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As we have seen in Sections 4, 5, and 6.2, current data show that WLyα and fescLyα are influenced by a large number of physical properties. In recent years much attention has been devoted to determining their order of precedence: i.e. whether covering fraction is more important than kinematic properties, which in turn is more important than dust reddening. Mostly we have been driven to find a way to predict the emergent Lyα flux, EW or fescLyα from a given set of conditions. We have now assembled significant samples of low-z observations, selected by Lyα, Hα, and UV continuum, and have studied various subsets of them between the X-ray and radio, measuring all the physical properties discussed in Section 6. By combining this literature we now have substantial power to determine how Lyα is regulated and test for the primary effects in homogeneously selected galaxies that do and do not emit Lyα.

Simultaneously we need to explain:

In doing so we must remain cognizant of the fact that data have been assembled from different selection functions, measurements have been made in apertures that probe a variety of physical sizes, and that large scale halo emission may affect some, but not all, of our results.

We first address stellar properties, as these dictate the intrinsic WLyα but do not affect transmission (i.e. they have no direct influence over fescLyα, and only set a limit on the emergent WLyα). Since Lyα is reprocessed ionizing continuum, WLyα will exceed 20Å only during for ages below ≈ 6 Myr (Leitherer et al., 1999 and Section 2.1), assuming an SSP. The SSP assumption is probably over-simplistic for whole galaxies but it does serve to illustrate that the Lyα-bright period cannot be sustained if the SFR is declining, and that episodes must be young. The Lyα production must be most strongly correlated with the evolutionary stage of the stars.

However the observed WLyα is not strongly correlated with instantaneous SFR, and neither are the high-EW galaxies the most luminous in Lyα. If anything the reverse is true, at least within the current samples, and over the UV and Lyα luminosity ranges probed at low-z high-EW galaxies are among the less luminous. Indeed similar can be said for galaxy samples selected by other emission lines such as Hα or [Oiii]λ 5007 (e.g. Atek et al., 2011): the requirement for high EW line emission necessitates not only ongoing star formation, but at a given SFR the UV continuum must be faint enough for the EW to be high. This at least partially explains why local LAEs are drawn from galaxies with higher Hα EWs (as seen by, e.g. Cowie et al., 2011), and at lower stellar age and mass. Considering the well-known mass-metallicity relationship (Tremonti et al., 2004), it equally well explains why LAEs should be more prevalent at lower metallicities. Note, however, that according to current spectroscopic data, this relationship does not extend indefinitely to the lowest metallicity, gas-rich dwarf galaxies; a point to which we will return below.

Lyα transfer however is not affected by any of the above considerations: stellar age, mass, and nebular oxygen abundance are not properties that influence radiation, although they may correlate with quantities that do. What matters from this point is the properties of dust and Hi. fescLyα is anticorrelated with the EB−V, as would be expected, but the spread is very large. Moreover the slope of the fescLyαEB−V relationship in LAE samples is flatter than would be expected for pure extinction (Atek et al., 2014), indicating that the role of dust is diminished. At the dust-free end the under-luminous Lyα can be most easily be explained by the presence of Hi, as it may scatter Lyα photons many times, and increase the probability of dust absorption. This is supported by, for example, small aperture spectroscopic observations of almost dust-free dwarf galaxies that show not only a lack of nebular Lyα but also the absorption of continuum photons in the Lyα resonance.

If this dust were distributed purely as a screen surrounding the star-forming regions, the apparent over-luminous Lyα observed in some LAEs cannot be explained without severely modifying extinction laws. Lyα would have to see at least the expected attenuation, plus an excess of absorption because of scattering. To explain this we must invoke geometrical effects. Evenly mixing dust into the Hii regions would produce an effective attenuation of the form fescLyα ∝ 1/τdust at high τdust, and asymptotically sets a lower limit to Lyα / Hα ratio of ≈ 2 (without scattering). However such a dust geometry cannot make high a Hα/Hβ ratio, which saturates for optically thick nebulae at ≈ 4. What can explain the simultaneous high Lyα / Hα and Hα/Hβ ratios is a clumpy distribution of dust, as advocated by Scarlata et al., (2009). This model, originally implemented by Natta & Panagia, (1984) and Caplan & Deharveng, (1986), assumes dust to be distributed in dense clumps and the effective attenuation law changes significantly with the average number of clumps along the line-of-sight. E.g. again without scattering, varying τdust within 10 clumps may produce Lyα / Hα > 2 with Hα / Hβ ≈ 7, and can explain the line ratios seen in the dustiest local LAEs. The fact that Lyα is seen at all from local ULIRGs (Martin et al., 2015) also suggests that Lyα must find paths of low dust optical depth.

Then we need to explain why the local dwarf galaxies (e.g. I Zw 18, SBS 0335-052) centrally absorb at Lyα despite their very low dust contents. Indeed HST spectroscopy shows some absorption component in every object observed, demonstrating that Hi has effects that range between small dips and very broad, damped absorption features. Tenorio-Tagle et al., (1999) presented an evolutionary sequence for the Lyα spectral profile expected from a star cluster (assuming an SSP). This model assumes that during the earliest stages of a cluster's evolution (≲ 2 Myr) local Lyα absorption would be expected because the surrounding medium is completely static. Over the subsequent ∼ 4 Myr mechanical feedback from O star winds and the first supernovae accelerate the Hi outwards, producing P Cygni-shaped Lyα profiles. The application of this model to dwarf galaxies suggests that their star-formation episodes may be too young and that feedback has not yet had time to accelerate the neutral ISM (Mas-Hesse et al., 2003).

This scenario is probably an over-simplistic representation of whole galaxies, where stars form in different regions over extended timescales, but nevertheless the qualitative arguments may be helpful in understanding the influence of galaxy winds. All the observed line profiles, including those of the local dwarf galaxies, can in principle be unified within such a scenario (Mas-Hesse et al., 2003). In the complete literature of low-z galaxies only one example shows symmetric Lyα emission without an obvious absorption component (Tol 1214-277, Thuan & Izotov, 1997), and as Figure 6 shows, an outflow in the neutral medium appears to be a requirement (but not uniquely sufficient) for net Lyα emission (Kunth et al., 1998, Wofford et al., 2013, Rivera-Thorsen et al., 2015).

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