Is there enough star formation in simulated protoclusters?
  As progenitors of the most massive objects, protoclusters are key to tracing
the evolution and star-formation history of the Universe, and are responsible
for ${\gtrsim}\,20$ per cent of the cosmic star formation at $z\,{>}\,2$. Using
a combination of state-of-the-art hydrodynamical simulations and empirical
models, we show that current galaxy-formation models do not produce enough star
formation in protoclusters to match observations. We find that the
star-formation rates (SFRs) predicted from the models are an order of magnitude
lower than what is seen in observations, despite the relatively good agreement
found for their mass-accretion histories, specifically that they lie on an
evolutionary path to become Coma-like clusters at $z\,{\simeq}\, 0$. Using a
well-studied protocluster core at $z\,{=}\,4.3$ as a test case, we find that
star-formation efficiency of protocluster galaxies is higher than predicted by
the models. We show that a large part of the discrepancy can be attributed to a
dependence of SFR on the numerical resolution of the simulations, with a
roughly factor of 3 drop in SFR when the spatial resolution decreases by a
factor of 4. We also present predictions up to $z\,{\simeq}\,7$. Compared to
lower redshifts, we find that centrals (the most massive member galaxies) are
more distinct from the other galaxies, while protocluster galaxies are less
distinct from field galaxies. All these results suggest that, as a rare and
extreme population at high-$z$, protoclusters can help constrain galaxy
formation models tuned to match the average population at $z\,{\simeq}\,0$.
