Helium is the second most abundant element in the Universe, and, when singly ionized, is hydrogenic. This means HeII has a hydrogen-like absorption spectrum but with transition energies a factor of 4 higher. This places HeII Ly α forest lines deep into the ultraviolet, the consequences of which highly limit the redshift visibility of HeII studies – only favorable quasar sightlines can be used to study HeII Ly α and Ly β absorption. The column density ratio of HeII to HI is highly sensitive to the shape and intensity of the cosmic ultraviolet background (UVB), and thus is a key quantity for constraining the evolution and patchiness of the UVB. An Epoch of HeII Reionization stretching into the Cosmic Noon era provides insights into the appearance of the first quasars in the Universe. In this chapter, we describe the redshift visibility of HeII absorbers, discuss the cosmic impact of HeII absorption, and describe key observational results, including the so-called hardness parameter, the HeII Gunn-Peterson trough, and HeII Ly α spikes.

Studies of the intermediate-ionization metal-line absorbers provide insights into warm/hot lower-density gas that has been processed through stars in galaxies. These absorbers have been studied primarily using doubly and triply ionized carbon and silicon ions (CIII, CIV, SiIII, and SiIV). CIII arises deep within the spectral range of the Ly α forest and is thus mostly visible at low redshifts where the Ly α forest line density is much smaller. SiIII is adjacent to the Ly α line and is also best surveyed at low redshift. The CIV and SiIV lines are well redward of the Ly α line and thus have visibility over a wide range of redshift. UV and IR spectrographs expanded the redshift coverage from z = 0 to z = 7. 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 these ions.

Quasar absorption line studies have matured into a modern science that has contributed to the development of our contemporary cosmological paradigm, ranging from the Big Bang, across Cosmic Noon, to the Present Epoch. Researchers focus on key ions, transitions, and absorption lines because they are most common in the Universe. Each of these lines has a unique cosmic visibility in that there is a strong relationship between the observed wavelength of a redshifted line, the cosmic era in which it originated, and the type of astrophysical environment it probes. In this chapter, we outline the main eras of the evolution of the Universe, describe the phases and ionization conditions of the gas in the Universe, and show the connection between ions/transitions and the cosmic era and gas phases they probe.

Hydrogen is the most abundant element in the Universe and neutral hydrogen, HI, is present in virtually all astrophysical structures ranging from the filamentary cosmic web to the inner regions of galaxies to the intracluster medium. The absorption transition from ground state to the lowest excitation state in neutral hydrogen gives rise to the countless optically thin Ly α forest lines and, in the highest column density structures, the damped Ly α absorption lines (DLAs). In optically thick structures, radiative ionization creates sharp “breaks” in quasar spectra called Lyman-limit systems (LLSs). HI correlates with the overdensity of the astrophysical environment, but this relationship evolves with redshift. HI also traces the mass density of neutral gas and the ionization history of the Universe. In this chapter, we describe the cosmic evolution of Ly α absorbers as recorded in quasar spectra from the Epoch of Reionization to the present epoch. At the highest redshifts, the transition from a dense Ly α forest to Ly α spikes to the famous Gunn-Peterson trough is described.

In this chapter, we begin by writing out the full reaction rate matrix accounting for the radiative and collisional processes presented in Chapter 34. The radiation field is assumed to originate externally and is thus not in equilibrium with the gas. We then derive the closed-form equilibrium solution for a pure hydrogen gas. Important to achieving equilibrium are the photoionization and recombination timescales. The industry standard ionization code is Cloudy; we describe how one uses this code to create model clouds. Important concepts such as the ionization parameter, cloud ionization structure, and shelf shielding of ionizing photons are discussed in detail. The building of grids of models is explained and example grids showing predictions of ionic column densities and ionization corrections are presented for commonly observed ions. Non-equilibrium collisional ionization models are described, and grids are presented. Sensitivities of the models to variations in the ionizing spectrum are explored. Finally, homology relationships useful for scaling cloud models to infer cloud densities, sizes, masses, and cloud stability are derived.

In this chapter, we apply the formalism of hydrogenic and multi-electron atoms and build the periodic table of ground-state elements. Examination of the table shows that all elements in a given column share the same Russell-Saunders state symbol; they have identical orbital and total angular momentum states and valence electron multiplicities. These columns are formally grouped, and we show how each group shares the same spectral characteristics (the transition energies differ, but the relationships between transitions are identical from one element to another in a group). We then introduce the idea of iso-electronic sequences, which neatly explain the many lithium-like and sodium-like ions (CIV, NV, OVI, NeVIII, MgII, etc.) that have hydrogenic-like spectral series, including zero-volt resonant fine-structure doublets. We then provide accurate tables of ionization potentials and describe the physical reasons for the ion-to-ion trends in these potentials. We conclude the chapter with a complete suite of Grotrian diagrams (visual representations of the energy states and allowed electron transitions) for ions commonly studied using quasar absorption lines.

In the 1950s, Lyman Spitzer predicted that a hot gaseous medium surrounded the Milky Way in a halo/corona and that this gas should be detectable in strong absorption from highly ionized oxygen and nitrogen. It was confirmed in the 1970s using the Copernicus satellite. In the early 1990s, the first hydrodynamic cosmological simulations predicted that a warm-hot intergalactic medium (WHIM) was pervasive and extended out to the mildly overdense regions in the Universe. At low redshifts, the WHIM was predicted to harbor most of the baryons in the Universe. This was a bold prediction in which five-, six-, and seven-times oxygen (OVI, OVII, and OVIII) was predicted to trace this gas in absorption. The latter two require the X-ray spectroscopy, which has its challenges. The WHIM is also believed to be the source of the so-called broad Ly α absorbers (BLAs) in the Ly α forest and can be probed using fast radio bursts. In this chapter, we describe the discovery and confirmation of the WHIM and its characteristic properties. This includes a review of cooling flows, astrophysical plasmas, shocks, and interfaces.

The fundamental quantity of the expansion dynamics of the Universe is the time-dependent scale factor. However, neither time nor the scale factor is a measurable quantity. The measurable quantity due to universal expansion is the cosmological redshift of observed radiation. This redshift gives the ratio by which the Universe has expanded relative to the present epoch. In this chapter, we rewrite the expands dynamics in terms of redshift and define proper and co-moving coordinates. Using the radial and transverse components of the Robertson-Walker metric, we derive relations for cosmic time and multiple useful distance measures as a function of redshift. These include the radial and transverse proper and co-moving distances, the angular diameter distance, the luminosity distance, and the “absorption” distance. We also derive the equations for the redshift dependence of the line-of-sight separations of gravitationally lensed quasars. The redshift path density is derived. Finally, the redshift dependence of line-of-sight peculiar velocities and cosmological recessional velocities are derived from the metric.

The energy structures and transition energies of single-electron atoms and ions are presented. Five Nobel Prizes in Physics were awarded for the theories discussed in this chapter. We first review the Bohr model, which was based on quantized angular momentum and classical circular orbits. The wave model of Schrödinger followed, in which spherical boundary conditions quantized polar and azimuthal standing waves. The energies were identical to Bohr’s, but transition selection rules dictated the change in angular momentum of the system during absorption and emission. Dirac incorporated electron spin and relativistic energies, resulting in energy shifts and fine structure splitting of the energy levels for non-zero angular momentum states. Feynman and Swinger incorporated quantization of the electric vector potential. This physics broke energy degeneracies in the Dirac model and correctly predicted the famous Lamb shift. In this chapter, each of these models are described in detail. The final full characterization of the energy levels and transitions are presented. The chapter ends with a discussion on isotope shifting and transitions to the continuum (ionization/recombination).