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We investigate the vertical gradient of the magnetic field of sunspots in the photospheric layer. Independent observations were obtained with the SOT/SP onboard the Hinode spacecraft and with the TIP-2 mounted at the VTT. We apply state-of-the-art inversion techniques to both data sets to retrieve the magnetic field and the corresponding vertical gradient. 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. MHD simulations also show negative gradients in the inner penumbrae, also at the locations of filaments. Both in the observations and 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, both in the observations and, to a lesser extent, also in MHD simulations. We interpret the observed localized presence of the 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.
Context. It has been reported that the boundary between the umbra and the penumbra of sunspots occurs at a canonical value of the strength of the vertical magnetic field, independently of the size of the spot. This critical field strength is interpre
Context: In sunspots, the geometric height of continuum optical depth unity is depressed compared to the quiet Sun. This so-called Wilson depression is caused by the Lorentz force of the strong magnetic field inside the spots. However, it is not unde
Observations of a relation between continuum intensity and magnetic field strength in sunspots have been made during nearly five decades. This work presents full-Stokes measurements of the full-split (g = 3) line Fe I 1564.85 nm with spatial resoluti
Understanding the characteristics of the solar magnetic field is essential for interpreting solar activities and dynamo. In this research, we investigated the asymmetric distribution of the solar photospheric magnetic field values, using synoptic cha
We investigate subsurface moat flow system around symmetrical sunspots of McIntosh type H and compare it to the flow system within supergranular cells. Representatives of both types of flows are constructed by means of statistical averaging of flow maps obtained by time--distance helioseismic