Testing the lognormality of the galaxy and weak lensing convergence distributions from Dark Energy Survey maps

L. Clerkin; D. Kirk; M. Manera; O. Lahav; F. Abdalla; A. Amara; D. Bacon; C. Chang; E. Gaztañaga; A. Hawken; B. Jain; B. Joachimi; V. Vikram; T. Abbott; S. Allam; R. Armstrong; A. Benoit-Lévy; G. M. Bernstein; R. A. Bernstein; E. Bertin; D. Brooks; D. L. Burke; A. Carnero Rosell; M. Carrasco Kind; M. Crocce; C. E. Cunha; C. B. D'Andrea; L. N. da Costa; S. Desai; H. T. Diehl; J. P. Dietrich; T. F. Eifler; A. E. Evrard; B. Flaugher; P. Fosalba; J. Frieman; D. W. Gerdes; D. Gruen; R. A. Gruendl; G. Gutierrez; K. Honscheid; D. J. James; S. Kent; K. Kuehn; N. Kuropatkin; M. Lima; P. Melchior; R. Miquel; B. Nord; A. A. Plazas; A. K. Romer; A. Roodman; E. Sanchez; M. Schubnell; I. Sevilla-Noarbe; R. C. Smith; M. Soares-Santos; F. Sobreira; E. Suchyta; M. E.C. Swanson; G. Tarle; A. R. Walker

doi:10.1093/mnras/stw2106

Testing the lognormality of the galaxy and weak lensing convergence distributions from Dark Energy Survey maps

L. Clerkin, D. Kirk, M. Manera, O. Lahav, F. Abdalla, A. Amara, D. Bacon, C. Chang, E. Gaztañaga, A. Hawken, B. Jain, B. Joachimi, V. Vikram, T. Abbott, S. Allam, R. Armstrong, A. Benoit-Lévy, G. M. Bernstein, R. A. Bernstein, E. BertinD. Brooks, D. L. Burke, A. Carnero Rosell, M. Carrasco Kind, M. Crocce, C. E. Cunha, C. B. D'Andrea, L. N. da Costa, S. Desai, H. T. Diehl, J. P. Dietrich, T. F. Eifler, A. E. Evrard, B. Flaugher, P. Fosalba, J. Frieman, D. W. Gerdes, D. Gruen, R. A. Gruendl, G. Gutierrez, K. Honscheid, D. J. James, S. Kent, K. Kuehn, N. Kuropatkin, M. Lima, P. Melchior, R. Miquel, B. Nord, A. A. Plazas, A. K. Romer, A. Roodman, E. Sanchez, M. Schubnell, I. Sevilla-Noarbe, R. C. Smith, M. Soares-Santos, F. Sobreira, E. Suchyta, M. E.C. Swanson, G. Tarle, A. R. Walker

Research output: Contribution to journal › Article › peer-review

54 Scopus citations

Abstract

It is well known that the probability distribution function (PDF) of galaxy density contrast is approximately lognormal; whether the PDF of mass fluctuations derived from weak lensing convergence (κ_WL) is lognormal is less well established. We derive PDFs of the galaxy and projected matter density distributions via the counts-in-cells (CiC) method. We use maps of galaxies and weak lensing convergence produced from the Dark Energy Survey Science Verification data over 139 deg². We test whether the underlying density contrast is well described by a lognormal distribution for the galaxies, the convergence and their joint PDF. We confirm that the galaxy density contrast distribution is well modelled by a lognormal PDF convolved with Poisson noise at angular scales from 10 to 40 arcmin (corresponding to physical scales of 3-10 Mpc). We note that as κ_WL is a weighted sum of the mass fluctuations along the line of sight, its PDF is expected to be only approximately lognormal. We find that the κ_WL distribution is well modelled by a lognormal PDF convolved with Gaussian shape noise at scales between 10 and 20 arcmin, with a best-fitting χ²/dof of 1.11 compared to 1.84 for a Gaussian model, corresponding to p-values 0.35 and 0.07, respectively, at a scale of 10 arcmin. Above 20 arcmin a simple Gaussian model is sufficient. The joint PDF is also reasonably fitted by a bivariate lognormal. As a consistency check, we compare the variances derived from the lognormal modelling with those directly measured via CiC. Our methods are validated against maps from the MICE Grand Challenge N-body simulation.

