Papers › Computing the Small-Scale Galaxy Power Spectrum and Bispectrum in Configuration-Space
Computing the Small-Scale Galaxy Power Spectrum and Bispectrum in Configuration-Space
Oliver H. E. Philcox, Daniel J. Eisenstein
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We present a new class of estimators for computing small-scale 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 R₀∼100h⁻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(NnR₀³) (or 𝒪(Nn²R₀⁶) for the bispectrum), measuring N galaxies with number density n. Our estimators are corrected for the survey geometry and have neither self-count contributions nor discretization artifacts, making them ideal for high-k analysis. Unlike conventional Fourier transform based approaches, our algorithm becomes more efficient on small scales (since a smaller R₀ may be used), thus we may efficiently estimate spectra across k-space 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 high-k power spectrum and its covariance. In addition, we derive a theoretical rescaled-Gaussian covariance matrix, which incorporates the survey geometry and is found to be in good agreement with that from mocks. Computing configuration- and Fourier-space 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 cross-covariance between the two-point correlation function and the small-scale power spectrum.
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