Studies of the high-ionization metal-line absorbers provide insights into hot diffuse gas that has been processed through stars in galaxies. In the ultraviolet and optical bands, these absorbers have been studied primarily using five-times ionized oxygen (OVI), six-times ionized nitrogen (NV), and seven-times ionized neon (NeVIII). Both OVI and NeVIII arise within the spectral range of the Ly α forest and are thus mostly visible at low redshifts where the Ly α forest line density is much smaller. NV is adjacent to the Ly α line and in principle can be surveyed over the full range of redshift; however, this ion is found in only a narrow range of astrophysical conditions. 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.

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.

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.

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.