Original language	English
Pages (from-to)	1444-1461
Number of pages	18
Journal	Monthly Notices of the Royal Astronomical Society
Volume	466
Issue number	2
DOIs	https://doi.org/10.1093/mnras/stw2106
State	Published - Apr 1 2017
Externally published	Yes

Funding

The MICE simulations have been developed at the MareNos-trum supercomputer (BSC-CNS) thanks to grants AECT-2006-2-0011 through AECT-2015-1-0013. Data products have been stored at the Port d’Informació Científica (PIC), and distributed through the CosmoHub webportal (cosmohub.pic.es). Funding for this project was partially provided by the Spanish Minis-terio de Ciencia e Innovacion (MICINN), projects 200850I176, AYA2009-13936, AYA2012-39620, AYA2013-44327, ESP2013-48274, ESP2014-58384, Consolider-Ingenio CSD2007-00060, research project 2009-SGR-1398 from Generalitat de Catalunya, and the Ramon y Cajal MICINN programme. This paper has gone through internal review by the DES collaboration. LC thanks the Perren Fund for a studentship. OL, DK and MM acknowledge support from a European Research Council Advanced Grant FP7/291329. Funding for the DES Projects has been provided by the US Department of Energy, the US National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundac¸ão Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desen-volvimento Científico e Tecnológico and the Ministério da Ciência, Tecnologia e Inovac¸ão, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey. We would like to thank Ludovic Van Waerbeke for extremely useful exchanges on the formalism for the calculation of the convergence second moment. We thank the anonymous referee for suggesting that the skewness of the convergence PDF can be used to estimate the amplitude of fluctuations, ?8, as presented in Section 6.1. The MICE simulations have been developed at the MareNostrum supercomputer (BSC-CNS) thanks to grants AECT-2006-2-0011 through AECT-2015-1-0013. Data products have been stored at the Port d'Informaci? Cient?fica (PIC), and distributed through the CosmoHub webportal (cosmohub.pic.es). Funding for this project was partially provided by the Spanish Ministerio de Ciencia e Innovacion (MICINN), projects 200850I176, AYA2009-13936, AYA2012-39620, AYA2013-44327, ESP2013-48274, ESP2014-58384, Consolider-Ingenio CSD2007-00060, research project 2009-SGR-1398 from Generalitat de Catalunya, and the Ramon y Cajal MICINN programme. We are grateful for the extraordinary contributions of our CTIO colleagues and the DECam Construction, Commissioning and Science Verification teams in achieving the excellent instrument and telescope conditions that have made this work possible. The success of this project also relies critically on the expertise and dedication of the DES Data Management group. Funding for the DES Projects has been provided by the US Department of Energy, the US National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Funda??o Carlos Chagas Filho de Amparo ? Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico and the Minist?rio da Ci?ncia, Tecnologia e Inova??o, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energ?ticas, Medioambientales y Tecnol?gicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgen?ssische Technische Hochschule (ETH) Z?rich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ci?ncies de l'Espai (IEEC/CSIC), the Institut de F?sica d'Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universit?t M?nchen and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, the Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, Texas A&M University and the OzDES Membership Consortium. The DES data management system is supported by the National Science Foundation under Grant Number AST-1138766. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2012-39559, ESP2013-48274, FPA2013-47986, and Centro de Excelencia Severo Ochoa SEV-2012-0234. Research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) including ERC grant agreements 240672, 291329 and 306478. This paper has gone through internal review by the DES collaboration. LC thanks the Perren Fund for a studentship. OL, DK and MM acknowledge support from a European Research Council Advanced Grant FP7/291329. The DES data management system is supported by the National Science Foundation under Grant Number AST-1138766. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2012-39559, ESP2013-48274, FPA2013-47986, and Centro de Excelencia Severo Ochoa SEV-2012-0234. Research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) including ERC grant agreements 240672, 291329 and 306478.

