Lag-luminosity relation in γ-ray burst X-ray flares: A direct link to the prompt emission

The temporal and spectral analysis of 9 bright X-ray flares out of a sample of 113 flares observed by Swift reveals that the flare phenomenology is strictly analogous to the prompt γ-ray emission: high energy flare profiles rise faster, decay faster and peak before the low energy emission. However, flares and prompt pulses differ in one crucial aspect: flares evolve with time. As time proceeds flares become wider, with larger peak lag, lower luminosities and softer emission. The flare spectral peak energy Ep,i evolves to lower values following an exponential decay which tracks the decay of the flare flux. The two flares with best statistics show higher than expected isotropic energy Eiso and peak luminosity Lp,iso when compared to the Ep,i Eiso and Ep,i Liso prompt correlations. Ep,i is found to correlate with Liso within single flares, giving rise to a time resolved Ep,i(t) Liso(t). Like prompt pulses, flares define a lag-luminosity relation: L 0.3 10keV p,iso / t 0.95±0.23 lag . The lag-luminosity is proven to be a fundamental law extending �5 decades in time and �5 in energy. Moreover, this is direct evidence that GRB X-ray flares and prompt gamma-ray pulses are produced by the same mechanism. Finally we establish a flare- afterglow morphology connection: flares are preferentially detected superimposed to one-break or canonical X-ray afterglows.