How do the magnetic field strengths and intensities of sunspots vary over the solar cycle?

Many efforts have been made to determine if sunspot umbrae continuum intensities and magnetic field strengths are different at sunspot maximum than at sunspot minimum. The results are inconsistent, probably due to differences in sample size and analysis methodology. However, five out of six studies reviewed in this paper agree that sunspots are darker and stronger at sunspot maximum than later in the same cycle, i.e. sunspots brighten during the declining phase of the sunspot cycle. The trend during the rising phase is not agreed upon. Better statistics during the rising phase is crucial to determine if umbrae exhibit a cyclical or linear brightness trend over the cycle. We further this work by analyzing the intensities of 179 sunspots observed with the Helioseismic Magnetic Imager (HMI) for the rising phase of Sunspot Cycle 24. We find no significant trend in the brightness of sunspot umbrae in HMI data during Carrington Rotations 2097-2129 in either hemisphere. Future studies should place limits on sunspots included in the data sample, i.e. use only the leading sunspot in a bipolar active region after most of the flux has emerged but prior to sunspot decay, hopefully separating the effects of surface conditions from those of the interior where the magnetic flux is generated