  If a planetary nebula (PN) is shown to be a member of a star cluster, we
obtain important new constraints on the mass and chemical composition of the
PN's progenitor star, which cannot be determined for PNe in the field. Cluster
membership can be tested by requiring the projected separation between the PN
and cluster to be within the tidal radius of the cluster, and the objects to
have nearly identical radial velocities (RVs) and interstellar extinctions, and
nearly identical proper motions (PMs). In an earlier study, we used PMs to
confirm that three PNe, which had already passed the other tests, are highly
likely to be members of Galactic globular clusters (GCs). For a fourth object,
the PN JaFu 1, which lies in the Galactic bulge near the GC Palomar 6 on the
sky and has a similar RV, the available PM measurement gave equivocal results.
We have now obtained new high-resolution images of the central star of JaFu 1
with the Hubble Space Telescope (HST) which, combined with archival HST frames
taken 14 and 16 years earlier, provide a high-precision PM. Unfortunately, we
find that the PM of the central star differs from that of the cluster with high
statistical significance, and thus is unlikely to be a member of Palomar 6.
Nevertheless, JaFu 1 is of astrophysical interest because its nucleus appears
to be a member of the rare class of "EGB 6-type" central stars, which are
associated with compact emission-line knots.
