Optimal linear reconstruction of dark matter from halo catalogues
Abstract
The dark matter lumps (or "halos") that contain galaxies have locations in the Universe that are to some extent random with respect to the overall matter distributions. We investigate how best to estimate the total matter distribution from the locations of the halos. We derive the weight function w(M) to apply to darkmatter haloes that minimizes the stochasticity between the weighted halo distribution and its underlying mass density field. The optimal w(M) depends on the range of masses of halos being used. While the standard biasedPoisson model of the halo distribution predicts that bias weighting is optimal, the simple fact that the mass is comprised of haloes implies that the optimal w(M) will be a mixture of massweighting and biasweighting. In Nbody simulations, the Poisson estimator is up to 15× noisier than the optimal. Optimal weighting could make cosmological tests based on the matter power spectrum or crosscorrelations much more powerful and/or cost effective.
 Authors:

 Univ. of Pennsylvania, Philadelphia, PA (United States)
 Publication Date:
 Research Org.:
 Univ. of Pennsylvania, Philadelphia, PA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 OSTI Identifier:
 1203600
 Grant/Contract Number:
 FG0295ER40893
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Monthly Notices of the Royal Astronomical Society
 Additional Journal Information:
 Journal Volume: 412; Journal Issue: 2; Journal ID: ISSN 00358711
 Publisher:
 Royal Astronomical Society
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTRONOMY AND ASTROPHYSICS; darkmatter halos; haloscosmology; theorydark matter; gravitational lensing; analyticalmethods; numerical
Citation Formats
Cai, Yan Chuan, Bernstein, Gary, and Sheth, Ravi K. Optimal linear reconstruction of dark matter from halo catalogues. United States: N. p., 2011.
Web. doi:10.1111/j.13652966.2010.17969.x.
Cai, Yan Chuan, Bernstein, Gary, & Sheth, Ravi K. Optimal linear reconstruction of dark matter from halo catalogues. United States. doi:10.1111/j.13652966.2010.17969.x.
Cai, Yan Chuan, Bernstein, Gary, and Sheth, Ravi K. Fri .
"Optimal linear reconstruction of dark matter from halo catalogues". United States. doi:10.1111/j.13652966.2010.17969.x. https://www.osti.gov/servlets/purl/1203600.
@article{osti_1203600,
title = {Optimal linear reconstruction of dark matter from halo catalogues},
author = {Cai, Yan Chuan and Bernstein, Gary and Sheth, Ravi K.},
abstractNote = {The dark matter lumps (or "halos") that contain galaxies have locations in the Universe that are to some extent random with respect to the overall matter distributions. We investigate how best to estimate the total matter distribution from the locations of the halos. We derive the weight function w(M) to apply to darkmatter haloes that minimizes the stochasticity between the weighted halo distribution and its underlying mass density field. The optimal w(M) depends on the range of masses of halos being used. While the standard biasedPoisson model of the halo distribution predicts that bias weighting is optimal, the simple fact that the mass is comprised of haloes implies that the optimal w(M) will be a mixture of massweighting and biasweighting. In Nbody simulations, the Poisson estimator is up to 15× noisier than the optimal. Optimal weighting could make cosmological tests based on the matter power spectrum or crosscorrelations much more powerful and/or cost effective.},
doi = {10.1111/j.13652966.2010.17969.x},
journal = {Monthly Notices of the Royal Astronomical Society},
number = 2,
volume = 412,
place = {United States},
year = {2011},
month = {4}
}
Web of Science
Works referenced in this record:
Strong clustering of underdense regions and the environmental dependence of clustering from Gaussian initial conditions
journal, June 2007
 Abbas, U.; Sheth, R. K.
 Monthly Notices of the Royal Astronomical Society, Vol. 378, Issue 2
The statistics of peaks of Gaussian random fields
journal, May 1986
 Bardeen, J. M.; Bond, J. R.; Kaiser, N.
 The Astrophysical Journal, Vol. 304
Dark Energy Constraints from Weak‐Lensing Cross‐Correlation Cosmography
journal, January 2004
 Bernstein, G.; Jain, B.
 The Astrophysical Journal, Vol. 600, Issue 1
Halo stochasticity in global clustering analysis
journal, July 2009
 Bonoli, S.; Pen, U. L.
 Monthly Notices of the Royal Astronomical Society, Vol. 396, Issue 3
Biased clustering in the cold dark matter cosmogony
journal, April 1989
 Cole, S.; Kaiser, N.
 Monthly Notices of the Royal Astronomical Society, Vol. 237, Issue 4
The evolution of largescale structure in a universe dominated by cold dark matter
journal, May 1985
 Davis, M.; Efstathiou, G.; Frenk, C. S.
 The Astrophysical Journal, Vol. 292
Stochastic Nonlinear Galaxy Biasing
journal, July 1999
 Dekel, Avishai; Lahav, Ofer
 The Astrophysical Journal, Vol. 520, Issue 1
A New Method For Galaxy Cluster Detection. I. The Algorithm
journal, October 2000
 Gladders, Michael D.; Yee, H. K. C.
