Correlation between peak energy and Fourier power density spectrum slope in gamma-ray bursts

Context. The origin of the gamma-ray burst (GRB) prompt emission still defies explanation, in spite of recent progress made, for example, on the occasional presence of a thermal component in the spectrum along with the ubiquitous non-thermal component that is modelled with a Band function. The combination of finite duration and aperiodic modulations make GRBs hard to characterise temporally. Although correlations between GRB luminosity and spectral hardness on one side and time variability on the other side have long been known, the loose and often arbitrary definition of the latter makes the interpretation uncertain. Aims. We characterise the temporal variability in an objective way and search for a connection with rest-frame spectral properties for a number of well-observed GRBs. Methods. We studied the individual power density spectra (PDS) of 123 long GRBs with measured redshift, rest-frame peak energy E_p,i of the time-averaged ν F_ν spectrum, and well-constrained PDS slope α detected with Swift, Fermi and past spacecraft. The PDS were modelled with a power law either with or without a break adopting a Bayesian Markov chain Monte Carlo technique. Results. We find a highly significant E_p,i-α anti-correlation. The null hypothesis probability is ∼10^-9. Conclusions. In the framework of the internal shock synchrotron model, the E_p,i-α anti-correlation can hardly be reconciled with the predicted E_p,i ∝ Γ^-2, unless either variable microphysical parameters of the shocks or continual electron acceleration are assumed. Alternatively, in the context of models based on magnetic reconnection, the PDS slope and E_p,i are linked to the ejecta magnetisation at the dissipation site, so that more magnetised outflows would produce more variable GRB light curves at short timescales (≲ 1 s), shallower PDS, and higher values of E_p,i.