3.6 Galaxy Properties and Biasing

The large number of galaxies available in the nearby dense surveys has made it possible to examine in greater detail the clustering properties of galaxies of different types. Such studies may contribute to our understanding of the relation between galaxies and LSS and help constrain galaxy biasing models. Recent works based on the SSRS2 (Benoist et al. 1996 Willmer et al. 1998) have shown evidence of strong, scale-independent luminosity bias, with more luminous galaxies showing a much stronger correlation than sub-L_* galaxies. This result is in marked contrast with the findings based on the Stromlo-APM survey (Loveday et al. 1995). The scale-independence suggests that this bias may be established at the time of galaxy formation. While several models of galaxy formation predict some degree of luminosity bias (Mo & White 1996), none can reproduce the observed dependence on the luminosity. An interesting spin-off of this analysis has been to find that very bright galaxies (L 3L_*) show a large correlation length (~ 15 h^-1 Mpc), comparable to that observed for clusters (Cappi et al. 1998). Interestingly, these galaxies are not found preferentially in prominent association of galaxies such as clusters or even loose groups. One possible interpretation is that these galaxies may be associated with more massive dark halos forming systems with atypically large M / L, which would naturally account for their large correlation length.

Using the SSRS2, one also finds that the relative bias between early and late types is scale-dependent (Figure 4), varying from about 1.4 on small scales to 1 at ~ 8 h^-1 Mpc, which may suggest that environmental effects may play a role. The mean relative bias is found to be b_E / b_L ~ 1.2. This small value, when compared to previous surveys (e.g., Guzzo et al. 1997), probably reflects the paucity of rich clusters in the surveyed region. Both early and late types separately show a luminosity-dependent bias similar to the sample as a whole further suggesting that the luminosity bias is primordial in nature while the excess clustering of early types relative to spirals on small scales may be caused by environmental effects. The relative bias between red and blue galaxies is similar to that observed between early and late type galaxies. However, it levels off on smaller scales ~ 4 h^-1 Mpc at a constant value of about 1.2. The mean relative bias of galaxies selected by colors is greater than when selected by morphologies. It is important to emphasize that although galaxy morphology and color are related, the scatter is large. This means that these properties may be considered as independent characteristics with colors reflecting the star formation history of galaxies. These results are in qualitative agreement with theoretical predictions of Kauffmann et al. (1997). Finally, one finds that the relative bias between optical and IRAS galaxies also varies with scale at least out to ~ 10 h^-1 Mpc and shows a strong luminosity dependence. The mean relative bias between optical and IRAS is b_o / b_I ~ 1.5 in real space.

Figure 5. The measured skewness S3 of different volume-limited sub-samples (full squares) compared to the expected skewness in the linear bias scenario (open squares). Two estimates of the errors are displayed. For sake of clarity, they are slightly shifted in magnitude. The left error bars are estimated from mock volume-limited samples extracted from a standard CDM simulation having the same geometry of the SSRS2, and the right error bars are estimated from the bootstrap method (for details see Benoist et al. 1998).

Additional information on the nature of bias can be extracted by investigating the higher order moments of the galaxy distribution. This type of investigation has been conducted using the the two-dimensional APM catalog (Gaztñaga & Frieman 1994) and in three-dimensions by Bouchet et al. (1993) using the 1.2 Jy IRAS Catalog. More recently, Benoist et al. (1998) have carried out similar analysis by comparing the measured skewness in volume-limited catalogs extracted from the SSRS2. Using the large number of galaxies they measured S₃ for different volume-limited samples finding S₃ scale- and luminosity-independent. As shown in Figure 5, the weak dependence of S₃ on luminosity is in marked contrast to what would be expected from the strong dependence of the two-point correlation function on luminosity in the framework of a linear biasing model. This result seems to argue in favor of some degree of non-linear bias.

The information derived from studies of clustering as a function of the internal properties of galaxies such as luminosity, color. morphology and internal dynamics, are essential for understanding the connection between galaxy formation and LSS. The present results are merely a preview of what will be possible with the data from a complete redshift survey of a multicolor sample of galaxies as envisioned by SDSS nearby and the ongoing work at high-redshift.