The Canada-France deep fields survey-II: Lyman-break galaxies and galaxy clustering at z~3

(abridged) We present a large sample of z~3 U- band dropout galaxies extracted from the Canada-France deep fields survey (CFDF). Our catalogue covers an effective area of ~1700 arcmin^2 divided between three large, contiguous fields separated widely on the sky. To IAB=24.5, the survey contains 1294 Lyman-break candidates, in agreement with previous measurements by other authors. Based on comparisons with spectroscopic observations and simulations, we estimate that our sample of Lyman-break galaxies is contaminated by stars and interlopers at no more than ~30%. We find that \omega(\theta) is well fitted by a power-law of fixed slope, \gamma=1.8, even at small (\theta<10'') angular separations. In two of our three fields, we are able to fit simultaneously for both the slope and amplitude and find a slope \gamma ~ 1.81. Our data marginally indicates in one field (at a 3 \sigma level) that the Lyman-break correlation length r_0 depends on sample limiting magnitude: brighter Lyman-break galaxies are more clustered than fainter ones. For the entire CFDF sample, assuming a fixed slope \gamma = 1.8 we find r_0 = (5.9\pm0.5)h^{-1} Mpc. Using these clustering measurements and prediction for the dark matter density field, we derive a linear bias of b = 3.5 +/- 0.3. Finally we show that the dependence of the correlation length with the surface density of Lyman-break galaxies is in good agreement with a simple picture where more luminous galaxies are hosted by more massive dark matter halos with a simple one-to-one correspondence.