摘要：Aims. We investigate the vertical gradient of the magnetic field of sunspots in the photospheric layer.
Methods. Independent observations were obtained with the Solar Optical Telescope/Spectropolarimeter (SOT/SP) on board the Hinode spacecraft and with the Tenrife Infrared Polarimeter-2 (TIP-2) mounted at the German Vacuum Tower Telescope (VTT). We apply state-of-the-art inversion techniques to both data sets to retrieve the magnetic field and the corresponding vertical gradient along with other atmospheric parameters in the solar photosphere.
Results. In the sunspot penumbrae we detected patches of negative vertical gradients of the magnetic field strength, i.e., the magnetic field strength decreases with optical depth in the photosphere. The negative gradient patches are located in the inner and partly in the middle penumbrae in both data sets. From the SOT/SP observations we found that the negative gradient patches are restricted mainly to the deep photospheric layers and are concentrated near the edges of the penumbral filaments. Magnetohydrodynamic (MHD) simulations also show negative gradients in the inner penumbrae, also at the locations of filaments. In the observations and the simulation negative gradients of the magnetic field vs. optical depth dominate at some radial distances in the penumbra. The negative gradient with respect to optical depth in the inner penumbrae persists even after averaging in the azimuthal direction in the observations and, to a lesser extent, in the MHD simulations. If the gradients in the MHD simulations are determined with respect to geometrical height, then the azimuthal averages are always positive within the sunspot (above log τ = 0), corresponding to magnetic field increasing with depth, as generally expected.
Conclusions. We interpret the observed localized presence of negative vertical gradient of the magnetic field strength in the observations as a consequence of stronger field from spines expanding with height and closing above the weaker field inter-spines. The presence of the negative gradients with respect to optical depth after azimuthal averaging can be explained by two different mechanisms: the high corrugation of equal optical depth surfaces and the cancellation of polarized signal due to the presence of unresolved opposite polarity patches in the deeper layers of the penumbra.
