We regard the Sun-as-a-star magnetic field (i.e. the mean field) as a filter for the spherical harmonic components of the photospheric field, and calculate the transmission coefficients of this filter. The coefficients for each harmonic, $Y_{ l}^{ m}$, are listed in three tables according to their dependence on $B_{ 0}$, the observer's latitude in the star's polar coordinate system. These coefficients are used to interpret the 46-yr sequence of daily mean-field measurements at the Wilcox Solar Observatory. We find that the non-axisymmetric part of the field originates in the $Y_{ 1}^{ 1}$, $Y_{ 2}^{ 2}$, and a combination of the $Y_{ 3}^{ 3}$ and $Y_{ 3}^{ 1}$ harmonic components. The axisymmetric part of the field originates in $Y_{ 2}^{ 0}$ plus a $B_{ 0}$-dependent combination of the $Y_{ 1}^{ 0}$ and $Y_{ 3}^{ 0}$ components. The power spectrum of the field has peaks at frequencies corresponding to the ~27-day synodic equatorial rotation period and its second and third harmonics. Each of these peaks has fine structure on its low-frequency side, indicating magnetic patterns that rotate slowly under the influence of differential rotation and meridional flow. The sidebands of the fundamental mode resolve into peaks corresponding to periods of ~28.5 and ~30 days, which tend to occur at the start of sunspot maximum, whereas the ~27-day period tends to occur toward the end of sunspot maximum. We expect similar rotational sidebands to occur in magnetic observations of other Sun-like stars and to be a useful complement to asteroseismology studies of convection and magnetic fields in those stars.
Categories: astro-ph.SR