The depths, widths, and shapes of absorption lines are the code of optical depth profiles. Line depth is the amplitude of the optical depth, which is absorber column density. Line width and shape mirror the total cross section. This is the atomic cross section convolved with a wavelength redistribution function, usually a Gaussian attributable to thermal Doppler broadening. The resulting optical depth profile is a Voigt function. In this chapter, we quantitatively described Voigt profiles in detail. The total absorption is the equivalent width and its functional dependence on column density and Doppler broadening is called the curve of growth. Expressions are derived for its three major regimes: the linear, flat, and damped “parts.” The measured equivalent width increases with increasing absorption redshift, and this must be calibrated out. Inverting absorption line profiles yields apparent optical depth (AOD) profiles, which can be converted into integrable column density profiles. We also describe how to compute the covering factor from doublets showing signs of partial covering and conclude with an in-depth discussion of Lyman-limit ionization breaks from optically thick absorbers.

Black holes were hypothesized as far back as the 1770s, but were not theoretically formalized until 1916, nor observationally identified until the 1970s. Since then, they have been recognized as a ubiquitous and important component of galaxy evolution and the baryon cycle. At the heart of AGN/quasars, they generate powerful outflows, which are believed to be radiatively driven. The nature of these outflows depends on the luminosity generated by the black hole accretion disks and the radiative efficiency of the accretion process. The luminosity is characterized by the Eddington ratio, the ratio of the bolometric luminosity to the Eddington luminosity, which is the value at which radiation pressure propels infalling gas outward. Quasars are observed to have a Schechter function distribution of Eddington ratios. Based on arguments of force multipliers, the case for radiative line-driven winds is advanced. A simplified picture in which outflows can be predicted on a plot of Eddington ratio versus black hole mass is discussed, as well as a black hole evolution H-R type of diagram based on “downsizing.”

In this chapter we discuss the energetic outflows from quasars, which achieve velocities 10–20% of the speed of light. BALs are quantified using the “balnicity index,” an imperfect measure of a complex phenomenon that includes variability, saturation, self-blending, and partial covering. BALs have several subclasses, including HiBALs, LoBALs, and mini-BALs. BAL evolution is not well understood and selected competing models are discussed. Associated narrow line absorption (NALs) can also be present with equally high velocities. Four subclasses of NALs are discussed but characterizing NALs is challenging. Variability, partial covering, and line locking can help their identification. Line locking, in particular, is described in detail as it is a key aspect of radiatively line-driven outflows. Efforts and challenges for determining the fraction of quasars with BALs and NALs are described. In this chapter, we also discuss the quasar CGM, including the proximity effect (both line-of-sight and transverse). The technique of quasars probing quasars (QPQs) is described as are the observed properties of the quasar CGM learned from QPQ experiments.

The “many electrons problem” for determining atomic energy levels cannot be solved analytically. It must be solved numerically using approximation techniques applied to each ion for each element. The industry standard approach is called the Hartree-Fock method, which incorporates a three-tiered Hamiltonian approximation. In this chapter we describe how these approximations yield the Russell-Saunders vector model, for which we describe quantized vector addition. We then summarize the Russell-Saunders term and state symbols so commonly used to precisely notate atomic transitions. It is through this formalism that we come to understand that a given energy structure/transition does not describe a single active or optical electron but applies to the full bound multi-electron ionic system. We also describe intermediate coupling schemes and the j-j coupling scheme for heavier nuclei. We then derive the line strengths and oscillator strengths for both term-averaged and fine-structure transitions. Line emission power and line absorption cross sections are derived and the dipole selection rules for multi-electron ions are presented.

