Computing the Small-Scale Galaxy Power Spectrum and Bispectrum in Configuration-Space. (arXiv:1912.01010v1 [astro-ph.CO])

<a href="http://arxiv.org/find/astro-ph/1/au:+Philcox_O/0/1/0/all/0/1">Oliver H. E. Philcox</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Eisenstein_D/0/1/0/all/0/1">Daniel J. Eisenstein</a>

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

$R_0sim 100h^{-1},mathrm{Mpc}$ 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 $mathcal{O}(NnR_0^3)$

(or $mathcal{O}(Nn^2R_0^6)$ for the bispectrum), measuring $N$ galaxies with

number density $n$. Our estimators are corrected for the survey geometry and

have neither 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 $R_0$ 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.

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

$R_0sim 100h^{-1},mathrm{Mpc}$ 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 $mathcal{O}(NnR_0^3)$

(or $mathcal{O}(Nn^2R_0^6)$ for the bispectrum), measuring $N$ galaxies with

number density $n$. Our estimators are corrected for the survey geometry and

have neither 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 $R_0$ 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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