Clustering Segregation with Ultraviolet Luminosity in Lyman Break Galaxies at z~3 and Its Implications

We report on the clustering properties of Lyman break galaxies (LBGs) at z ~ 3. The correlation length of flux-limited samples of LBGs depends on their rest-frame ultraviolet (UV) luminosity at λ ~ 1700 Å, with fainter galaxies being less strongly clustered in space. We have used three samples with progressively fainter flux limits: two extracted from our ground-based survey and one from the Hubble Deep Fields (both North and South). The correlation length decreases by a factor of ≈3 over the range of limiting magnitudes that we have probed, namely, 25 ≲ ℛ ≲ 27, suggesting that samples with a fainter UV luminosity limit include galaxies with smaller mass. We have compared the observed scaling properties of the clustering strength with those predicted for cold dark matter (CDM) halos and found that (1) the clustering strength of LBGs follows, within the errors, the same scaling law with the volume density as the halos; and (2) the scaling law predicted for the galaxies using the halo mass spectrum and a number of models for the relationship that maps the halos' mass into the galaxies' UV luminosity depends only on how tightly mass and UV luminosity correlate but is otherwise insensitive to the details of the models. We interpret these results as additional evidence that the strong spatial clustering of LBGs is due to galaxy biasing, supporting the theory of biased galaxy formation and gravitational instability as the primary physical mechanism for the formation of structure. We have also fitted models of the mass-UV luminosity relationship to the data to reproduce simultaneously from the CDM halo mass spectrum the dependence of the correlation length with the UV luminosity and the luminosity function. We have found that (1) a scale invariant relationship between mass and UV luminosity (e.g., a power law) is not supported by the observations, suggesting that the properties of star formation of galaxies change along the mass spectrum of the observed LBGs; (2) the scatter of the UV luminosity of LBGs of given mass must be relatively small for massive LBGs, suggesting that the mass is an important parameter in regulating the activity of star formation in these systems; and (3) the fraction of massive halos at z ~ 3 that are not observed in UV-selected surveys is not large. From the fits, for a given choice of the cosmology, one can assign a scale of mass to the LBGs. For example, if Ω = 0.3 and ΩΛ = 0.7, the average mass of galaxies with luminosity ℛ = 23, 25.5, and 27.0 is = 2.5, 0.9, and 0.4 × 1012 M☉, respectively. The numbers are ≈2 times larger and ≈10 times smaller in an open universe with Ω = 0.2 and ΩΛ = 0 and in the Einstein-de Sitter cosmologies, respectively.