Sigmoid Formation, Filament Destabilization, and Initiation of Weak Flare by Tether-Cutting Reconnection

We have studied a B-class solar flare and an associated filament eruption through multi-wavelength observations. The flare triggers at 16:24~UT on June 7$^{th}$, 2017 from an active region (AR) 12661, and it maximizes at 16:54~UT. The magnetic flux cancellation occurs near the polarity inversion line (PIL) preceding the flare, and ultraviolet (UV) brightenings occur in the pre-flare phase at the flux cancellation sites, suggesting the reconnection occurs in the lower atmosphere, initially. The S-shaped sigmoid forms through successive steps in corona, i.e., small-scale brightenings, helical/twisted field lines, bright patches, and finally, a developed sigmoid. It justifies that runaway reconnection within the coronal arcades forms the sigmoid within the filament. The differential emission-measure (DEM) analysis reveals the existence of the plasma at a temperature of more than 10 MK within the sigmoid. The initial magnetic reconnection reorganizes the field overlying the filament as per the tether-cutting model. Therefore, it enables the filament to rise slowly, and around~16:41~UT, the eruption phase of the filament begins. The filament eruption removes the overlying coronal field, including the sigmoid. During the eruption phase, we have found intersecting/crossing of coronal loops and jet-like structures far away from the sigmoid-filament system. In conclusion, all the observational findings (e.g., magnetic flux convergence, cancellation, UV brightenings, and spatial and temporal correlation between formation/evolution of the sigmoid and rise/eruption of the filament) suggest that the formation of a solar flare and the eruption of the filament are consistent with the tether-cutting model of solar eruption.