# Disentangling Redshift-Space Distortions and Nonlinear Bias using the 2D Power Spectrum

## Abstract

We present the nonlinear 2D galaxy power spectrum, P(k, µ), in redshift space, measured from the Dark Sky simulations, using galaxy catalogs constructed with both halo occupation distribution and subhalo abundance matching methods, chosen to represent an intermediate redshift sample of luminous red galaxies. We find that the information content in individual µ (cosine of the angle to the line of sight) bins is substantially richer then multipole moments, and show that this can be used to isolate the impact of nonlinear growth and redshift space distortion (RSD) effects. Using the µ < 0.2 simulation data, which we show is not impacted by RSD effects, we can successfully measure the nonlinear bias to an accuracy of ~ 5% at k < 0.6hMpc-1 . This use of individual µ bins to extract the nonlinear bias successfully removes a large parameter degeneracy when constraining the linear growth rate of structure. We carry out a joint parameter estimation, using the low µ simulation data to constrain the nonlinear bias, and µ > 0.2 to constrain the growth rate and show that f can be constrained to ~ 26(22)% to a kmax < 0.4(0.6)hMpc-1 from clustering alone using a simple dispersion model, for amore »

- Authors:

- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Univ. of Chicago, IL (United States)
- Stanford Univ., CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1221340

- Report Number(s):
- FERMILAB-PUB-15-339-A

Journal ID: ISSN 0035-8711; arXiv eprint number arXiv:1508.01803

- Grant/Contract Number:
- AC02-07CH11359

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Monthly Notices of the Royal Astronomical Society

- Additional Journal Information:
- Journal Volume: 457; Journal ID: ISSN 0035-8711

- Publisher:
- Royal Astronomical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; N-body simulations; cosmology:theory; large-scale structure of the Universe

### Citation Formats

```
Jennings, Elise, and Wechsler, Risa H. Disentangling Redshift-Space Distortions and Nonlinear Bias using the 2D Power Spectrum. United States: N. p., 2015.
Web. doi:10.1093/mnras/stv2989.
```

```
Jennings, Elise, & Wechsler, Risa H. Disentangling Redshift-Space Distortions and Nonlinear Bias using the 2D Power Spectrum. United States. doi:10.1093/mnras/stv2989.
```

```
Jennings, Elise, and Wechsler, Risa H. Fri .
"Disentangling Redshift-Space Distortions and Nonlinear Bias using the 2D Power Spectrum". United States. doi:10.1093/mnras/stv2989. https://www.osti.gov/servlets/purl/1221340.
```

```
@article{osti_1221340,
```

title = {Disentangling Redshift-Space Distortions and Nonlinear Bias using the 2D Power Spectrum},

author = {Jennings, Elise and Wechsler, Risa H.},

abstractNote = {We present the nonlinear 2D galaxy power spectrum, P(k, µ), in redshift space, measured from the Dark Sky simulations, using galaxy catalogs constructed with both halo occupation distribution and subhalo abundance matching methods, chosen to represent an intermediate redshift sample of luminous red galaxies. We find that the information content in individual µ (cosine of the angle to the line of sight) bins is substantially richer then multipole moments, and show that this can be used to isolate the impact of nonlinear growth and redshift space distortion (RSD) effects. Using the µ < 0.2 simulation data, which we show is not impacted by RSD effects, we can successfully measure the nonlinear bias to an accuracy of ~ 5% at k < 0.6hMpc-1 . This use of individual µ bins to extract the nonlinear bias successfully removes a large parameter degeneracy when constraining the linear growth rate of structure. We carry out a joint parameter estimation, using the low µ simulation data to constrain the nonlinear bias, and µ > 0.2 to constrain the growth rate and show that f can be constrained to ~ 26(22)% to a kmax < 0.4(0.6)hMpc-1 from clustering alone using a simple dispersion model, for a range of galaxy models. Our analysis of individual µ bins also reveals interesting physical effects which arise simply from different methods of populating halos with galaxies. We also find a prominent turnaround scale, at which RSD damping effects are greater then the nonlinear growth, which differs not only for each µ bin but also for each galaxy model. These features may provide unique signatures which could be used to shed light on the galaxy–dark matter connection. Furthermore, the idea of separating nonlinear growth and RSD effects making use of the full information in the 2D galaxy power spectrum yields significant improvements in constraining cosmological parameters and may be a promising probe of galaxy formation models.},

doi = {10.1093/mnras/stv2989},

journal = {Monthly Notices of the Royal Astronomical Society},

number = ,

volume = 457,

place = {United States},

year = {2015},

month = {8}

}

*Citation information provided by*

Web of Science

Web of Science

Works referenced in this record:

