Understanding redshift space distortions in density-weighted peculiar velocity

Naonori S. Sugiyama, Teppei Okumura, David N. Spergel

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


Observations of the kinetic Sunyaev-Zel'dovich (kSZ) effect measure the density-weighted velocity field, a potentially powerful cosmological probe. This paper presents an analytical method to predict the power spectrum and two-point correlation function of the density-weighted velocity in redshift space, the direct observables in kSZ surveys. We show a simple relation between the density power spectrum and the density-weighted velocity power spectrum that holds for both dark matter and halos. Using this relation, we can then extend familiar perturbation expansion techniques to the kSZ power spectrum. One of the most important features of density-weighted velocity statistics in redshift space is the change in sign of the cross-correlation between the density and density-weighted velocity at mildly small scales due to nonlinear redshift space distortions. Our model can explain this characteristic feature without any free parameters. As a result, our results can precisely predict the non-linear behavior of the density-weighted velocity field in redshift space up to ∼ 30 h-1 Mpc for dark matter particles at the redshifts of z=0.0, 0.5, and 1.0.

Original languageEnglish (US)
Article number001
JournalJournal of Cosmology and Astroparticle Physics
Issue number7
StatePublished - Jul 1 2016

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics


  • cosmological simulations
  • galaxy clusters
  • power spectrum
  • redshift surveys


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