Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

The quasi-linear nearby Universe

Abstract

The local Universe provides a unique opportunity for testing cosmology and theories of structure formation. As the velocities of galaxies respond to the distribution of matter—both visible and dark—the velocity field provides structural information. Here, we present an original method for the reconstruction of the quasi-linear matter density and velocity fields from galaxy peculiar velocities and apply it to the Cosmicflows-2 database of velocites. The method consists of constructing an ensemble of cosmological simulations, constrained by the standard cosmological model and the observational data. The quasi-linear density field is the geometric mean and variance of the fully nonlinear density fields of the simulations. The main nearby clusters (Virgo, Centaurus and Coma), superclusters (Shapley and Perseus–Pisces) and voids (Dipole Repeller) are robustly reconstructed. Galaxies are born ‘biased‘ with respect to the underlying dark matter distribution. Using our quasi-linear framework, we demonstrate that the luminosity-weighted density field derived from the 2M++ redshift compilations is nonlinearly biased with respect to the matter density field. The bias diminishes in the linear regime.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Three-dimensional visualization of the density field by means of isosurfaces.
Fig. 2: Contour maps of the QL density field and its statistical uncertainty.
Fig. 3: Comparison of the QL, 2M++ raw and the 2M++ bias-free density fields.
Fig. 4: Comparison and probability distribution functions of the raw and bias-free 2M++ and QL density fields.
Fig. 5: Bias power index α plotted against the Gaussian smoothing length, Rs.
Fig. 6: Local Group-centric spherical mean densities as a function of depth.
Fig. 7: Virgocentric density and velocity profiles.

References

  1. Dekel, A., Bertschinger, E. & Faber, S. M. Potential, velocity, and density fields from sparse and noisy redshift-distance samples—method. Astrophys. J. 364, 349–369 (1990).

    ADS  Article  Google Scholar 

  2. Zaroubi, S., Hoffman, Y., Fisher, K. B. & Lahav, O. Wiener reconstruction of the large-scale structure. Astrophys. J. 449, 446 (1995).

    ADS  Article  Google Scholar 

  3. Hoffman, Y. & Ribak, E. Constrained realizations of Gaussian fields—a simple algorithm. Astrophys. J. Lett. 380, L5–L8 (1991).

    ADS  Article  Google Scholar 

  4. Ganon, G. & Hoffman, Y. Constrained realizations of Gaussian fields—reconstruction of the large-scale structure. Astrophys. J. Lett. 415, L5–L8 (1993).

    ADS  Article  Google Scholar 

  5. Zaroubi, S., Hoffman, Y. & Dekel, A. Wiener reconstruction of large-scale structure from peculiar velocities. Astrophys. J. 520, 413–425 (1999).

    ADS  Article  Google Scholar 

  6. Tully, R. B., Courtois, H., Hoffman, Y. & Pomarède, D. The Laniakea supercluster of galaxies. Nature 513, 71–73 (2014).

    ADS  Article  Google Scholar 

  7. Libeskind, N. I. et al. Planes of satellite galaxies and the cosmic web. Mon. Not. R. Astron. Soc. 452, 1052–1059 (2015).

    ADS  Article  Google Scholar 

  8. Lavaux, G. Bayesian 3D velocity field reconstruction with VIRBIUS. Mon. Not. R. Astron. Soc. 457, 172–197 (2016).

    ADS  Article  Google Scholar 

  9. Hoffman, Y., Pomarède, D., Tully, R. B. & Courtois, H. M. The dipole repeller. Nat. Astron. 1, 0036 (2017).

    ADS  Article  Google Scholar 

  10. Strauss, M. A. & Davis, M. in Large-Scale Motions in the Universe 255–274 (Princeton Univ. Press, Princeton, NJ, 1988).

  11. Nusser, A., Dekel, A., Bertschinger, E. & Blumenthal, G. R. Cosmological velocity–density relation in the quasi-linear regime. Astrophys. J. 379, 6–18 (1991).

    ADS  Article  Google Scholar 

  12. Lahav, O., Fisher, K. B., Hoffman, Y., Scharf, C. A. & Zaroubi, S. Wiener reconstruction of all-sky galaxy surveys in spherical harmonics. Astrophys. J. Lett. 423, L93 (1994).

    ADS  Article  Google Scholar 

  13. Dekel, A. et al. IRAS galaxies versus POTENT mass—density fields, biasing, and Omega. Astrophys. J. 412, 1–21 (1993).

    ADS  Article  Google Scholar 

  14. Fisher, K. B., Lahav, O., Hoffman, Y., Lynden-Bell, D. & Zaroubi, S. Wiener reconstruction of density, velocity and potential fields from all-sky galaxy redshift surveys. Mon. Not. R. Astron. Soc. 272, 885–908 (1995).

