Alcock-Paczynski effects on wide-angle galaxy statistics. (arXiv:2103.08126v2 [astro-ph.CO] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Shiraishi_M/0/1/0/all/0/1">Maresuke Shiraishi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Akitsu_K/0/1/0/all/0/1">Kazuyuki Akitsu</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Okumura_T/0/1/0/all/0/1">Teppei Okumura</a>
The Alcock-Paczynski (AP) effect is a geometrical distortion in
three-dimensional observed galaxy statistics. In anticipation of precision
cosmology based on ongoing and upcoming all-sky galaxy surveys, we build an
efficient method to compute the AP-distorted correlations of galaxy number
density and peculiar velocity fields for any larger angular scale not relying
on the conventionally used plane-parallel (PP) approximation. Here, instead of
the usual Legendre polynomial basis, the correlation functions are decomposed
using tripolar spherical harmonic basis; hence, characteristic angular
dependence due to the wide-angle AP effect can be rigorously captured. By means
of this, we demonstrate the computation of the AP-distorted correlations over
the various scales. Comparing our results with the PP-limit ones, we confirm
that the errors due to the PP approximation become more remarkable as the
visual angle of separation between target galaxies, $Theta$, enlarges, and
especially for the density auto correlation, the error exceeds $10%$ when
$Theta gtrsim 30^circ$. This highlights the importance of the analysis
beyond the PP approximation.
The Alcock-Paczynski (AP) effect is a geometrical distortion in
three-dimensional observed galaxy statistics. In anticipation of precision
cosmology based on ongoing and upcoming all-sky galaxy surveys, we build an
efficient method to compute the AP-distorted correlations of galaxy number
density and peculiar velocity fields for any larger angular scale not relying
on the conventionally used plane-parallel (PP) approximation. Here, instead of
the usual Legendre polynomial basis, the correlation functions are decomposed
using tripolar spherical harmonic basis; hence, characteristic angular
dependence due to the wide-angle AP effect can be rigorously captured. By means
of this, we demonstrate the computation of the AP-distorted correlations over
the various scales. Comparing our results with the PP-limit ones, we confirm
that the errors due to the PP approximation become more remarkable as the
visual angle of separation between target galaxies, $Theta$, enlarges, and
especially for the density auto correlation, the error exceeds $10%$ when
$Theta gtrsim 30^circ$. This highlights the importance of the analysis
beyond the PP approximation.
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