6.6 Is the mean solar magnetic field really axisymmetric?

While the large-scale solar magnetic field is axisymmetric about the Sun’s rotation axis to a good first approximation, various lines of observational evidence point to a persistent, low-level non-axisymmetric component; such evidence includes the so-called active longitudes (see Henney and Harvey, 2002 , and references therein), rotationally-based periodicity in cycle-related eruptive phenomena (Bai, 1987 ), and the shape of the white-light corona in the descending phase of the cycle.

Various mean-field-based dynamo models are known to support non-axisymmetric modes over a substantial portion of their parameter space (see, e.g., Moss, 1999 ; Bigazzi and Ruzmaikin, 2004 , and references therein). At high $Rm$ , strong differential rotation (in the sense that $C_O_ » Ca$ ) is known to favor axisymmetric modes, because it efficiently destroys any non-axisymmetric component on a timescale much faster than diffusive ( $oc Rm1/3$ at high $Rm$ , instead of $oc Rm$ ). Although it is not entirely clear that the Sun’s differential rotation is strong enough to place it in this regime (see, e.g., Rüdiger and Elstner, 1994 ), some 3D models do show this symmetrizing effect of differential rotation (see, e.g., Zhang et al., 2003a ).

While all poloidal field regeneration mechanisms considered above must rely on some break of axisymmetry to circumvent Cowling’s theorem, some are of a fundamentally non-axisymmetric nature even at the largest scales. This is the case with the $a$ -effect based on both the buoyant instability of toroidal magnetic flux tubes (see Section 4.7), and on the hydrodynamical shear instability in the tachocline (see Section 4.5). In either cases stability analyses indicate that the most readily excited modes have low azimuthal wave numbers ( $m = 1$ or $m = 2$ ). This is subsumed in an axisymmetric dynamo model upon invoking azimuthal averaging, which amounts to assuming that successive destabilization events are uncorrelated in longitude; if they are, however, then the corresponding $a$ -effect should be itself longitude-dependent, which is known to favor the excitation of non-axisymmetric dynamo modes (see, e.g., Moss et al., 1991 ). This avenue should definitely be explored.