The Global History of Reionisation
  Using a Bayesian framework, we quantify what current observations imply about the history of the epoch of reionisation (EoR). We use a popular, three-parameter EoR model, flexible enough to accommodate a wide range of physically-plausible reionisation histories. We study the impact of various EoR observations: (i) the optical depth to the CMB measured by Planck 2016; (ii) the dark fraction in the Lyman $\alpha$ and $\beta$ forests; (iii) the redshift evolution of galactic Ly$\alpha$ emission (so-called "Ly$\alpha$ fraction"); (iv) the clustering of Ly$\alpha$ emitters; (v) the IGM damping wing imprint in the spectrum of QSO ULASJ1120+0641; (vi) and the patchy kinetic Sunyaev-Zel'dovich signal. Combined, (i) and (ii) already place interesting constraints on the reionisation history, with the epochs corresponding to an average neutral fraction of (75, 50, 25) per cent, constrained at 1$\sigma$ to $z= (9.21\substack{+1.22 -1.15}, 8.14\substack{+1.08 -1.00}, 7.26\substack{+1.13 -0.96})$. Folding-in more model-dependent EoR observations [(iii--vi)], strengthens these constraints by tens of per cent, at the cost of a decrease in the likelihood of the best-fit model, driven mostly by (iii). The tightest constraints come from (v). Unfortunately, no current observational set is sufficient to break degeneracies and constrain the astrophysical EoR parameters. However, model-dependent priors on the EoR parameters themselves can be used to set tight limits by excluding regions of parameter space with strong degeneracies. Motivated by recent observations of $z\sim7$ faint, lensed galaxies, we show how a conservative upper limit on the virial temperature of haloes which host reionising galaxies can constrain the escape fraction of ionising photons to $f_{\rm esc} = 0.14\substack{+0.26 -0.09}$ 
Bradley Greig and Andrei Mesinger
astro-ph.CO