Kavli Affiliate: Masahiro Takada
| Summary:
We investigate the angular power spectrum ($C_ell)$ and angular correlation function ($w(θ)$) 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 $w(θ)$ extends across a wide range of angular scales, including those below the nonlinear scale. Therefore, the equivalence between $C_ell$ and $w(θ)$ 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 $w(θ)$ assuming different scale cuts in the multipoles or angular scales, respectively. Our results imply that the PNG information can be extracted from $w(θ)$ on relatively small angular scales such as $lesssim 10$ degree for a high-redshift galaxy sample or from $w(θ)$ measured in a survey with partial area coverage.
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