Empirically demonstrating the association of metal-line absorber lines with galaxies has a long, rich history from the earliest theoretical predictions in the mid 1960s to observational confirmation in the 1990s. From that point onward, quasar absorption line studies became a powerful tool for characterizing the gaseous halos of galaxies. Countless works have provided valuable insights into the chemical, ionization, and kinematic conditions of what is now called the circumgalactic medium. A new concept called the baryon cycle was birthed in which the balance of accretion modes, stellar feedback, gas recycling, and outflow dynamics of galactic gas was found to be closely linked to how baryons respond to dark matter halos of a given mass. Modern theory known as halo abundance matching has helped us empirically connect the average stellar mass to dark matter halos of a given mass. Powerful hydrodynamics simulations tell a story in which the average baryon cycle processes in a galaxy are closely linked to dark matter halo mass. In this chapter, we discuss how synthesizing both the observational data and theoretical insights has yielded a simple composite model of the baryon cycle.

Chapter 1 begins by introducing the quantum world as part of the physical world, not in opposition to or separate from the classical world. It then introduces the basic tools needed to work with quantum mechanics, and describes the scope and purpose of this textbook. It discusses how despite its successes, current quantum mechanics lacks adequate explanations for important observed atomic properties, suggesting an incompleteness of the theory. After a brief overview of its main interpretative issues , the chapter concludes with an introduction of the vacuum or zero-point field as the physical element that restores causality and serves to complete the quantum picture by providing a causal explanation of characteristic quantum phenomena.

The 1960s through the 1970s was an exciting era of the discovery of quasars. During this time the study of these cosmologically distant luminous sources developed into a powerful tool that changed the course of the science of astronomy. This story runs in parallel with technological advances in both light-gathering capability and computing power. In this chapter, we chart the development of the study of quasars and show how quasar absorption lines provide a tool for studying the properties of diffuse gas across the full dynamic range of astrophysical environment out to the highest redshifts.

The wave model of hydrogenic ions naturally yields transition probabilities. These probabilities are written in terms of three Einstein coefficients, which are determined from “overlap integrals” for spontaneous emission. Under the assumption that a simple dipole describes the moment between the charge densities of the initial and final stationary states of an electron transition, the transition probabilities yield selection rules, emission line intensities, and absorption cross sections. The former governs whether a transition is permitted or forbidden. The amplitudes of the latter two are often written as oscillator strengths. In this chapter, we describe the formalism for determining selection rules and oscillator strengths. We begin with the Schrödinger model and generalize to fine structure transitions for bound-bound transitions. We then address the oscillator strengths of bound-free transitions. Finally, we derive the line spread function describing the natural line width, which depends on the magnitude of the Einstein coefficients and is written in terms of the damping constant. Full expressions for the bound-bound and bound-free absorption cross sections are provided.

Chapter 16 begins by showing how quantum mechanics explains the structure and basic properties of multielectron atoms and their position in the periodic table of elements. It introduces the main approximation methods that have been developed to study such systems, explains the atomic shell structure, and discusses the helium atom in detail. It then looks at the different types of forces that bind atoms together to form molecules, focusing on diatomic molecules and the hydrogen molecule in particular. It discusses the long-range intermolecular forces that are responsible for many of the chemical and structural properties of matter, and identifies the zero-point or vacuum field as being responsible for the van der Waals and Casimir forces. In the final section, the properties of atomic nuclei are shown to reveal an internal structure with periodicities reminiscent of those of atoms and to disclose the effect of the nuclear spin–orbit interaction.

Chapter 18 is entirely devoted to the quantum theory of scattering, which is normally covered in more detail in a course on quantum field theory. We introduce the main concepts, including scattering amplitude, differential and total cross sections, and form factors, and derive the main formulas for elastic scattering, in a nonrelativistic framework; this allows us to appreciate how the information obtained from scattering experiments is used to explore the intricacies of quantum particles that are otherwise inaccessible. The Born approximation is studied and applied to scattering by a periodic potential, a weak potential, and Rutherford scattering. The partial wave expansion is derived and applied to obtain the optical theorem. The chapter concludes with a complementary section on resonant scattering.

It is time to take a deep dive into several of the “key quantitie” introduced in Chapter 3. Above all are the population density functions, which describe the number of absorbers per unit redshift per unit column density (or equivalent width). In this chapter, we present practical equations for obtaining maximum likelihood estimates of the population parameters for commonly adopted distribution functions: the power law, the exponential, and Schechter. Summing absorber counts and/or integrating these parameterized distribution functions in absorber subspaces (i.e., bins of redshift and column density) – or along one axis of the absorber survey space (i.e., across all equivalent widths at fixed redshift, etc.) – allows absorber evolution to be quantified. Examples include the redshift path density, absorber cross sections, the column density and equivalent width distributions, and the mass density of absorbers. We derive these quantities from first principles and then show how they can be computed accounting for the detection completeness, the redshift path sensitivity, and the total redshift sensitivity path of the survey.

