Beyond Yamamoto: Anisotropic Power Spectra and Correlation Functions with Pairwise Lines-of-Sight

Understand

Conventional estimators of the anisotropic power spectrum and two-point correlation function (2PCF) adopt the `Yamamoto approximation', fixing the line-of-sight of a pair of galaxies to that of just one of its members.

• Whilst this is accurate only to first-order in the characteristic opening angle $\theta_\max$, it allows for efficient implementation via Fast Fourier Transforms (FFTs).
• This work presents practical algorithms for computing the power spectrum and 2PCF multipoles using pairwise lines-of-sight, adopting either the galaxy midpoint or angle bisector definitions.
• Using newly derived infinite series expansions for spherical harmonics and Legendre polynomials, we construct estimators accurate to arbitrary order in $\theta_\max$, though note that the midpoint and bisector formalisms themselves differ at fourth order.