Constraints on the temperature of the intergalactic medium atz= 8.4 with 21-cm observations

We compute robust lower limits on the spin temperature, TS, of the z = 8.4 intergalactic medium (IGM), implied by the upper limits on the 21-cm power spectrum recently measured by PAPER–64. Unlike previous studies which used a single epoch of reionization (EoR) model, our approach samples a large parameter space of EoR models: the dominant uncertainty when estimating constraints on TS. Allowing TS to be a free parameter and marginalizing over EoR parameters in our Markov Chain Monte Carlo code |21|CMMC, we infer TS ≥ 3 K (corresponding approximately to 1σ) for a mean IGM neutral fraction of |x̄_H\, I 0.1|⁠. We further improve on these limits by folding-in additional EoR constraints based on: (i) the dark fraction in QSO spectra, which implies a strict upper limit of |x̄_H\, I[z=5.9]≤ 0.06+0.05 \,(1σ )|⁠; and (ii) the electron scattering optical depth, τe = 0.066 ± 0.016 (1σ) measured by the Planck satellite. By restricting the allowed EoR models, these additional observations tighten the approximate 1σ lower limits on the spin temperature to TS ≥ 6 K. Thus, even such preliminary 21-cm observations begin to rule out extreme scenarios such as ‘cold reionization’, implying at least some prior heating of the IGM. The analysis framework developed here can be applied to upcoming 21-cm observations, thereby providing unique insights into the sources which heated and subsequently reionized the very early Universe.