Impact of the Hall effect in star formation and the issue of angular
  momentum conservation
  We present an implementation of the Hall term in the non-ideal
magnetohydrodynamics equations into the adaptive-mesh-refinement code RAMSES to
study its impact on star formation. Recent works show that the Hall effect
heavily influences the regulation of the angular momentum in collapsing dense
cores, strengthening or weakening the magnetic braking. Our method consists of
a modification of the two-dimensional constrained transport scheme. Our scheme
shows convergence of second-order in space and the frequency of the propagation
of whistler waves is accurate. We confirm previous results, namely that during
the collapse, the Hall effect generates a rotation of the fluid with a
direction in the mid-plane that depends on the sign of the Hall resistivity,
while counter-rotating envelopes develop on each side of the mid-plane.
However, we find that the predictability of our numerical results is severely
limited. The angular momentum is not conserved in any of our dense
core-collapse simulations with the Hall effect: a large amount of angular
momentum is generated within the first Larson core, a few hundred years after
its formation, without compensation by the surrounding gas. This issue is not
mentioned in previous studies and may be correlated to the formation of the
accretion shock on the Larson core. We expect that this numerical effect could
be a serious issue in star formation simulations.
