923578.fig.007
Figure 7: Visual representations of the first few spherical harmonics. Red portions represent regions where the function is positive, and green, negative, respectively. The right hand side of the figure shows numbers, and the left side, negative numbers, so the pattern solutions shown distinguish the symmetric from the antisymmetric solutions. As usual, the number denotes the total number of nodes, with being the number of vertical nodes, so denotes axisymmetric solutions, vertically downward from the top. The mode denotes sectoral nodes, having no vertical nodes, as a vertically sliced orange would. These sectoral nodes are shown diagonally downward on the right hand side, and the antisymmetric form diagonally downward on the left. The original solar sector pattern had an , form, shown in the third row downward on the right or left. The very top spherically symmetric node is the monopole term, positive everywhere, or alternatively negative everywhere, and the second one vertically downward is the quadrupole term ( , ), negative in the equatorial plane and positive at both poles, or vice-versa. The coefficient can multiply the form to be negative of the actual spherical harmonic.