The VIMOS Public Extragalactic Redshift Survey (VIPERS): Hierarchical scaling and biasing

A. Cappi, F. Marulli, J. Bel, O. Cucciati, E. Branchini, S. De La Torre, L. Moscardini, M. Bolzonella, L. Guzzo, U. Abbas, C. Adami, S. Arnouts, D. Bottini, J. Coupon, I. Davidzon, G. De Lucia, A. Fritz, P. Franzetti, M. Fumana, B. GarilliB. R. Granett, O. Ilbert, A. Iovino, J. Krywult, V. Le Brun, O. Le Fèvre, D. MacCagni, K. Małek, H. J. McCracken, L. Paioro, M. Polletta, A. Pollo, M. Scodeggio, L. A M Tasca, R. Tojeiro, D. Vergani, A. Zanichelli, A. Burden, C. Di Porto, A. Marchetti, C. Marinoni, Y. Mellier, R. C. Nichol, J. A. Peacock, W. J. Percival, S. Phleps, C. Schimd, H. Schlagenhaufer, M. Wolk, G. Zamorani

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Aims. Building on the two-point correlation function analyses of the VIMOS Public Extragalactic Redshift Survey (VIPERS), we investigate the higher-order correlation properties of the same galaxy samples to test the hierarchical scaling hypothesis at z ∼ 1 and the dependence on galaxy luminosity, stellar mass, and redshift. With this work we also aim to assess possible deviations from the linearity of galaxy bias independently from a previously performed analysis of our survey. Methods. We have measured the count probability distribution function in spherical cells of varying radii (3 ≤ R ≤ 10h <sup>-1</sup> Mpc), deriving σ <inf>8g</inf> (the galaxy rms at 8 h <sup>-1</sup> Mpc), the volume-averaged two-, three-, and four-point correlation functions and the normalized skewness S<inf>3g</inf> and kurtosis S<inf>4g</inf> for different volume-limited subsamples, covering the following ranges: -19.5 ≤ MB(z = 1.1) - 5log(h) ≤ -21.0 in absolute magnitude, 9.0 ≤ log(M<inf>∗</inf>/M<inf>⊙</inf>h<sup>-2</sup>) ≤ 11.0 in stellar mass, and 0.5 ≤ z ≤ 1.1 in redshift. Results. We have performed the first measurement of high-order correlation functions at z ∼ 1 in a spectroscopic redshift survey. Our main results are the following. 1) The hierarchical scaling between the volume-averaged two- and three-point and two- and four-point correlation functions holds throughout the whole range of scale and redshift we could test. 2) We do not find a significant dependence of S <inf>3g</inf> on luminosity (below z = 0.9 the value of S<inf>3g</inf> decreases with luminosity, but only at 1σ-level). 3) We do not detect a significant dependence of S<inf>3g</inf> and S<inf>4g</inf> on scale, except beyond z ∼ 0.9, where S<inf>3g</inf> and S4<inf>g</inf> have higher values on large scales (R 10 h <sup>-1</sup> Mpc): this increase is mainly due to one of the two CFHTLS Wide Fields observed by VIPERS and can be explained as a consequence of sample variance, consistently with our analysis of mock catalogs. 4) We do not detect a significant evolution of S <inf>3g</inf> and S4<inf>g</inf> with redshift (apart from the increase of their values with scale in the last redshift bin). 5) σ <inf>8g</inf> increases with luminosity, but does not show significant evolution with redshift. As a consequence, the linear bias factor b = σ <inf>8g</inf>/σ <inf>8m</inf>, where σ<inf>8m</inf> is the rms of matter at a scale of 8 h <sup>-1</sup> Mpc, increases with redshift, in agreement with the independent analysis of VIPERS and of other surveys such as the VIMOS-VLT Deep Survey (VVDS). We measure the lowest bias b = 1.47 ± 0.18 for galaxies with M<inf>B</inf>(z = 1.1) - 5 log(h) ≤ -19.5 in the first redshift bin (0.5 ≤ z ≤ 0.7) and the highest bias b = 2.12 ± 0.28 for galaxies with MB(z = 1.1) - 5 log(h) ≤ -21.0 in the last redshift bin (0.9 ≤ z ≤ 1.1).6) We quantify deviations from the linear bias by means of the Taylor expansion parameter b<inf>2</inf>. We obtain b<inf>2</inf> = -0.20 ± 0.49 for 0.5 ≤ z 0.7 and b<inf>2</inf> = -0.24 ± 0.35 for 0.7 ≤ z ≤ 0.9, while for the redshift range 0.9 ≤ z < 1.1 we find b<inf>2</inf> = +0.78 ± 0.82. These results are compatible with a null non-linear bias term, but taking into account another analysis for VIPERS and the analysis of other surveys, we argue that there is evidence for a small but non-zero non-linear bias term.

Original languageEnglish
Article numberA70
JournalAstronomy & Astrophysics
Publication statusPublished - 1 Jul 2015


  • Cosmology: observations
  • Dark matter
  • Galaxies: statistics
  • Large-scale structure of Universe


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