Lyman α emitters in ionized bubbles: constraining the environment and ionized fraction

Lyman-alpha emitters (LAEs) are excellent probes of the reionization process, as they must be surrounded by large ionized bubbles in order to be visible during the reionization era. Large ionized regions are thought to correspond to over-dense regions and may be protoclusters, making them interesting test-beds for early massive structures. Close associations containing several LAEs are often assumed to mark over-dense, ionized bubbles. Here, we develop the first framework to quantify the ionization and density fields of high-z galaxy associations. We explore the interplay between (i) the large-scale density of a survey field, (ii) Poisson noise due to the small number density of bright sources at high redshifts (z~7), and (iii) the effects of the ionized fraction on the observation of LAEs. We use Bayesian statistics, a simple model of reionization, and a Monte-Carlo simulation to construct a more comprehensive method for calculating the large-scale density of LAE regions than previous works. We find that Poisson noise has a strong effect on the inferred density of a region and show how the ionized fraction can be inferred. We then apply our framework to the strongest association yet identified: Hu et al. (2021) found 14 LAEs in a volume of ~50,000 cMpc^3 inside the COSMOS field at z~7. We show that this is most likely a 2.5-sigma over-density inside of an ionized or nearly ionized bubble. We also show that this LAE association implies that the global ionized fraction is Q = 0.60 (+0.08,-0.09), within the context of a simple reionization model.