Photometric Flattening Index of the Solar Corona in the Solar Cycle

The photometric flattening index as a quantitative characteristic of the shape of the solar corona observed during a total solar eclipse was proposed by Ludendorff in the 1930s. The work collected the values of the flattening index for 69 total solar eclipses in 1851–2020 and investigated their relationship with the parameters of the solar cycle. The value of the flattening index varies from approximately 0.3–0.4 at the cycle minimum to 0.0–0.1 at the cycle maximum. The flattening index correlates with the relative sunspot numbers and the phase of the solar cycle. The correlation coefficients between the flattening index and the daily, monthly and smoothed monthly sunspot numbers are –0.577 (р < 4 × 10^–7), –0.595 (p < 8 × 10^–8) and –0.598 (p < 7 × 10^–8), respectively. The correlation coefficients between the flattening index and the phase of the solar cycle for the rising and declining phases of the cycle are –0.759 (p < 5 × 10^–6) and 0.660 (p < 2 × 10^–6), respectively. The observed shape of the solar corona, in particular the value of the flattening index, is determined by the global magnetic field of the Sun, mainly by its dipole component.