An update of Leighton's solar dynamo model

In 1969, Leighton developed a quasi-1D mathematical model of the solar dynamo, building upon the phenomenological scenario of Babcock published in 1961. Here we present a modification and extension of Leighton's model. Using the axisymmetric component (longitudinal average) of the magnetic field, we consider the radial field component at the solar surface and the radially integrated toroidal magnetic flux in the convection zone, both as functions of latitude. No assumptions are made with regard to the radial location of the toroidal flux. The model includes the e ff ects of (i) turbulent di ff usion at the surface and in the convection zone; (ii) poleward meridional flow at the surface and an equatorward return flow a ff ecting the toroidal flux; (iii) latitudinal di ff erential rotation and the near-surface layer of radial rotational shear; (iv) downward convective pumping of magnetic flux in the shear layer; and (v) flux emergence in the form of tilted bipolar magnetic regions treated as a source term for the radial surface field. While the parameters relevant for the transport of the surface field are taken from observations, the model condenses the unknown properties of magnetic field and flow in the convection zone into a few free parameters (turbulent di ff usivity, e ff ective return flow, amplitude of the source term, and a parameter describing the e ff ective radial shear). Comparison with the results of 2D flux transport dynamo codes shows that the model captures the essential features of these simulations. We make use of the computational e ffi ciency of the model to carry out an extended parameter study. We cover an extended domain of the 4D parameter space and identify the parameter ranges that provide solar-like solutions. Dipole parity is always preferred and solutions with periods around 22 yr and a correct phase di ff erence between flux emergence in low latitudes and the strength of the polar fields are found for a return flow speed around 2 ms(-1), turbulent di ff usivity below about 80 km(2) s(-1), and dynamo excitation not too far above the threshold (linear growth rate less than 0.1 yr 1).