Magnetic reconnection rate and flux-rope acceleration of two-ribbon flares

Forbes & Lin derived simple equations to link the properties of magnetic reconnection in the corona to observed signatures of solar flares. We measured the photospheric magnetic fields and the flare ribbon separation speeds then applied these equations to derive two physical terms for the magnetic reconnection rates: the rate of magnetic flux change phi(rec) involved in magnetic reconnection in the low corona and the electric field E-rec inside the reconnecting current sheet (RCS) that is generated during magnetic reconnection. The central interest in this work is to investigate and quantify the statistical correlation between the magnetic reconnection rate and the corresponding flux-rope acceleration. From a sample of 13 well-observed two- ribbon flares, which are associated with filament eruptions or coronal mass ejections (CMEs), the acceleration of erupting filaments is found mainly in the range of 0.05 - 0.4 km s(-2), up to 3 km s(-2). Correspondingly, the maximum E-rec and phi(rec) mostly occur in the range of 0.2 - 5 V cm(-1) and 0.5 - 6 x 10(18) Mx s(-1), respectively. A positive and strong correlation is found with a cross-correlation coefficient of 0.94 - 0.97 between the magnetic reconnection rate and the acceleration of erupting filaments that represents the early stages of flux-rope eruptions in the low corona. However, the inferred reconnection rate is not correlated to the acceleration of CME fronts measured by the Large Angle and Spectrometric Coronagraph (LASCO) observations in the range of 2 - 30 solar radii ( the correlation coefficient is less than 0.2). A reasonable correlation is found between the reconnection rate and the velocity of CMEs, which indicates the cumulative acceleration of CMEs from the low corona to the LASCO C2 field of view. The temporal correlation between the magnetic reconnection rate and the flare nonthermal emissions has also been verified in this paper.