Hydrogen selects a little ultraviolet light
A beam that looks continuous contains many wavelengths. A spectrum lays out how much light arrives at each wavelength. If something absorbs light on the journey, the corresponding part becomes dimmer and an absorption line appears.
A hydrogen atom has a set of allowed electron energies. An atom in its lowest energy state can absorb a photon that lifts its electron to the next level. That transition is called Lyman-alpha. For hydrogen at rest, its wavelength is about 121.567 nanometres, in the ultraviolet, beyond human vision.
The absorbing atom still needs its electron. This is neutral hydrogen. Radiation has ionized most hydrogen in the intergalactic gas, separating electrons from protons, but the small neutral remainder can still leave strong marks along a long path. The gaps record absorption by that remainder; they are an indirect view of the gas.
Reading: Tepper García, Voigt profile fitting to quasar absorption lines, arXiv:astro-ph/0602124v1 · Peeples et al., Pressure Support versus Thermal Broadening in the Lyman-alpha Forest, arXiv:0910.0256v3
One transition appears at many wavelengths
Imagine the beam passing several patches of gas. In each patch’s own rest frame, hydrogen absorbs the same ultraviolet transition. Light continues travelling after the interaction. Cosmic expansion stretches its wavelength, so patches at different distances leave their marks at different places in the spectrum we receive.
Redshift describes this stretch. At redshift three, the wavelength has grown by a factor of four: an absorption mark at 121.567 nanometres moves to about 486.268 nanometres. A gap in visible light today can therefore record ultraviolet absorption when the light met the gas.
Gas near the quasar and gas closer to us have different expansion histories along the remaining path. Absorption by the closer gas usually appears at a shorter wavelength. The forest lies to the blue of the quasar’s own Lyman-alpha emission line. Motion relative to the overall expansion shifts the marks a little further.
Reading: Peeples et al., Pressure Support versus Thermal Broadening in the Lyman-alpha Forest, arXiv:0910.0256v3 · Independent hydrogen and sightline calculation materials
A dip need not surround a separate cloud
It is natural to begin with one cloud making one line, then many clouds making the forest. A more detailed picture can use a continuously varying gas density instead: denser ridges, thinner regions and velocities that change along the path.
A strong absorber often contains more neutral hydrogen, but ionization and temperature also matter. Two patches with the same total hydrogen density can have different neutral abundances if one experiences a stronger ionizing background. Hotter atoms have a wider spread of thermal velocities, spreading absorption over a wider wavelength range.
The correspondence between spatial location and spectral location can also fold. Two distant patches can share a similar recession velocity and absorb in the same part of the spectrum. Several broadened contributions can combine into one wide depression. Assigning a unique distance to every dip needs more information and a model of those effects.
Reading: Peeples et al., Pressure Support versus Thermal Broadening in the Lyman-alpha Forest, arXiv:0910.0256v3 · Tepper García, Voigt profile fitting to quasar absorption lines, arXiv:astro-ph/0602124v1
Join the losses along the path
Let the light cross one short segment and then another. Each segment keeps a fraction of the light delivered by the previous segment. The total transmitted fraction is the product of these fractions. Optical depth is a convenient measure of absorption strength because the optical depths of successive segments add.
For pure attenuation, imagine that the first segment leaves one fifth of the incoming light. A second segment lets half of that remainder through. The observer receives one tenth of the original light. This simple accounting works separately at every wavelength: one segment may remove a colour strongly while its neighbour absorbs a slightly shifted colour.
The expression below converts the total optical depth back into the fraction of light left. The transmitted fraction compares the received light with the background expected without intervening absorption; optical depth sums absorption at that wavelength. Increasing optical depth leaves less light.
A very deep line centre is already almost black. More absorbing material may make little visible difference there, while changing the wings is easier to notice. Line width, wings and the surrounding spectrum help distinguish absorbers whose centres look much alike.
The forest turns otherwise elusive gas into measurable missing light. Density, ionization, temperature and motion all help write the marks. The following calculation starts with a short piece of gas and joins those contributions one at a time.
Reading: Tepper García, Voigt profile fitting to quasar absorption lines, arXiv:astro-ph/0602124v1 · Independent hydrogen and sightline calculation materials