Flattening Index of the Solar Corona and the Sun’s Magnetic Field

Abstract

The photometric-flattening index of the solar corona was introduced by Ludendorff in the 1930s. It characterizes the white-light corona’s shape as observed during total solar eclipses. We compiled all of the published values of this parameter for total solar eclipses observed since 1976 and additionally calculated the flattening index for seven total solar eclipses in 2012 – 2020. One value for each of 29 total solar eclipses in 1976 – 2020 was chosen for further analysis (18 were calculated by the author). Then all these chosen values were compared with some parameters of the magnetic field of the Sun as observed and calculated at the Wilcox Solar Observatory for corresponding dates or Carrington rotations since 1976 (such parameters as amplitude and power of harmonic terms for dipole, quadrupole, and octupole, heliospheric current-sheet tilts, polar magnetic-field strength, and total photospheric magnetic flux). It is found that among all the harmonic terms of the solar magnetic field the flattening index best correlates with the axial-dipole term ${g}^{0}_{1}$ (correlation coefficient [c.c.] equal to 0.700, $P < 0.0005$). The shape of the solar corona is defined mainly by the axial-dipole field during most of the solar cycle. In addition, it is found that the flattening index also strongly correlates with observed polar magnetic-field strength (c.c. $= 0.796$, $P < 5 \times 10^{-7}$) and is in strong negative correlation with heliospheric current-sheet tilts (c.c. $= -0.803$, $P < 2 \times 10^{-7}$ for classic tilts and c.c. $= -0.820$, $P < 7 \times 10^{-8}$ for radial tilts). The flattening index is also in moderate negative correlation with the total photospheric magnetic flux and tends to be higher in the minimum of a stronger solar cycle.