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

The temporal and spectral analysis of nine bright X-ray flares out of a sample of 113 flares observed by <it>Swift</it> 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 <it>E</it><inf>p,i</inf> 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 <it>E</it><inf>iso</inf> and peak luminosity <it>L</it><inf>p,iso</inf> when compared to the <it>E</it><inf>p,i</inf>–<it>E</it><inf>iso</inf> and <it>E</it><inf>p,i</inf>–<it>L</it><inf>iso</inf> prompt correlations. <it>E</it><inf>p,i</inf> is found to correlate with <it>L</it><inf>iso</inf> within single flares, giving rise to a time-resolved <it>E</it><inf>p,i</inf>(<it>t</it>)–<it>L</it><inf>iso</inf>(<it>t</it>). Like prompt pulses, flares define a lag–luminosity relation: <it>L</it>0.3–10 keV<inf>p,iso</inf>∝<it>t</it>−0.95±0.23<inf>lag</inf>. The lag–luminosity is proven to be a fundamental law extending ∼5 decades in time and ∼5 decades in energy. Moreover, this is direct evidence that γ-ray burst (GRB) X-ray flares and prompt γ-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.

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