Bulk Motions in Large-Scale Void Models

To explain the puzzling situation in the observed bulk flows on scales $\sim 150 h^{-1}$ Mpc ($H_0 = 100 h^{-1}$ km sec$^{-1}$ Mpc$^{-1}$), we consider the observational behavior of spherically symmetric inhomogeneous cosmological models, which consist of inner and outer homogeneous regions connected by a shell or an intermediate self-similar region. It is assumed that the present matter density parameter in the inner region is smaller than that in the outer region, and the present Hubble parameter in the inner region is larger than that in the outer region. Then galaxies in the inner void-like region can be seen to have a bulk motion relative to matter in the outer region, when we observe them at a point O deviated from the center C of the inner region. Their velocity $v_p$ in the CD direction is equal to the difference of two Hubble parameters multiplied by the distance between C and O. It is found also that the velocity $v_d$ corresponding to CMB dipole anisotropy observed at O is by a factor $\approx 10$ small compared with $v_p$. This behavior of $v_d$ and $v_p$ is consistent with the observed cosmic flow of cluster galaxies, when the radius of the inner region and the distance CD are about 200 $h^{-1}$ Mpc and 40 $h^{-1}$ Mpc, respectively, and when the gaps of density and Hubble parameters are $\approx 0.5$ and 18%, respectively. Moreover, the [m, z] relation in these models is discussed in connection with SNIa data.