Are the double-mode bulge RR Lyrae stars with identical period-ratios
  the relic of a disrupted stellar system?
  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.
