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

Abstract: 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 gamma-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 E_{p,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 E_{iso} and peak luminosity L_{p,iso} when compared to the E_{p,i}-E_{iso} and E_{p,i}-L_{iso} prompt correlations. E_{p,i} is found to correlate with L_{iso} within single flares, giving rise to a time resolved E_{p,i}(t)-L_{iso}(t). Like prompt pulses, flares define a lag-luminosity relation: L_{p,iso}^{0.3-10 keV} t_{lag}^{-0.95+/-0.23}. 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.