Radial velocities of fifteen double-mode bulge RR Lyrae (RR01) stars are presented, six of which belong to a compact group of RR01 stars in pulsation space, with the ratio of first-overtone period to fundamental-mode period, P_{fo}/P_{f}~0.74, and P_{f}~0.44. It has been suggested that these pulsationally clumped RR01 stars are a relic of a disrupted dwarf galaxy or stellar cluster, as they also appear to be spatially coherent in a vertical strip across the bulge. However, the radial velocities of the stars presented here, along with proper motions from Gaia DR2, show a large range of radial velocities, proper motions and distances for the bulge RR01 stars in the pulsation clump, much larger than the RR01 stars in the Sagittarius dwarf galaxy (Sgr). Therefore, in contrast to the kinematics of the RRL stars belonging to Sgr, and those in and surrounding the bulge globular cluster NGC~6441, there is no obvious kinematic signature within the pulsationally clumped RR01 stars. If the pulsationally clumped RR01 stars belonged to the same system in the past and were accreted, their accretion in the inner Galaxy was not recent, as the kinematic signature of this group has been lost (i.e., these stars are now well-mixed within the inner Galaxy). We show that the apparent spatial coherence reported for these stars could have been caused by small number statistics. The orbits of the RR01 stars in the inner Galaxy suggest they are confined to the innermost ~4~kpc of the Milky Way.
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