Joint analysis constraints on the physics of the first galaxies with low frequency radio astronomy data

The first billion years of cosmic history remains largely unobserved. We demonstrate, using a novel machine learning technique, how combining upper limits on the spatial fluctuations in the 21-cm signal with observations of the sky-averaged 21-cm signal from neutral hydrogen can improve our understanding of this epoch. By jointly analysing data from SARAS3 (redshift $z\approx15-25$) and limits from HERA ($z\approx8$ and $10$), we show that such a synergetic analysis provides tighter constraints on the astrophysics of galaxies 200 million years after the Big Bang than can be achieved with the individual data sets. Although our constraints are weak, this is the first time data from a sky-averaged 21-cm experiment and power spectrum experiment have been analysed together. In synergy, the two experiments leave only $64.9^{+0.3}_{-0.1}$% of the explored broad theoretical parameter space to be consistent with the joint data set, in comparison to $92.3^{+0.3}_{-0.1}$% for SARAS3 and $79.0^{+0.5}_{-0.2}$% for HERA alone. We use the joint analysis to constrain star formation efficiency, minimum halo mass for star formation, X-ray luminosity of early emitters and the radio luminosity of early galaxies. The joint analysis disfavours at 68% confidence a combination of galaxies with X-ray emission that is $\lesssim 33$ and radio emission that is $\gtrsim 32$ times as efficient as present day galaxies. We disfavour at $95$% confidence scenarios in which power spectra are $\geq126$ mK$^{2}$ at $z=25$ and the sky-averaged signals are $\leq-277$ mK.