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We use the Fisher matrix formalism and semi-numerical simulations to derivequantitative predictions of the constraints that power spectrum measurements onnext-generation interferometers, such as the Hydrogen Epoch of ReionizationArray (HERA) and the Square Kilometre Array (SKA), will place on thecharacteristics of the X-ray sources that heated the high redshiftintergalactic medium. Incorporating observations between $z=5$ and $z=25$, wefind that the proposed 331 element HERA and SKA phase 1 will be capable ofplacing $\lesssim 10\%$ constraints on the spectral properties of these firstX-ray sources, even if one is unable to perform measurements within theforeground contaminated "wedge" or the FM band. When accounting for theenhancement in power spectrum amplitude from spin temperature fluctuations, wefind that the observable signatures of reionization extend well beyond the peakin the power spectrum usually associated with it. We also find that lowerredshift degeneracies between the signatures of heating and reionizationphysics lead to errors on reionization parameters that are significantlygreater than previously predicted. Observations over the heating epoch are ableto break these degeneracies and improve our constraints considerably. For thesetwo reasons, 21\,cm observations during the heating epoch significantly enhanceour understanding of reionization as well.

Constraining High Redshift X-ray Sources with Next Generation 21 cm Power Spectrum Measurements