Kavli Affiliate: Masahiro Takada
| First 5 Authors: Ryo Terasawa, Yue Nan, Masahiro Takada, ,
| Summary:
We investigate the angular power spectrum ($C_ell)$ and angular correlation
function ($w(theta)$) of galaxy number density field in the presence of the
local-type primordial non-Gaussianity (PNG), explicitly accounting for the
integral constraint in an all-sky survey. We show that the PNG signature in
$C_{ell}$ is confined to low multipoles in the linear regime, whereas its
signature in $w(theta)$ extends across a wide range of angular scales,
including those below the nonlinear scale. Therefore, the equivalence between
$C_ell$ and $w(theta)$ can be violated when scale cuts of multipoles or
angular scales — for example, to mitigate systematic effects — are applied in
the analysis. Assuming samples of photometric galaxies divided into multiple
redshift bins in the range $0<z<7$, we forecast the precision of constraining
the PNG parameter ($f_{rm NL}$) from the hypothetical measurements of $C_ell$
or $w(theta)$ assuming different scale cuts in the multipoles or angular
scales, respectively. Our results imply that the PNG information can be
extracted from $w(theta)$ on relatively small angular scales such as $lesssim
10$ degree for a high-redshift galaxy sample or from $w(theta)$ measured in a
survey with partial area coverage.
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