Computing the smallscale galaxy power spectrum and bispectrum in configuration space
Abstract
We present a new class of estimators for computing smallscale power spectra and bispectra in configuration space via weighted pair and triple counts, with no explicit use of Fourier transforms. Particle counts are truncated at R_0∼ 100 h^{1} Mpc via a continuous window function, which has negligible effect on the measured power spectrum multipoles at small scales. This gives a power spectrum algorithm with complexity O(NnR_0^3) (or O(Nn^2R_0^6) for the bispectrum), measuring N galaxies with number density n. Our estimators are corrected for the survey geometry and have neither selfcount contributions nor discretization artefacts, making them ideal for highk analysis. Unlike conventional Fouriertransformbased approaches, our algorithm becomes more efficient on small scales (since a smaller R_{0} may be used), thus we may efficiently estimate spectra across kspace by coupling this method with standard techniques. We demonstrate the utility of the publicly available power spectrum algorithm by applying it to BOSS DR12 simulations to compute the highk power spectrum and its covariance. In addition, we derive a theoretical rescaledGaussian covariance matrix, which incorporates the survey geometry and is found to be in good agreement with that from mocks. Computing configuration and Fourierspace statistics in the same manner allows us to consider joint analyses, which can place stronger bounds on cosmological parameters; to this end we also discuss the crosscovariance between the twopoint correlation function and the smallscale power spectrum.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 February 2020
 DOI:
 10.1093/mnras/stz3335
 arXiv:
 arXiv:1912.01010
 Bibcode:
 2020MNRAS.492.1214P
 Keywords:

 methods: numerical;
 methods: statistical;
 galaxies: statistics;
 largescale structure of Universe;
 cosmology: theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Astrophysics  Instrumentation and Methods for Astrophysics
 EPrint:
 29 pages, 14 figures, accepted by MNRAS. Code is available at https://github.com/oliverphilcox/HIPSTER with documentation at https://HIPSTER.readthedocs.io