## 1. IntroductionThere has been a considerable theoretical effort in the last decade to understand the origin, time evolution, and space distribution of magnetic fields in galaxies. Direct numerical calculations are limited by the inability of present-day computers to span the whole size range from the large galactic scales down to the small diffusive scales. The traditional way to circumvent this problem is to focus on the large-scale (or mean) magnetic field, and to split the velocity field into a large-scale velocity, which is either prescribed or easily calculable, and a small-scale turbulent velocity, whose effects on the large-scale magnetic field are parametrized in terms of two tensors: the alpha-tensor, , and the diffusivity tensor, . This approach leads to an evolution equation for the large-scale magnetic field, known as the dynamo equation. In virtually all dynamo calculations, the alpha- and diffusivity tensors take on simple analytical forms, which are based on their expected behavior at vanishing and infinite galactic heights and on order-of-magnitude estimates of their characteristic values. A first attempt to obtain realistic expressions for the various components of and in our Galaxy was made by Ferrière (1998b). Proceeding from the hypothesis that supernova (SN) explosions constitute the primary source of turbulence in the interstellar medium (ISM), she numerically followed the time evolution of a large number of supernova remnants (SNRs) and superbubbles (SBs) in the axisymmetric model ISM presented by Ferrière (1998a), she computed their final size, lifetime, and other quantities relevant to dynamo action, and she introduced these into the analytical formulae derived by Ferrière (1993a) for the alpha-tensor and by Ferrière (1993b) for the diffusivity tensor due to a distribution of axisymmetric explosions. The purpose of this paper is to solve the Galactic dynamo equation, using the expressions for and obtained by Ferrière (1998b) together with a realistic rotation curve inferred from observations. Both are functions of Galactic radius and height only, i.e., they are independent of Galactic longitude, time, and magnetic field strength. Although the emphasis will be placed on axisymmetric solutions, we will also consider nonaxisymmetric magnetic configurations. We will make several series of runs to investigate the influence of each of the input parameters. In particular, we will examine how the magnetic field growth and morphology are affected by anisotropies in the alpha-tensor, the existence of an escape velocity, the vertical dependence of the Galactic rotation velocity, the conductivity of the surrounding medium In Sect. 2, we formulate the dynamo equation, specify the reference values adopted for the various model parameters, and describe the numerical code. In Sect. 3, we analyze a special simple case which makes it possible to understand physically how each of the basic mechanisms affects the large-scale magnetic field evolution. In Sect. 4, we present the computation results in different parameter regimes and interpret them physically. In Sect. 5, we discuss the relevance and results of nonlinear models in which either the alpha-tensor alone or both the alpha- and the diffusivity tensors are assigned a simple dependence on the magnetic field strength. And in Sect. 6, we comment on the validity of our theoretical predictions and compare them to the available observations. © European Southern Observatory (ESO) 2000 Online publication: June 26, 2000 |