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

We compute robust lower limits on the spin temperature, T-S, 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 T-S. Allowing T-S to be a free parameter and marginalizing over EoR parameters in our Markov ChainMonte Carlo code 21CMMC, we infer TS >= 3 K (corresponding approximately to 1 sigma) for a mean IGM neutral fraction of x(HI) greater than or similar to 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 (x) over bar (HI) [z = 5.9] <= 0.06 + 0.05 (1 sigma); and (ii) the electron scattering optical depth, tau(e) = 0.066 +/- 0.016 (1 sigma) measured by the Planck satellite. By restricting the allowed EoR models, these additional observations tighten the approximate 1 sigma lower limits on the spin temperature to T-S >= 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.