Oscillations on the Sun in regions with a vertical magnetic field

II. On the calculation of the sunspot umbral oscillations

The Central Astronomical Observatory of Russian Academy of Sciences, 65 Pulkovo, 196 140 St. Petersburg, Russia e-mail: leapsy@mail.ru (Zhukova Svetlana)

Received: 17 June 2004
Accepted: 3 December 2004

Abstract

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.