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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