The literature makes use of several observable quantities that pertain to Lyα, that often are specific to how much escapes or aim to illustrate how ‘strong' the feature is. This Section summarizes some of these quantities and conventions, and lists several caveats that may be considered while reading.
2.1. Flux, Luminosity, and Equivalent Width
Lyα is mainly produced by recombinations in photoionized nebulae, where under standard Case B assumptions 68% of ionizing photons absorbed by hydrogen are reprocessed into Lyα in the following radiative cascade (See Dijkstra, 2014 for an intuitive explanation). For continuously star-forming galaxies, with constant star formation rate (SFR), the Lyα equivalent width (EW) ranges between ≈ 80Å. For very young systems the EW peaks around 300Å (Charlot & Fall, 1993), while very high EWs that exceed 1000 Å may in principle be expected for very low metallicity, population iii stellar systems (Schaerer, 2003, Raiter et al., 2010). Naturally if the SFR is declining the intrinsic Lyα EW may take any value less than these, and it is worth noting that for a simple stellar population (SSP), WLyα exceeds 20 Å only during the first 6 Myr (Leitherer et al., 1999).
Measuring the flux and EW of most emission lines is straightforward. However for Lyα this is not necessarily so and these quantities may depend upon both methodology and definition. As a resonant transition, both nebular Lyα and continuum radiation with wavelength λ = 1216 Å may be absorbed by Hi. Depending upon the column density, this absorption may reach equivalent widths of several tens of Å, which is a substantial fraction of the nebular flux. Fluxes measured in a given aperture may or may not be reduced by this amount. Narrowband imaging, for example, needs to be continuum-subtracted and therefore measures the sum of nebular emission and absorption. Spectroscopic observations, on the other hand, may enable the observer to isolate the components and separate nebular emission from ISM absorption, should this be the goal of the measurement. However even with in spectroscopic mode isolating the emission-only flux depends upon the spectral resolution, and the separation will be much easier with high-resolution slit spectrographs than low-resolution survey telescopes.
Not only is Lyα absorbed in the ISM but also, depending on temperature and the properties of their winds, in the atmospheres of stars. For the hottest O stars Lyα EWs may be negligible, but as the population ages or the star formation rate declines, the dominant source of UV continuum will shift to progressively cooler stars. Valls-Gabaud, 1993 showed that Lyα measurements from some local galaxies may be subject to significant uncertainties from stellar absorption, and recent models by Peña-Guerrero & Leitherer, 2013 demonstrate that stellar Lyα absorption may reach EWs of −30 Å. For example, the effect of stellar absorption may also vary from O-star dominated systems where the nebular EW is high and the stellar feature is negligible, to later B-star systems where the reverse is true. The stellar feature may therefore shorten the timescale over which an episode of star-formation remains bright in Lyα, and the effect may even be seen on resolved scales within a galaxy.
2.2. Lyα/Balmer Ratios and Escape Fraction
Equivalent widths have the advantage that only a short range in wavelength is needed to make the measurement, over which the effects of interstellar dust (reddening curve, total extinction) should have a negligible effect. As discussed above, the evolutionary phase of star formation dominates the intrinsic EW. Lyα/Balmer line ratios, however, may also be used as a measure of the strength of Lyα, and because the intrinsic ratios are limited to a narrow range of values, have other advantages. For example the Hα line (λ = 6564.61Å) is a well-known, calibrated tracer of current star-formation activity in nearby galaxies (e.g. Kennicutt, 1983). For Case B nebulae at temperatures in the range 5,000–20,000 K and electron density in the range ne = 102 – 104 cm−3, the Lyα / Hα ratio ranges between 8.1 and 11.6 (Hummer & Storey, 1987). Thus deviations from the intrinsic line ratios encode information about the Hi scattering and dust absorption. While different authors do tend to adopt slightly different values, the range of permitted values is relatively narrow. For this review we will adopt the value of Lyα / Hα = 8.7, which for T = 104 K gas corresponds to ne ≈ 350 cm−3, and as a convention can be traced back to at least Hu et al., 1998.
Frequently we make reference to the Lyα escape fraction (fescLyα), in an effort to find a quantity that most closely reflects the combined impact that gas and dust have on suppressing the emission line. We define fescLyα as the ratio of the emitted Lyα luminosity to that intrinsically produced, but naturally a number of assumptions can enter our estimates of the intrinsic value. The most robust estimates of fescLyα will naturally come from comparing Lyα with other hydrogen recombination lines, where in practice Hα is the strongest and easiest to observe. Assuming that Hα is unobscured, fescLyα will simply be the observed Lyα / Hα ratio divided by its intrinsic case B value (8.7 as mentioned above). Of course Hα can also be significantly absorbed by dust, and in local ‘normal' galaxies suffers about 1 magnitude of extinction on average (Kennicutt & Kent, 1983). Obviously redder hydrogen lines would be better as they suffer less extinction but also become systematically weaker in flux, and become harder to observe in the near infrared. Radio recombination lines would be optimal, suffering no extinction at all, but are even more challenging to observe beyond the very local universe. Thus often the best route to fescLyα is to dust-correct Hα using the Hβ line, which should recover all the star formation down to moderate optical depths (Hayes et al., 2005, Atek et al., 2009a). However when Hα becomes very optically thick, in very dusty star-forming galaxies (e.g. Martin et al., 2015), even dust-corrected Hα traces only a small fraction of the true ionized gas, making the inferred escape fraction prone to strong biases. In such instances, one may do better by comparing the Lyα-derived SFR with that estimated from dust emission in the FIR, under the assumption that systematic errors on the SFR calibrations are smaller than the fraction of Hα that is recoverable. In the highest optical depth regimes this is probably true.