Funders	Funder number
Centro de Excelencia Severo Ochoa	SEV-2012-0234
Collaborating Institutions are Argonne National Laboratory
Collaborating Institutions in the Dark Energy Survey
Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico
FP7/2007
Institut de Ci?ncies de l'Espai
Institut de F?sica d'Altes Energies
Kavli Institute of Cosmological Physics at the University of Chicago
Ludwig-Maximilians Universit?t M?nchen
Minist?rio da Ci?ncia
Ministry of Science and Education of Spain
Ministério da Ciência
Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University
National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign
Perren Fund
Science and Technology Facilities Council of the United Kingdom
Spanish Minis-terio de Ciencia e Innovacion
Spanish Ministerio de Ciencia e Innovacion
US Department of Energy
US National Science Foundation
National Science Foundation	AST-1138766
U.S. Department of Energy
University of Illinois at Urbana-Champaign
Stanford University
Lawrence Berkeley National Laboratory
University of California, Santa Cruz
University of Pennsylvania
Ohio State University
University of Chicago
University of Michigan
Texas A and M University
University of Portsmouth
National Centre for Supercomputing Applications
Seventh Framework Programme	1138766, 240672, 306478, 291329
SLAC National Accelerator Laboratory
Higher Education Funding Council for England
Center for Cosmology and Astroparticle Physics, Ohio State University
Science and Technology Facilities Council
University College London
European Research Council	FP7/291329
University of Nottingham
University of Sussex
University of Edinburgh
Deutsche Forschungsgemeinschaft
Generalitat de Catalunya
EidgenÃ¶ssische Technische Hochschule ZÃ¼rich
Ministerio de Economía y Competitividad	FPA2013-47986, AYA2012-39559, ESP2013-48274
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro
Financiadora de Estudos e Projetos
Ministerio de Ciencia e Innovación	200850I176, 2009-SGR-1398, AYA2012-39620, CSD2007-00060, AYA2009-13936, AYA2013-44327, ESP2014-58384
Seventh Framework Programme
Universidade do Estado do Rio de Janeiro
Ministry of Education and Science of Ukraine

Keywords

Cosmology: observations
Gravitational lensing: weak
Large-scale structure of Universe

Access to Document

10.1093/mnras/stw2106

Cite this

Clerkin, L., Kirk, D., Manera, M., Lahav, O., Abdalla, F., Amara, A., Bacon, D., Chang, C., Gaztañaga, E., Hawken, A., Jain, B., Joachimi, B., Vikram, V., Abbott, T., Allam, S., Armstrong, R., Benoit-Lévy, A., Bernstein, G. M., Bernstein, R. A., ... Walker, A. R. (2017). Testing the lognormality of the galaxy and weak lensing convergence distributions from Dark Energy Survey maps. Monthly Notices of the Royal Astronomical Society, 466(2), 1444-1461. https://doi.org/10.1093/mnras/stw2106

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title = "Testing the lognormality of the galaxy and weak lensing convergence distributions from Dark Energy Survey maps",

abstract = "It is well known that the probability distribution function (PDF) of galaxy density contrast is approximately lognormal; whether the PDF of mass fluctuations derived from weak lensing convergence (κWL) is lognormal is less well established. We derive PDFs of the galaxy and projected matter density distributions via the counts-in-cells (CiC) method. We use maps of galaxies and weak lensing convergence produced from the Dark Energy Survey Science Verification data over 139 deg2. We test whether the underlying density contrast is well described by a lognormal distribution for the galaxies, the convergence and their joint PDF. We confirm that the galaxy density contrast distribution is well modelled by a lognormal PDF convolved with Poisson noise at angular scales from 10 to 40 arcmin (corresponding to physical scales of 3-10 Mpc). We note that as κWL is a weighted sum of the mass fluctuations along the line of sight, its PDF is expected to be only approximately lognormal. We find that the κWL distribution is well modelled by a lognormal PDF convolved with Gaussian shape noise at scales between 10 and 20 arcmin, with a best-fitting χ2/dof of 1.11 compared to 1.84 for a Gaussian model, corresponding to p-values 0.35 and 0.07, respectively, at a scale of 10 arcmin. Above 20 arcmin a simple Gaussian model is sufficient. The joint PDF is also reasonably fitted by a bivariate lognormal. As a consistency check, we compare the variances derived from the lognormal modelling with those directly measured via CiC. Our methods are validated against maps from the MICE Grand Challenge N-body simulation.",

keywords = "Cosmology: observations, Gravitational lensing: weak, Large-scale structure of Universe",