##
The Rockstar Phase-Space Temporal halo Finder and the Velocity Offsets of Cluster Cores

journal, December 2012

- Behroozi, Peter S.; Wechsler, Risa H.; Wu, Hao-Yi
- The Astrophysical Journal, Vol. 762, Issue 2

##
Gravitationally Consistent halo Catalogs and Merger Trees for Precision Cosmology

journal, December 2012

- Behroozi, Peter S.; Wechsler, Risa H.; Wu, Hao-Yi
- The Astrophysical Journal, Vol. 763, Issue 1

##
Mergers and mass Accretion for Infalling Halos both end well Outside Cluster Virial Radii

journal, May 2014

- Behroozi, Peter S.; Wechsler, Risa H.; Lu, Yu
- The Astrophysical Journal, Vol. 787, Issue 2

##
The Halo Occupation Distribution: Toward an Empirical Determination of the Relation between Galaxies and Mass

journal, August 2002

- Berlind, Andreas A.; Weinberg, David H.
- The Astrophysical Journal, Vol. 575, Issue 2

##
The 6dF Galaxy Survey: z≈ 0 measurements of the growth rate and σ8: 6dFGS: z≈ 0 measurements of fσ8 and σ8

journal, June 2012

- Beutler, Florian; Blake, Chris; Colless, Matthew
- Monthly Notices of the Royal Astronomical Society, Vol. 423, Issue 4

##
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: testing gravity with redshift space distortions using the power spectrum multipoles

journal, July 2014

- Beutler, Florian; Saito, Shun; Seo, Hee-Jong
- Monthly Notices of the Royal Astronomical Society, Vol. 443, Issue 2

##
Halo velocity bias

journal, November 2014

- Biagetti, Matteo; Desjacques, Vincent; Kehagias, Alex
- Physical Review D, Vol. 90, Issue 10

##
Improving the modelling of redshift-space distortions – I. A bivariate Gaussian description for the galaxy pairwise velocity distributions

journal, November 2014

- Bianchi, Davide; Chiesa, Matteo; Guzzo, Luigi
- Monthly Notices of the Royal Astronomical Society, Vol. 446, Issue 1

##
The WiggleZ Dark Energy Survey: the growth rate of cosmic structure since redshift z=0.9: WiggleZ Survey: growth of structure

journal, June 2011

- Blake, Chris; Brough, Sarah; Colless, Matthew
- Monthly Notices of the Royal Astronomical Society, Vol. 415, Issue 3

##
Galaxy halo occupation at high redshift

journal, January 2002

- Bullock, James S.; Wechsler, Risa H.; Somerville, Rachel S.
- Monthly Notices of the Royal Astronomical Society, Vol. 329, Issue 1

##
Clustering of luminous red galaxies - I. Large-scale redshift-space distortions

journal, March 2009

- Cabré, Anna; Gaztañaga, Enrique
- Monthly Notices of the Royal Astronomical Society, Vol. 393, Issue 4

##
The 2dF Galaxy Redshift Survey: power-spectrum analysis of the final data set and cosmological implications

journal, September 2005

- Cole, Shaun; Percival, Will J.; Peacock, John A.
- Monthly Notices of the Royal Astronomical Society, Vol. 362, Issue 2

##
Modeling Luminosity‐dependent Galaxy Clustering through Cosmic Time

journal, August 2006

- Conroy, Charlie; Wechsler, Risa H.; Kravtsov, Andrey V.
- The Astrophysical Journal, Vol. 647, Issue 1