    ADS  Google Scholar 

  15. Strauss, M. A. & Willick, J. A. The density and peculiar velocity fields of nearby galaxies. Phys. Rep. 261, 271–431 (1995).

    ADS  Article  Google Scholar 

  16. Kolatt, T., Dekel, A., Ganon, G. & Willick, J. A. Simulating our cosmological neighborhood: mock catalogs for velocity analysis. Astrophys. J. 458, 419 (1996).

    ADS  Article  Google Scholar 

  17. Bistolas, V. & Hoffman, Y. Nonlinear constrained realizations of the large-scale structure. Astrophys. J. 492, 439–451 (1998).

    ADS  Article  Google Scholar 

  18. Mathis, H. et al. Simulating the formation of the local galaxy population. Mon. Not. R. Astron. Soc. 333, 739–762 (2002).

    ADS  Article  Google Scholar 

  19. Wang, H., Mo, H. J., Yang, X., Jing, Y. P. & Lin, W. P. ELUCID—Exploring the Local Universe with the reConstructed Initial Density field. I. Hamiltonian Markov chain Monte Carlo method with particle mesh dynamics. Astrophys. J. 794, 94 (2014).

    ADS  Article  Google Scholar 

  20. Van de Weygaert, R. & Hoffman, Y. In Cosmic Flows 1999: Towards an Understanding of Large-Scale Structures (eds Courteau, S. & Willick, J.) 169 (Conference Series Volume 201, Astronomical Society of the Pacific, 2000).

  21. Sorce, J. G., Gottlöber, S., Hoffman, Y. & Yepes, G. How did the Virgo cluster form? Mon. Not. R. Astron. Soc. 460, 2015–2024 (2016).

    ADS  Article  Google Scholar 

  22. Sorce, J. G. et al. Cosmicflows constrained Local UniversE Simulations. Mon. Not. R. Astron. Soc. 455, 2078–2090 (2016).

    ADS  Article  Google Scholar 

  23. Gottlöber, S., Hoffman, Y. & Yepes, G. in High Performance Computing in Science and Engineering (eds Wagner, S., Steinmetz, M., Bode, A. & Müller, M. M.) 309–323 (Springer, Berlin, 2010).

  24. Gottlöber, S., Hoffman, Y. & Yepes, G. Constrained Local UniversE Simulations (CLUES). Preprint at https://arxiv.org/abs/1005.2687 (2010).

  25. Hoffman, Y. in Data Analysis in Cosmology Vol. 665 (eds Martnez, V. J., Saar, E., Martnez-González, E. & Pons-Bordera, M.-J.) 565–583 (Springer, Berlin, 2009).

  26. Hoffman, Y., Martinez-Vaquero, L. A., Yepes, G. & Gottlöber, S. The local Hubble flow: is it a manifestation of dark energy? Mon. Not. R. Astron. Soc. 386, 390–396 (2008).

    ADS  Article  Google Scholar 

  27. Klypin, A., Hoffman, Y., Kravtsov, A. V. & Gottlöber, S. Constrained simulations of the real universe: the local supercluster. Astrophys. J. 596, 19–33 (2003).

    ADS  Article  Google Scholar 

  28. Kravtsov, A. V., Klypin, A. & Hoffman, Y. Constrained simulations of the real universe. II. Observational signatures of intergalactic gas in the local supercluster region. Astrophys. J. 571, 563–575 (2002).

    ADS  Article  Google Scholar 

  29. Kitaura, F.-S. et al. Cosmic structure and dynamics of the local Universe. Mon. Not. R. Astron. Soc. 427, L35–L39 (2012).

    ADS  Google Scholar 

  30. Lavaux, G. & Jasche, J. Unmasking the masked Universe: the 2M++ catalogue through Bayesian eyes. Mon. Not. R. Astron. Soc. 455, 3169–3179 (2016).

    ADS  Article  Google Scholar 

  31. Desmond, H., Ferreira, P. G., Lavaux, G. & Jasche, J. Reconstructing the gravitational field of the local Universe. Mon. Not. R. Astron. Soc. 474, 3152–3161 (2018).

    ADS  Article  Google Scholar 

  32. Tully, R. B. et al. Cosmicflows-2: the data. Astron. J. 146, 86 (2013).

    ADS  Article  Google Scholar 

  33. Peebles, P. J. E. The Large-Scale Structure of the Universe (Princeton Univ. Press, Princeton, NJ, 1980).

  34. Weinberg, S. Cosmology (Oxford Univ. Press, Oxford, 2008).

  35. Pomarède, D., Tully, R. B., Hoffman, Y. & Courtois, H. M. The Arrowhead mini-supercluster of galaxies. Astrophys. J. 812, 17 (2015).

