The three-dimensional power spectrum of dark and luminous matter from the VIRMOS-DESCART cosmic shear survey

We present the first optimal power spectrum estimation and three-dimensional deprojections for the dark and luminous matter and their cross-correlations. The results are obtained using a new optimal fast estimator, deprojected using minimum variance and Singular Value Decomposition (SVD) techniques. We show the resulting 3D power spectra for dark matter and galaxies, and their covariance for the VIRMOS-DESCART weak lensing shear and galaxy data. The survey is most sensitive to non-linear scales k(NL) similar to 1 h Mpc(-1). On these scales, our 3D power spectrum of dark matter is in good agreement with the RCS 3D power spectrum found by Tegmark & Zaldarriaga. Our galaxy power is similar to that found by the 2MASS survey, and larger than that of SDSS, APM and RCS, consistent with the expected difference in galaxy population. We find an average bias b = 1.24 +/- 0.18 for the I-selected galaxies, and a cross-correlation coefficient r = 0.75 +/- 0.23. Together with the power spectra, these results optimally encode the entire two point information about dark matter and galaxies, including galaxy-galaxy lensing. We address some of the implications regarding galaxy haloes and mass-to-light ratios. The best-fitting 'halo' parameter h = r/b = 0.57 +/- 0.16, suggesting that dynamical masses estimated using galaxies systematically underestimate total mass. Ongoing surveys, such as the Canada-France-Hawaii Telescope Legacy Survey, will significantly improve on the dynamic range, and future photometric redshift catalogues will allow tomography along the same principles.