The 2dF Galaxy Redshift Survey: the nature of the relative bias between galaxies of different spectral type

We present an analysis of the relative bias between early‐ and late‐type galaxies in the Two‐degree Field Galaxy Redshift Survey (2dFGRS) – as defined by the η parameter of Madgwick et al., which quantifies the spectral type of galaxies in the survey. We calculate counts in cells for flux‐limited samples of early‐ and late‐type galaxies, using approximately cubical cells with sides ranging from 7 to 42 h −1 Mpc . We measure the variance of the counts in cells using the method of Efstathiou et al., which we find requires a correction for a finite volume effect equivalent to the integral constraint bias of the autocorrelation function. Using a maximum‐likelihood technique we fit lognormal models to the one‐point density distribution, and develop methods of dealing with biases in the recovered variances resulting from this technique. We then examine the joint density distribution function, f (δ E , δ L ) , and directly fit deterministic bias models to the joint counts in cells. We measure a linear relative bias of ≈1.3, which does not vary significantly with ℓ. A deterministic linear bias model is, however, a poor approximation to the data, especially on small scales (ℓ≤ 28  h −1 Mpc) where deterministic linear bias is excluded at high significance. A power‐law bias model with index b 1 ≈ 0.75 is a significantly better fit to the data on all scales, although linear bias becomes consistent with the data for ℓ≳ 40  h −1 Mpc .