    ADS  Article  Google Scholar 

  36. Yepes, G., Gottlöber, S. & Hoffman, Y. Dark matter in the local Universe. New Astron. Rev. 58, 1–18 (2014).

    ADS  Article  Google Scholar 

  37. Sorce, J. G., Courtois, H. M., Gottlöber, S., Hoffman, Y. & Tully, R. B. Simulations of the local Universe constrained by observational peculiar velocities. Mon. Not. R. Astron. Soc. 437, 3586–3595 (2014).

    ADS  Article  Google Scholar 

  38. Doumler, T., Hoffman, Y., Courtois, H. & Gottlöber, S. Reconstructing cosmological initial conditions from galaxy peculiar velocities—I. Reverse Zeldovich approximation. Mon. Not. R. Astron. Soc. 430, 888–901 (2013).

    ADS  Article  Google Scholar 

  39. Doumler, T., Gottlöber, S., Hoffman, Y. & Courtois, H. Reconstructing cosmological initial conditions from galaxy peculiar velocities—III. Constrained simulations. Mon. Not. R. Astron. Soc. 430, 912–923 (2013).

    ADS  Article  Google Scholar 

  40. Doumler, T., Courtois, H., Gottlöber, S. & Hoffman, Y. Reconstructing cosmological initial conditions from galaxy peculiar velocities—II. The effect of observational errors. Mon. Not. R. Astron. Soc. 430, 902–911 (2013).

    ADS  Article  Google Scholar 

  41. Bardeen, J. M., Bond, J. R., Kaiser, N. & Szalay, A. S. The statistics of peaks of Gaussian random fields. Astrophys. J. 304, 15–61 (1986).

    ADS  Article  Google Scholar 

  42. Dekel, A. & Rees, M. J. Physical mechanisms for biased galaxy formation. Nature 326, 455–462 (1987).

    ADS  Article  Google Scholar 

  43. Branchini, E., Davis, M. & Nusser, A. The linear velocity field of 2MASS Redshift Survey, K s = 11.75 galaxies: constraints on β and bulk flow from the luminosity function. Mon. Not. R. Astron. Soc. 424, 472–481 (2012).

    ADS  Article  Google Scholar 

  44. Simon, P. & Hilbert, S. Scale dependence of galaxy biasing investigated by weak gravitational lensing: an assessment using semi-analytic galaxies and simulated lensing data. Preprint at https://arxiv.org/abs/1711.02677 (2017).

  45. Desjacques, V., Jeong, D. & Schmidt, F. Large-scale galaxy bias. Phys. Rep. 733, 1–193 (2018).

    ADS  MathSciNet  Article  Google Scholar 

  46. Zaroubi, S., Branchini, E., Hoffman, Y. & da Costa, L. N. Consistent β values from density–density and velocity–velocity comparisons. Mon. Not. R. Astron. Soc. 336, 1234–1246 (2002).

    ADS  Article  Google Scholar 

  47. Davis, M. et al. Local gravity versus local velocity: solutions for β and non-linear bias. Mon. Not. R. Astron. Soc. 413, 2906–2922 (2011).

    ADS  Article  Google Scholar 

  48. Carrick, J., Turnbull, S. J., Lavaux, G. & Hudson, M. J. Cosmological parameters from the comparison of peculiar velocities with predictions from the 2M++ density field. Mon. Not. R. Astron. Soc. 450, 317–332 (2015).

    ADS  Article  Google Scholar 

  49. Nusser, A. Velocity–density correlations from the Cosmicflows-3 distance catalogue and the 2MASS Redshift Survey. Mon. Not. R. Astron. Soc. 470, 445–454 (2017).

    ADS  Article  Google Scholar 

  50. Lavaux, G. & Hudson, M. J. The 2M++ galaxy redshift catalogue. Mon. Not. R. Astron. Soc. 416, 2840–2856 (2011).

    ADS  Article  Google Scholar 

  51. Pomarède, D., Courtois, H. M., Hoffman, Y. & Tully, R. B. Cosmography and data visualization. Publ. Astron. Soc. Pac. 129, 058002 (2017).

    ADS  Article  Google Scholar 

  52. Huchra, J. P. et al. The 2MASS Redshift Survey—description and data release. Astrophys. J. Suppl. Ser. 199, 26 (2012).

    ADS  Article  Google Scholar 

  53. Abazajian, K. N. et al. The seventh data release of the Sloan Digital Sky Survey. Astrophys. J. Supple. Ser. 182, 543–558 (2009).

    ADS  Article  Google Scholar 

  54. Jones, D. H. et al. The 6dF Galaxy Survey: final redshift release (DR3) and southern large-scale structures. Mon. Not. R. Astron. Soc. 399, 683–698 (2009).

