Hydrodynamical Simulation of Clusters of Galaxies in X-Ray, mm, and submm Bands: Determination of Peculiar Velocity and the Hubble Constant

We have performed a series of simulations of clusters of galaxies on the basis of the smoothed particle hydrodynamics technique in a spatially-flat cold dark matter universe with $\Omega=0.3$, $\lambda=0.7$, and H_0=70 km/s/Mpc as one of the most successful representative cosmological scenarios. In particular, we focus on the Sunyaev--Zel'dovich effect in submm and mm bands, and estimate the reliability of the estimates of the global Hubble constant $H_0$ and the peculiar velocity of clusters $v_r$. Our simulations indicate that fractional uncertainties of the estimates of $H_0$ amount to $\sim 20%$ mainly due to the departure from the isothermal and spherical gas density distribution. We find a systematic underestimate bias of $H_0$ by $\sim 20%$ for clusters $z\approx 1$, but not at $z\approx 0$. The gas temperature drop in the central regions of our simulated clusters leads to the underestimate bias of $v_r$ by $\sim 5%$ at $z\approx 0$ and by $\sim 15%$ at $z\approx 1$ in addition to the statistical errors of the comparable amount due to the non-spherical gas profile.