Many previous studies have shown that magnetic fields as well as sunspot structures present rapid and irreversible changes associated with solar flares. In this paper we first use five X-class flares observed by SDO/HMI to show that not only the magnetic fields and sunspot structures do show rapid, irreversible changes but also these changes are closely related, both spatially and temporally. The magnitudes of the correlation coefficients between the temporal variations of horizontal magnetic field and sunspot intensity are all larger than 0.90, with a maximum value of 0.99 and an average value of 0.96. Then using four active regions in quiescent times, three observed and one simulated, we show that in sunspot penumbra regions there also exists a close correlation between sunspot intensity and horizontal magnetic field strength, in addition to the well-known one between sunspot intensity and normal magnetic field strength. Connecting these two observational phenomena, we show that the sunspot structure change and the magnetic field change are the two facets of the same phenomena of solar flares, one change might be induced by the change of the other due to a linear correlation between sunspot intensity and magnetic field strength out of a local force balance.
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