The sunspot as a self-excited dynamo

Observations show that there is downflow in and around sunspots. Following Henoux and Somov, Heyvaerts and Hagyard, Hirayama, and Lorrain and Koutchmy, we show that sunspots are self-excited magnetic-flux-tube dynamos run by the downflowing plasma. The azimuthal current results from an azimuthal upsilon x B field generated by the radial inflow of the plasma. Comparison between various observations on sunspots with the fields of various coils seems to indicate that the azimuthal current is distributed nearly uniformly over the umbra and penumbra, with a slight excess near the axis. The resulting ohmic power density is negligible. The flux tube radius, at depth, is inversely proportional to the fourth root of the ambient pressure. The Standard Solar Model of Bahcall and Pinsonneau provides the pressure as a function of depth below -36 Mm.