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Using the latest upper limits on the 21-cm power spectrum at $z\approx9.1$from the Low Frequency Array (LOFAR), we explore regions of parameter spacewhich are inconsistent with the data. We use 21CMMC, a Monte Carlo Markov Chainsampler of 21cmFAST which directly forward models the 3D cosmic 21-cm signal ina fully Bayesian framework. We use the astrophysical parameterisation from21cmFAST, which includes mass-dependent star formation rates and ionisingescape fractions as well as soft-band X-ray luminosities to place limits on theproperties of the high-$z$ galaxies. Further, we connect the disfavouredregions of parameter space with existing observational constraints on the Epochof Reionisation such as ultra-violet (UV) luminosity functions, background UVphotoionisation rate, intergalactic medium (IGM) neutral fraction and theelectron scattering optical depth. We find that all models exceeding the 21-cmsignal limits set by LOFAR at $z\approx9.1$ are excluded at $\gtrsim2\sigma$ byother probes. Finally, we place limits on the IGM spin temperature from LOFAR,disfavouring at 95 per cent confidence spin temperatures below $\sim2.6$ Kacross an IGM neutral fraction range of $0.15 \lesssim\bar{x}_{H{\scriptscriptstyle I}} \lesssim 0.6$. Note, these limits are onlyobtained from 141 hrs of data in a single redshift bin. With tighter upperlimits, across multiple redshift bins expected in the near future from LOFAR,more viable models will be ruled out. Our approach demonstrates the potentialof forward modelling tools such as 21CMMC in combining 21-cm observations withother high-$z$ probes to constrain the astrophysics of galaxies.

Interpreting LOFAR 21-cm signal upper limits at z~9.1 in the context of high-z galaxy and reionisation observations