Direct Collapse to Supermassive Black Hole Seeds: Comparing the AMR and
  SPH Approaches
  We provide detailed comparison between the AMR code Enzo-2.4 and the SPH/N-
body code GADGET-3 in the context of isolated or cosmological direct baryonic
collapse within dark matter (DM) halos to form supermassive black holes. Gas
flow is examined by following evolution of basic parameters of accretion flows.
Both codes show an overall agreement in the general features of the collapse,
however, many subtle differences exist. For isolated models, the codes increase
their spatial and mass resolutions at different pace, which leads to
substantially earlier collapse in SPH than in AMR cases due to higher
gravitational resolution in GADGET-3. In cosmological runs, the AMR develops a
slightly higher baryonic resolution than SPH during halo growth via cold
accretion permeated by mergers. Still, both codes agree in the buildup of DM
and baryonic structures. However, with the onset of collapse, this difference
in mass and spatial resolution is amplified, so evolution of SPH models begins
to lag behind. Such a delay can have effect on formation/destruction rate of H2
due to UV background, and on basic properties of host halos. Finally, isolated
non-cosmological models in spinning halos, with spin parameter {\lambda} ~ 0.01
- 0.07, show delayed collapse for greater {\lambda}, but pace of this increase
is faster for AMR. Within our simulation setup, GADGET-3 requires significantly
larger computational resources than Enzo- 2.4 during collapse, and needs
similar resources, during the pre-collapse, cosmological structure formation
phase. Yet it benefits from substantially higher gravitational force and
hydrodynamic resolutions, except at the end of collapse.
