The VIMOS Public Extragalactic Redshift Survey (VIPERS)

Hierarchical scaling and biasing^⋆

¹ INAF–Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italy
e-mail: alberto.cappi@oabo.inaf.it
² Laboratoire Lagrange, UMR 7293, Université de Nice-Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, 06300 Nice, France
³ Dipartimento di Fisica e Astronomia – Alma Mater Studiorum Università di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴ INFN, Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy
⁵ Centre de Physique Théorique, UMR 6207 CNRS-Université de Provence, Case 907, 13288 Marseille, France
⁶ Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, via della Vasca Navale 84, 00146 Roma, Italy
⁷ INFN, Sezione di Roma Tre, via della Vasca Navale 84, 00146 Roma, Italy
⁸ INAF–Osservatorio Astronomico di Roma, via Frascati 33, 00040 Monte Porzio Catone ( RM), Italy
⁹ Aix-Marseille Université, CNRS, LAM (Laboratoire d’Astrophysique de Marseille) UMR 7326, 13388 Marseille, France
¹⁰ INAF–Osservatorio Astronomico di Brera, via Brera 28, 20122 Milano, via E. Bianchi 46, 23807 Merate, Italy
¹¹ Dipartimento di Fisica, Università di Milano-Bicocca, P.zza della Scienza 3, 20126 Milano, Italy
¹² INAF – Osservatorio Astronomico di Torino, 10025 Pino Torinese, Italy
¹³ Canada-France-Hawaii Telescope, 65–1238 Mamalahoa Highway, Kamuela, HI 96743, USA
¹⁴ INAF–Istituto di Astrofisica Spaziale e Fisica Cosmica Milano, via Bassini 15, 20133 Milano, Italy
¹⁵ Astronomical Observatory of the University of Geneva, Ch. d’Écogia 16, 1290 Versoix, Switzerland
¹⁶ INAF–Osservatorio Astronomico di Trieste, via G. B. Tiepolo 11, 34143 Trieste, Italy
¹⁷ Institute ofPhysics, Jan Kochanowski University, ul. Swietokrzyska 15, 25-406 Kielce, Poland
¹⁸ Department of Particle and Astrophysical Science, Nagoya University, Furo-cho, Chikusa-ku, 464-8602 Nagoya, Japan
¹⁹ National Centre for Nuclear Research, ul. Hoza 69, 00-681 Warszawa, Poland
²⁰ Institut d’Astrophysique de Paris, UMR 7095 CNRS, Université Pierre et Marie Curie, 98bis boulevard Arago, 75014 Paris, France
²¹ Astronomical Observatory of the Jagiellonian University, Orla 171, 30-001 Cracow, Poland
²² Institute of Cosmology and Gravitation, Dennis Sciama Building, University of Portsmouth, Burnaby Road, Portsmouth, PO1 3FX, UK
²³ INAF–Istituto di Astrofisica Spaziale e Fisica Cosmica Bologna, via Gobetti 101, 40129 Bologna, Italy
²⁴ INAF–Istituto di Radioastronomia, via Gobetti 101, 40129 Bologna, Italy
²⁵ Università degli Studi di Milano, via G. Celoria 16, 20130 Milano, Italy
²⁶ SUPA, Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
²⁷ Max-Planck-Institut für Extraterrestrische Physik, 84571 Garching b. München, Germany
²⁸ Universitätssternwarte München, Ludwig-Maximillians Universität, Scheinerstr. 1, 81679 München, Germany

Received: 23 January 2015
Accepted: 5 May 2015

Abstract

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 ≤ 10 h^-1 Mpc), deriving σ_8g (the galaxy rms at 8 h^-1 Mpc), the volume-averaged two-, three-, and four-point correlation functions and the normalized skewness S_3g and kurtosis S_4g for different volume-limited 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 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_3g on luminosity (below z = 0.9 the value of S_3g decreases with luminosity, but only at 1σ-level). 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 VIMOS-VLT 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 b₂. We obtain b₂ = −0.20 ± 0.49 for 0.5 ≤ z< 0.7 and b₂ = −0.24 ± 0.35 for 0.7 ≤ z< 0.9, while for the redshift range 0.9 ≤ z< 1.1 we find b₂ = + 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.