CLUSTER CORRELATIONS FOR COLD PLUS HOT DARK MATTER AND OTHER MODELS

Calculations of the autocorrelation function of rich clusters of galaxies are presented for several nonstandard variants of cold dark matter (CDM) that have an enhanced power spectrum on large scales compared to '' standard '' OMEGA = 1 CDM. The models considered are (1) cold + hot dark matter (C + HDM) models with OMEGA(CDM) + OMEGA(nu) + OMEGA(b) = 1 (where OMEGA(nu), the fraction of the critical density in one or three species of light neutrinos, is comparable to OMEGA(CDM), (2) OMEGA(CDM) + OMEGA(b) = 0.2 or 1 (where OMEGA(b) the fraction of critical density in baryonic matter, is comparable to OMEGA(CDM)), and (3) CDM with a non-Zel'dovich fluctuation spectrum that arises in a particular inflationary model. For models of types (1) and (2), calculations of bulk velocities and microwave background anisotropies have been presented previously; for the third model considered, these are presented here. The cluster correlation functions are calculated using the theory of linear Gaussian fluctuations, and are compared to the currently available data on both spatial (three-dimensional) and angular (two-dimensional) correlations of rich (R greater-than-or-equal-to 1) Abell clusters, including corrections for projection effects. Although '' standard '' CDM is now in serious conflict with observed cluster correlations, several of the models considered here-in particular, C + HDM models with OMEGA(nu) almost-equal-to 0.3-are consistent with the available cluster correlation data as well as with other observations, including the COBE microwave background quadrupole anisotropy.