We present high-level four-component coupled cluster and multireference configuration interaction calculations of potential energy curves, dipole moment, Franck-Condon factors and spectroscopic constants of the newly formed RbYb molecule. From finite-field calculations we obtain an electric dipole moment for RbYb of almost 1 D. In combination with its magnetic dipole moment this makes RbYb an excellent candidate for trapping and for studying dipolar interaction in the ultracold regime. Significant Franck-Condon factors are found between the rovibronic ground state and the lowest rovibrational levels of the first excited 2Sigma1/2+ state but also between a broad range of rovibrational levels of the 2Pi1/2 and 2Pi3/2 states. This allows for several two-step approaches to reach the rovibronic ground state after initial photoassociation.