Studies of the low-ionization metal-line absorbers provide insights into cool/warm higher-density gas that has been processed through stars in galaxies. These absorbers have been studied primarily using the abundant neutral atoms sodium, oxygen, and carbon (NaI, OI, and CI), as well as the singly ionized ions of carbon, silicon, calcium, and magnesium (CII, SiII, CaII, and MgII). For optical quasar spectroscopy, these ions have limited visibilities over different redshift ranges. The advent of sensitive UV and IR spectrographs expanded the redshift coverage of MgII absorbers from z = 0 to z = 7. However, the redshift visibility of OI, CI, CII, and SiII remain limited because of their far-ultraviolet transitions. The population statistics measured include the redshift path density, the equivalent width and column density distributions, the cosmic mass densities, and the kinematics (broadening parameters, velocity splitting distributions, and absorber velocity widths). In this chapter, we discuss multiple observational programs and their reported findings for several of the ions.

Astrophysical gases are characterized by their macro variables, which describe the radiation field and the particle field. Radiation can be described by its frequency-dependent energy density or photon number density. Both these quantities can be integrated over frequency, yielding total radiative energy density and/or photon number density. Particles are described by their number and/or mass densities, thermal motions, partial pressures, and the charge density of ions and free electrons. Ion number densities depend on the abundances of elements in the gas and their ionization fractions. In this chapter, we describe the formalisms of the quantities describing the radiation and particle fields in astrophysical gases. We describe the cosmic ultraviolet ionizing background and starburst galaxies ionizing spectra. The principles of particle density and charge density conservation are derived, and the equation of state is presented. This chapter provides the fundamental formalism for studying the micro processes of ionization and the detailed balancing of partially ionized astrophysical gases key to modeling the ionization balance of these gases.

Each quasar sightline provides only a “pencil beam” core sample of the Universe. Quasar absorption lines surveys that employ numerous quasar sightlines aim to measure several key quantities (known as absorber population statistics) that characterize the astrophysical properties of absorbers. Creative methods and experimental approaches have been developed over the past decades. These include rudimentary tomography experiments using close groupings of multiple quasars for measuring transverse properties of absorbers, stacking of spectra, peering “down-the-barrel,” and the use of Gamma-ray bursts. In this chapter, we describe these “key” population statistics and how they are measured in principle. We also describe the innovative ways that multiple sightlines are used experimentally adopting modern techniques.

The abundance of deuterium, an isotope of hydrogen, is sensitive to the ratio of the cosmic baryon density to the photon density. This ratio is fixed (or “frozen in”) well before Big Bang nucleosynthesis begins. Competing with the timescale over which fusion is building up helium-4 nuclei is the timescale for the photodissociation of deuterium and the β-decay rate of free neutrons. Together, these form the highly sensitive “deuterium bottleneck.” In the 1990s, measurements of the cosmic deuterium abundance using quasar absorption line techniques varied by an order of magnitude. After 25 years of effort, the scatter has been reduced to sub-1% precision and the highly sought cosmic D/H ratio has been pinned down. Additional constraints are obtained using the cosmic microwave background, but these can be in tension with quasar absorption line results. In this chapter, we describe efforts to measure the cosmic deuterium abundance and reconcile them with theoretical predictions, which may be limited by the accuracy of the reaction rates used for Big Bang nucleosynthesis calculations.

Chapter 4 shows that, just as Heisenberg’s matrix mechanics represented a break with classical physics and the beginning of a new physics, Schrödinger’s wave mechanics represented another, no less radical, break with classical physics and at the same time opened up another path to the quantum world. Schrödinger’s theory is shown to make substantial use of de Broglie’s waves and related phenomena. The Schrödinger equation, being wave-like, constitutes mathematically an eigenvalue problem for bounded systems, and thus naturally leads to quantization, as is illustrated with a couple of simple examples. The chapter ends with Dirac’s abstract formulation, which has the advantage of being suitable for any description, be it Heisenberg’s, Schrödinger’s or any other.

Chapter 8 is devoted to the study of the dynamics of quantum systems, based on the formalism presented in Chapter 7 and previous chapters. The operator notation and its matrix representation are used without distinction, moving freely from one to the other as convenient. This allows us to study the evolution of the system from different perspectives, depending on the description adopted. The chapter includes a discussion of the statistical information contained in the quantum formalism, a formal derivation of the Heisenberg inequalities and a clarification of their physical meaning. A section is dedicated to quantum canonical and related transformations. More advanced topics, which provide a valuable complement, include Noether’s theorem on the relationship between the symmetry properties and the conserved dynamical variables of the system.

Over the last quarter century, studies of the circumgalactic medium (CGM) have evolved from small, isolated cottage-industry efforts to a few dozen factory-scale assembly-line collaborations. The advent and continued development of large galaxy surveys, the refinement of photometric redshifts, and the honing of color selection of quasars have all combined to yield more than a million object-searchable catalogs for building large samples of galaxy-quasar pairs on the sky. Though the largest body of work has focused on low- and intermediate-redshifts, where detailed galaxy properties can be measured, wholesale studies of the CGM have now reached redshifts of 4 using Lyman break galaxies (LBGs) and the stacking of the spectra of thousands of Lyman alpha emitters. In this chapter, we provide an overview of CGM studies with a focus on sample building and experimental approaches and techniques. The three main types of survey strategies are discussed. Concepts such as the characterization of CGM absorption properties as a function of impact parameters, covering fractions, and galaxy-absorber morphokinematic and morphospatial analysis are presented.