Reconciliating the Vertical and Horizontal Gradients of the Sunspot Magnetic Field

In the literature, we found 15 references showing that the sunspot photospheric magnetic field vertical gradient is on the order of 3-4 G/km, with field strength decreasing with height, whereas the horizontal gradient is nine times weaker on the order of 0.4-0.5 G/km. This is confirmed by our recent THEMIS observations. As a consequence, the vanishing of divB→ is not realized. In other words, a loss of magnetic flux is observed with increasing height, which is not compensated for by an increase of the horizontal flux. We show that the lack of spatial resolution, vertical as well as horizontal, cannot be held responsible for the nonvanishing observed divB→. The present paper is devoted to the investigation of this problem. We investigate how the magnetic field is influenced by the plasma anisotropy due to the stratification, which is responsible for an “aspect ratio” between horizontal and vertical typical lengths. On the example of our THEMIS observations, made of two spectral lines formed at two different depths, which enables the retrieval of the three components entering divB→, it is shown that once this aspect ratio is applied, the rescaled divB→ vanishes, which suggests a new methodology for MHD modeling in the photosphere