Accreting Matter around Clusters of Galaxies: One-Dimensional Considerations

During the formation of the large scale structure of the Universe, matter accretes onto high density peaks. Accreting collisionless dark matter (DM) forms caustics around them, while accreting collisional baryonic matter (BM) forms accretion shocks. The properties of the accreting matter depend upon the power spectrum of the initial perturbations on a given scale as well as the background expansion in a given cosmological model. In this paper, we have calculated the accretion of DM particles in one-dimensional spherical geometry under various cosmological models including the Einstein-de Sitter universe, the open universe with $\Omega_o<1$, and the flat universe with $\Omega_{\Lambda}=1-\Omega_o$. A density parameter in the range $0.1\le \Omega_o \le 1$ has been considered. The initial perturbation characterized by a point mass at the origin has been considered. Since the accretion shock of BM is expected to form close to the first caustic of DM, the properties of the accreting BM are common with those of the DM. Hence, the accretion calculations with DM particles have been used to find the position and velocity of the accretion shock and the cluster mass inside it. The average temperature of BM has been estimated by adopting simplifying assumptions. The velocity of the accreting BM around clusters of a given temperature is smaller in a universe with smaller $\Omega_o$, but only by up to $\sim24\%$ in the models with $0.1\le \Omega_o \le 1$. Thus, it would be difficult to use that quantity to discriminate among the cosmological models. However, the accretion velocity around clusters of a given mass or a given radius depends more sensitively on the cosmological models. It is smaller in a universe with smaller $\Omega_o$ by up to $\sim41\%$ and $\sim65\%$, respectively. So, it can provide a better