On the α-intensity correlation in gamma-ray bursts: Subphotospheric heating with varying entropy

The emission mechanism during the prompt phase in gamma-ray bursts (GRBs) can be investigated through correlations between spectral properties. Here, we revisit the correlation relatingtheinstantaneousflux,F,andthephotonindexbelowthespectralbreak,α,inindividual emission pulses, by studying the 38 most prominent pulses in the Fermi/Gamma-ray Burst Monitor GRB catalogue. First, we search for signatures of the bias in the determination of α due to the limited spectral coverage (window effect) expected in the synchrotron case. The absence of such a characteristic signature argues against the simplest synchrotron models. We instead find that the observed correlation between F and α can, in general, be described by the relation F(t) ∝ e^kα(t⁾, for which the median k = 3. We suggest that this correlation is a manifestation of subphotospheric heating in a flow with a varying entropy. Around the peak of the light curve, a large entropy causes the photosphere to approach the saturation radius, leading to an intense emission with a narrow spectrum. As the entropy decreases the photosphere secedes from the saturation radius, and weaker emission with a broader spectrum is expected. This simple scenario naturally leads to a correlated variation of the intensity and spectral shape, covering the observed range.