Oscillations on the Sun in regions with a vertical magnetic field - II. On the calculation of the sunspot umbral oscillations

We calculated the spectrum of oscillations for the model of the sunspot umbra described in Zhukov (2002, A&A, 386, 653). The calculations were carried out both by resonant filtering and from the solution of the eigenvalue problem. Both methods yield the same results, thus confirming the concept according to which both 5-min and 3-min oscillations of the umbra represent the same set of p-like mode oscillations of the sunspot. The calculated frequencies of the oscillations and corresponding eigenfunctions are consistent with observations.