##
Halo models of large scale structure

journal, December 2002

- Cooray, A.; Sheth, R.
- Physics Reports, Vol. 372, Issue 1

##
A survey of galaxy redshifts. V - The two-point position and velocity correlations

journal, April 1983

- Davis, M.; Peebles, P. J. E.
- The Astrophysical Journal, Vol. 267

##
Power-spectrum analysis of three-dimensional redshift surveys

journal, May 1994

- Feldman, Hume A.; Kaiser, Nick; Peacock, John A.
- The Astrophysical Journal, Vol. 426

##
DESI and other Dark Energy experiments in the era of neutrino mass measurements

journal, May 2014

- Font-Ribera, Andreu; McDonald, Patrick; Mostek, Nick
- Journal of Cosmology and Astroparticle Physics, Vol. 2014, Issue 05

##
`emcee` : The MCMC Hammer

journal, March 2013

- Foreman-Mackey, Daniel; Hogg, David W.; Lang, Dustin
- Publications of the Astronomical Society of the Pacific, Vol. 125, Issue 925

##
Velocity bias from the small-scale clustering of SDSS-III BOSS galaxies

journal, November 2014

- Guo, Hong; Zheng, Zheng; Zehavi, Idit
- Monthly Notices of the Royal Astronomical Society, Vol. 446, Issue 1

##
A test of the nature of cosmic acceleration using galaxy redshift distortions

journal, January 2008

- Guzzo, L.; Pierleoni, M.; Meneux, B.
- Nature, Vol. 451, Issue 7178

##
An improved model for the non-linear velocity power spectrum

journal, September 2012

- Jennings, Elise
- Monthly Notices of the Royal Astronomical Society: Letters

##
Non-linear stochastic growth rates and redshift space distortions

journal, April 2015

- Jennings, E.; Jennings, D.
- Monthly Notices of the Royal Astronomical Society, Vol. 449, Issue 4

##
Velocity and mass bias in the distribution of dark matter haloes

journal, November 2014

- Jennings, E.; Baugh, C. M.; Hatt, D.
- Monthly Notices of the Royal Astronomical Society, Vol. 446, Issue 1

##
Clustering in real space and in redshift space

journal, July 1987

- Kaiser, Nick
- Monthly Notices of the Royal Astronomical Society, Vol. 227, Issue 1

##
The Dark Side of the Halo Occupation Distribution

journal, July 2004

- Kravtsov, Andrey V.; Berlind, Andreas A.; Wechsler, Risa H.
- The Astrophysical Journal, Vol. 609, Issue 1

##
Mapping Growth and Gravity with Robust Redshift Space Distortions

journal, March 2012

- Kwan, Juliana; Lewis, Geraint F.; Linder, Eric V.
- The Astrophysical Journal, Vol. 748, Issue 2

##
Cosmological parameters from CMB and other data: A Monte Carlo approach

journal, November 2002

- Lewis, Antony; Bridle, Sarah
- Physical Review D, Vol. 66, Issue 10

##
Deriving the Nonlinear Cosmological Power Spectrum and Bispectrum from Analytic Dark Matter Halo Profiles and Mass Functions

journal, November 2000

- Ma, Chung‐Pei; Fry, J. N.
- The Astrophysical Journal, Vol. 543, Issue 2

##
Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture

journal, October 2008

- Matsubara, Takahiko
- Physical Review D, Vol. 78, Issue 8

##
The effect of redshift-space distortions on projected two-point clustering measurements: Redshift distortions and projected clustering

journal, June 2010

- Nock, Kelly; Percival, Will J.; Ross, Ashley J.
- Monthly Notices of the Royal Astronomical Society, Vol. 407, Issue 1

##
Reconstructing the linear power spectrum of cosmological mass fluctuations

journal, April 1994

- Peacock, J. A.; Dodds, S. J.
- Monthly Notices of the Royal Astronomical Society, Vol. 267, Issue 4

##
Testing cosmological structure formation using redshift-space distortions

journal, February 2009

- Percival, Will J.; White, Martin
- Monthly Notices of the Royal Astronomical Society, Vol. 393, Issue 1

##
*Planck* 2013 results. I. Overview of products and scientific results

journal, October 2014

- Ade, P. A. R.; Aghanim, N.; Alves, M. I. R.
- Astronomy & Astrophysics, Vol. 571

