Measurements of maximum magnetic flux, minimum intensity, and size are presented for 12 967 sunspot umbrae detected on the National Aeronautics and Space Administration/National Solar Observatory (NASA/NSO) spectromagnetograms between 1993 and 2004 to study umbral structure and strength during the solar cycle. The umbrae are selected using an automated thresholding technique. Measured umbral intensities are first corrected for center-to-limb intensity dependence. Log-normal fits to the observed size distribution confirm that the size-spectrum shape does not vary with time. The intensity -aEuro parts per thousand magnetic-flux relationship is found to be steady over the solar cycle. The dependence of umbral size on the magnetic flux and minimum intensity are also independent of the cycle phase and give linear and quadratic relations, respectively. While the large sample size does show a low-amplitude oscillation in the mean minimum intensity and maximum magnetic flux correlated with the solar cycle, this can be explained in terms of variations in the mean umbral size. These size variations, however, are small and do not substantiate a meaningful change in the size spectrum of the umbrae generated by the Sun. Thus, in contrast to previous reports, the observations suggest the equilibrium structure, as manifested by the invariant size-magnetic field relationship, as well as the mean size (i.e., strength) of sunspot umbrae do not significantly depend on the solar-cycle phase.
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