Sunspot geometry and pressure balance

Abstract

Measurements on magnetic canopies extending from sunspots show that, at the outer penumbral edge, heights of the bases are independent of sunspot diameter and average 180 km. This places a lower limit on the outer penumbral base; with an assumed thickness of 250 km, the top is ∼ 430 km above z = 0 (τ c = 1) in the photosphere. Chistyakov's (1962) observations require the penumbral surface to be convex in radial section. The Wilson depression, able thus to be found only from limb-side penumbras, is 1360 km from his selected measurements. Averaged over all regular sunspots without special selection, this drops to 1040 km. Thus τ* = 1 in umbras lies around z = -610 km. Magnetic field-strength measurements relate probably to τ* ∼ 0.02, some 160 km higher, where z ≈ -450 km. The magnetic pressure of the typical 3250 G sunspot field would support the external-axial gas-pressure difference at z = -330 km, the difference of 120 km lying well within the uncertainties. Tension forces, commonly invoked to achieve pressure balance, do not exceed the uncertainties of measurement. Beyond the sunspot, the base of the sunspot field rises only slowly over at least 16 000 km horizontally, whereas Beckers (1963) found the inclination of Hα superpenumbral fibrils to be some 13°. These results are nicely compatible since the field angle is typically of this magnitude at the minimum heights where Hα fibrils will be observed, say 1400 km.