New results on the gamma-ray burst variability-luminosity relation

At the dawn of the gamma-ray burst (GRB) afterglow era, a Cepheid-like correlation was discovered between time variability V and isotropic-equivalent peak luminosity Liso of the prompt emission of about a dozen long GRBs with measured redshift available at that time. Soon afterwards, the correlation was confirmed against a sample of about 30 GRBs, despite being affected by significant scatter. Unlike the minimum variability timescale (MVT), V measures the relative power of short-to-intermediate timescales. We aim to test the correlation using about two hundred long GRBs with spectroscopically measured redshift, detected by Swift, Fermi, and Konus/WIND, for which both observables can be accurately estimated. For all the selected GRBs, variability was calculated according to the original definition using the 64-ms background-subtracted light curves of Swift/BAT (Fermi/GBM) in the 15-150 (8-900) keV energy passband. Peak luminosities were either taken from literature or derived from modelling broad-band spectra acquired with either Konus/WIND or Fermi/GBM. The statistical significance of the correlation has weakened to <~2%, mostly due to the appearance of a number of smooth and luminous GRBs characterised by a relatively small V. At odds with most long GRBs, 3 out of 4 long-duration merger candidates have high V and low Liso. Luminosity is more tightly connected with shortest timescales measured by MVT rather than short-to-intermediate ones, measured by V. We discuss the implications on internal dissipation models and the role of the e+- photosphere. We identified a few, smooth GRBs with a single broad pulse and low V, that might have an external shock origin, in contrast with most GRBs. The combination of high variability (V>~0.1), low luminosity (Liso<~10^51 erg s^-1) and short MVT (<~ 0.1 s) could be a good indicator for a compact binary merger origin.