Reconstructing the velocity field beyond the local universe

  • R. JohnstonEmail author
  • D. Bacon
  • L. F. A. Teodoro
  • R. C. Nichol
  • M. S. Warren
  • C. Cress
Editor's Choice (Research Article)


We present a maximum probability approach to reconstructing spatial maps of the peculiar velocity field at redshifts \(z\sim 0.1\), where the velocities have been measured from distance indicators (DI) such as \(D_n-\sigma \) relations or Tully–Fisher. With the large statistical uncertainties associated with DIs, our reconstruction method aims to recover the underlying true peculiar velocity field by reducing these errors with the use of two physically motivated filtering prior terms. The first constructs an estimate of the velocity field derived from the galaxy over-density \(\delta _g\) and the second makes use of the matter linear density power spectrum \(P_k\). Using \(N\)-body simulations we find, with an SDSS-like sample (\(N_{gal}\simeq 33\) per deg\(^2\) ), an average correlation coefficient value of \(r=0.55\pm {0.02}\) between our reconstructed velocity field and that of the true velocity field from the simulation. However, with a suitably high number density of galaxies from the next generation surveys (e.g. \(N_{gal}\simeq 140\) per deg\(^2\)) we can achieve an average \(r=0.70\pm {0.02}\) out to moderate redshifts \(z\sim 0.1\). This will prove useful for future tests of gravity, as these relatively deep maps are complementary to weak lensing maps at the same redshift. LA-UR 12-24505.


Methods: data analysis, numerical, statistical Galaxies: distances and redshifts Cosmology: large-scale structure of universe 



We would like to extend special thanks to Enzo Branchini and Adi Nusser for stimulating discussions, their comments and reading several drafts of this paper. We also would like to thank Martin Hendry, Mat Smith, Andreas Faltenbacher, Roy Maartens, Daniele Bertacca, Rafal Szepietowski, Yong-Seon Song, Kazuya Koyama, Prina Patel, Emma Beynon, Robert Crittenden and Philip Marshall for useful discussions. RJ acknowledges the support of the SKA-South Africa and the National Research Foundation (NRF), as well as the hospitality of the Institute of Cosmology and Gravitation (ICG) at the University of Portsmouth where some of this work was carried out. DB and RN are supported by the UK Science and Technology Facilities Council (Grant Nos. ST/H002774/1 and ST/K0090X/1). The analysis was performed with the SCIAMA High Performance Computing cluster supported by the ICG, at the University of Portsmouth. We would like to thank the SCIAMA cluster administrator, Gary Burton, for all his help. Please contact the authors to request access to research materials discussed in this paper.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • R. Johnston
    • 1
    Email author
  • D. Bacon
    • 2
  • L. F. A. Teodoro
    • 3
  • R. C. Nichol
    • 2
  • M. S. Warren
    • 4
  • C. Cress
    • 5
  1. 1.Department of PhysicsUniversity of Western CapeCape TownSouth Africa
  2. 2.Institute of Cosmology and GravitationUniversity of PortsmouthPortsmouthUK
  3. 3.BAER Institute, Space Science and Astrobiology DivisionNASA Ames Research CenterMoffett FieldUSA
  4. 4.Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA
  5. 5.Centre for High Performance ComputingCape TownSouth Africa

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