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A&A 439, 887-900 (2005)
DOI: 10.1051/0004-6361:20041964

The VIMOS VLT deep survey

Computing the two point correlation statistics and associated uncertainties

A. Pollo¹, B. Meneux², L. Guzzo¹, O. Le Fèvre², J. Blaizot², A. Cappi³, A. Iovino⁴, C. Marinoni², H. J. McCracken^{5, 6}, D. Bottini⁷, B. Garilli⁷, V. Le Brun², D. Maccagni⁷, J. P. Picat⁸, R. Scaramella⁹, M. Scodeggio⁷, L. Tresse², G. Vettolani¹⁰, A. Zanichelli¹⁰, C. Adami², M. Arnaboldi¹¹, S. Arnouts², S. Bardelli³, M. Bolzonella³, S. Charlot^{5, 12}, P. Ciliegi¹⁰, T. Contini⁸, S. Foucaud⁷, P. Franzetti⁷, I. Gavignaud⁸, O. Ilbert², B. Marano¹³, G. Mathez⁸, A. Mazure², R. Merighi³, S. Paltani², R. Pellò⁸, L. Pozzetti³, M. Radovich¹¹, G. Zamorani³, E. Zucca³, M. Bondi¹⁰, A. Bongiorno³, G. Busarello¹¹, L. Gregorini¹⁰, F. Lamareille⁸, Y. Mellier^{5, 6}, P. Merluzzi¹¹, V. Ripepi¹¹ and D. Rizzo<sup>8

1</sup>  INAF - Osservatorio Astronomico di Brera, via Bianchi 46, Merate (LC), Italy
    e-mail: apollo@merate.mi.astro.it
²  Laboratoire d'Astrophysique de Marseille, UMR 6110 CNRS, Université de Provence, Traverse du Siphon-Les trois Lucs, 13012 Marseille, France
³  INAF - Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italy
⁴  INAF - Osservatorio Astronomico di Brera, via Brera, 20121 Milan, Italy
⁵  Institut d'Astrophysique de Paris, UMR 7095, 98bis Bd. Arago, 75014 Paris, France
⁶  Observatoire de Paris, LERMA, UMR 8112, 61 Av. de l'Observatoire, 75014 Paris, France
⁷  IASF - INAF, 20133 Milano, Italy
⁸  Laboratoire d'Astrophysique - Observatoire Midi-Pyrénées, 31400 Toulouse, France
⁹  INAF - Osservatorio Astronomico di Roma, Italy
¹⁰  INAF - Istituto di Radio-Astronomia, Bologna, Italy
¹¹  INAF - Osservatorio Astronomico di Capodimonte, via Moiariello 16, 80131 Napoli, Italy
¹²  Max-Planck-Institut für Astrophysik, 85741 Garching, Germany
¹³  Università di Bologna, Departimento di Astronomia, via Ranzani 1, 40127 Bologna, Italy

(Received 6 September 2004 / Accepted 10 March 2005 )

Abstract
We present a detailed description of the methods used to compute the three-dimensional two-point galaxy correlation function in the VIMOS-VLT deep survey (VVDS). We investigate how instrumental selection effects and observational biases affect the measurements and identify the methods to correct for them. We quantify the accuracy of our corrections using an ensemble of 50 mock galaxy surveys generated with the GalICS semi-analytic model of galaxy formation which incorporate the selection biases and tiling strategy of the real data. We demonstrate that we are able to recover the real-space two-point correlation function and the projected correlation function to an accuracy better than 10% on scales larger than 1 h^-1 Mpc with the sampling strategy used for the first epoch VVDS data. The large number of simulated surveys allows us to provide a reliable estimate of the cosmic variance on the measurements of the correlation length r₀ at , of about 15-20% for the first epoch VVDS observation while any residual systematic effect in the measurements of r₀ is always below . The error estimation and measurement techniques outlined in this paper are being used in several parallel studies which investigate in detail the clustering properties of galaxies in the VVDS.

Key words: cosmology: large scale structure of Universe -- methods: statistical -- galaxies: evolution -- surveys

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