Astron. Astrophys. 347, L27-L30 (1999)

5. Conclusions

The two main results of our analysis, the lower canopy base height of the sunspot and the similarity of relative expansion of sunspots and magnetic elements, have consequences that we now briefly explore. The lower values agree with those of Giovanelli & Jones (1982) and confirm that in active regions large areas are filled with magnetic field already in the mid-photosphere. In addition to having almost the same field strength, when averaged over their cross-sections, it is now clear that the smallest and largest photospheric flux tubes expand in an almost identical manner, although they carry 6 orders of magnitude different amounts of flux. This result provides a new constraint on models of the sunspot magnetic field. It also shows that at least in some important aspects sunspots behave like thin flux tubes, although they definitely do not fulfill the conditions under which the thin tube approximation is valid, since their diameter is far larger than a scale height. The thin-tube approximation even predicts that , as follows from flux () conservation: .

Solanki et al. (1994) have argued that due to the order of magnitude lower gas density above than in the penumbra (since the density scale height km) only 6-20% of the mass transported by the Evershed flow within the penumbra continues in the canopy.

We find that due to the lower the gas density above is larger by a factor of 2-2.5 compared to that used by Solanki et al. (1994). The density jump at , caused by the imposed pressure balance, only partially compensates for the 100-150 km lower . Taking the new numbers we find that 15-50% of the mass transported by the Evershed effect in the penumbra also passes through the canopy. Inspite of this higher fraction over half of the matter flowing through the penumbra must return to the solar interior at the penumbral edge (cf. Westendorp Plaza et al. 1997).

The expansion of large and small tubes differs clearly only rather close to the flux-tube boundary, between and 1.2. This implies that whatever the distribution of electric currents within these sunspots, they influence the expansion of the field only in a minor manner. Unfortunately, close to the sunspot boundary stray light can be a problem, complicating the issue.

It follows from Figs. 3 and 4 that in the low photosphere slender tubes expand more rapidly with height than sunspots, whereas their field strength decreases less rapidly with . The difference in behaviour between the sunspot field and that of thin flux tubes may be due to the presence of some return flux at the outer penumbral boundary, as proposed by Westendorp Plaza et al. (1997). Such a disappearance of the penumbral horizontal field component into the solar interior is expected to cause the field strength to drop rapidly as r becomes greater than , since less flux can now fill the available space. Also a less rapid relative expansion of sunspot fields with height (relative to slender flux tubes) is expected to be produced because only the more vertical magnetic component is left at , so that increases rapidly with near the spot boundary.

To test this conjecture it is necessary, however, to compare MHD models of the magnetic structure of sunspots with observations of the type presented in Figs. 1 and 2.

© European Southern Observatory (ESO) 1999

Online publication: June 30, 1999
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