The evolution of the hot dark matter (HDM) model containing both baryonic matter and dark matter is computed for a postrecombination Friedmann-Robertson-Walker universe. We use a locally valid Newtonian approximation to model a representative piece of the universe with size much less than the horizon. A highly developed Eulerian hydrodynamic code is used (for a detailed methodological description see Cen 1992) for the gas with a standard particle-mesh (PM) code for the motion of collisionless dark matter particles. We model a standard HDM scenario (Bardeen et al. 1986), adopting the following set of parameters: h = 0.75, OMEGA = 1.0, OMEGA(b) = 0.027, consistent with light-element nucleosynthesis (Walker et al. 1991; Schramm 1991). The simulation box size is L = 64 h-1 Mpc with 128(3) approximately 10(6.3) baryonic cells and an equal number of dark matter particles. The initial amplitude of the perturbation is fixed by the requirement that (deltaM/M)rms = 1 on an 8 h-1 Mpc top-hat sphere at z = 0, which is consistent with recent COBE differential microwave radiometer measurements (cf. Wright et al. 1992). 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 followed in detail, with allowance made for bremsstrahlung and recombination radiation input as well as ionization losses. However, in computing the thermal changes of the gas, we allow for both line and continuum processes as well as Compton interactions with the cosmic microwave background radiation (CBR) and X-ray background radiation (XBR) fields. The final mean Sunyaev-Zel'dovich y-parameter is estimated to be yBAR = (3.2 +/- 1.6) x 10(-6), below current attainable observations, with a rms fluctuation of approximately deltayBAR = (3.6 + 1.8) x 10(-6) on arcminute scales and deltaT/T almost-equal-to 1 x 10(-6) on the COBE 7-degrees scale. Of greater interest, this model can make a nontrivial (approximately 10%) fraction of the XBR in the 1-10 keV range and does not produce overrich X-ray clusters (cf. Evrard & Davis 1988) as compared with observations. The model with our chosen parameters fails to produce enough ionization either by shocks or radiation (UV from stars not included in this simulation) to satisfy the Gunn-Peterson test (Gunn & Peterson 1965). It appears that for this model with low OMEGA(b) only a very small fraction of the baryons (< 1%) will condense out as galaxies. This conclusion results from our input parameters (low OMEGA(b), low amplitude) and is not in disagreement with prior work which found significant galaxy formation for larger values of these parameters. We also examine the relations among four kinds of objects: (1) initial high-density peaks, (2) galaxies, (3) final high-density peaks, and (4) bright X-ray spots. They show very interesting properties which are tightly related to the special feature of the HDM power spectrum: cutoff of short-wavelength power due to neutrino free streaming. We can set limits on (OMEGA(b), amplitude) by the requirement that the 1 keV cosmic X-ray background not exceed its observed value and the distortion of the CBR not exceed COBE observations. The HDM models that other investigators (with high-resolution one-dimensional simulations) have found could successfully put over 10% of the baryons into galaxies are not permitted according to our calculations; they overproduce 1 keV X-rays and CBR distortions.
