Baryonic fraction in the cold plus hot dark matter universe

We report a study to constrain the fraction of baryonic matter in the cold plus hot dark matter (CHDM) universe by numerical simulations which include the hydrodynamics of baryonic matter as well as the particle dynamics of dark matter. Spatially flat, COBE-normalized CHDM models with the fraction of hot component $\Omega_h\leq0.2$ are considered. We show that the models with $h/n/\Omega_h=0.5/0.9/0.1$ and $0.5/0.9/0.2$ give a linear power spectrum which agrees well with observations. Here, $h$ is the Hubble constant in unit of $100~km/s/Mpc$ and $n$ is the spectral index of the initial power spectrum. Then, for the models with $h/n/\Omega_h=0.5/0.9/0.2$ and baryonic fraction $\Omega_b=0.05$ and 0.1 we calculate the properties of X-ray clusters, such as luminosity function, temperature distribution function, luminosity-temperature relation, histogram of gas to total mass ratio, and change of average temperature with redshift $z$. Comparison with the observed data of X-ray clusters indicates that the model with $\Omega_b=0.05$ is preferred. The COBE-normalized CHDM model with $\Omega_b>0.1$ may be ruled out by the present work, since it produces too many X-ray bright clusters.