Penumbral filaments: A dissipation form of the magnetic field

In this paper we suggest that penumbral filaments are a phenomenon of magnetohydrodynamic instability, developed in a stable and uniform magnetic field of sunspots during a dissipation process. We have solved local magnetohydrodynamic disturbance equations and have obtained the necessary condition for filament instability mode, that the ratio of filament length to width must be larger than the ratio of Alfvén speed to sound speed. We have also obtained correlations between two fluctuations from their phase difference. Although there are two correlations between the fluctuation of temperature (or filament intensity) and (1) the fluctuation of magnetic field, and (2) the fluctuation of the flow during the phases of developing and dissipating of the filament, we cannot distinguish whether the correlation is associated with the light filament or dark filament and we cannot decide whether the phase difference is 0° or 180° from tg() = 0. However, we can make a judgment: if the correlation is associated with a light filament during its development phase, it will be associated with a dark filament during its dissipation phase, andvice versa. In addition, there are no correlations between the fluctuations mentioned above for a stable filament, because the phase difference of the filament is changing with time.The phase differences of filaments are related to the existence of a gravitational field.