In this chapter, selected observational programs of merging galaxies, groups, and clusters are presented, and their reported results summarized. For each, neutral, low-, intermediate-, and high-ionization gas is examined separately. Various findings appear to indicate that comparing absorption to the “nearest galaxy,” the “most massive galaxy,” or the “central galaxy,” can strongly influence the inferred conclusions from the studies. The results that appear to agree between the various studies, show that compared to the CGM of member galaxies, the metal-line selected IGrM gas appears to be both relatively optically thin and kinematically quiescent in both its low- (MgII) and high-ionization (OVI) phases. Clusters, on the other hand, surprisingly appear to have neutral gas deep into their cores and, within the virial radius of the cluster, the sizes of the CGM of the individual member galaxies appears to be diminished compared to galaxies residing outside the virial radius. At the time of this writing, the study of the CGM in the IGrM and ICM environment is a developing area of study.

In this chapter, the taxonomy of the emission spectra of starbursts, active galactic nuclei (AGN), and quasars are compared. These spectra are discussed in terms of their emission line diagnostics as measured on Baldwin-Phillips-Terlevich (BPT) diagrams. The non-unique typing of AGN/quasars as Markarian galaxies, LINERs, Seyfert galaxies, radio galaxies, blazars, BL Lac objects, and flat-radio spectrum quasars is explained. The taxonomic subclassification of Seyfert galaxies and quasars based on the relative strengths of permitted broad lines and forbidden narrow lines are discussed. The quasar main sequence, which is based on the kinematics of the H β emission line and the luminosity ratio of the FeII/H β emission lines, is introduced. Insights into the nature of AGN/quasars can be gleaned from the fact that their luminosities and spectral energy distributions can be highly variable on timescales of hours to decades. Broad absorption lines (BALs) and narrow absorption lines (NALs) arise in strong outflows. The BALs may provide clues about viewing angles, leading to radio-quiet and radio-loud unified models of AGN and quasars.

Absorption line studies have shown that the circumgalactic medium (CGM) is an extended complex multiphase gas reservoir of galaxies. It is a kinematically diverse region that interfaces the baryon cycle activity within galaxies to the intergalactic environment in which the galaxies are embedded. In this chapter, selected observational programs and their reported results are presented. The focus is on empirical bivariate relations, such as absorption strength and covering fractions, versus impact parameter, stellar mass, star formation rate, etc. The CGM is presented as viewed through several commonly targeted ions, in particular HI, MgII, CIV, OVI, and NeVIII. Though this allows the various ionization stages of CGM gas to be examined in isolation, it glosses over the multiphase nature of the CGM. The practical design of high-redshift experiments is such that they are much more statistical in nature than the more granular experiments at low redshift. Thus, high-redshift studies are discussed separately.

This chapter covers the most challenging aspect of quasar absorption line studies – estimating the densities, dynamic conditions, metallicities, ionization conditions, and general cloud properties (masses, sizes, stability) that match the observed data. The techniques have evolved from single-cloud single phase models that were simply constrained by the measure column densities, to kinematically complex, multi-cloud multiphase models that are constrained by absorption profile morphologies on a pixel-by-pixel basis. In this chapter, we cover the modeling methods by describing them in order of complexity and ambition. These methods are the chi-square method, the density-metallicity locus method, and Bayesian approaches, including Markov Chain Monte Carlo (MCMC) methods and profile-based multiphase Bayesian modeling. Methods are discussed and examples are provided, but modeling absorbers is a scientific artform that requires a deep intuition that can only be developed through lots of practice.

In this chapter, we describe how blended multi-component absorption profiles can be modeled. Simple deblending that bypasses radiative transfer and atomic and gas physics can be performed using multi-component Gaussian fitting. We show how further sophistication can be added by tying doublets or multiplets and forcing Gaussian components to match known line spacings. To extract column densities and Doppler broadening parameters for each component, we use Voigt profile fitting. We begin with a general expression for a multi-component absorption profile for which each component has a unique column density and Doppler broadening parameter. We then discuss progressively more complex Voigt profile fitting, starting with multiple components for a single transition, then multiple components for a doublet (two transitions from a single ion), and then generalize to multi-component multi-transition multi-ion absorption systems. We also discuss methods for measuring the turbulent velocity component and approaches to multiphase decomposition for ions of different ionization levels. We conclude by discussing fitters and fitting philosophies. Optimized AOD column densities are also discussed.

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.