In this Letter , we investigate the long-duration quasi-static evolution of 12 pre-eruptive filaments ( 4 active region and 8 quiescent filaments ) , mainly focusing on the evolution of the filament height in three dimension ( 3D ) and the decay index of the background magnetic field .
The filament height in 3D is derived through two-perspective observations of Solar Dynamics Observatory and Solar TErrestrial RElations Observatory .
The coronal magnetic field is reconstructed using the potential field source surface model .
A new finding is that the filaments we studied show two types of long-duration evolution : one type is comprised of a long-duration static phase and a short slow rise phase with a duration of less than 12 hours and a speed of 0.1–0.7 km s ^ { -1 } , while the other one only presents a slow rise phase but with an extremely long duration of more than 60 hours and a smaller speed of 0.01–0.2 km s ^ { -1 } .
At the moment approaching the eruption , the decay index of the background magnetic field at the filament height is similar for both active region and quiescent filaments .
The average value and upper limit are \sim 0.9 and \sim 1.4 , close to the critical index of torus instability .
Moreover , the filament height and background magnetic field strength are also found to be linearly and exponentially related with the filament length , respectively .