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We present constraints on both the kinetic temperature of the intergalacticmedium (IGM) at z=8.4, and on models for heating the IGM at high-redshift withX-ray emission from the first collapsed objects. These constraints are derivedusing a semi-analytic method to explore the new measurements of the 21 cm powerspectrum from the Donald C. Backer Precision Array for Probing the Epoch ofReionization (PAPER), which were presented in a companion paper, Ali et al.(2015). Twenty-one cm power spectra with amplitudes of hundreds of mK^2 can begenerically produced if the kinetic temperature of the IGM is significantlybelow the temperature of the Cosmic Microwave Background (CMB); as such, thenew results from PAPER place lower limits on the IGM temperature at z=8.4.Allowing for the unknown ionization state of the IGM, our measurements find theIGM temperature to be above ~5 K for neutral fractions between 10% and 85%,above ~7 K for neutral fractions between 15% and 80%, or above ~10 K forneutral fractions between 30% and 70%. We also calculate the heating of the IGMthat would be provided by the observed high redshift galaxy population, andfind that for most models, these galaxies are sufficient to bring the IGMtemperature above our lower limits. However, there are significant ranges ofparameter space that could produce a signal ruled out by the PAPERmeasurements; models with a steep drop-off in the star formation rate densityat high redshifts or with relatively low values for the X-ray to star formationrate efficiency of high redshift galaxies are generally disfavored. The PAPERmeasurements are consistent with (but do not constrain) a hydrogen spintemperature above the CMB temperature, a situation which we find to begenerally predicted if galaxies fainter than the current detection limits ofoptical/NIR surveys are included in calculations of X-ray heating.

PAPER-64 Constraints On Reionization II: The Temperature Of The z=8.4 Intergalactic Medium