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Recently, the Hydrogen Epoch of Reionization Array (HERA) collaboration hasproduced the experiment's first upper limits on the power spectrum of 21-cmfluctuations at z~8 and 10. Here, we use several independent theoretical modelsto infer constraints on the intergalactic medium (IGM) and galaxies during theepoch of reionization (EoR) from these limits. We find that the IGM must havebeen heated above the adiabatic cooling threshold by z~8, independent ofuncertainties about the IGM ionization state and the nature of the radiobackground. Combining HERA limits with galaxy and EoR observations constrainsthe spin temperature of the z~8 neutral IGM to 27 K < T_S < 630 K (2.3 K < T_S< 640 K) at 68% (95%) confidence. They therefore also place a lower bound onX-ray heating, a previously unconstrained aspects of early galaxies. Forexample, if the CMB dominates the z~8 radio background, the new HERA limitsimply that the first galaxies produced X-rays more efficiently than local ones(with soft band X-ray luminosities per star formation rate constrained toL_X/SFR = { 10^40.2, 10^41.9 } erg/s/(M_sun/yr) at 68% confidence), consistentwith expectations of X-ray binaries in low-metallicity environments. The z~10limits require even earlier heating if dark-matter interactions (e.g., throughmillicharges) cool down the hydrogen gas. Using a model in which an extra radiobackground is produced by galaxies, we rule out (at 95% confidence) thecombination of high radio and low X-ray luminosities of L_{r,\nu}/SFR > 3.9 x10^24 W/Hz/(M_sun/yr) and L_X/SFR<10^40 erg/s/(M_sun/yr). The new HERA upperlimits neither support nor disfavor a cosmological interpretation of the recentEDGES detection. The analysis framework described here provides a foundationfor the interpretation of future HERA results.

HERA Phase I Limits on the Cosmic 21-cm Signal: Constraints on Astrophysics and Cosmology During the Epoch of Reionization