On the topological evolution of the coronal magnetic field during the solar cycle

Using an axisymmetric model that includes the effects of flux emergence and surface transport processes, we calculate the evolution of the photospheric magnetic field over the solar cycle and derive a corresponding sequence of coronal configurations by means of a potential-field source-surface extrapolation. By identifying magnetic neutral points and tracking changes in the total flux within each topological domain, we construct an overall picture of how open and closed flux is transported as the coronal field reverses its polarity: 1. During the rising phase of the cycle, an X-point forms above the emerging flux (represented by a bipole structure) in each hemisphere, and the overlying, opposite-polarity field lines are stripped away'' (reconnected to each side); at the same time, as the Sun's axial dipole strength decreases, open field lines from the polar coronal holes begin to merge at the equator and close down. 2. As the rate of flux emergence peaks, the X-point rises toward the source surface and the bipole opens up, forming a trailing-polarity hole on its poleward side, which evolves into the new-cycle polar hole; the leading-polarity open flux on the equatorward side of the bipole progressively closes down by merging with its opposite-hemisphere counterpart. 3. Later in the declining phase of the cycle, the opposite-hemisphere bipoles begin to reconnect with each other at an equatorial X-point, producing long trailing-polarity loops that rise toward the source surface and continue to feed flux into the new-cycle polar holes, and short leading-polarity loops that collapse toward the photosphere and eventually submerge. We compare the case in which the transport of the photospheric field is by supergranular diffusion alone with that in which both diffusion and a 20 m s(-1) poleward flow are present; the latter model is shown to reproduce more closely the coronal topologies inferred from the observed photospheric field.