# 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 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 wave number k, as is usually done, linearity is guaranteed because both the LOS and transverse wave numbers 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 frommore »

- Authors:

- Institute for Strings, Cosmology and Astroparticle Physics (ISCAP), New York, New York 10027 (United States)
- (United States)
- (Hong Kong)
- Institut de Ciencies de l'Espai, IEEC-CSIC, F. de Ciencies, Torre C5 par-2, Barcelona 08193 (Spain)

- Publication Date:

- OSTI Identifier:
- 21249810

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 77; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.77.063526; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ANISOTROPY; BARYONS; CORRELATION FUNCTIONS; CORRELATIONS; FLUCTUATIONS; GALAXIES; IMPACT PARAMETER; MATHEMATICAL SPACE; NONLINEAR PROBLEMS; OSCILLATIONS; RED SHIFT; SPECTRA

### Citation Formats

```
Hui Lam, Department of Physics, Columbia University, New York, New York 10027, Institute of Theoretical Physics, Chinese University of Hong Kong, Gaztanaga, Enrique, LoVerde, Marilena, and Department of Physics, Columbia University, New York, New York 10027.
```*Anisotropic magnification distortion of the 3D galaxy correlation. II. Fourier and redshift space*. United States: N. p., 2008.
Web. doi:10.1103/PHYSREVD.77.063526.

```
Hui Lam, Department of Physics, Columbia University, New York, New York 10027, Institute of Theoretical Physics, Chinese University of Hong Kong, Gaztanaga, Enrique, LoVerde, Marilena, & Department of Physics, Columbia University, New York, New York 10027.
```*Anisotropic magnification distortion of the 3D galaxy correlation. II. Fourier and redshift space*. United States. doi:10.1103/PHYSREVD.77.063526.

```
Hui Lam, Department of Physics, Columbia University, New York, New York 10027, Institute of Theoretical Physics, Chinese University of Hong Kong, Gaztanaga, Enrique, LoVerde, Marilena, and Department of Physics, Columbia University, New York, New York 10027. Sat .
"Anisotropic magnification distortion of the 3D galaxy correlation. II. Fourier and redshift space". United States. doi:10.1103/PHYSREVD.77.063526.
```

```
@article{osti_21249810,
```

title = {Anisotropic magnification distortion of the 3D galaxy correlation. II. Fourier and redshift space},

author = {Hui Lam and Department of Physics, Columbia University, New York, New York 10027 and Institute of Theoretical Physics, Chinese University of Hong Kong and Gaztanaga, Enrique and LoVerde, Marilena and Department of Physics, Columbia University, New York, New York 10027},

abstractNote = {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 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 wave number k, as is usually done, linearity is guaranteed because both the LOS and transverse wave numbers 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.},

doi = {10.1103/PHYSREVD.77.063526},

journal = {Physical Review. D, Particles Fields},

number = 6,

volume = 77,

place = {United States},

year = {Sat Mar 15 00:00:00 EDT 2008},

month = {Sat Mar 15 00:00:00 EDT 2008}

}