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We study 7530 sunspot umbrae and pores measured by the HinodeSpectropolarimeter (SP) between November 2006 and November 2012. We primarilyseek confirmation of the long term secular decrease in the mean magnetic fieldstrength of sunspot umbrae found by Penn and Livingston (2011, IAU Symp.273,126) between 1998 and 2011. The excellent SP photometric properties andfull vector magnetic field determinations from full-Stokes Milne-Eddingtoninversions are used to address the interrelated properties of the magneticfield strength and brightness temperature for all umbral cores. We findnon-linear relationships between magnetic field strength and umbral temperature(and continuum contrast), as well as between umbral radius and magnetic fieldstrength. Using disambiguated vector data, we find that the azimuths measuredin the umbral cores reflect an organization weakly influenced by Joy's law. Thelarge selection of umbrae displays a log-normal size spectrum similar toearlier solar cycles. Influenced by the amplitude of the solar cycle and thenonlinear relationship between umbral size and core magnetic field strength,the distribution of core magnetic field strengths, fit most effectively with askew-normal distribution, shows a weak solar cycle dependence. Yet, the meanmagnetic field strength does not show a significant long term trend.

On the Collective Magnetic Field Strength and Vector Structure of Dark Umbral Cores Measured by the Hinode Spectropolarimeter