author = "L. Clerkin and D. Kirk and M. Manera and O. Lahav and F. Abdalla and A. Amara and D. Bacon and C. Chang and E. Gazta{\~n}aga and A. Hawken and B. Jain and B. Joachimi and V. Vikram and T. Abbott and S. Allam and R. Armstrong and A. Benoit-L{\'e}vy and Bernstein, {G. M.} and Bernstein, {R. A.} and E. Bertin and D. Brooks and Burke, {D. L.} and {Carnero Rosell}, A. and {Carrasco Kind}, M. and M. Crocce and Cunha, {C. E.} and D'Andrea, {C. B.} and {da Costa}, {L. N.} and S. Desai and Diehl, {H. T.} and Dietrich, {J. P.} and Eifler, {T. F.} and Evrard, {A. E.} and B. Flaugher and P. Fosalba and J. Frieman and Gerdes, {D. W.} and D. Gruen and Gruendl, {R. A.} and G. Gutierrez and K. Honscheid and James, {D. J.} and S. Kent and K. Kuehn and N. Kuropatkin and M. Lima and P. Melchior and R. Miquel and B. Nord and Plazas, {A. A.} and Romer, {A. K.} and A. Roodman and E. Sanchez and M. Schubnell and I. Sevilla-Noarbe and Smith, {R. C.} and M. Soares-Santos and F. Sobreira and E. Suchyta and Swanson, {M. E.C.} and G. Tarle and Walker, {A. R.}",

note = "Publisher Copyright: {\textcopyright} 2016 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society",

year = "2017",

month = apr,

day = "1",

doi = "10.1093/mnras/stw2106",

language = "English",

volume = "466",

pages = "1444--1461",

journal = "Monthly Notices of the Royal Astronomical Society",

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Clerkin, L, Kirk, D, Manera, M, Lahav, O, Abdalla, F, Amara, A, Bacon, D, Chang, C, Gaztañaga, E, Hawken, A, Jain, B, Joachimi, B, Vikram, V, Abbott, T, Allam, S, Armstrong, R, Benoit-Lévy, A, Bernstein, GM, Bernstein, RA, Bertin, E, Brooks, D, Burke, DL, Carnero Rosell, A, Carrasco Kind, M, Crocce, M, Cunha, CE, D'Andrea, CB, da Costa, LN, Desai, S, Diehl, HT, Dietrich, JP, Eifler, TF, Evrard, AE, Flaugher, B, Fosalba, P, Frieman, J, Gerdes, DW, Gruen, D, Gruendl, RA, Gutierrez, G, Honscheid, K, James, DJ, Kent, S, Kuehn, K, Kuropatkin, N, Lima, M, Melchior, P, Miquel, R, Nord, B, Plazas, AA, Romer, AK, Roodman, A, Sanchez, E, Schubnell, M, Sevilla-Noarbe, I, Smith, RC, Soares-Santos, M, Sobreira, F, Suchyta, E, Swanson, MEC, Tarle, G & Walker, AR 2017, 'Testing the lognormality of the galaxy and weak lensing convergence distributions from Dark Energy Survey maps', Monthly Notices of the Royal Astronomical Society, vol. 466, no. 2, pp. 1444-1461. https://doi.org/10.1093/mnras/stw2106

TY - JOUR

T1 - Testing the lognormality of the galaxy and weak lensing convergence distributions from Dark Energy Survey maps

AU - Clerkin, L.

AU - Kirk, D.

AU - Manera, M.

AU - Lahav, O.

AU - Abdalla, F.

AU - Amara, A.

AU - Bacon, D.

AU - Chang, C.

AU - Gaztañaga, E.

AU - Hawken, A.

AU - Jain, B.

AU - Joachimi, B.

AU - Vikram, V.

AU - Abbott, T.

AU - Allam, S.

AU - Armstrong, R.

AU - Benoit-Lévy, A.

AU - Bernstein, G. M.

AU - Bernstein, R. A.

AU - Bertin, E.

AU - Brooks, D.

AU - Burke, D. L.

AU - Carnero Rosell, A.

AU - Carrasco Kind, M.

AU - Crocce, M.

AU - Cunha, C. E.

AU - D'Andrea, C. B.

AU - da Costa, L. N.

AU - Desai, S.

AU - Diehl, H. T.

AU - Dietrich, J. P.

AU - Eifler, T. F.

AU - Evrard, A. E.

AU - Flaugher, B.

AU - Fosalba, P.

AU - Frieman, J.

