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We compute robust lower limits on the spin temperature, $T_{\rm S}$, of the$z=8.4$ intergalactic medium (IGM), implied by the upper limits on the 21-cmpower spectrum recently measured by PAPER-64. Unlike previous studies whichused a single epoch of reionization (EoR) model, our approach samples a largeparameter space of EoR models: the dominant uncertainty when estimatingconstraints on $T_{\rm S}$. Allowing $T_{\rm S}$ to be a free parameter andmarginalizing over EoR parameters in our Markov Chain Monte Carlo code 21CMMC,we infer $T_{\rm S}\ge3 {\rm K}$ (corresponding approximately to $1\sigma$) fora mean IGM neutral fraction of $\bar{x}_{\rm H{\scriptsize I}}\gtrsim0.1$. Wefurther improve on these limits by folding-in additional EoR constraints basedon: (i) the dark fraction in QSO spectra, which implies a strict upper limit of$\bar{x}_{\rm H{\scriptsize I}}[z=5.9]\leq 0.06+0.05 \,(1\sigma)$; and (ii) theelectron scattering optical depth, $\tau_{\rm e}=0.066\pm0.016\,(1\sigma)$measured by the Planck satellite. By restricting the allowed EoR models, theseadditional observations tighten the approximate $1\sigma$ lower limits on thespin temperature to $T_{\rm S} \ge 6$ K. Thus, even such preliminary 21-cmobservations begin to rule out extreme scenarios such as `cold reionization',implying at least some prior heating of the IGM. The analysis frameworkdeveloped here can be applied to upcoming 21-cm observations, thereby providingunique insights into the sources which heated and subsequently reionized thevery early Universe.

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