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Measurements of maximum magnetic flux, minimum intensity, and size arepresented for 12 967 sunspot umbrae detected on the NASA/NSOspectromagnetograms between 1993 and 2004 to study umbral structure andstrength during the solar cycle. The umbrae are selected using an automatedthresholding technique. Measured umbral intensities are first corrected for aconfirming observation of umbral limb-darkening. Log-normal fits to theobserved size distribution confirm that the size spectrum shape does not varywith time. The intensity-magnetic flux relationship is found to be steady overthe solar cycle. The dependence of umbral size on the magnetic flux and minimumintensity are also independent of cycle phase and give linear and quadraticrelations, respectively. While the large sample size does show a low amplitudeoscillation in the mean minimum intensity and maximum magnetic flux correlatedwith the solar cycle, this can be explained in terms of variations in the meanumbral size. These size variations, however, are small and do not substantiatea meaningful change in the size spectrum of the umbrae generated by the Sun.Thus, in contrast to previous reports, the observations suggest the equilibriumstructure, as testified by the invariant size-magnetic field relationship, aswell as the mean size (i.e. strength) of sunspot umbrae do not significantlydepend on solar cycle phase.

Structural Invariance of Sunspot Umbrae Over the Solar Cycle: 1993-2004