AU - Gerdes, D. W.

AU - Gruen, D.

AU - Gruendl, R. A.

AU - Gutierrez, G.

AU - Honscheid, K.

AU - James, D. J.

AU - Kent, S.

AU - Kuehn, K.

AU - Kuropatkin, N.

AU - Lima, M.

AU - Melchior, P.

AU - Miquel, R.

AU - Nord, B.

AU - Plazas, A. A.

AU - Romer, A. K.

AU - Roodman, A.

AU - Sanchez, E.

AU - Schubnell, M.

AU - Sevilla-Noarbe, I.

AU - Smith, R. C.

AU - Soares-Santos, M.

AU - Sobreira, F.

AU - Suchyta, E.

AU - Swanson, M. E.C.

AU - Tarle, G.

AU - Walker, A. R.

PY - 2017/4/1

Y1 - 2017/4/1

N2 - It is well known that the probability distribution function (PDF) of galaxy density contrast is approximately lognormal; whether the PDF of mass fluctuations derived from weak lensing convergence (κWL) is lognormal is less well established. We derive PDFs of the galaxy and projected matter density distributions via the counts-in-cells (CiC) method. We use maps of galaxies and weak lensing convergence produced from the Dark Energy Survey Science Verification data over 139 deg2. We test whether the underlying density contrast is well described by a lognormal distribution for the galaxies, the convergence and their joint PDF. We confirm that the galaxy density contrast distribution is well modelled by a lognormal PDF convolved with Poisson noise at angular scales from 10 to 40 arcmin (corresponding to physical scales of 3-10 Mpc). We note that as κWL is a weighted sum of the mass fluctuations along the line of sight, its PDF is expected to be only approximately lognormal. We find that the κWL distribution is well modelled by a lognormal PDF convolved with Gaussian shape noise at scales between 10 and 20 arcmin, with a best-fitting χ2/dof of 1.11 compared to 1.84 for a Gaussian model, corresponding to p-values 0.35 and 0.07, respectively, at a scale of 10 arcmin. Above 20 arcmin a simple Gaussian model is sufficient. The joint PDF is also reasonably fitted by a bivariate lognormal. As a consistency check, we compare the variances derived from the lognormal modelling with those directly measured via CiC. Our methods are validated against maps from the MICE Grand Challenge N-body simulation.

AB - It is well known that the probability distribution function (PDF) of galaxy density contrast is approximately lognormal; whether the PDF of mass fluctuations derived from weak lensing convergence (κWL) is lognormal is less well established. We derive PDFs of the galaxy and projected matter density distributions via the counts-in-cells (CiC) method. We use maps of galaxies and weak lensing convergence produced from the Dark Energy Survey Science Verification data over 139 deg2. We test whether the underlying density contrast is well described by a lognormal distribution for the galaxies, the convergence and their joint PDF. We confirm that the galaxy density contrast distribution is well modelled by a lognormal PDF convolved with Poisson noise at angular scales from 10 to 40 arcmin (corresponding to physical scales of 3-10 Mpc). We note that as κWL is a weighted sum of the mass fluctuations along the line of sight, its PDF is expected to be only approximately lognormal. We find that the κWL distribution is well modelled by a lognormal PDF convolved with Gaussian shape noise at scales between 10 and 20 arcmin, with a best-fitting χ2/dof of 1.11 compared to 1.84 for a Gaussian model, corresponding to p-values 0.35 and 0.07, respectively, at a scale of 10 arcmin. Above 20 arcmin a simple Gaussian model is sufficient. The joint PDF is also reasonably fitted by a bivariate lognormal. As a consistency check, we compare the variances derived from the lognormal modelling with those directly measured via CiC. Our methods are validated against maps from the MICE Grand Challenge N-body simulation.

KW - Cosmology: observations

KW - Gravitational lensing: weak

KW - Large-scale structure of Universe

UR - http://www.scopus.com/inward/record.url?scp=85018869339&partnerID=8YFLogxK

U2 - 10.1093/mnras/stw2106

DO - 10.1093/mnras/stw2106

M3 - Article

AN - SCOPUS:85018869339

SN - 0035-8711

VL - 466

SP - 1444

EP - 1461

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

IS - 2

ER -

Testing the lognormality of the galaxy and weak lensing convergence distributions from Dark Energy Survey maps

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