We compute the evolution of spatially flat, mixed cold and hot dark matter models containing both baryonic matter and two kinds of dark matter. Hydrodynamics is treated with a highly developed dynamic code (see Cen 1992). A standard particle-mesh (PM) code is also used in parallel to calculate the motion of the dark matter components. We adopt the following parameters: h = H-0/100 km s-1 Mpc-1 = 0.5, OMEGA(c) = 0.64, OMEGA(h) = 0.3, and OMEGA(b) = 0.06, with amplitude of the perturbation spectrum fixed by the COBE DMR measurements (Smoot et al. 1992) being sigma8 = 0.67. Four different boxes are simulated with box sizes of L = (64, 16, 4, 1)h-1 Mpc, respectively, the two small boxes providing good resolution but little valid information due to the absence of large-scale power. We use 128(3) approximately 10(6.3) baryonic cells, 128(3) cold dark matter particles, and 2 x 128(3) hot dark matter particles. In addition to the dark matter we follow separately six baryonic species (H, H+, He, He+, He++, e-) with allowance for both (nonequilibrium) collisional and radiative ionization in every cell. The background radiation field is also followed in detail with allowance made for both continuum and line processes, to allow nonequilibrium heating and cooling processes to be followed in detail. The mean final Zeldovich-Sunyaev y parameter is estimated to be yBAR = (5.4 +/- 2.7) x 10(-7) below currently attainable observations, with a rms fluctuation of approximately deltayBAR = (6.0 +/- 3.0) x 10(-7) on arcminute scales. The rate of galaxy formation peaks at an even later epoch (z approximately 0.3) than in the standard (OMEGA = 1, sigma8 = 0.67) cold dark matter (CDM) model (z approximately 0.5) and, at a redshift of z = 4, is nearly a factor of 100 lower than for the CDM model with the same value of sigma8. With regard to mass function, the smallest objects are stabilized against collapse by thermal energy: the mass-weighted mass spectrum has a broad peak in the vicinity of m(b) = 10(9.5) M. with a reasonable fit to the Schechter luminosity function if the ratio of baryon mass to blue light is approximately 4. In addition, one very large PM simulation was made in a box with size (320 h-1 Mpc) containing 3 x 200(3) = 10(7.4) particles. Utilizing this simulation we find that the model yields a cluster mass function which is about a factor of 4 higher than observed, but a cluster-cluster correlation length marginally lower than observed, but that both are closer to observations than in the COBE-normalized CDM model. The one-dimensional pairwise velocity dispersion is 605 +/- 8 km s-1 at 1 h-1 separation, lower than that of the CDM model normalized to COBE, but still significantly higher than observations (Davis & Peebles 1983). A plausible velocity bias b(v) = 0.8 +/- 0.1 on this scale will reduce but not remove the discrepancy. The velocity autocorrelation function has a coherence length of 40 h-1 Mpc, which is somewhat lower than the observed counterpart. In all these respects the model would be improved by decreasing the cold fraction of the dark matter and could be brought into agreement with these constraints for a somewhat smaller value of OMEGA(CDM)/(OMEGA(CDM) + OMEGA(HDM)). But formation of galaxies and clusters of galaxies is much later in this model than in COBE-normalized CDM, perhaps too late. To improve on these constraints a larger ratio of OMEGA(CDM)/(OMEGA(CDM) + OMEGA(HDM)) is required than the value of 0.67 adopted here. It does not seem possible to find a value for this ratio which would satisfy all tests. Overall, the model is similar both on large and intermediate scales to the standard CDM model normalized to the same value of sigma8, but the problem with regard to late formation of galaxies is more severe in this model than in that CDM model. Adding hot dark matter, significantly improves the ability of the COBE-normalized CDM scenario to fit existing observations, but the model. is in fact not as good as the CDM model with the same sigma8 and is still probably unsatisfactory with regard to several critical tests.
