The Spatial Distribution of Hard X-Ray Spectral Index and Local Magnetic Reconnection Rate

The rare phenomenon of ribbon-like hard X-ray (HXR) sources up to 100 keV found in the 2005 May 13 M8.0 flare observed with the \textit{Reuven Ramaty High Energy Solar Spectroscopic Imager} provides detailed information on the spatial distribution of flare HXR emission. In this Letter, we further investigate the characteristics of HXR emission in this event using imaging spectroscopy, from which we obtain spatially resolved HXR spectral maps during the flare impulsive phase. As a result we found, along a flare ribbon, an anticorrelation relationship between the local HXR flux and the local HXR spectral index. We suggest that this can be regarded as a spatial analog of the well-known temporal soft-hard-soft spectral evolution pattern of the integrated HXR flux. We also found an anticorrelation between HXR spectral index and local electric field along the ribbon, which suggests the electron acceleration by the electric field during flares.