Dipolarization fronts and magnetic flux transport
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We have measured the synodic rotation rates of a sample of compact X-ray emission features lasting from 1 day to 7 days, thus bridging the transition between X-ray bright points and active regions. The rotation rate is found to be a function of the lifetime, or size, of the feature; shorter-lived smaller features rotate more slowly than long-lived ones. The rotation rate for features lasting 2 days or less is consistent with that of the photospheric gas. The longest-lived features rotate at a rate about 5% higher, consistent with the sunspot rotation rate.
Analysis of the dynamical stability of a large flux tube suggests that the field of a sunspot must divide into many separate tubes within the first 1000 km below the surface. Buoyancy of the Wilson depression at the visible surface and probably also a downdraft beneath the sunspot hold the separate tubes in a loose cluster. Convective generation of Alfven waves, which are emitted preferentially downward, cools the tubes. Aerodynamic drag on a slender flux tube stretched vertically across a convective cell is also studied. Since the drag is approximately proportional to the local kinetic energy density, the density stratification weights the drag in favor of the upper layers. Horizontal motions concentrated in the bottom of the convective cell may reverse this density effect. A downdraft of about two km/sec through the flux tubes beneath the sunspot is hypothesized.
The mutual hydrodynamic forces between parallel cylinders in a moving fluid are illustrated through several formal examples. Parallel tubes in a uniform flow are attracted or repelled depending on whether they are side by side or one ahead of the other, respectively. A pulsating or undulating tube attracts all other neighboring tubes toward itself. These hydrodynamic effects suggest that the separate flux tubes beneath the sunspots exert significant attractive forces on each other.
The effect of negative aerodynamic drag in an ideal fluid subject to convective instability is considered. It is shown that a cylinder moving in such a fluid is propelled forward in its motion by the convective forces and that the characteristic acceleration time is comparable to the onset time of convective motions in the fluid. It is suggested that convective propulsion plays an important role in the dynamics of flux tubes extending through the surface of the sun. The suppression of the upward heat flow in a Boussinesq convective cell with free upper and lower boundaries by a downdraft is then analyzed. Application to the solar convection zone indicates that downdrafts of 1 to 2 km/s at depths of 1000 to 4000 km beneath the visible surface of the sun are sufficient to reduce the upward heat flux to a small fraction of the ambient value.
The magnetohydrodynamics of flux tubes are considered. The sections on equilibrium of flux tubes, and stability and waves deal with sunspots, the largest members of the general class of photospheric flux tubes.
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Resonant absorption of MHD waves on a nonuniform flux tube is investigated as a driven problem for a 1D cylindrical equilibrium. The variation of the fractional absorption is studied as a function of the frequency and its relation to the eigenvalue problem of the MHD radiating eigenmodes of the nonuniform flux tube is established. The optimal frequencies producing maximal fractional absorption are determined and the condition for total absorption is obtained. This condition defines an impedance matching and is fulfilled for an equilibrium that is fine tuned with respect to the incoming wave. The variation of the spatial wave solutions with respect to the frequency is explained as due to the variation of the real and imaginary parts of the dispersion relation of the MHD radiating eigenmodes with respect to the real driving frequency.
There were no publications associated with this grant. Instead, we used the funds to place IRM, Prognoz-10, and GOES-5/6/7 data sets on-line. The included copies of WWW pages indicate the nature of these services at APL. Since the time when the work was performed, a more complete set of IRM data has been placed on-line at the University of New Hampshire.
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