Relative bias parameters from angular correlations of optical and Iras galaxies

We compare the galaxy distributions in the optical catalogs UGC and ESO with those in the IRAS sample by calculating the auto- and cross-angular correlation functions. We find that each angular correlation function is well approximated by the form w(θ) = Aθ^1-γ out to an angular distance of 5°, with γ ≈ 1.7. The corresponding three-dimensional correlation lengths are r₀(OO) ≈ 6, r₀(11) ≈ 4 and r₀(IO) ≈ 4h^-1 Mpc. The discrepancy in the correlation lengths of optical and IRAS galaxies may be interpreted as being due to different degree of biasing relative to the total matter distribution. The bias parameter b is defined as the ratio of the galaxy to matter density contrasts. The above correlation lengths yield somewhat inconsistent estimates of the optical to IRAS biasing ratios: b_O/b_I = 1.0, 1.4, or 2.0. However, a combined analysis of the data yields b_O/b_I ≈ 1.7, in good agreement with the ratio deduced from dynamical tests.