A HYDRODYNAMIC APPROACH TO COSMOLOGY - NONLINEAR EFFECTS ON COSMIC BACKGROUNDS IN COLD DARK-MATTER MODEL

Using the CDM model as a testbed, we produce and analyze sky maps of fluctuations in the cosmic background radiation field due to Sunyaev-Zel'dovich effect, as well as those seen in X-ray background at 1 keV and at 2 keV. These effects are due to the shock heating of baryons in the nonlinear phases of cosmic collapses. Comparing observations with computations provides a powerful tool to constrain cosmological models. We use a highly developed Eulerian mesh code with 128(3) cells and 2 x 10(6) particles. Most of our information comes from simulations with box size 64 h-1 Mpc, but other calculations were made with L = 16 h-1 and L = 4 h-1 Mpc. A standard CDM input spectrum was used with amplitude defined by the requirement (DELTAM/M)rms = 1/1.5 on 8 h-1 Mpc scales (lower than the COBE normalization by a factor of 1.6 +/- 0.4), with H-0 = 50 km s-1 Mpc-1 and OMEGA(b) = 0.05. For statistical validity a large number of independent simulations must be run. In all, over 60 simulations were run from z = 20 to z = 0. We produce maps of 50' x 50' with almost-equal-to 1' effective resolution by randomly stacking along the past light cone for 0.02 less-than-or-equal-to z less-than-or-equal-to 10 appropriate combinations of computational boxes of different comoving lengths, which are picked from among different realizations of initial conditions. We also compute time evolution, present intensity pixel distributions, and the autocorrelation function of sky fluctuations as a function of angular scale. Our most reliable results are obtained after deletion of bright sources having 1 keV intensity greater than 0.1 keV cm-2 sr-1 s-1 keV-1. Then for the Sunyaev-Zel'dovich parameter y the mean and dispersion are [yBAR, sigma(y)] = (4, 3) x 10(-7) with a lognormal distribution providing a good fit for values of y greater than average. The angular correlation function (less secure) is roughly exponential with scale length approximately 2.5'. For the X-ray intensity fluctuations, in units of keV s-1 sr-1 cm-2 keV-1 we find I(X1,X2)BAR = (0.02, 0.006) and sigma(X1,X2) = (0.06, 0.03). The pixel distribution is roughly a power law in the intermediate range -f(I(X))dI(X) is-proportional-to I(X)-1.8 DI(X). Also in these cases the angular autocorrelation function is roughly exponential with decay angles of theta0;X1,X2 found to be 1.6' and 1.3' but probably below our numerical resolution of 1.0' in fact. If we scale our results to the COBE normalization, y values increase by approximately a factor of 9 and X-ray intensity by a factor of 8 to give a (deltaT/T)rms,SZ = 3.5 x 10(-6) on the 1.0' scale and I1keVBAR = 0.2 keV cm-2 sr-1 s-1 keV-1 with both making nontrivial contributions to the observed background radiation fields.