should be such that, starting from relatively structureless density enhancements at high redshifts (z ≳ 25), one is capable of producing such a variety at z = 0. Second, the observational situation as regards galaxylike structures at high redshifts is still very unsatisfactory. The samples are small in number and often we have to decide how to make the correspondence between the sources seen at high redshifts and those seen at low redshifts. This issue is further complicated by the fact that a certain kind of population could have existed at a certain interval of time and could have vanished outside this epoch. Such a conjecture of invoking new populations is often convenient, but is not very satisfactory unless we could back it with some physical reasoning.

Introduction

Cosmic microwave background radiation (CMBR) is a relic from the redshift z ≈ 103, beyond which the universe is optically thick in most of the wave bands. This radiation therefore carries vital information about the state of the universe at an epoch that is probably as early as we could probe by direct electromagnetic measurements. A considerable amount of theoretical and observational progress has been achieved in this topic in the past decade, and future observations of CMBR hold the promise for allowing us to determine the parameters of the universe with unprecedented accuracy.

The temperature anisotropies in CMBR and related issues are discussed in this chapter. Anisotropies that are due to peculiar velocities and fluctuations in the gravitational potential are derived in Section 6.3 and discussed in detail in Sections 6.4 and 6.5. The damping of anisotropies and the distortions that arise because of the astrophysical processes are studied in Section 6.7.

Processes Leading to Distortions in CMBR

We have seen in Chap. 4 that the photons in the universe decoupled from matter at a redshift of ~ 103. These photons have been propagating freely in space–time since then and can be detected today. In an ideal Friedmann universe, a comoving observer will see these photons as a blackbody spectrum at some temperature T0.

Atoms and ions of the working gas and trace impurities emit radiation when transitions of electrons occur between the various energy levels of the atomic system. The radiation is in the form of narrow spectral lines, unlike the continuum of free-electron radiation such as bremsstrahlung. It was, of course, the study of these spectral lines that originally led to the formation of the quantum theory of atoms.

Because of the enormous complexity of the spectra of multielectron atoms it would be inappropriate here to undertake an introduction to atomic structure and spectra. Many excellent textbooks exist [e.g., Thorne (1974) or, for a more complete treatment, Slater (1968)] that can provide this introduction at various levels of sophistication. Instead we shall assume that the energy level structure of any species of interest is known, because of experimental or theoretical spectroscopic research. Then we shall discuss those aspects of spectroscopy that more directly relate to our main theme, plasma diagnostics. It is fairly well justified for neutral atoms and for simpler atomic systems with only a few electrons, to assume that spectral structure is known (speaking of the scientific enterprise as a whole, not necessarily for the individual student!). It is not so well justified for highly ionized heavy ions that occur in hot plasmas. The spectra of such species are still a matter of active research; therefore, it should not automatically be assumed that all aspects of these spectra are fully understood. However, for those diagnostic purposes that we shall discuss, the gaps in our knowledge are not particularly important.

In many plasmas it is unsatisfactory to use material probes to determine internal plasma parameters, so we require nonperturbing methods for diagnosis. Some of the most successful and accurate of these use electromagnetic waves as a probe into the plasma. Provided their intensity is not too great, such waves cause negligible perturbation to the plasma, but can give information about the internal plasma properties with quite good spatial resolution. In this chapter we are concerned with the uses of the refractive index of the plasma, that is, the modifications to free space propagation of the electromagnetic waves due to the electrical properties of the plasma.

The way waves propagate in magnetized plasmas is rather more complicated than in most other media because the magnetic field causes the electrical properties to be highly anisotropic. This is due to the difference in the electron dynamics between motions parallel and perpendicular to the magnetic field. Therefore, we begin with a brief review of the general problem of wave propagation in anisotropic media before specializing to the particular properties of plasmas.

Interferometry is the primary experimental technique for measuring the plasma's refractive properties and we shall discuss the principles of its use as well as some of the practical details that dominate plasma diagnostic applications.

Electromagnetic waves in plasma

Waves in uniform media

We must first consider the nature and properties of electromagnetic waves in a plasma. We treat the plasma as a continuous medium in which current can flow, but that is otherwise governed by Maxwell's equations in a vacuum.