Galaxy clustering from COMBO-17: the halo occupation distribution at

We present measurements of galaxy clustering at redshift $\langle z \rangle=0.6$ using $10\,360$ galaxies with photometric redshifts over an area of 0.78 deg2 from the COMBO-17 survey. To obtain a result that is unaffected by redshift uncertainties, we calculate the projected correlation function $w(r_{\rm p})$, giving results for red sequence and blue cloud galaxies separately. The correlation function of the red galaxies displays clear deviations from a power law at comoving separations around 1 to $3{\,h^{-1}\,\rm Mpc}$, and similar but weaker trends are suggested by the data for the blue galaxies. To interpret these results, we fit the correlation functions with analytical predictions derived from a simple halo occupation model. This combines linear clustering of the underlying mass with a description of the number of galaxies occupying each dark-matter halo (the halo occupation distribution). If the occupation numbers are taken to be a simple power law $N \propto \smash{M^\alpha}$, then $\alpha \simeq 0.5$ and $\alpha \simeq 0.2$ for red and blue galaxies respectively. These figures are little different from the values required to fit present-day clustering data. The power-spectrum shape is assumed to be known in this exercise, but we allow the data to determine the preferred value of $\sigma_8$, the linear power-spectrum normalization. The average normalization inferred from red and blue galaxies at $\langle z \rangle=0.6$ is $\sigma_8=1.02\pm0.17$ at zero redshift, consistent with independent estimates of this local value. This agreement can be regarded as a verification of the hierarchical growth of the halo mass function.