Clustering segregation with ultraviolet luminosity in Lyman break galaxiesat z similar to 3 and its implications

We report on the clustering properties of Lyman break galaxies (LBGs) at z similar to 3. The correlation length of flux-limited samples of LBGs depend s on their rest-frame ultraviolet (UV) luminosity at lambda similar to 1700 Angstrom, with fainter galaxies being less strongly clustered in space. We have used three samples with progressively fainter flux limits : two extra cted from our ground-based survey and one from the Hubble Deep Fields (both North and South). The correlation length decreases by a factor of approxim ate to 3 over the range of limiting magnitudes that we have probed, namely, 25 less than or similar to R less than or similar to 27, suggesting that s amples with a fainter UV luminosity limit include galaxies with smaller mas s. We have compared the observed scaling properties of the clustering stren gth with those predicted for cold dark matter (CDM) halos and found that (1 ) the clustering strength of LBGs follows, within the errors, the same scal ing law with the volume density as the halos; and (2) the scaling law predi cted for the galaxies using the halo mass spectrum and a number of models f or the relationship that maps the halos' mass into the galaxies' UV luminos ity depends only on how tightly mass and UV luminosity correlate but is oth erwise insensitive to the details of the models. We interpret these results as additional evidence that the strong spatial clustering of LBGs is due t o galaxy biasing, supporting the theory of biased galaxy formation and grav itational instability as the primary physical mechanism for the formation o f structure. We have also fitted models of the mass-UV luminosity relations hip to the data to reproduce simultaneously from the CDM halo mass spectrum the dependence of the correlation length with the UV luminosity and the lu minosity function. We have found that (1) a scale invariant relationship be tween mass and UV luminosity (e.g., a power law) is not supported by the ob servations, suggesting that the properties of star formation of galaxies ch ange along the mass spectrum of the observed LBGs; (2) the scatter of the U V luminosity of LBGs of given mass must be relatively small for massive LBG s, suggesting that the mass is an important parameter in regulating the act ivity of star formation in these systems; and (3) the fraction of massive h alos at z similar to 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 Omega = 0.3 and Omega (Lambda) = 0.7, the average mass of galaxies with luminosity R = 23, 25.5, and 27.0 is [M] = 2.5, 0.9, and 0.4 x 10(12) M ., respectively. The numbers are appr oximate to 2 times larger and approximate to 10 times smaller in an open un iverse with Omega = 0.2 and Omega (Lambda) = 0 and in the Einstein-de Sitte r cosmologies, respectively.