    ADS  Article  Google Scholar 

  55. Pahwa, I. et al. The alignment of galaxy spin with the shear field in observations. Mon. Not. R. Astron. Soc. 457, 695–703 (2016).

    ADS  Article  Google Scholar 

  56. Wang, H. et al. ELUCID IV: Galaxy quenching and its relation to halo mass, environment, and assembly bias. Preprint at https://arxiv.org/abs/1707.09002 (2017).

  57. Shaya, E. J., Tully, R. B., Hoffman, Y. & Pomarède, D. Action dynamics of the local supercluster. Astrophys. J. 850, 207 (2017).

    ADS  Article  Google Scholar 

  58. Tully, R. B., Courtois, H. M. & Sorce, J. G. Cosmicflows-3. Astron. J. 152, 50 (2016).

    ADS  Article  Google Scholar 

  59. Teerikorpi, P., Bottinelli, L., Gouguenheim, L. & Paturel, G. Investigations of the local supercluster velocity field. I—observations close to Virgo, using Tully–Fisher distances and the Tolman–Bondi expanding sphere. Astron. Astrophys. 260, 17–32 (1992).

    ADS  Google Scholar 

  60. Peirani, S. & de Freitas Pacheco, J. A. Mass determination of groups of galaxies: effects of the cosmological constant. New Astron. 11, 325–330 (2006).

    ADS  Article  Google Scholar 

  61. Karachentsev, I. D., Tully, R. B., Wu, P.-F., Shaya, E. J. & Dolphin, A. E. Infall of nearby galaxies into the Virgo Cluster as traced with Hubble Space Telescope. Astrophys. J. 782, 4 (2014).

    ADS  Article  Google Scholar 

  62. Wang, H. et al. ELUCID IV: Galaxy quenching and its relation to halo mass, environment, and assembly bias. Preprint at https://arxiv.org/abs/1707.09002v1 (2017).

  63. Planck Collaboration et al. Planck 2013 results. XVI. Cosmological parameters. Astron. Astrophys. 571, A16 (2014).

    Article  Google Scholar 

  64. Hoffman, Y., Nusser, A., Courtois, H. M. & Tully, R. B. Goodness-of-fit analysis of the Cosmicflows-2 data base of velocities. Mon. Not. R. Astron. Soc. 461, 4176–4181 (2016).

    ADS  Article  Google Scholar 

  65. Freedman, W. L. Cosmology at a crossroads. Nat. Astron. 1, 0121 (2017).

    ADS  Article  Google Scholar 

  66. Springel, V. The cosmological simulation code GADGET-2. Mon. Not. R. Astron. Soc. 364, 1105–1134 (2005).

    ADS  Article  Google Scholar 

  67. Coles, P. & Jones, B. A lognormal model for the cosmological mass distribution. Mon. Not. R. Astron. Soc. 248, 1–13 (1991).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

The help provided by G. Lavaux in using the 2M++ density field is highly appreciated. A. Nusser is gratefully acknowledged for careful reading of the paper and critical remarks. Support has been provided by the Israel Science Foundation (1013/12), Institut Universitaire de France, US National Science Foundation, Space Telescope Science Institute (observations with Hubble Space Telescope), Jet Propulsion Lab (observations with the Spitzer Space Telescope) and NASA (analysis of data from the Wide-field Infrared Survey Explorer). J.G.S. acknowledges support from the Astronomy ESFRI and Research Infrastructure Cluster ASTERICS project, funded by the European Commission under the Horizon 2020 Programme (GA 653477), as well as from the l′Oréal-UNESCO Pour les Femmes et la Science and Centre National d′Études Spatiales postdoctoral fellowship programmes. G.Y. thanks MINECO/FEDER (Spain) for financial support under project grant AYA2015-63810-P. We thank the Red Española de Supercomputación for granting us computing time using the MareNostrum Supercomputer at the BSC-CNS where the simulations used for this paper were performed.

Author information

Authors and Affiliations

Authors

Contributions

Y.H. and S.G. analysed the simulations. Y.H., D.P. and R.B.T. analysed the cosmography. Y.H. and D.P. prepared the figures. E.C. ran numerical simulations. D.P. produced the online visualization. R.B.T and H.M.C. prepared the CF2 data. Y.H. wrote the manuscript, with contributions from all co-authors.

Corresponding author

Correspondence to Yehuda Hoffman.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Table 1 and Supplementary Figures 1–4 with links to a video and Sketchfab visualization

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hoffman, Y., Carlesi, E., Pomarède, D. et al. The quasi-linear nearby Universe. Nat Astron 2, 680–687 (2018). https://doi.org/10.1038/s41550-018-0502-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41550-018-0502-4

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing