7.6. Galaxy Clustering at High Redshift

Astronomers generally assume that the galaxy distribution traces the underlying matter distribution; comparisons of the large-scale distribution of galaxies at early cosmic epoch therefore is a potentially powerful means of discriminating cosmology and mechanisms of structure formation (e.g., White 1997). A simple constant of proportionality known as the "bias parameter," b, relating galaxy and mass fluctuations, is the conventional parametrization: _gal = b_mass. In principle, many physical mechanisms could lead to a relation of this form (e.g., Dekel & Rees 1987), although gravitational instability in a massive dark matter halo is currently popular as numerical simulations and semianalytic models of this "dark halo" model are consistent with observations (e.g., Baugh et al. 1998; Mo, Mao, & White 1999).

Sufficient numbers of galaxies at z 3 have now been reliably identified that observational measurements of their spatial distribution is now possible. Giavalisco et al. (1998) reports on the angular clustering of Lyman-break galaxies at z ~ 3. The slope of a power-law parametrization of the angular correlation function, w() = A_w^-, is ~ 0.9, similar to galaxy samples in the local and intermediate-redshift universe. Applying the Limber transform to w() yields the comoving spatial correlation length. Giavalisco et al. (1998) report r₀ = 4.2_-1.0^+0.9 h₅₀^-1 Mpc (q₀ = 0.5) at the median redshift of their Lyman-break survey, = 3.04. The value is similar to that of local spiral galaxies and approximately half that of local early-type galaxies; it is comparable or slightly larger than comoving spatial correlation lengths determined for intermediate-redshift galaxies. The strong clustering is broadly consistent with biased galaxy formation theories, suggesting that the Lyman-break systems are associated with massive dark matter halos.

Steidel et al. (1998) report a large structure of Lyman-break galaxies at z 3.09 in the SSA 22 field which they interpret in the context of cold dark matter cosmological models. Dark halo models of galaxy formation predict that galaxies of a given mass should form first in regions of the highest density and that these regions should be strongly clustered spatially. Adelberger et al. (1998) measure the bias parameter, b, for the Steidel et al. (1998) z 3.09 structure: considering 268 Lyman-break galaxies in six 9' × 9' fields with spectroscopic redshifts at z 3, Adelberger et al. (1998) perform a counts-in-cell analysis, measuring the fluctuations in galaxy counts in cells of differing comoving volume. They find that the variance in cubes of comoving side length (15.4, 23.8, 22.8) h₅₀^-1 Mpc is _gal² ~ 1.3 ± 0.4. Following the methodology of Peacock & Dodds (1994), the implied bias factor is b = (6.0 ± 1.1, 1.9 ± 0.4, 4.0 ± 0.7) for these spatial scales. The result is broadly consistent with simple dark halo models of structure formation, in which matter fluctuations are Gaussian, have a linear power spectrum shape similar to that determined locally ( ~ 0.2), and Lyman-break galaxy luminosities are correlated with their mass. The results are largely independent of cosmology. Adelberger et al. (1998) note that measurements of the Lyman-break galaxy masses could, in principal, distinguish cosmological scenarios.