The VIMOS Public Extragalactic Redshift Survey (VIPERS). Hierarchical scaling and biasing
Abstract
Aims: Building on the twopoint correlation function analyses of the VIMOS Public Extragalactic Redshift Survey (VIPERS), we investigate the higherorder 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 ≤ 10 h^{1} Mpc), deriving σ_{8g} (the galaxy rms at 8 h^{1} Mpc), the volumeaveraged two, three, and fourpoint correlation functions and the normalized skewness S_{3g} and kurtosis S_{4g} for different volumelimited subsamples, covering the following ranges: 19.5 ≤ M_{B}(z = 1.1)  5log (h) ≤ 21.0 in absolute magnitude, 9.0 ≤ log (M_{∗}/M_{☉}h^{2}) ≤ 11.0 in stellar mass, and 0.5 ≤ z< 1.1 in redshift.
Results: We have performed the first measurement of highorder correlation functions at z ~ 1 in a spectroscopic redshift survey. Our main results are the following. 1) The hierarchical scaling between the volumeaveraged two and threepoint and two and fourpoint correlation functions holds throughout the whole range of scale and redshift we could test. 2) We do not find a significant dependence of S_{3g} on luminosity (below z = 0.9 the value of S_{3g} decreases with luminosity, but only at 1σlevel). 3) We do not detect a significant dependence of S_{3g} and S_{4g} on scale, except beyond z ~ 0.9, where S_{3g} and S_{4g} have higher values on large scales (R ≥ 10 h^{1} 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_{3g} and S_{4g} with redshift (apart from the increase of their values with scale in the last redshift bin). 5) σ_{8g} increases with luminosity, but does not show significant evolution with redshift. As a consequence, the linear bias factor b = σ_{8g}/σ_{8m}, where σ_{8m} is the rms of matter at a scale of 8 h^{1} Mpc, increases with redshift, in agreement with the independent analysis of VIPERS and of other surveys such as the VIMOSVLT Deep Survey (VVDS). We measure the lowest bias b = 1.47 ± 0.18 for galaxies with M_{B}(z = 1.1)  5log (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 M_{B}(z = 1.1)  5log (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_{2}. We obtain b_{2} = 0.20 ± 0.49 for 0.5 ≤ z< 0.7 and b_{2} = 0.24 ± 0.35 for 0.7 ≤ z< 0.9, while for the redshift range 0.9 ≤ z< 1.1 we find b_{2} = + 0.78 ± 0.82. These results are compatible with a null nonlinear 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 nonzero nonlinear bias term.
Based on observations collected at the European Southern Observatory, Cerro Paranal, Chile, using the Very Large Telescope under programs 182.A0886 and partly 070.A9007. Also based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the CanadaFranceHawaii Telescope (CFHT), which is operated by the National Research Council (NRC) of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. This work is based in part on data products produced at TERAPIX and the Canadian Astronomy Data Centre as part of the CanadaFranceHawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS. The VIPERS web site is http://www.vipers.inaf.it
 Publication:

Astronomy and Astrophysics
 Pub Date:
 July 2015
 DOI:
 10.1051/00046361/201525727
 arXiv:
 arXiv:1505.05347
 Bibcode:
 2015A&A...579A..70C
 Keywords:

 largescale structure of Universe;
 cosmology: observations;
 dark matter;
 galaxies: statistics;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 20 pages, 14 figures, accepted for publication in Astronomy and Astrophysics