10. Biasing and the development of nonlinear mass density fluctuations

Elements of the physics of cluster formation in test (9) appear in this test of the early stages in the nonlinear growth of departures from homogeneity. An initially Gaussian mass distribution becomes skew as low density fluctuations start to bottom out and high density fluctuations start to develop into prominent mass peaks. The early signature of this nonlinear evolution is the disconnected three-point mass autocorrelation function, <(, t) (, t) (, t)>, where (, t) = / is the dimensionless mass contrast. If galaxies are useful mass tracers the galaxy three-point function is a good measure of this mass function.

The form for the mass three-point function, for Gaussian initial conditions at high redshift, in lowest nonzero order in perturbation theory, is worked out in Fry (1984), and Fry (1994) makes the point that measurements of the galaxy three-point function test how well galaxies trace mass. ⁽⁸⁸⁾ There are now two sets of measurements of the galaxy three-point function on scales ~ 10 to 20 Mpc, where the density fluctuations are not far from Gaussian. One uses infrared-selected IRAS galaxies, ⁽⁸⁹⁾ the other optically-selected galaxies (Verde et al., 2001). The latter is consistent with the perturbative computation of the mass three-point function for Gaussian initial conditions. The former says infrared-selected galaxies are adequate mass tracers apart from the densest regions, which IRAS galaxies avoid. That has a simple interpretation in astrophysics: galaxies in dense regions tend to be swept clear of the gas and dust that make galaxies luminous in the infrared.

This test gives evidence of consistency of three ideas: galaxies are useful mass tracers on scales ~ 10 Mpc, the initial conditions are close to Gaussian, and conventional gravity physics gives an adequate description of this aspect of the growth of structure. It is in principle sensitive to ₀, through the suppression of the growth of small departures from homogeneity at low redshift, but the effect is small.

⁸⁸ Other notable contributions to the development of this point include Bernardeau and Schaeffer (1992), Fry and Gaztañaga (1993), and Hivon et al. (1995). Back.

⁸⁹ Two sub-samples of IRAS galaxies are analyzed by Scoccimarro et al. (2001) and by Feldman et al. (2001). Back.