Mean magnetic field and energy balance of Parker ’ s surface - wave dynamo

We study the surface-wave dynamo proposed by Parker (1993) as a model for the solar dynamo, by solving equations for the mean magnetic field B0, as well as for the mean ’magnetic energy tensor’ T = 〈BB〉/8π. This tensor provides information about the energy balance, rms field strengths and correlation coefficients between field components. The main goal of this paper is to check whether the equations forB0 and T are compatible, i.e. whether both have ”reasonable” solutions for a set of ”reasonable” parameters. We apply the following constraints: B0 has a period of 22 years and, taking into account the effect of period variations, a decay time of 10 dynamo periods, and T is marginally stable. We find that under these constraints, the equations forB0 and T are compatible only if, apart from turbulent transport out of the dynamo region, an additional energy sink is introduced. If this extra term is omitted, then marginal stability of T requires a turbulent diffusion in the convection zone of the order β2 >∼ 3 × 1014 cm2 s−1, whereas the conditions onB0 require β2 ≈ 1012 cm2 s−1. Furthermore, the rms surface field strength, the maximum rms field strength and the magnetic energy flux through the upper surface of the convection zone cannot simultaneously assume solar values.We explore the possibility that the extra energy sink is provided by resistive dissipation, hitherto not accounted for in the equation for T, by considering various cases. We demonstrate that with a heuristically modified equation for T, the inconsistencies can be removed. Our results suggest that resistive dissipation is the dominant sink of magnetic energy, and that resistive heating may amount to several percent of the solar luminosity.