The VLT LBG Redshift Survey - I. Clustering and dynamics of ≈ 1000 galaxies at z ≈ 3

We present the initial imaging and spectroscopic data acquired as part of the Very Large Telescope (VLT) VIMOS Lyman-break galaxy Survey. UBR (or UBVI) imaging covers five approximate to 36 x 36 arcmin(2) fields centred on bright z > 3 quasi-stellar objects (QSOs), allowing approximate to 21 000 2 < z < 3.5 galaxy candidates to be selected using the Lyman-break technique. We performed spectroscopic follow-up using VLT VIMOS, measuring redshifts for 1020 z > 2 Lyman-break galaxies and 10 z > 2 QSOs from a total of 19 VIMOS pointings. From the galaxy spectra, we observe a 625 +/- 510 km s(-1) velocity offset between the interstellar absorption and Lyman a emission-line redshifts, consistent with previous results. Using the photometric and spectroscopic catalogues, we have analysed the galaxy clustering at z approximate to 3. The angular correlation function, w(theta), is well fitted by a double power law with clustering scalelength, r(0) = 3.19(-0.54)(+0.32) h(-1) Mpc and slope gamma = 2.45 for r < 1 h(-1) Mpc and r(0) = 4.37(-0.55)(+0.43) h(-1) Mpc with gamma = 1.61 +/- 0.15 at larger scales. Using the redshift sample we estimate the semiprojected correlation function, w(p)(sigma), and, for a gamma = 1.8 power law, find r(0) = 3.67(-0.24)(+0.23) h(-1) Mpc for the VLT sample and r(0) = 3.98(-0.15)(+0.14) h(-1) Mpc for a combined VLT+Keck sample. From xi (s) and xi(sigma, pi), and assuming the above xi(r) models, we find that the combined VLT and Keck surveys require a galaxy pairwise velocity dispersion of approximate to 700 km s(-1), higher than approximate to 400 km s(-1) assumed by previous authors. We also measure a value for the gravitational growth rate parameter of beta(z = 3) = 0.48 +/- 0.17, again higher than that previously found and implying a low value for the bias of b = 2.06(-0.5)(+1.1). This value is consistent with the galaxy clustering amplitude which gives b = 2.22 +/- 0.16, assuming the standard cosmology, implying that the evolution of the gravitational growth rate is also consistent with Einstein gravity. Finally, we have compared our Lyman-break galaxy clustering amplitudes with lower redshift measurements and find that the clustering strength is not inconsistent with that of low-redshift L* spirals for simple 'long-lived' galaxy models.