Vertical Gradients of Sunspot Magnetic Fields

In this paper, we describe results of a Solar Maximum Mission (SMM) guest investigation to determine vertical gradients of sunspot magnetic fields for the first time from coordinated observations of photospheric and transition-region fields. Both the photospheric vector field of a sunspot, derived from observations using the NASA Marshall Space Flight Center vector magnetograph, and the line-of-sight component in the transition region, obtained from the SMM Ultraviolet Spectrometer and Polarimeter instrument, are described. From these data, vertical gradients of the line-of-sight magnetic field component are calculated using three methods. (1) The vertical gradient is derived directly from the observations assuming a height difference of 2000 km between the photosphere and transition region. (2) Using the observed transverse photospheric field, the initial gradient (ΔB_z/Δz)_{z = 0}, is calculated from the condition ▽ . B = 0. (3) Using the photospheric line-of-sight component as the boundary condition in a potential-field calculation, the extrapolated potential field at different heights is compared to the observed transition-region field; from these comparisons, an average height difference is derived and used to calculate the average vertical gradient (ΔB_z/Δz). Comparisons of gradients derived from these three methods show consistent results for methods (2) and (3). Deviations of the calculated potential transverse field at z = 0 from the observed transverse component are investigated to assess the validity of gradient calculations using method (3). Since the field is shown to be very close to a potential distribution, we conclude that the vertical gradient of B_z is lower than values from previous studies and the transition-region field occurs at a height of ≈ 4000-6000 km above the photosphere.