Appendices are only available in electronic form at http://www.aanda.org

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NRAO Jansky Fellow.

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... yield

Since coordinates on the observing plane are scaled (see the text below Eq. (2)), $\omega$ is also scaled. The replacement $\omega \rightarrow (D_{\rm LS}/D_{\rm S})\omega$ converts to observational quantities. This replacement is insubstantial in most cases under consideration since the modifying factor is of order unity.

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... unimportant

Note that the form of the power spectrum differs slightly to that considered in M04, where the power spectrum of mass density (not mass surface density), $\Phi_\rho$ , fluctuations was specified directly. The previous formulation is too simple for treating intensity fluctuations, as it included no power beyond the outer scale.

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... cosmology

An example of clustering between dissimilar populations in cosmological contexts is the galaxy-cluster two point correlation, which can be compared against the galaxy-galaxy and cluster-cluster two-point correlation functions (see Peebles 1980b; Bahcall 1988). The galaxy-cluster two-point correlation function is empirically determined to contain two terms, the first of which is important at short scales and is due to the tendency of galaxies to cluster in clusters. In our treatment we assume that stars of a certain type have no tendency to cluster around stars of a different type, so this term is unimportant. The second term is related to the clustering of clusters themselves, and is important in our case. This contribution is given approximately by the geometric mean of the two-point correlation functions for objects of either type: $\xi_{\rm GC} \approx \xi_{\rm CC}^{1/2} \xi_{\rm GG}^{1/2}$ .

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