 The Astronomical Journal, Vol. 120, Issue 4
Minimizing the stochasticity of halos in largescale structure surveys
journal, August 2010
 Hamaus, Nico; Seljak, Uroš; Desjacques, Vincent
 Physical Review D, Vol. 82, Issue 4
MaxBCG: A Red‐Sequence Galaxy Cluster Finder
journal, May 2007
 Koester, Benjamin P.; McKay, Timothy A.; Annis, James
 The Astrophysical Journal, Vol. 660, Issue 1
Largescale bias and the inaccuracy of the peakbackground split: Largescale bias
journal, December 2009
 Manera, M.; Sheth, Ravi K.; Scoccimarro, R.
 Monthly Notices of the Royal Astronomical Society, Vol. 402, Issue 1
An analytic model for the spatial clustering of dark matter haloes
journal, September 1996
 Mo, H. J.; White, S. D. M.
 Monthly Notices of the Royal Astronomical Society, Vol. 282, Issue 2
Inductively Coupled Plasma Sources and Applications
journal, January 2010
 Okumura, Tomohiro
 Physics Research International, Vol. 2010
Combined Effects of Galaxy Interactions and LargeScale Environment on Galaxy Properties
journal, February 2009
 Park, Changbom; Choi, YunYoung
 The Astrophysical Journal, Vol. 691, Issue 2
Gravitational Potential Environment of Galaxies. i. Simulation
journal, April 2010
 Park, Hyunbae; Kim, Juhan; Park, Changbom
 The Astrophysical Journal, Vol. 714, Issue 1
Beating lensing cosmic variance with galaxy tomography
journal, June 2004
 Pen, UeLi
 Monthly Notices of the Royal Astronomical Society, Vol. 350, Issue 4
Fourier analysis of luminositydependent galaxy clustering
journal, January 2004
 Percival, W. J.; Verde, L.; Peacock, J. A.
 Monthly Notices of the Royal Astronomical Society, Vol. 347, Issue 2
Transients from initial conditions: a perturbative analysis
journal, October 1998
 Scoccimarro, R.
 Monthly Notices of the Royal Astronomical Society, Vol. 299, Issue 4
How Many Galaxies Fit in a Halo? Constraints on Galaxy Formation Efficiency from Spatial Clustering
journal, January 2001
 Scoccimarro, Roman; Sheth, Ravi K.; Hui, Lam
 The Astrophysical Journal, Vol. 546, Issue 1
Largescale bias and stochasticity of haloes and dark matter
journal, November 2004
 Seljak, Uroš; Warren, Michael S.
 Monthly Notices of the Royal Astronomical Society, Vol. 355, Issue 1
A LineofSight Integration Approach to Cosmic Microwave Background Anisotropies
journal, October 1996
 Seljak, Uros; Zaldarriaga, Matias
 The Astrophysical Journal, Vol. 469
How to Suppress the Shot Noise in Galaxy Surveys
journal, August 2009
 Seljak, Uroš; Hamaus, Nico; Desjacques, Vincent
 Physical Review Letters, Vol. 103, Issue 9
The halomodel description of marked statistics
journal, December 2005
 Sheth, R. K.
 Monthly Notices of the Royal Astronomical Society, Vol. 364, Issue 3
Peculiar velocities of galaxies and clusters
journal, April 2001
 Sheth, Ravi K.; Diaferio, Antonaldo
 Monthly Notices of the Royal Astronomical Society, Vol. 322, Issue 4
Substructure and the halo model of largescale structure
journal, October 2003
 Sheth, Ravi K.; Jain, Bhuvnesh
 Monthly Notices of the Royal Astronomical Society, Vol. 345, Issue 2
Biasing and the distribution of dark matter haloes
journal, April 1999
 Sheth, R. K.; Lemson, G.
 Monthly Notices of the Royal Astronomical Society, Vol. 304, Issue 4
Largescale bias and the peak background split
journal, September 1999
 Sheth, Ravi K.; Tormen, Giuseppe
 Monthly Notices of the Royal Astronomical Society, Vol. 308, Issue 1
An excursion set model of hierarchical clustering: ellipsoidal collapse and the moving barrier
journal, January 2002
 Sheth, Ravi K.; Tormen, Giuseppe
 Monthly Notices of the Royal Astronomical Society, Vol. 329, Issue 1
Scale dependence of halo and galaxy bias: Effects in real space
journal, March 2007
 Smith, Robert E.; Scoccimarro, Román; Sheth, Ravi K.
 Physical Review D, Vol. 75, Issue 6
The cosmological simulation code gadget2
journal, December 2005
 Springel, Volker
 Monthly Notices of the Royal Astronomical Society, Vol. 364, Issue 4
Simulations of the formation, evolution and clustering of galaxies and quasars
journal, June 2005
 Springel, Volker; White, Simon D. M.; Jenkins, Adrian
 Nature, Vol. 435, Issue 7042
Karhunen‐Loeve Eigenvalue Problems in Cosmology: How Should We Tackle Large Data Sets?
journal, May 1997
 Tegmark, Max; Taylor, Andy N.; Heavens, Alan F.
 The Astrophysical Journal, Vol. 480, Issue 1
The Luminosity and Color Dependence of the Galaxy Correlation Function
journal, September 2005
 Zehavi, Idit; Zheng, Zheng; Weinberg, David H.
 The Astrophysical Journal, Vol. 630, Issue 1
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