The Sun's Mean Line-of-sight Field

In this paper, I 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 then 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. I find that the nonaxisymmetric 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 might 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.