SpringerLink
Forum Springer Astron. Astrophys.
Forum Whats New Search Orders


Astron. Astrophys. 337, 887-896 (1998)

Previous Section Next Section Title Page Table of Contents

4. Current-carrying magnetic flux tubes in the photosphere

The formation of intensive axially symmetric flux tubes with [FORMULA]([FORMULA]), j ([FORMULA]) in the steady-state situation in the case of axially symmetric [FORMULA]), converging, [FORMULA], flux of partially ionized photospheric plasma, supposing the tubes to be vertical inside the convective zone, was considered by Zaitsev (1996, 1997), and Zaitsev & Khodachenko (1997).

Supposing [FORMULA], [FORMULA], [FORMULA], where [FORMULA], [FORMULA], and [FORMULA] are Alfvén, sound and free-fall velocities, respectively we obtain from Eqs. (2) and (3) the following expressions for the magnetic field components of a steady-state flux tube (Zaitsev 1996):

[EQUATION]

where

[EQUATION]

Let us suppose the following approximations for the plasma convection velocity field near a steady-state magnetic flux tube:

[EQUATION]

where [FORMULA] is the radius of a magnetic flux tube.

For such a model of the convective flow in the photosphere, where [FORMULA], the solution for Eq. (5) can be expressed as (Zaitsev & Khodachenko 1997):

[EQUATION]

[EQUATION]

where [FORMULA], and [FORMULA] = [FORMULA].

It follows from Eq. (6) that for [FORMULA] magnetic field [FORMULA] has a maximum on the axis of the tube and decreases with increasing [FORMULA]. Assuming that at the tube boundary the magnetic field value [FORMULA] appears to be much less than [FORMULA], we can estimate from Eq. (6) the radius of flux tube (Zaitsev & Khodachenko 1997):

[EQUATION]

In particular, if on the tube boundary [FORMULA], then for the height [FORMULA] km upon the level [FORMULA], where [FORMULA]cm-3, [FORMULA] cm-3, and [FORMULA]K, and the magnetic field on the axis of the flux tube [FORMULA] G, we obtain from Eq. (8) the tube radius [FORMULA]. This yields for the convection velocity [FORMULA] m/s the radius of the magnetic flux tube [FORMULA] cm.

Keeping in mind that on the boundary of the tube, in the region [FORMULA], the magnetic field becomes rather small and consequently the photospheric parameters, [FORMULA] and Eq. (5), give the spatial behavior of the magnetic field:

[EQUATION]

where

[EQUATION]

is the magnetic Reynolds number. Thus, we have very rapid power-law decrease of the magnetic field vs. distance for [FORMULA], because [FORMULA] in the photosphere.

Taking Eq. (7) into account we obtain the total longitudinal current [FORMULA] in the magnetic flux tube driven by the photospheric convection (Zaitsev 1997):

[EQUATION]

Using Eq. (8) we have

[EQUATION]

Under the physical conditions of the upper photosphere in height h = 500 km upon the level [FORMULA], for the plasma flow velocity [FORMULA] m/s, and the magnetic field [FORMULA] G, Eq. (10) yields for [FORMULA] the longitudinal current value [FORMULA] A.

Thus, thin magnetic flux tubes with strong magnetic field and longitudinal currents of about 1011-1012 A can be generated in the photosphere-convection zone. We assume that these currents flow from one footpoint to another through the coronal part of a loop, and close deep down in the photosphere forming an electric circuit.

Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1998

Online publication: August 27, 1998
helpdesk.link@springer.de