A faster Fourier transform? Computing smallscale power spectra and bispectra for cosmological simulations in ğ�'ª(N^{2}) time
Abstract
We present $\mathcal {O}(N^2)$ estimators for the smallscale power spectrum and bispectrum in cosmological simulations. In combination with traditional methods, these allow spectra to be efficiently computed across a vast range of scales, requiring orders of magnitude less computation time than Fast Fourier Transform based approaches alone. These methods are applicable to any tracer; simulation particles, haloes or galaxies, and take advantage of the simple geometry of the box and periodicity to remove almost all dependence on large random particle catalogues. By working in configurationspace, both power spectra and bispectra can be computed via a weighted sum of particle pairs up to some radius, which can be reduced at larger k, leading to algorithms with decreasing complexity on small scales. These do not suffer from aliasing or shotnoise, allowing spectra to be computed to arbitrarily large wavenumbers. The estimators are rigorously derived and tested against simulations, and their covariances discussed. The accompanying code, HIPSTER, has been publicly released, incorporating these algorithms. Such estimators will be of great use in the analysis of large sets of highresolution simulations.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 March 2021
 DOI:
 10.1093/mnras/staa3882
 arXiv:
 arXiv:2005.01739
 Bibcode:
 2021MNRAS.501.4004P
 Keywords:

 methods: numerical;
 methods: statistical;
 galaxies: statistics;
 cosmology: theory;
 cosmology: largescale structure of Universe;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 General Relativity and Quantum Cosmology;
 Physics  Computational Physics;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 31 pages, 6 figures, accepted by MNRAS. Code available at https://HIPSTER.readthedocs.io