## 4. Effects of the currents in the photosphereWithout radial and vertical currents, the dependence of the radial velocity would be linear in the photosphere. However, the electromagnetic forces generated by the currents modify the law, and at a height of 350 km the radial velocity of neutral changes of sign and stops the influx of angular momentum. Consequently, the layers at 350 km and above cannot act as current generator and the radial current density is null at km. The radial currents are generated near the boundary of the flux tube in low field regions as it can be seen by comparison of Figs. 2a,b,c with Fig. 1. The vertical current density profile shows a negative and a positive peak indicating the presence of two cylindrical shells of currents flowing in opposite directions. In each shell, the vertical current density changes of sign at about 200 km, as shown on Fig. 2c. As it can be seen in Fig. 2d, since the two cylindrical shells of current flowing in opposite directions are generating repulsive forces they create a depression between them. On the other hand, the most internal current shell of current produces a pinch effect and increases the gas pressure inside the flux tube. ## 4.1. Photospheric upflows inside the internal current shellIn the flux tube the pressure enhancement due to the internal current shell reaches 10 and it can generate upward flows and modify consequently the pressure of the upper atmospheric layers. The amplitude of the upflow can be estimated by solving the system of fluid dynamics equations for vertical motions in presence of some local overpressure Here The equations (13) and (14) lead to This equation is independent of density. Using the numerical expression of its coefficients at an altitude of about 50 km we obtain At the height of 50 km, the relative pressure increase is , and in the photospheric layers the vertical gradient of the relative pressure increase is negative or null. A lower limit of the vertical velocity gradient is found for a null value of this gradient. This limit is Consequently, assuming a constant value of ,
up to the height where the electric current goes through zero and
changes of sign, i.e. over a vertical distance of 250 km, the vertical
velocity can reach 3.5 km s ## 4.2. Upflows between the two current shellsBetween the two current shells, the dominant force is the vertical force. This force is directed upwards in the low photosphere and downwards in the upper photosphere where the sign of reverses. However, the dominant contribution comes from the denser lower photospheric layers. The velocity gradient is such that where is the density. Assuming that the density is equal to the density in the hydrostatic atmosphere, equation (17) simplifies as At km, reaches Newton. This force is nearly equal to the gravity force. Consequently, a significant velocity gradient is present and In the hypothesis of constant density, a vertical velocity of about
7 km s © European Southern Observatory (ESO) 1997 Online publication: July 3, 1998 |