A new way of setting the phases for cosmological multi-scale Gaussian
  initial conditions
  We describe how to define an extremely large discrete realisation of a
Gaussian white noise field that has a hierarchical structure and the property
that the value of any part of the field can be computed quickly. Tiny
subregions of such a field can be used to set the phase information for
Gaussian initial conditions for individual cosmological simulations of
structure formation. This approach has several attractive features: (i) the
hierarchical structure based on an octree is particular well suited for
generating follow up resimulation or zoom initial conditions; (ii) the phases
are defined for all relevant physical scales in advance so that resimulation
initial conditions are, by construction, consistent both with their parent
simulation and with each other; (iii) the field can easily be made public by
releasing a code to compute it - once public, phase information can be shared
or published by specifying a spatial location within the realisation. In this
paper we describe the principles behind creating such realisations. We define
an example called PANPHASIA and in a companion paper on arXiv (Jenkins &
Booth), make public a code to compute it. With fifty octree levels Panphasia
spans a factor of more than 10^15 in linear scale - a range that significantly
exceeds the ratio of the current Hubble radius to the putative CDM
free-streaming scale. We show how to modify a code used for making cosmological
and resimulation initial conditions so that it can take the phase information
from Panphasia and, using this code, we demonstrate that it is possible to make
good quality resimulation initial conditions. We define a convention for
publishing phase information from Panphasia and publish the initial phases for
several of the Virgo Consortium's most recent cosmological simulations
including the 303 billion particle MXXL simulation.
