Interpreting LOFAR 21-cm signal upper limits at z~9.1 in the context of
  high-z galaxy and reionisation observations
  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 space
which are inconsistent with the data. We use 21CMMC, a Monte Carlo Markov Chain
sampler of 21cmFAST which directly forward models the 3D cosmic 21-cm signal in
a fully Bayesian framework. We use the astrophysical parameterisation from
21cmFAST, which includes mass-dependent star formation rates and ionising
escape fractions as well as soft-band X-ray luminosities to place limits on the
properties of the high-$z$ galaxies. Further, we connect the disfavoured
regions of parameter space with existing observational constraints on the Epoch
of Reionisation such as ultra-violet (UV) luminosity functions, background UV
photoionisation rate, intergalactic medium (IGM) neutral fraction and the
electron scattering optical depth. We find that all models exceeding the 21-cm
signal limits set by LOFAR at $z\approx9.1$ are excluded at $\gtrsim2\sigma$ by
other probes. Finally, we place limits on the IGM spin temperature from LOFAR,
disfavouring at 95 per cent confidence spin temperatures below $\sim2.6$ K
across an IGM neutral fraction range of $0.15 \lesssim
\bar{x}_{H{\scriptscriptstyle I}} \lesssim 0.6$. Note, these limits are only
obtained from 141 hrs of data in a single redshift bin. With tighter upper
limits, across multiple redshift bins expected in the near future from LOFAR,
more viable models will be ruled out. Our approach demonstrates the potential
of forward modelling tools such as 21CMMC in combining 21-cm observations with
other high-$z$ probes to constrain the astrophysics of galaxies.
