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 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 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^{0.3-10 keV}_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 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.