Annu. Rev. Astron. Astrophys. 2005. 43: 727-768 Copyright © 2005 by Annual Reviews. All rights reserved

6. CLUSTERING

Measuring clustering gives information about the distribution of galaxies with respect to the dark matter. The strength of clustering is correlated with the mass of extended halos that host luminous galaxies. At redshift lower than 1.3, large-scale structures have been mapped by the DEEP2, 2dF and SDSS surveys (Coil et al. 2004; Peacock et al. 2001; Doroshkevich et al. 2004). At higher redshifts, correlation lengths r₀ have been measured for different galaxy populations such as the LBGs and EROs. Values of about r₀ = 4 h^-1 Mpc (Porciani & Giavalisco 2002) and r₀ = 11 h^-1 Mpc (Daddi et al. 2000; Firth et al. 2002; Roche et al. 2003) are reported with mean redshift of about 3 and 1-1.5 for the LBGs and EROs, respectively. Getting information on the clustering of the infrared galaxies is essential to see how they relate to the other galaxy populations and to understand their formation process. As an example, one of the key questions is to see if the most massive SMGs are associated with the most massive dark matter halo.

Up to now, very little information is available on the clustering of infrared galaxies. A clustering signal can tentatively be measured, although the small number of objects in the deep narrow-pencil ISOCAM and SCUBA beams prevents accurate measurements of the autocorrelation function. At z ~ 1, Moy & Elbaz (2005) study the large-scale and close environment of ISOCAM galaxies. They find that infrared galaxies are more strongly clustered than optical galaxies. Eighty percents of ISOCAM galaxies are found preferentially in redshift peaks, versus 68% for the optically selected galaxies. Moy & Elbaz (2005) find indirect evidences that the triggering mechanism of dusty starbursts is small-scale (~ 100 kpc) galaxy-galaxy interactions. Such interactions do not lead to major mergers most of the time but are more likely simple fly-by, tidal interactions or minor mergers. At much higher redshift, there are some indirect evidences of strong clustering of SMGs when compared to other classes of high-redshift galaxies. For example, Chapman et al. (2001) identified SMGs within the most overdense structure of LBGs at z ~ 3.1 (Steidel et al. 2000). De Breuck et al. (2004) detected an overdensity of MAMBO sources likely at z 4.1 in a proto-cluster containing also overdensities of Ly emitters and LBGs. The first three-dimensional quantitative measurement of the clustering strength of SMGs has been made by Blain et al. (2004a). They find spectroscopic evidence for clustering. Using 73 spectroscopically identified galaxies, they find a surprisingly large number of "associations" with redshifts separated by less than 1200 km s^-1. They provide tentative evidence for strong clustering of SMGs at z 2-3 with a correlation length of ~ (6.9 ± 2.1) h^-1 Mpc using a simple pair-counting approach appropriate for the small and sparse SMG sample. This correlation length appears to be somewhat larger than that for both LBG and QSO galaxies at comparable redshifts. It is thus unlikely that the SMGs form a simple evolutionary sequence with either population. On the contrary, the correlation length could be consistent with a form of evolution that subsequently matches the large comoving correlation length typical of evolved EROs at z 1 and of clusters of galaxies at z = 0 (Figure 10). From this figure, we see that the correlation function of SMGs appears to be consistent with the hypothesis that they are associated with the most massive dark matter halos at high redshifts. These are more massive than the host halos of LBGs and QSOs at comparable redshift. These preliminary conclusions have to be investigated in more detail. In particular, the SMG masses inferred from clustering measurements have to be compared to the dynamical masses derived from millimeter wave CO spectroscopy. To go deeper in understanding the clustering properties of infrared galaxies, Spitzer 24 µm surveys will be best suited. With a large number of sources detected in quite large surveys, Spitzer will unambiguously constrain the clustering of infrared galaxies from redshift 0.5 to 2.5. Conjointly, the physics of galaxy clustering can be probed by the CIB fluctuation analysis (Knox et al. 2001). CIB fluctuations measure, on large angular scales, the linear clustering bias in dark-matter halo and, at small angular scales, the nonlinear clustering within a dark-matter halo (Cooray & Sheth 2002). They thus probe both the dark-matter halo mass scale and the physics governing the formation of infrared galaxies within a halo. Promising attempts are underway using the 170 µm ISO FIRBACK fields (Lagache et al., in preparation).

Figure 10. Comoving correlation length of the SMGs (triangle) in contrast to other populations of low- and high-redshift galaxies (see the summary in Overzier et al. 2003). The horizontal error bar on the SMG point spans the range of redshifts over which SMG associations are found. The solid line shows a representative model for the evolution of a certain overdensity. The dashed lines show the expected correlation length of dark matter halos as a function of mass and redshift. From Blain et al. (2004a).