Wide-Angle Effects in the Power Spectrum Multipoles in Next-Generation Redshift Surveys

As galaxy redshift surveys expand to larger areas on the sky, effects coming from the curved nature of the sky become important, introducing wide-angle (WA) corrections to the power spectrum multipoles at large galaxy-pair separations. These corrections particularly impact the measurement of physical effects that are predominantly detected on large scales, such the local primordial non-Gaussianities. In this paper, we examine the validity of the perturbative approach to modeling WA effects in the power spectrum multipoles for upcoming surveys by comparing to measurements on simulated galaxy catalogs using the Yamamoto estimator. We show that on the scales $k \lesssim 2\pi/\chi$, where $\chi$ is the comoving distance to the galaxies, the estimated power spectrum monopole differs by up to $5\%$ from the second-order perturbative result, with similar absolute deviations for higher multipoles. To enable precision comparison, we pioneer an improved treatment of the $\mu$-leakage effects in the Yamamoto estimator. Additionally, we devise a solution to include $f_{\rm NL}$ in the perturbative WA calculations, avoiding divergences in the original framework through the integral constraint. This allows us to conclude that WA effects can mimic a $f_{\rm NL}\sim5$ signal in the lowest SPHEREx redshift bin. We recommend using non-perturbative methods to model large scale power spectrum multipoles for $f_{\rm NL}$ measurements. A companion paper, Wen et al. 2024, addresses this by introducing a new non-perturbative method going through the spherical Fourier-Bessel basis.