On the Oosterhoff dichotomy in the Galactic bulge: II. kinematical distribution

We present a kinematical study of RR~Lyrae stars associated with two Oosterhoff groups in the Galactic bulge. We used data published in the first paper of the series, plus proper motions from the {\it Gaia} Data Release 2, and radial velocities from the literature. A 6D kinematical and spatial solution was obtained for 429 RR~Lyrae stars. We use a model of the Galactic gravitational potential to infer stellar orbits. We did not find a difference between the Oosterhoff groups in the individual components of the space velocity. We report that \textit{foreground} and \textit{background} stars with respect to the Galactic bulge stand out in the mean $V$ velocity component, which we interpret as a sign of the Galactic rotation. The movement of the studied stars in the central region of the Galactic bulge is consistent with random motions expected for a classical bulge component. From the orbital integration, we estimate that 8\,\% of the RR~Lyrae stars are halo interlopers currently located in the Galactic bulge. The majority of the stars' orbits are within a 3\,kpc radius from the Galactic bulge. The fraction of Oosterhoff\,II stars increases with increasing Galactic latitude, as well as towards longer orbital periods. We found several RR~Lyrae stars with high space velocities, one of which has an extremely long orbital period of $\sim$1\,Gyr. We conclude that based on their kinematics, the vast majority of the stars in our sample do not seem to contribute to the boxy/peanut component of the Galactic bulge.