##
The Connection Between Galaxies and dark Matter Structures in the Local Universe

journal, June 2013

- Reddick, Rachel M.; Wechsler, Risa H.; Tinker, Jeremy L.
- The Astrophysical Journal, Vol. 771, Issue 1

##
Constraining the Luminous red Galaxy halo Occupation Distribution Using Counts-In-Cylinders

journal, May 2009

- Reid, Beth A.; Spergel, David N.
- The Astrophysical Journal, Vol. 698, Issue 1

##
Towards an accurate model of the redshift-space clustering of haloes in the quasi-linear regime: Redshift-space distortions

journal, August 2011

- Reid, Beth A.; White, Martin
- Monthly Notices of the Royal Astronomical Society, Vol. 417, Issue 3

##
A 2.5 per cent measurement of the growth rate from small-scale redshift space clustering of SDSS-III CMASS galaxies

journal, August 2014

- Reid, Beth A.; Seo, Hee-Jong; Leauthaud, Alexie
- Monthly Notices of the Royal Astronomical Society, Vol. 444, Issue 1

##
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological constraints from the full shape of the clustering wedges

journal, June 2013

- Sánchez, Ariel G.; Kazin, Eyal A.; Beutler, Florian
- Monthly Notices of the Royal Astronomical Society, Vol. 433, Issue 2

##
The spatial correlation function of IRAS galaxies on small and intermediate scales

journal, September 1992

- Saunders, W.; Rowan-Robinson, M.; Lawrence, A.
- Monthly Notices of the Royal Astronomical Society, Vol. 258, Issue 1

##
Statistics of primordial density perturbations from discrete seed masses

journal, November 1991

- Scherrer, Robert J.; Bertschinger, Edmund
- The Astrophysical Journal, Vol. 381

##
Redshift-space distortions, pairwise velocities, and nonlinearities

journal, October 2004

- Scoccimarro, Román
- Physical Review D, Vol. 70, Issue 8

##
Distribution function approach to redshift space distortions

journal, November 2011

- Seljak, Uroš; McDonald, Patrick
- Journal of Cosmology and Astroparticle Physics, Vol. 2011, Issue 11

##
Baryon acoustic oscillations in 2D: Modeling redshift-space power spectrum from perturbation theory

journal, September 2010

- Taruya, Atsushi; Nishimichi, Takahiro; Saito, Shun
- Physical Review D, Vol. 82, Issue 6

##
Redshift-space distortions with the halo occupation distribution - I. Numerical simulations

journal, May 2006

- Tinker, J. L.; Weinberg, D. H.; Zheng, Z.
- Monthly Notices of the Royal Astronomical Society, Vol. 368, Issue 1

##
Linking halo mass to galaxy luminosity

journal, September 2004

- Vale, A.; Ostriker, J. P.
- Monthly Notices of the Royal Astronomical Society, Vol. 353, Issue 1

##
The Dependence of Halo Clustering on Halo Formation History, Concentration, and Occupation

journal, November 2006

- Wechsler, Risa H.; Zentner, Andrew R.; Bullock, James S.
- The Astrophysical Journal, Vol. 652, Issue 1

##
Tests of redshift-space distortions models in configuration space for the analysis of the BOSS final data release

journal, December 2014

- White, Martin; Reid, Beth; Chuang, Chia-Hsun
- Monthly Notices of the Royal Astronomical Society, Vol. 447, Issue 1

##
Theoretical Models of the Halo Occupation Distribution: Separating Central and Satellite Galaxies

journal, November 2005

- Zheng, Zheng; Berlind, Andreas A.; Weinberg, David H.
- The Astrophysical Journal, Vol. 633, Issue 2

##
Halo Occupation Distribution Modeling of Clustering of Luminous red Galaxies

journal, November 2009

- Zheng, Zheng; Zehavi, Idit; Eisenstein, Daniel J.
- The Astrophysical Journal, Vol. 707, Issue 1

##
Determination of the large scale volume weighted halo velocity bias in simulations

journal, June 2015

- Zheng, Yi; Zhang, Pengjie; Jing, Yipeng
- Physical Review D, Vol. 91, Issue 12

##
CosmoSIS: Modular cosmological parameter estimation

journal, September 2015

- Zuntz, J.; Paterno, M.; Jennings, E.
- Astronomy and Computing, Vol. 12