  We determine and analyze collective normal modes of a finite disk-shaped
two-dimensional vortex crystal formed in a compressible bosonic superfluid in
an artificial magnetic field. Using the microscopic Gross-Pitaevskii theory in
the lowest Landau level approximation, we generate vortex crystal ground states
and solve the Bogoliubov-de Gennes equations for small amplitude collective
oscillations. We find chiral surface waves that propagate at frequencies larger
than those of the bulk Tkachenko modes. Furthermore, we study low frequency
bulk excitations and identify a torsional Ruderman mode, which we find is
well-described by a previously developed low-energy effective field theory.
