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 .