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Context.The interaction between magnetic fields and convection in sunspots during their decay process remains poorly understood, whereas the formation of sunspots is relatively well studied and fully modeled. Works on the velocity scales at the solar surface have pointed to the existence of the family of granules, whose interaction with the magnetic field leads to the formation of supergranules and their networks, which are visible at the solar surface. Aims.The aim of this paper is to consider relationship between the decay of sunspots and convection via the motion of the family of granules and how the diffusion mechanism of magnetic field operates in a decaying sunspot. Methods.We report the decay of a sunspot observed by the 1.6 m Goode Solar Telescope (GST) with the TiO Broadband Filter Imager (BFI) and the Near-InfraRed Imaging Spectropolarimeter (NIRIS). The analysis was aided by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO). In the first step, we followed the decay of the sunspot with HMI data over three days by constructing its evolving area and total magnetic flux. In the second step, the high spatial and temporal resolution of the GST instruments allowed us to analyze the causes of the decay of the sunspot. Afterward, we followed the emergence of granules in the moat region around the sunspot over six hours. The evolution of the trees of fragmenting granules (TFGs) was derived based on their relationship with the horizontal surface flows. Results.We find that the area and total magnetic flux display an exponential decrease over the course of the sunspot decay. We identified 22 moving magnetic features (MMFs) in the moats of pores, which is a signature of sunspot decay through diffusion. We note that the MMFs were constrained to follow the borders of TFGs during their journey away from the sunspot. Conclusions.The TFGs and their development contribute to the diffusion of the magnetic field outside the sunspot. The conclusion of our analysis shows the important role of the TFGs in sunspot decay. Finally, the family of granules evacuates the magnetic field. 

Abstract We have developed a comprehensive catalog of the variable differential rotation measured near the solar photosphere. This catalog includes measurements of these flows obtained using several techniques: direct Doppler, granule tracking, magnetic pattern tracking, global helioseismology, as well as both time-distance and ring-diagram methods of local helioseismology. We highlight historical differential rotation measurements to provide context, and thereafter provide a detailed comparison of the MDI-HMI-GONG-Mt. Wilson overlap period (April 2010 – Jan 2011) and investigate the differences between velocities obtained from different techniques and attempt to explain discrepancies. A comparison of the rotation rate obtained by magnetic pattern tracking with the rotation rates obtained using local and global helioseismic techniques shows that magnetic pattern tracking measurements correspond to helioseismic flows located at a depth of 25 to 28 Mm. In addition, we show the torsional oscillation from Sunspot Cycles 23 and 24 and discuss properties that are consistent across measurement techniques. We find that acceleration derived from torsional oscillation is a better indicator of long-term trends in torsional oscillation compared to the residual velocity magnitude. Finally, this analysis will pave the way toward understanding systematic effects associated with various flow measurement techniques and enable more accurate determination of the global patterns of flows and their regular and irregular variations.