We determine and analyze the collective normal modes of a finite disk-like two-dimensional vortex crystal formed in a compressible bosonic superflow in an artificial magnetic field. Using the microscopic Gross-Pitaevsky theory with the lowest Landau level approximation, we generate the ground state of the vortex crystal and solve the Bogoliubov-De Genes equation for small-amplitude collective oscillations. We find a chiral surface wave propagating at a frequency higher than that of the bulk Tkachenko mode. In addition, we study low-frequency bulk excitations and identify torsional Ludermann modes that are well described by previously developed low-energy effective-field theories.
