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 relating the instantaneous flux, F, and the photon index below the spectral break, alpha, in individual 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 alpha 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 alpha can, in general, be described by the relation F(t) proportional to e(k alpha(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.