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

Context. At the dawn of the gamma–ray burst (GRB) afterglow era, a Cepheid-like correlation was discovered between the time variability V and the isotropic-equivalent peak luminosity L_iso of the prompt emission of about a dozen long GRBs with measured redshift available at that time. Soon afterwards, the correlation was confirmed in a sample of about 30 GRBs, even though it was affected by significant scatter. Unlike the minimum variability timescale (MVT), V measures the relative power of short-to-intermediate timescales. Aims. We aim to test the correlation using about 200 long GRBs with spectroscopically measured redshift, detected by Swift, Fermi, and Konus/WIND, for which both observables can be accurately estimated. Methods. The variability for all selected GRBs 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 the literature or derived from modelling broad-band spectra acquired with either Konus/WIND or Fermi/GBM. Results.The statistical significance of the correlation has weakened to ≲2%, mostly due to the appearance of a number of smooth and luminous GRBs that are characterised by a relatively small V. At odds with most long GRBs, three out of four long-duration merger candidates have high V and low L_iso. Conclusions. The luminosity is more tightly connected with shortest timescales measured by MVT than the short to intermediate timescales measured by V. We discuss the implications for 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 L_iso ≲ 10⁵¹ erg s^‑1, and short MVT (≲0.1 s) could be a good indicator for a compact binary merger origin.