SUNSPOT ROTATION AND THE FIELD STRENGTHS OF SUBSURFACE FLUX TUBES

Observations show that bipolar magnetic regions (BMRs) have differenti al rotation profiles that are faster than the local Doppler velocity p rofiles by about 5%, and the p-spots in the growing sunspot groups rot ate faster than the f-spots. Also, the smaller spots rotate faster tha n the larger ones. We present detailed observations of the functional dependence of the residual rotation of sunspots on the spot size of th e p- and f-spots of growing sunspot groups. Through numerical calculat ions of the dynamics of thin flux tubes we show that flux loops emergi ng from the bottom of the convection zone acquire a rotation velocity faster than the local plasma velocities, in complete contradiction to what angular momentum conservation would demand. The sunspot flux tube s need not be anchored to regions rotating faster than the surface pla sma velocities to exhibit the observed faster rotation; we show that t his occurs through a subtle interplay between the forces of magnetic b uoyancy and drag, coupled with the important role of the Coriolis forc e acting on rising flux tubes. The dynamics of rising flux tubes also explains the faster rotation of smaller sunspots; we show that there i s no need to evoke a radial differential rotation and anchoring of sma ller spots to faster rotating regions. The simulated differential rota tion profiles of the p- and f-legs of flux loops emerging in the conve ction zone, with a latitudinal differential rotation and velocity cont ours constant along cones, mimic the observed profiles for growing sun spot groups only when the flux loops emerge radially and obey Joy's la w. (The 'legs' are defined to be the vertical part of the loops.) Also the rotation-size relation of growing sunspots is obeyed only by radi ally emerging loops which obey Joy's law. This constrains the fields a t the bottom of the convection zone that are possible for producing th e BMRs we see, to lie between 60 and 160 kG, which is in agreement wit h previous claims.