A new way of setting the phases for cosmological multi-scale Gaussian initial conditions

Abstract: 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.