The secular evolution of a uniform density star cluster immersed in a
  compressible galactic tidal field
  Nuclear stellar clusters are common in the center of galaxies. We consider
the possibility that their progenitors assumed to be globular clusters may have
formed elsewhere, migrated to and assembled near their present location. The
main challenge for this scenario is whether globular clusters can withstand the
tidal field of their host galaxies. Our analysis suggests that provided the
mass-density distribution of background potential is relatively shallow, as in
some galaxies with relatively flat surface brightness profiles, the tidal field
near the center of galaxies may be shown to be able to compress rather than
disrupt a globular cluster at a distance from the center much smaller than the
conventionally defined `tidal disruption radius', $r_t$. To do so, we adopt a
previously constructed formalism and consider the secular evolution of star
clusters with a homogeneous mass density distribution. We analytically solve
the secular equations in the limit that the mass density of stars in the
galactic center approaches a uniform distribution. Our model indicates that a
star cluster could travel to distances much smaller than $r_t$ without
disruption, thus potentially contributing to the formation of the nuclear
cluster. However, appropriate numerical N-body simulations are needed to
confirm our analytic findings.
