Mon. Not. R. Astron. Soc. **369** (2006) 1611-1624.
doi:10.1111/j.1365-2966.2006.10480.x
## Converging and diverging convection around axisymmetric magnetic flux tubes

G.J.J. Botha(1),
A.M.Rucklidge(1) and
N.E. Hurlburt(2)

(1) Department of Applied Mathematics,

University of Leeds, Leeds LS2 9JT, UK

(2) Lockheed Martin Solar and Astrophysics Laboratory,

Organization L9-41 Building 252, Palo Alto, CA 94304, USA

**Abstract.**
A numerical model of idealized sunspots and pores is presented, where
axisymmetric cylindrical domains are used with aspect ratios (radius versus
depth) up to 4. The model contains a compressible plasma with density and
temperature gradients simulating the upper layer of the Sun's convection zone.
Non-linear magnetohydrodynamic equations are solved numerically and
time-dependent solutions are obtained where the magnetic field is pushed to the
centre of the domain by convection cells. This central magnetic flux bundle is
maintained by an inner convection cell, situated next to it and with a flow
such that there is an inflow at the top of the numerical domain towards the
flux bundle. For aspect ratio 4, a large inner cell persists in time, but for
lower aspect ratios it becomes highly time dependent. For aspect ratios 2 and 3
this inner convection cell is smaller, tends to be situated towards the top of
the domain next to the flux bundle, and appears and disappears with time. When
it is gone, the neighbouring cell (with an opposite sense of rotation, i.e.
outflow at the top) pulls the magnetic field away from the central axis. As
this happens a new inner cell forms with an inflow which pushes the magnetic
field towards the centre. This suggests that to maintain their form, both pores
and sunspots need a neighbouring convection cell with inflow at the top towards
the magnetic flux bundle. This convection cell does not have to be at the top
of the convection zone and could be underneath the penumbral structure around
sunspots. For an aspect ratio of 1, there is not enough space in the numerical
domain for magnetic flux and convection to separate. In this case the solution
oscillates between two steady states: two dominant convection cells threaded by
magnetic field and one dominant cell that pushes magnetic flux towards the
central axis.

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