Separating angular and radial modes with spherical-Fourier Bessel power spectrum on all scales and implications for systematics mitigation

Current and upcoming large-scale structure surveys place stringent requirements on the mitigation of observational systematics in order to achieve their unprecedented constraining power. In this work, we investigate the potential use of the spherical Fourier-Bessel (SFB) power spectrum in controlling systematics, leveraging its capability of disentangling angular and radial scales. We first clarify how the discrete SFB basis describes radial scales via the index $n$ and demonstrate that the SFB power spectrum reduces to the clustering wedge $P(k,μ)$ in the plane-parallel limit, enabling it to inherit results from past literature based on the clustering wedge. While the parallel and perpendicular Fourier mode $(k_{||}, k_\perp)$ decomposition underlying the wedge is only valid for surveys of small angular coverage with a well-defined global line-of-sight, the SFB basis provides a natural generalization that can be applied to the full sky. Crucially, the separation of angular and radial scales allows systematics to be localized in SFB space. In particular, systematics with broad and smooth radial distributions primarily concentrate in the $n=0$ modes corresponding to the largest radial scales. This localization behavior enables one to selectively remove only particular angular and radial modes contaminated by systematics. This is in contrast to standard 3D clustering analyses of wide-field surveys based on power spectrum multipoles, where systematic effects necessitate the removal of all modes below a given $k_{\rm min}$. Our findings advocate for adopting the SFB basis in 3D clustering analyses where systematics have become a limiting factor.

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