The Sun’s Mean Line-of-Sight Field. (arXiv:2208.03216v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Sheeley_N/0/1/0/all/0/1">Neil R. Sheeley Jr</a>
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.
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.
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