Spherical harmonic decomposition of solar magnetic fields

¹ Institute of Astronomy, ETH-Zentrum, 8092 Zürich, Switzerland e-mail: rknaack@astro.phys.ethz.ch
² Faculty of Mathematics and Science, University of Zurich, 8057 Zürich, Switzerland e-mail: stenflo@astro.phys.ethz.ch

Received: 25 January 2005
Accepted: 5 April 2005

Abstract

We have investigated the temporal evolution of large-scale magnetic fields in the solar photosphere during the time interval 1966–2004 by means of spherical harmonic decomposition and subsequent time series analysis. Two data sets of daily magnetograms recorded at the Mt. Wilson and Kitt Peak observatories were used to calculate the spherical harmonic coefficients of the radial magnetic field for axisymmetric () and non-axisymmetric () modes. Time series analysis was then applied to deduce their temporal variations. A third data set of synoptic Carrington rotation maps from Kitt Peak was also analyzed for completeness. Besides the obvious magnetic cycle, we have found evidence for intermittent oscillations with periods of , and . The biennial oscillation occurred during the solar maxima of cycles 20–22 (and likely also during the current cycle 23) and was most pronounced for modes that resemble non-linear dynamo waves (Stix 1972, A&A, 20, 9). The period was stronger during the odd cycles 21 and 23 than during the even cycles 20 and 22, whereas the opposite was the case for the period. Similar variations of have recently been detected in the north-south asymmetry of the magnetic flux (Knaack et al. 2004, A&A, 418, L17), while quasi-periodicities of ~1.3 yr have been observed in the rotation rate near the base of the convection zone (Howe et al. 2000, Science, 287, 2456), in the heliosphere and geomagnetic activity (Lockwood 2001, J. Geophys. Res., 106, 16 021) in sunspot areas (Krivova & Solanki 2002, A&A, 394, 701), and in the large-scale photospheric magnetic field (Knaack et al. 2005, A&A, in press). In agreement with the latter study, we have found additional quasi-periodicities in the range and rotational periods of , , and . Compared to earlier decompositions by Stenflo & Vogel (1986, Nature, 319, 285) and Stenflo & Güdel (1988, A&A, 191, 137), we can confirm the main features of their results, although several modifications need to be considered.