We use the overdensity field reconstructed in the volume of the COSMOS area to study the nonlinear biasing of the zCOSMOS galaxies. The galaxy overdensity field is reconstructed using the current sample of ~8500 accurate zCOSMOS redshifts at I(AB)<22.5 out to z~1 on scales R from 8 to 12 Mpc/h. By comparing the probability distribution function (PDF) of galaxy density contrast delta_g to the lognormal approximation of the PDF of the mass density contrast delta, we obtain the mean biasing function b(delta,z,R) between the galaxy and matter overdensity field and its second moments b(hat) and b(tilde) up to z~1. Over the redshift interval 0.4<z<1 the conditional mean function <delta_g|delta> = b(delta,z,R) delta is of the following characteristic shape. The function vanishes in the most underdense regions and then sharply rises in a nonlinear way towards the mean densities. <delta_g|delta> is almost a linear tracer of the matter in the overdense regions, up to the most overdense regions in which it is nonlinear again and the local effective slope of <delta_g|delta> vs. delta is smaller than unity. The <delta_g|delta> function is evolving only slightly over the redshift interval 0.4<z<1. The linear biasing parameter increases from b(hat)=1.24+/-0.11 at z=0.4 to b(hat)=1.64+/-0.15 at z=1 for the M_B<-20-z sample of galaxies. b(hat) does not show any dependence on the smoothing scale from 8 to 12 Mpc/h, but increases with luminosity. The measured nonlinearity parameter b(tilde)/b(hat) is of the order of a few percent (but it can be consistent with 0) and it does not change with redshift, the smoothing scale or the luminosity. By matching the linear bias of galaxies to the halo bias, we infer that the M_B<-20-z galaxies reside in dark matter haloes with a characteristic mass of about 3-6 x 10^12 Msol, depending on the halo bias fit.
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