Analysis and modelling of recurrent solar flares observed with Hinode/EIS on March 9, 2012

Three homologous C-class flares and one last M-class flare were observed by both the Solar Dynamics Observatory (SDO) and the Hinode EUV Imaging Spectrometer (EIS) in the AR 11429 on March 9, 2012. All the recurrent flares occurred within a short interval of time (less than 4 hours), showed very similar plasma morphology and were all confined, until the last one when a large-scale eruption occurred. The C-class flares are characterized by the appearance, at approximatively the same locations, of two bright and compact footpoint sources of $approx$~3--10~MK evaporating plasma, and a semi-circular ribbon. During all the flares, the continuous brightening of a spine-like hot plasma ($approx$~10~MK) structure is also observed. Spectroscopic observations with Hinode/EIS are used to measure and compare the blueshift velocities in the fexxiii emission line and the electron number density at the flare footpoints for each flare. Similar velocities, of the order of 150--200~km~s$^{-1}$, are observed during the C2.0 and C4.7 confined flares, in agreement with the values reported by other authors in the study of the last M1.8 class flare. On the other hand, lower electron number densities and temperatures tend to be observed in flares with lower peak soft X-ray flux.In order to investigate the homologous nature of the flares, we performed a Non-Linear Force-Free Field (NLFFF) extrapolation of the 3D magnetic field configuration in the corona. The NLFFF extrapolation and the Quasi-Separatrix Layers (QSLs) provide the magnetic field context which explains the location of the kernels, spine-like and semi-circular brightenings observed in the (non-eruptive) flares. Given the absence of a coronal null point, we argue that the homologous flares were all generated by the continuous recurrence of bald patch reconnection.