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In paper I of this series we discuss how magnification bias distorts the 3Dcorrelation function by enhancing the observed correlation in the line-of-sight(LOS) orientation, especially on large scales. This lensing anisotropy isdistinctive, making it possible to separately measure the galaxy-galaxy,galaxy-magnification {\it and} magnification-magnification correlations. Herewe extend the discussion to the power spectrum and also to redshift space. Inreal space, pairs oriented close to the LOS direction are not protected againstnonlinearity even if the pair separation is large; this is because nonlinearfluctuations can enter through gravitational lensing at a small transverseseparation (or i.e. impact parameter). The situation in Fourier space isdifferent: by focusing on a small wavenumber $k$, as is usually done, linearityis guaranteed because both the LOS and transverse wavenumbers must be small.This is why magnification distortion of the galaxy correlation appears lesssevere in Fourier space. Nonetheless, the effect is non-negligible, especiallyfor the transverse Fourier modes, and should be taken into account ininterpreting precision measurements of the galaxy power spectrum, for instancethose that focus on the baryon oscillations. The lensing induced anisotropy ofthe power spectrum has a shape that is distinct from the more well knownredshift space anisotropies due to peculiar motions and the Alcock-Paczynskieffect. The lensing anisotropy is highly localized in Fourier space whileredshift space distortions are more spread out. This means that one couldseparate the magnification bias component in real observations, implying thatpotentially it is possible to perform a gravitational lensing measurementwithout measuring galaxy shapes.

Anisotropic Magnification Distortion of the 3D Galaxy Correlation: II. Fourier and Redshift Space