The three-dimensional structure of sunspots. I. The height dependence of the magnetic field
Balthasar H.1, Gömöry P.2,
1 Astrophysikalishes Institut Potsdam, An der Sternwarte 16,
14482 Potsdam, Germany
2 Astronomical Institute of the Slovak Academy of Sciences,
SK-05960 Tatranská Lomnica, Slovakia
Abstract:
Aims. We investigate the height dependence of the magnetic field of a sunspot, which has been until now a
controversial issue.
Methods. Full-Stokes profiles of a sunspot, derived from infrared spectro-polarimetric measurements, were
investigated. The magnetic field strength, inclination and azimuth were obtained using an inversion code. The results
from two different spectral lines deliver the height dependence of the magnetic vector field. Vertical current densities
and helicities as well as the vertical derivative of the vertical component of the magnetic field strength are calculated
using Maxwell's equations.
Results. Inside the spot, the total magnetic field strength decreases with height, even in the outer penumbra,
where the opposite trend was reported by other investigators. Outside the spot, the field strength increases with height
apart from at a few small locations. This result is interpreted in terms of magnetic canopies. Magnetic field lines are
less inclined in higher layers everywhere in the field of view. In the umbra, the vertical component of the magnetic
field decreases by values in the range 0.5 - 2.2 G/km, depending on the applied method. Mean values in the inner penumbra
are smaller than in the umbra. In the outer penumbra, the vertical magnetic component increases independently of the
local intensity distribution. A pore close to the spot exhibits a more rapid decrease with height than the spot itself.
The electric current densities and helicities depend on the fine structure of the sunspots. Typical values of
the current densities vary in the range +-40 mA/m^(2). The mean values are -11 mA/m(2) for the umbra and -2 mA/m(2)
for the penumbra, respectively, but the propagated errors are of the same order as the mean values. There are
indications that the radial structure of the penumbra is related to enhanced current densities, but at the present
resolution we are unable to establish a correlation with local intensity fluctuations.
Conclusions. If the spatial resolution is sufficiently high, electric current densities and helicities could
be applied as reliable diagnostic tools for understanding penumbral fine structure.