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

Abstract

In paper I of this series we discuss how magnification bias distorts the 3D correlation function by enhancing the observed correlation in the line-of-sight (LOS) orientation, especially on large scales. This lensing anisotropy is distinctive, making it possible to separately measure the galaxy-galaxy, galaxy-magnification {\it and} magnification-magnification correlations. Here we extend the discussion to the power spectrum and also to redshift space. In real space, pairs oriented close to the LOS direction are not protected against nonlinearity even if the pair separation is large; this is because nonlinear fluctuations can enter through gravitational lensing at a small transverse separation (or i.e. impact parameter). The situation in Fourier space is different: by focusing on a small wavenumber $k$, as is usually done, linearity is guaranteed because both the LOS and transverse wavenumbers must be small. This is why magnification distortion of the galaxy correlation appears less severe in Fourier space. Nonetheless, the effect is non-negligible, especially for the transverse Fourier modes, and should be taken into account in interpreting precision measurements of the galaxy power spectrum, for instance those that focus on the baryon oscillations. The lensing induced anisotropy of the power spectrum has a shape that is distinct from the more well known redshift space anisotropies due to peculiar motions and the Alcock-Paczynski effect. The lensing anisotropy is highly localized in Fourier space while redshift space distortions are more spread out. This means that one could separate the magnification bias component in real observations, implying that potentially it is possible to perform a gravitational lensing measurement without measuring galaxy shapes.

14 pages, minor revisions, as accepted for publication in Physical Review D

References in corpus (3)

• Anisotropic Magnification Distortion of the 3D Galaxy Correlation: I. Real Space
• Magnification-Temperature Correlation: the Dark Side of ISW Measurements
• Lensing Corrections to Features in the Angular Two-Point Correlation Function and Power Spectrum

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• Weak Lensing Effects on the Galaxy Three-Point Correlation Function
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• Universal Weak Lensing Distortion of Cosmological Correlation Functions
• Relativistic distortions in galaxy density-ellipticity correlations: gravitational redshift and peculiar velocity effects
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• Euclid preparation. The impact of relativistic redshift-space distortions on two-point clustering statistics from the Euclid wide spectroscopic survey
• Self calibration of galaxy bias in spectroscopic redshift surveys of baryon acoustic oscillations
• Investigating the imprint of quintessence in cosmic magnification