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We use the sky-average spectrum measured by EDGES High-Band ($90-190$ MHz) toconstrain parameters of early galaxies independent of the absorption feature at$78$~MHz reported by Bowman et al. (2018). These parameters representtraditional models of cosmic dawn and the epoch of reionization produced withthe 21cmFAST simulation code (Mesinger & Furlanetto 2007, Mesinger et al.2011). The parameters considered are: (1) the UV ionizing efficiency ($\zeta$),(2) minimum halo virial temperature hosting efficient star-forming galaxies($T^{\rm min}_{\rm vir}$), (3) integrated soft-band X-ray luminosity ($L_{\rmX\,<\,2\,keV}/{\rm SFR}$), and (4) minimum X-ray energy escaping the firstgalaxies ($E_{0}$), corresponding to a typical H${\rm \scriptstyle I}$ columndensity for attenuation through the interstellar medium. The High-Band spectrumdisfavors high values of $T^{\rm min}_{\rm vir}$ and $\zeta$, which correspondto signals with late absorption troughs and sharp reionization transitions. Italso disfavors intermediate values of $L_{\rm X\,<\,2\,keV}/{\rm SFR}$, whichproduce relatively deep and narrow troughs within the band. Specifically, werule out $39.4<\log_{10}\left(L_{\rm X\,<\,2\,keV}/{\rm SFR}\right)<39.8$($95\%$ C.L.). We then combine the EDGES High-Band data with constraints on theelectron scattering optical depth from Planck and the hydrogen neutral fractionfrom high-$z$ quasars. This produces a lower degeneracy between $\zeta$ and$T^{\rm min}_{\rm vir}$ than that reported in Greig & Mesinger (2017a) usingthe Planck and quasar constraints alone. Our main result in this combinedanalysis is the estimate $4.5$~$\leq \log_{10}\left(T^{\rm min}_{\rm vir}/\rmK\right)\leq$~$5.7$ ($95\%$ C.L.). We leave for future work the evaluation of$21$~cm models using simultaneously data from EDGES Low- and High-Band.

Results from EDGES High-Band: II. Constraints on Parameters of Early Galaxies