Resolution Convergence in Cosmological Hydrodynamical Simulations Using
  Adaptive Mesh Refinement
  We have explored the evolution of gas distributions from cosmological
simulations carried out using the RAMSES adaptive mesh refinement (AMR) code,
to explore the effects of resolution on cosmological hydrodynamical
simulations. It is vital to understand the effect of both the resolution of
initial conditions and the final resolution of the simulation. Lower initial
resolution simulations tend to produce smaller numbers of low mass structures.
This will strongly affect the assembly history of objects, and has the same
effect of simulating different cosmologies. The resolution of initial
conditions is an important factor in simulations, even with a fixed maximum
spatial resolution. The power spectrum of gas in simulations using AMR diverges
strongly from the fixed grid approach - with more power on small scales in the
AMR simulations - even at fixed physical resolution and also produces offsets
in the star formation at specific epochs. This is because before certain times
the upper grid levels are held back to maintain approximately fixed physical
resolution, and to mimic the natural evolution of dark matter only simulations.
Although the impact of hold back falls with increasing spatial and
initial-condition resolutions, the offsets in the star formation remain down to
a spatial resolution of 1 kpc. These offsets are of order of 10-20%, which is
below the uncertainty in the implemented physics but are expected to affect the
detailed properties of galaxies. We have implemented a new grid-hold-back
approach to minimize the impact of hold back on the star formation rate.
