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Transverse Galaxy Velocities from Multiple Topological Images
The study of the kinematics of galaxies within clusters or groups has the
limitation that only one of the three velocity components and only two of the
three spatial components of a galaxy position in six-dimensional phase space
can normally be measured. However, if multiple topological images of a cluster
exist, then the radial positions and sky plane mean velocities of galaxies in
the cluster may also be measurable from photometry of the two cluster images.
The vector arithmetic and principles of the analysis are presented. These are
demonstrated by assuming the suggested topological identification of the
clusters RX J1347.5-1145 and CL 09104+4109 to be correct and deducing the
sky-plane relative velocity component along the axis common to both images of
this would-be single cluster.
Three out of four of the inferred transverse velocities are consistent with
those expected in a rich cluster. A control sample of random `common' sky-plane
axes, independent of the topological hypothesis, implies that this is not
surprising. This shows that while galaxy kinematics are deducible from
knowledge of cosmological topology, it is not easy to use them to refute a
specific candidate manifold.Comment: 13 pages, 7 figures, accepted for MNRA
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