We combine the measurements of luminosity dependence of bias with the luminosity dependent weak lensing analysis of dark matter around galaxies to derive the galaxy bias and constrain amplitude of mass fluctuations. We take advantage of theoretical and simulation predictions that predict that, while halo bias is rapidly increasing with mass for high masses, it is nearly constant in low mass halos. We use a new weak lensing analysis around the same Sloan Digital Sky Survey (SDSS) galaxies to determine their halo mass probability distribution. We use these halo mass probability distributions to predict the bias for each luminosity subsample. Galaxies below $L_{*}$ are antibiased with $b<1$ and for these galaxies bias is only weakly dependent on luminosity. In contrast, for galaxies above $L_{*}$ bias is rapidly increasing with luminosity. These observations are in an excellent agreement with theoretical predictions based on weak lensing halo mass determination combined with halo bias-mass relations. We find that for standard cosmological parameters theoretical predictions are able to explain the observed luminosity dependence of bias over six magnitudes in absolute luminosity. We combine the bias constraints with those from the Wilkinson Microwave Anisotropy Probe (WMAP) and the SDSS power spectrum analysis to derive new constraints on bias and ${\sigma }_8$. For the most general parameter space that includes running and neutrino mass, we find ${\sigma }_8=0.88\pm 0.06$ and $b_{*}=0.99\pm 0.07$. In the context of spatially flat models we improve the limit on the neutrino mass for the case of three degenerate families from $m_{\nu }<0.6\mathrm{e}\mathrm{V}$ without bias to $m_{\nu }<0.18\mathrm{e}\mathrm{V}$ with bias (95% C.L.), which is weakened to $m_{\nu }<0.24\mathrm{e}\mathrm{V}$ if running is allowed. The corresponding limit for $3\mathrm{\text{massless}}+1\mathrm{\text{massive}}$ neutrino is 1.37 eV.

• Received 25 June 2004

DOI:https://doi.org/10.1103/PhysRevD.71.043511